AN IMPLANTABLE, STIMULATED MUSCLE POWERED PIEZOELECTRIC

GENERATOR

By

BETH ELAINE LEWANDOWSKI

Submitted in partial fulfillment of the requirements

For the degree of Doctor of Philosophy

Dissertation Advisor: Dr. Kenneth J. Gustafson

Department of Biomedical Engineering

CASE WESTERN RESERVE UNIVERSITY

May, 2009

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CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

__Beth Elaine Lewandowski_________________________

candidate for the ____PhD___________ degree *.

(signed) ______Kenneth Gustafson____________________ (chair of the committee) _______Kevin Kilgore________________________

_______Robert F. Kirsch______________________

_______Steven L. Garverick___________________

_______Dustin Tyler_________________________

(date) __3/5/09_____

*We also certify that written approval has been obtained for any proprietary material contained therein.

iii

Copyright © 2009 by Beth Elaine Lewandowski

All rights reserved

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TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................................................ 6

LIST OF FIGURES ...................................................................................................................................... 7

ACKNOWLEGEMENTS ............................................................................................................................. 9

ABSTRACT ................................................................................................................................................. 11

I. INTRODUCTION .............................................................................................................................. 12

A. BACKGROUND AND SIGNIFICANCE ........................................................................................ 12

B. SPECIFIC AIMS .............................................................................................................................. 14

C. EXISTING RESEARCH ON ENERGY HARVESTING TECHNOLOGY .................................... 16

D. GENERATOR CONCEPT ............................................................................................................... 19

1. GENERATOR DRIVEN BY MUSCLE POWER ........................................................................... 19

2. SELECTION OF MECHANICAL TO ELECTRICAL CONVERSION METHOD........................ 23

3. RELEVANT PIEZOELECTRIC MATERIAL PROPERTIES ........................................................ 27

4. APPLICATION POWER VS. ENERGY ....................................................................................... 32

5. PIEZOELECTRIC CIRCUIT MODELS ....................................................................................... 35

II. DESIGN CONSIDERATIONS ......................................................................................................... 40

A. ABSTRACT ..................................................................................................................................... 40

B. INTRODUCTION ............................................................................................................................ 41

C. METHODS ...................................................................................................................................... 46

1. SOFTWARE MODEL .................................................................................................................. 46

2. EXPERIMENTAL METHODS ..................................................................................................... 54

D. RESULTS ........................................................................................................................................ 56

1. MODEL RESULTS ...................................................................................................................... 56

2. EXPERIMENTAL RESULTS ....................................................................................................... 59

E. DISCUSSION .................................................................................................................................. 61

F. CONCLUSION ................................................................................................................................ 65

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G. ACKNOWLEDGEMENTS ............................................................................................................. 65

III. IN-VIVO DEMONSTRATION OF GENERATOR CONCEPT ................................................ 67

A. ABSTRACT ..................................................................................................................................... 67

B. INTRODUCTION ............................................................................................................................ 68

C. METHODS ...................................................................................................................................... 73

1. MECHANICAL MUSCLE ANALOG ........................................................................................... 73

2. PREPARATION FOR IN-VIVO DEMONSTRATION .................................................................. 75

3. IN-VIVO EXPERIMENTAL PROTOCOL .................................................................................... 77

D. RESULTS ........................................................................................................................................ 82

1. OUTPUT POWER CAPABILITIES OF THE GENERATOR ....................................................... 82

2. IN-VIVO DEMONSTRATION OF GENERATOR CONCEPT ..................................................... 83

3. COMPARISON OF IN-VIVO DATA TO MECHANICAL ANALOG DATA ................................ 86

4. STIMULATION PARAMETER EVALUATION............................................................................ 87

E. DISCUSSION .................................................................................................................................. 89

F. CONCLUSION ................................................................................................................................ 93

G. ACKNOWLEDGEMENTS ............................................................................................................. 94

IV. DISCUSSION ................................................................................................................................. 95

A. DISSERTATION IMPACT ............................................................................................................. 95

B. SIMPLIFIED ESTIMATE OF SYSTEM PARAMETERS .............................................................. 97

C. NEXT STEPS TO FURTHER ADVANCE THE TECHNOLOGY ................................................. 98

1. ATTACHMENT SITES ................................................................................................................. 99

2. BIOCOMPATIBILITY ................................................................................................................ 100

3. ENCAPSULATION .................................................................................................................... 101

4. IMPROVEMENTS TO THE ELECTRICAL CIRCUIT............................................................... 103

5. MEASUREMENT OF SYSTEM PERFORMANCE DURING CHRONIC STUDIES ................. 104

D. THE EFFECT OF OPTIMIZATION OF EACH PART OF THE SYSTEM ON GENERATOR

OUTPUT POWER .................................................................................................................................. 105

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1. MUSCLE SIZE ........................................................................................................................... 105

2. OPTIMAL MECHANICAL POWER OF MUSCLE ................................................................... 106

3. STIMULATOR POWER REQUIREMENTS ............................................................................... 107

4. MECHANICAL COUPLING ..................................................................................................... 108

5. STIMULATION PATTERNS ...................................................................................................... 109

E. PRACTICALITY OF REALIZING THE TECHNOLOGY IN A HUMAN APPLICATION ....... 109

V. CONCLUSION ................................................................................................................................. 113

APPENDIX A. REQUIREMENTS AND DESIGN SELECTION PROCESS ................................ 114

A. LINEAR ELECTROMAGNETIC INDUCTION ........................................................................... 116

1. THE THEORETICAL ANALYSIS OF THE MAGNET AND COIL SYSTEM ............................. 116

2. MAGNET AND COIL EXPERIMENTAL RESULTS .................................................................. 119

B. PIEZOELECTRIC GENERATOR................................................................................................. 121

1. THEORETICAL ANALYSIS OF THE PIEZOELECTRIC GENERATOR .................................. 121

2. PIEZOELECTRIC GENERATOR EXPERIMENTAL RESULTS ............................................... 122

C. SUMMARY OF THE TWO OPTIONS ......................................................................................... 123

APPENDIX B. SIMULATION MODEL ............................................................................................ 125

APPENDIX C. MECHANICAL MUSCLE ANALOG ...................................................................... 127

VI. BIBLIOGRAPHY ........................................................................................................................ 130

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LIST OF TABLES

Table I-1. Properties of example piezoelectric materials .................................................. 31

Table I-2. Comparison of energy capacity and charging time for different sizes of CL ... 33

Table I-3. Discharge rate of CL = 100 µF for various sizes of load resistors ................... 35

Table II-1. Summary of system parameter constraints ..................................................... 52

Table III-1. The load circuit tuning frequency for stimulation pattern combinations ...... 88

Table III-2. Predicted output power for different stimulation patterns ............................. 89

Table IV-1. Estimated increase in output power resulting from system improvements . 109

Table A-1. Evaluation of ideas for scavenging power from the body ............................ 115

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LIST OF FIGURES

Figure I-1. Muscle force produced from motor nerve stimulation.. ................................. 21

Figure I-2. The generator concept. .................................................................................... 23

Figure I-3. Mechanical to electrical energy conversion methods.. ................................... 27

Figure I-4. Circuit representation of the generator system. .............................................. 30

Figure I-5. Circuit representation of a piezoelectric stack generator ................................ 35

Figure I-6. Voltage source model. .................................................................................... 36

Figure I-7. Current source model.. .................................................................................... 37

Figure I-8. Force and the derivative of the force. ............................................................. 38

Figure I-9. Simulation results from application of the force ............................................ 39

Figure II-1. The generator concept. .................................................................................. 42

Figure II-2. Circuit representation of the generator system. ............................................ 47

Figure II-3. Relationship between piezoelectric and dielectric constants. ........................ 50

Figure II-4. Photo of the mechanical holder.. ................................................................... 56

Figure II-5. Predicted output power as a function of system parameters.. ....................... 57

Figure II-6. Predicted output power for three generator scenarios.. ................................. 58

Figure II-7. Output voltage resulting from repetitive force application. .......................... 60

Figure II-8. Simulation and experimental output power comparison. .............................. 61

Figure

III-1. The implantable, stimulated-muscle-powered piezoelectric energy generator

concept. ............................................................................................................................. 71

Figure III-2. Schematic of the mechanical muscle analog test bed.. ................................ 73

Figure III-3. Power analysis circuit schematic. ................................................................ 74

Figure III-4. Generator system circuit schematic. ............................................................ 76

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Figure III-5. In-vivo power generation matched the mechanical muscle analog.. ............ 83

Figure

III-6. Example stimulus pulse, twitch force and output voltage during the in-vivo

demonstration.. .................................................................................................................. 84

Figure III-7. Self-sustaining, in-vivo power generation. ................................................... 86

Figure B-1. Software simulation schematic. ................................................................... 125

Figure B-2. Example output of the software simulations. .............................................. 126

Figure C-1. Schematic of the mechanical muscle analog control system. ...................... 127

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ACKNOWLEGEMENTS

I would like to thank my advisor, Ken Gustafson, for his careful review of this

work, for his technical advice and for the nerve cuff electrode surgeries that he performed

with great patience and care. I would like to thank my advisor, Kevin Kilgore for

formulating the concept for an implantable, stimulated muscle powered generator, for his

careful review of this work and for the wealth of technical advice that he shared. I would

like to thank Steve Garverick for his review of this work and his valuable electrical

engineering advice and Bob Kirsch and Dustin Tyler for their review of this work and

their relevant advice.

Special thanks are due to Fred Montague, Tina Emancipator and Narendra Bhadra

for all of the help they offered throughout this project. Katie Hallahan, Alex Frayna and

Jess Snyder are each recognized for their contributions to the project. Roger Diamond is

recognized for his machining help.

I would like to recognize my NASA Glenn Research Center supervisors and co-

workers who provided tremendous amounts of support in a variety of ways, including,

Bruce Banks, William Brown, Chris Burke, Dave Ercegovic, Joe Flatico, Gus Fralick,

Kelly Gilkey, Paul Greenberg, DeVon Griffin, Mike Krasowski, Brad Lerch, Valerie

Lyons, Jerry Myers, Marsha Nall, Emily Nelson, Gail Perusek, Sergey Samorezov, John

Sankovic, Mark Savina, Ali Sayir, Bhim Singh, Amy Stalker, Bill Yanis and June

Zakrajsek.

I am thankful for the friendship of my classmates, especially Ravi Nataraj, Marc

Petre, Alicia Jensen, Matt Schiefer, Brian Wenzel, Adam Boger and Tim Bruns.

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I am grateful for the love provided by my extended family, for the unconditional

love and support from my father (William Jeremiah), my mother (Carolyn Jeremiah) and

my sister (Cathy Jeremiah) and especially for the love, support and encouragement from

my husband, Skip Lewandowski.

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An Implantable, Stimulated Muscle Powered Piezoelectric Generator

Abstract

by

BETH ELAINE LEWANDOWSKI

An implantable, stimulated muscle powered piezoelectric generator was designed

to exploit the fact that the mechanical output power of muscle is substantially greater than

the electrical power necessary to stimulate the motor nerve. We reduced to practice our

concept by building a generator prototype and demonstrating its feasibility in-vivo, using

a rabbit quadriceps to drive the generator. The generated power was sufficient for

continuous operation of the stimulator and a small amount of additional power was

dissipated through a load resistor. The power generating capabilities of the prototype

generator were tested with a mechanical muscle analog. Comparison of data from the

animal experiments with mechanical muscle analog data verified its usefulness as a test-

bed for future generator developments. Two key parameters of the generator system are

the magnitude and frequency of the muscle force used to drive the generator. These

parameters are dependent on the muscle stimulation patterns. Various stimulation

patterns were studied to identify patterns that may increase the output power capabilities

of future versions of the generator. A potential application for our generator is a self-

replenishing power source for implanted electronic medical devices.

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I. INTRODUCTION

The content of this introduction has been published in the following citation:

Lewandowski BE, Kilgore KL, Gustafson KJ, Feasibility of an implantable, stimulated

muscle-powered piezoelectric generator as a power source for implanted medical devices.

In: Priya S, Inman DJ, Energy Harvesting Technologies, Springer Science+Business

Media, LLC., New York, 2009, pp 389-404.

The objectives of this research are listed in B. SPECIFIC AIMS, within this Introduction.

A. BACKGROUND AND SIGNIFICANCE

Implanted electronic medical devices provide beneficial therapies and increase the

quality of life of many patients. In particular, functional electrical stimulation (FES)

devices, also referred to as neural prostheses, restore some neurological function in spinal

cord injured (SCI) patients. There are approximately 11,000 new cases of SCI each year

in the United States [1], resulting in various degrees of impairment of the many functions

humans take for granted. Motor function for reaching and grasping objects, interacting

with computers and other machines or appliances, bending and walking can be impaired

along with involuntary functions such as respiration and bladder control. FES devices use

electrical current pulses to artificially stimulate nerves in patterns that result in muscle

contractions that allow these various functions to be restored to some extent [2-6]. FES

devices improve the quality of life of persons with SCI by allowing them to perform

activities of daily living independently and in some cases return to work. FES devices are

implanted into the body and require electrical power for operation. Power is obtained

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from either batteries implanted along with the device or from an external transcutaneous

power source.

The majority of spinal cord injuries occur in young adults between the age of 16

and 30 [1]. Therefore, the timeframe over which the FES device is needed can be quite

long, potentially 50 years or longer, as life expectancy for SCI patients with less severe

injuries are only slightly less than people without SCI [1]. Batteries that are implanted

with an electronic device need to be replaced when they are depleted. Battery depletion

may occur several times over the lifetime of the device, requiring surgery each time

battery replacement is needed. Replacement of implanted batteries requires frequent,

costly surgeries with increased risk of complications. Documented clinical experience

with pacemakers and implanted defibrillators highlight the limitations of implanted

batteries. The mean time to when pacemaker battery replacement is needed is eight years

after the initial implantation [7]. Depletion of implanted batteries is the reason for more

than 70% of pacemaker replacement surgeries and the complication rate after a

replacement surgery is three times greater than for the initial implant [8]. For implanted

defibrillators, patients require battery replacement surgery 3-4 years after initial

implantation with costs up to $10,000 [9].

Transcutaneous energy transfer systems provide high levels of power to neural

prostheses through radio frequency energy transfer between external and internal coils.

These systems require bulky external equipment including a coil fixed to the chest, a coil

driver power supply and wire leads between the driver and the coil [10]. The external

equipment can be damaged and the wires can tangle, it is burdensome to carry,

cosmetically unappealing and it is unable to be used in the shower or in a rehabilitation

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pool. Small movements of the external or internal coils out of alignment will reduce the

efficiency of the power transferred and large misalignments can severely reduce the

power transferred, resulting in situations of device malfunction [10;11]. The resistance

inherent in the internal coil causes the coil to heat during operation. The heat that is

generated has the potential to cause tissue necrosis or an inflammatory reaction [10]. So

while implanted medical devices are very beneficial to patients, there is room for

improvement in how power is supplied to them. A totally implanted generator driven by a

physiological process resulting in a replenishable and sustainable source of power is an

attractive solution to the limitations of the power sources currently used to power FES

devices.

B. SPECIFIC AIMS

In this work we report the development efforts for an implantable generator

driven by electrically activated muscle as a self-replenishing power source that could

augment or replace FES power systems. With such a generator, the lifetime of implanted

batteries could be extended, reducing or possibly eliminating replacement surgeries.

Internally generated power could allow for periods of FES use without external

transcutaneous power system equipment during which a shower or other types of daily

activities could be performed independently. This objective-based project tested the

hypothesis that more electrical power can be generated from stimulated muscle than is

needed for muscle stimulation. To our knowledge this has not previously been

demonstrated and it is the basis upon which the concept for our generator was developed.

15

The work associated with this objective was broken into three specific aims. The three

aims are outlined below and the following two chapters describe the methods and results

of the experimentation performed to accomplish the objectives of the aims.

Aim 1: In order for a stimulated muscle powered generator to be feasible as a FES

power source, it must generate positive net output power. The objective of this aim was

to develop a method to predict the output power of the generator so that its feasibility

can be determined. A software model of the concept was developed, mechanical testing

was performed to verify the accuracy of the model and software simulations were

performed to predict output power. The predicted output power was compared to the

theoretical power necessary for muscle stimulation. Concept feasibility was demonstrated

through this power comparison. In addition, software simulations were used to study the

resulting generator output power as the system parameters were varied within their

constraints. This work is described in detail in Chapter II. DESIGN

CONSIDERATIONS.

Aim 2: The concept for the generator must be reduced to practice. The objective

of this aim was to demonstrate operation of the generator concept in an acute animal

model. A prototype generator system was built and operation was demonstrated when a

small animal muscle was used to drive the generator. A mechanical muscle analog was

built to aid in the development of the generator system. Data from the animal

experiments was compared to data from the mechanical muscle analog to verify that the

mechanical muscle analog can be used as a test bed for future generator development.

This work is described in detail in Chapter III. IN-VIVO DEMONSTRATION OF

GENERATOR CONCEPT.

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Aim 3: Key system parameters include the magnitude and frequency of the

muscle force. These parameters are dependent on the muscle stimulation patterns,

including number of pulses, stimulation frequency and repetition rate and affect the net

output power of the generator. The objective of this aim was to determine the most

advantageous muscle stimulation parameters for generator operation. Their effect on

generator output power was determined through software simulations and animal testing.

Understanding the effect of these parameters on generator output power was a first step

towards increasing generator output power in future versions of the generator. This work

is described in detail in Chapter III. IN-VIVO DEMONSTRATION OF GENERATOR

CONCEPT.

C. EXISTING RESEARCH ON ENERGY HARVESTING TECHNOLOGY

Interest in energy scavenging and power harvesting has grown over the past

decade. There has been interest in scavenging energy from the environment, mechanical

equipment and the human body for many reasons including, a method for increasing

energy efficiency, a power source for wireless sensors that monitor environmental,

structural or health conditions, a power source for robotic applications, a method for

decreasing the weight burden of batteries and a primary or emergency power source in

remote environments [12-18]. For example, research into the conversion of vibrations

from mechanical equipment to electrical energy has been conducted for possible

applications such as powering the monitoring sensors and operational control of heating,

air conditioning and ventilating equipment, for damping unwanted vibrations of

17

helicopter blades, for powering sensors that monitoring the structural integrity of aircraft

bodies and highway bridges, powering sensors that monitor operations within an aircraft

engine and for measuring performance within sports equipment [19-26].

Because of the interest in energy harvesting there has also been research to

advance the state of the art in energy harvesting methods. Work has been done on

creating nanogenerators with zinc oxide fibers [27], MEMS based microgenerators have

been developed [28-30], piezoelectric material is being specifically designed for energy

harvesting [31] and advances have been made in thermal to electrical energy conversion

[32]. In addition, advances have been made in the storage circuitry for use with energy

harvesting generators. These include thin film batteries which retain more charge and

withstand more charging cycles than traditional batteries [33]. Hybrid batteries are being

developed to combine the ease of charging found in capacitors with the low leakage

characteristics of batteries [34]. Power management systems are being developed to be

integrated with the MEMS generators [35]. Energy harvesting modules have been

developed to adapt the impedance of the storage circuit if changes occur in the frequency

of the driver of the generator [36].

The literature also shows that others have an interest in the generation of electrical

power from human energy sources, both external and internal to the body, for a variety of

applications. Applications include power sources for electronic equipment to increase

mobility or in remote locations and biomedical applications, such as a power source for

sensors or therapeutic devices. For example, the thermal energy produced by the body

has been converted to electrical energy for powering watches. External human powered

generators that convert mechanical motion to electricity include hand cranks for

18

powering radios, shake generators for flashlights, cycle driven portable generators, heel

strike generators for lessening the weight burden that soldiers carry, inductive generators

in hiking backpacks for powering mobile communication devices and a generator located

at the knee joint that operates using the negative work of locomotion for powering

prosthetic limbs. [37-41].

Research on implanted generators has focused on the conversion of thermal

energy or mechanical energy to electrical energy. An implantable, proprietary

thermoelectric power source is under development by researchers within industry [42].

Their target application is a power source for pacemakers, implantable cardioverter-

defibrillators, drug pumps or neurostimulators. Piezoelectric generators have been

developed, using different types of piezoelectric material with different loading

strategies, producing a range of power generation results. Elvin et al. used a single piece

of polyvinylidene fluoride (PVDF) piezoelectric material mounted on a simply supported

beam as a bone strain sensor and telemeter, which produced approximately 0.1 μW of

power [43]. Hausler et al. rolled PVDF piezoelectric material into a tube and connected it

between two ribs in a canine. The rib displacement during breathing produced a strain on

the piezoelectric material, which produced 17 μW of power [44]. Ko placed a mass on the

end of a single piezoelectric cantilever beam ceramic wafer (2 cm x 5 cm x 1 cm) and

packaged it in a box for attachment to the heart. When 80 bpm mechanical pulses shook

the box, the piezoelectric material was vibrated at 6.5 Hz, resulting in 160 μW of power

[45;46]. When chronically driven by actual canine heart contractions, the efficiency of

the generator was reduced to a sustained output power of 30 μW [46]. The reduction in

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efficiency was due to the reaction of the tissue to wall-off the generator thus minimizing

force transfer to the generator.

We seek to advance the state of the art in implantable generators by incorporating

the most relevant aspects of previous research on energy harvesting technologies into the

design for a generator with unique features that is capable of producing power sufficient

for the operation of FES devices, including those that are high power consuming and for

long durations.

D. GENERATOR CONCEPT

1. GENERATOR DRIVEN BY MUSCLE POWER

Our generator will be driven from the force and power associated with the

physiological process of muscle contraction. Muscle contraction is initiated through

natural or artificial electrical stimulation of the motor nerve, resulting in an action

potential traveling the length of the nerve. When the action potential reaches the nerve

ending acetylcholine is released. This causes acetylcholine-gated channels on the muscle

fibers to open, allowing sodium ions to flow through. The increase of sodium ions within

the muscle fibers causes an action potential to be generated and propagated throughout

the muscle fiber. The muscle fiber action potential causes the sarcoplasmic reticulum to

release calcium ions. These calcium ions play a role in activating the attraction between

the actin and myosin filaments within the muscle fiber, which is what causes the

contractile forces of the muscle to occur. Prior to the attraction between the actin and

myosin filaments, the chemical energy available from adenosine triphospate (ATP) is

20

utilized by the myosin filaments to cause a conformational change in a portion of the

filaments. The conformational change allows the myosin filament to be in the correct

position for interaction with the actin filament and to have the energy needed for the

muscle to produce contractile forces and mechanical power [47].

There is a large body of literature available reporting the force characteristics of

muscles when they are artificially stimulated with current pulses [48-56]. A single current

pulse, ranging in amplitude from 0.5 to 1 mA, with a pulse width ranging from 10 to 500

µs, applied to a motor nerve will cause the muscle to produce a single burst of force,

referred to as a twitch. Figure I-1A provides an illustration of a twitch force burst with a

generalized amplitude and time scale. The amplitude of the force burst depends on the

size of the muscle and its duration depends on the muscle fiber type. When a train of

current pulses are applied to the motor nerve multiple force bursts result. At lower

frequencies (1 – 30 Hz) the force bursts will look like individual twitches repeated at

regular intervals, at higher frequencies (30 – 50 Hz) the force bursts occur more quickly

resulting in each subsequent force burst in the train adding to the one before it, as

illustrated in Figure I-1B. When current pulse trains are applied to the motor nerve at

frequencies greater than approximately 50 Hz, the force bursts fuse together to form one

large force burst (Figure I-1C). As the frequency continues to increases, the amplitude of

this force burst will increase to a maximum level, after which increases in the frequency

will no longer result in increases in the force. An estimate of the maximum contraction

forces can be found by multiplying the muscle’s physiological cross sectional area by a

conversion factor of 35 Ncm-2 [47]. The force produced by a twitch contraction is

approximately 10 to 30% of the maximal contractive force of the muscle. The

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physiological cross-sectional area of the muscles of the limbs and trunk of the human

body range from 0.2 to 230 cm2 [57-60] and therefore have the capacity to produce

maximal forces of 8 to 8000 N.

Figure I-1. Muscle force produced from motor nerve stimulation. A. A single pulse of current produces a low amplitude burst of force. B. A train of current pulses applied at a mid-range frequency (30 – 50 Hz) results in a force burst with multiple peaks. C. A train of current pulses applied at high frequencies (>50 Hz) results in a fused, high amplitude force burst.

While the muscles have the capability to produce enormous amounts of force,

they are unable to sustain this force production for very long due to muscle fatigue. The

sustainable mechanical output power of a muscle is a function of the force produced by

the muscle, the distance traveled by the muscle fibers during contraction and the

contraction rate. As an example, a study experimentally quantifying the sustained output

power of muscle used a muscle contraction force over the range of 10 – 30 N, a change in

muscle length of 1 – 3 cm and a contraction rate of 30 - 60 contractions per minute [49].

The results of this study and others found a conservative estimate of the sustained output

power of stimulated, conditioned muscle producing isotonic maximal contractions is 1

mW/g [49;61;62]. The mass of the muscles of the limbs and trunk of the human body

range from 3 to 814 g [60] and therefore have the capacity to produce up to

approximately 800 mW of mechanical power. If this muscle power is generated from

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electrical stimulation, an estimate of the range of electrical stimulation power needed to

produce this amount of muscle output power is 0.05 to 6 µW. The high end of this range

is based on 1 mA, 500 µs current pulses, applied at 50 Hz for 250 ms per contraction at a

rate of 1 contraction per second, assuming a 1 kΩ impedance. The low end of the range is

based on single current pulse of 500 µA for 200µs through a resistance of 1kΩ, operating

at 1 Hz.

When comparing the mechanical output power to the electrical power necessary

for motor nerve stimulation, we see that muscle acts as a power amplifier. Just a small

amount of electrical power initiates the chemical reaction that converts the chemical

energy within the muscle to mechanical power. Our generator will exploit this power

amplification characteristic of muscle, a physiological phenomenon that, to our

knowledge, has not been previously utilized. An illustration of the fundamental concept

of our implantable generator is shown in Figure I-2. A generator that converts mechanical

energy to electrical energy is connected in series with a muscle-tendon unit and bone.

Repetitive stimulation of the nerve innervating the muscle results in repetitive muscle

contractions that are used to drive the generator. The generated power is stored in energy

storage circuitry. A portion of the generated output power will be used to power the nerve

stimulator and the remaining power will be available to power the targeted application.

Existing conversion techniques will be used to convert the mechanical power of the

muscle to electrical power.

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Figure I-2. The generator concept. A piezoelectric stack generator in a mechanical holder is surgically attached in series with a muscle-tendon unit. Stimulation of motor nerve causes sustained isometric muscle contractions, repetitively exerting force on the piezoelectric material. The charge developed in the strained piezoelectric material is stored and utilized in a circuit. A portion of the generated power is used to power the stimulator and the rest is used to power an application such as a neural prosthesis.

2. SELECTION OF MECHANICAL TO ELECTRICAL CONVERSION

METHOD

In addition to this section, further information on the conversion method selection

analysis is located in APPENDIX A. The most common method for converting

mechanical energy to electrical energy is an electromagnetic induction generator.

Electromagnetic induction generators convert kinetic energy to electricity through the

movement of a magnet through a coil, or visa versa. A simple example of a linear

electromagnetic generator is shown in Figure I-3A. A force pushes the magnet through

the coil, the spring reverses the motion and pushes it back through the coil, resulting in

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the magnet moving through the coil in a back and forth motion. The open circuit voltage

generated by the linear electromagnetic generator (VMag) is given in Eq. I-1:

vNBAV CoilMag =

Eq. I-1

Where, N = number of turns of the coil, B = the magnetic strength of the magnet,

ACoil is the cross-sectional area of the coil and v = the velocity of the magnet as it travels

through the coil [16]. While this method is appropriate for many different applications, it

is not an appropriate application for an implantable, muscle driven generator. The reason

for this is that the voltage produced in the coil is dependent on velocity. More voltage,

and ultimately power, is available from the system the faster the magnet moves relative to

the coil. As can be seen from the paragraphs above, fast, vibratory movement is not what

the muscle produces. It produces large amounts of force, but with small displacements.

To avoid fatiguing the muscle, contraction repetition rates must be kept at 1 Hz or less.

The velocity could potentially be increased with the use of a spring or other mechanical

device, but implantation complications will arise with such a design. When a device of

any type is implanted into the body, the body’s response is to encapsulate it with fibrous

growth. Previous attempts at chronically implanting power generating devices that

require movement for operation have resulted in reductions in the efficiency of the

generator due to the fibrous growth. For example, after 12 weeks of operation a 65%

reduction in output pressure was found with a device used to convert muscle power to

pneumatic pressure for cardiac assist [63].

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The method that will be used to convert mechanical energy to electrical energy in

our system is through the use of piezoelectric material, which has a unique property

where charge is generated when the material is strained by an external stress. There are

two popular types of piezoelectric generators, cantilever beam generators and stack

generators, as shown in Figure I-3B and Figure I-3C. Force is repetitively applied at the

tip of a cantilever beam made of piezoelectric material in the cantilever beam

piezoelectric generator. The resulting open circuit voltage of this generator (VPBG) is:

WtLFgVPBG

31

43

=

Eq. I-2

Where, g31 = the piezoelectric constant of the material for the case when the force

is applied perpendicular to the direction in which the material is poled, L = the length of

the piezoelectric beam, W = the width of the piezoelectric beam, t = the thickness of the

beam, and F = force application [64]. The displacement of the beam depends upon the

length of the beam and the elasticity of the material. An estimate of the displacement for

our application would be in the millimeter range. While this is less displacement than in

the case of the electromagnetic generator, this still would most likely suffer from a

decrease in efficiency after implantation, as was seen in a generator developed for

powering a pacemaker. A mass was placed on the end of a single piezoelectric cantilever

beam ceramic wafer (2 cm x 5 cm x 1 cm) and packaged in a box for attachment to the

heart. When 80 bpm mechanical pulses shook the box, the piezoelectric material was

vibrated at 6.5 Hz, resulting in 160 µW of power [45;46]. When chronically driven by

26

actual canine heart contractions, the efficiency of the generator was reduced to a

sustained output power of 30 µW [46]. The reduction in efficiency was due to the

reaction of the tissue to wall-off the generator thus minimizing force transfer to the

generator.

A piezoelectric stack generator is made up of many thin layers of piezoelectric

material mechanically connected in series and electrically connected in parallel. As

depicted in Fig. 1C, a compressive force applied to the stack will result in an open circuit

voltage (VPSG):

AtFgVPSG

33=

Eq. I-3

Where, g33 = the piezoelectric constant of the material for the case in which the

force is applied in the same direction the material is poled, A = cross-sectional area of the

piezoelectric material, t = the thickness of the individual layers of the stack and F is a

compressive force applied to the stack [16;64]. The displacement of the piezoelectric

stack generator is in the micrometer range for force applications in the range possible

from muscles. This amount of movement should be undetectable by the surrounding

tissue. This minimal excursion of the piezoelectric material dictates that isometric muscle

contractions be used. While shortening muscle contractions and long excursions of a

power generating device is the ideal scenario for power production by muscle and may

initially appear to be more advantageous, in the long term the efficiency of such a device

27

will decrease. In contrast, the efficiency of our conversion device should not decrease due

to tissue encapsulation.

Figure I-3. Mechanical to electrical energy conversion methods. A. Linear electromagnetic generator. B. Piezoelectric cantilever beam generator. C. Piezoelectric stack generator.

3. RELEVANT PIEZOELECTRIC MATERIAL PROPERTIES

An illustration of a circuit representation of a piezoelectric generator and a simple

load circuit that can be used to harness the charge developed from strained piezoelectric

material is shown in Figure I-4. A piezoelectric generator can be electrically represented

as a voltage source (Vp) in series with a capacitance (Cp). A simple load circuit includes a

diode bridge, a load capacitor (CL) and a load resistor (RL). Vp depends upon the type of

28

piezoelectric generator used and is describe by equations equating the piezoelectric

voltage to force such as in Eq. I-2 and Eq. I-3. Cp is described by Eq. I-4.

tAEnEC or

p =

Eq. I-4

Where, n = number of layers of piezoelectric material, Er = dielectric constant of

the piezoelectric material, Eo = the dielectric constant of free space = 8.9 pFm-1 and A and

t are as defined above [65]. The diode bridge rectifies the piezoelectric voltage and the

charge generated by the piezoelectric generator is stored in the load capacitor. The

charging time increases and the leakage current decreases as the size of the load capacitor

increases. The load resistor is matched to the impedance of the piezoelectric generator for

maximum power conversion:

pL fC

R 1=

Eq. I-5

Where, f = the frequency of force application [66]. Calculation of the output

power of the generator is achieved using the steady state voltage (VLss) across the load

resistor with Eq. I-6:

29

L

ssLout R

VP

2

=

Eq. I-6

When the impedances are matched, the steady state output voltage will equal one

half of the peak piezoelectric voltage, neglecting the voltage drop in the diodes:

mmp

ssL FV

V2A

tg 2

33==

Eq. I-7

Fm is the peak amplitude of the input force pulse and Vpm is the peak piezoelectric

voltage. Substituting Eq. I-4 into Eq. I-5 and Eq. I-5 and Eq. I-7 into Eq. I-6 results in Eq.

I-8 for the average optimal output power (Pout opt) in terms of the system parameters:

AfEtnEFgfCV

P ormpmpoptout 44

2233

2

==

Eq. I-8

30

Figure I-4. Circuit representation of the generator system. The piezoelectric generator is represented as a voltage source in series with a capacitance. The generator is connected to a half diode bridge, capacitor (CL) and a load resistor (RL). The load resistor is sized to match the impedance of the piezoelectric generator.

From the above equations it is evident that the output power of the generator is

dependent on the material properties of the piezoelectric generator. Ceramic and polymer

materials are the two main classes of material from which commercially available

piezoelectric material is made. Variations in the composition of materials within these

two classes have resulted in many different types of materials with different piezoelectric

properties. Table I-1 lists some different types of ceramic and polymer piezoelectric

material and their piezoelectric and dielectric material properties. The output power of

the generator is dependent on the square of the voltage generated by the piezoelectric

material, its capacitance and the frequency at which the generator is driven. The

piezoelectric voltage is dependent on the piezoelectric constant of the material and the

input force and the capacitance is dependent on the dielectric constant of the material.

While for maximum power all of these variables should be maximized, through

inspection of Table I-1, we see that a tradeoff exists since there is an inverse relationship

between the piezoelectric constants and the dielectric constant. The polymer materials

31

have much higher piezoelectric constants than the ceramic materials, but also have a

much lower dielectric constant.

Table I-1. Properties of example piezoelectric materials

Material type g31 (VmN-1)

g33 (VmN-1) Er

Ceramic Lead Magnesium Niobate - Lead Titanate -0.024 0.043 4629 Lead Zirconate Titanate -0.0095 0.013 5400 Lead Metaniobate -0.007 0.032 270 Barium Titanate -0.005 0.013 1250 Bismuth Titanate -0.004 0.017 120 Polymer Polyvinylidene Fluoride 0.216 N/A 12.5 Copolymer of Polyvinylidene Fluoride 0.162 N/A 7.5

PVDF is typically manufactured into a thin film. From the values in Table I-1 and

the above equations, one can see that the capacitance of PVDF thin films will be very

small in low frequency applications. This will cause the impedance to be large and

difficult to match in the load circuit. This is not well suited for use in a muscle driven

generator since the frequency of muscle contractions needs to be kept low to avoid

fatigue. In addition, application of large forces will result in the production of extremely

large piezoelectric voltages. Since the forces available from the muscle are high, a

method would be needed to step down the generated voltage to a usable level. This would

add more complexity and sources of loss to the system. However, others have

successfully used PVDF generators in their low power biological applications. The

feasibility of a PVDF piezoelectric material mounted on a simply supported beam for use

as a bone strain sensor and telemeter has been assessed. The prototype produced sub

microwatts of power [43]. In another application, PVDF piezoelectric material was rolled

32

into a tube and connected between two ribs in a canine. The rib displacement during

breathing produced a strain on the piezoelectric material, which produced 17 µW of

power for a microprocessor-controlled insulin delivery pump application [44]. While

PDVF was suitable for these low power applications, a ceramic piezoelectric stack was

selected for our application in an effort to achieve greater output power. A ceramic stack

will produce an operating voltage in a useable range in response to the force levels that

will be produced by the muscle and it has a larger capacitance so that the load impedance

can be more easily matched at the low operating frequencies.

4. APPLICATION POWER VS. ENERGY

There are two methods of comparison to determine if the generator can produce

enough power for the target application. The first method is an energy comparison. The

amount of energy needed by an application can be compared to the amount of energy that

can be produced by the generator. The second method, which is the approach we have

taken throughout this study, is to compare the average power needs of an application to

the average power generated. We chose to compare the average power needs to the

average power generated because the maximum power transfer occurs when the load

impedance matches the impedance of the piezoelectric generator and the generator is

producing continuous power through the load. Generation and storage of charge for use at

later time will incur losses, so to analyze the maximum power generation capabilities we

used an average power generation analysis.

33

a) Energy Comparison

The energy (E) needs of the target application depend on the amount of power

(P) it draws and the duty cycle (tC), or the time that it is operational. The amount of

power an application draws depends on the operating voltage (V) and the amount of

charge (Q) it uses per second (tQ). For a dc system, the equations to describe this are:

C

Q

PtEt

VQVIP

=

==

Eq. I-9

where the unit of P is Watts (W) and the unit of E is Joules (J). The amount of energy

needed by an application can be compared to the amount of energy that can be produced

by the generator. The energy that can be stored in the generator is given by:

2LssLVCE =

Eq. I-10

where CL is the storage capacitor and VLss is the steady state voltage of the system. The

time it takes to charge CL to this energy level depends on the size of CL, increasing as the

size increases. Table I-2 provides several sizes of CL, its energy capacity with VLss = 20 V

and the time it takes to charge the capacitor.

Table I-2. Comparison of energy capacity and charging time for different sizes of CL

CL (µF) Energy Capacity (J) Time to Charge (s) 1 0.0005 6 10 0.005 64 100 0.045 785

34

b) Average power comparison

The average power needs of an application can be compared to the average power

generated. For the application, the average power (PAveApp) is:

)( CQ

AveApp kt

VQP

=

Eq. I-11

where kC is the duty cycle fraction. The average power produced by the generator

(PAveGen) is:

L

LssAveGen Z

VP

2

=

Eq. I-12

where VLss is the steady state operating voltage of the generator and ZL is the impedance

of the generator load. The maximum energy transfer occurs when ZL matches the

impedance of the piezoelectric generator. If the load is not matched with the generator

impedance and power is dissipated through the load at variable times, then the power

dissipation will depend on the load impedance. When the switch in Figure I-5 is closed,

the energy in CL will dissipate through RL. If RL has a high impedance, the energy

dissipation will be very slow. If RL has a low impedance, the energy dissipation will be

very fast. If we assume that the application of force to the piezoelectric generator stops

once CL is at its steady state value, and close the switch, then the time it takes to dissipate

35

all of the energy in CL for different values of RL is given in Table I-3, along with the

associated power.

Table I-3. Discharge rate of CL = 100 µF for various sizes of load resistors

RL (kΩ) Discharge time (s) Power (mW) 10 8 5.7 100 84 0.54 1000 836 0.054

Figure I-5. Circuit representation of a piezoelectric stack generator and load circuitry for storage and usage of the generated power.

5. PIEZOELECTRIC CIRCUIT MODELS

A piezoelectric generator can be modeled as a voltage source in series with a

capacitor or a current source in parallel with a capacitor. The two models are equivalent

and produce the same predictions of generator output power. The piezoelectric voltage is

proportional to the applied force and the current source is proportional to the derivative of

the force. We chose to use the voltage source model throughout this study to avoid

differentiation of the force. Many of the simulations we conducted used experimental

force data files as the input, which could be used directly without modification. If the

36

current source model was used we would have had to differentiate the force first, adding

an extra step to the analysis.

a) The voltage source model

Figure I-6. Voltage source model. A piezoelectric stack generator modeled as a voltage source in series with a capacitor.

The piezoelectric voltage (Vp) is given by the equation:

FA

tgVp33=

Eq. I-13

Where, g33 is the piezoelectric constant, t is the thickness of one layer, F is the applied

force and A is the cross-sectional area. The capacitance (Cp) is given by the equation:

tAEnEC or

p =

Eq. I-14

37

Where, n is the number of layers, Er is the relative dielectric constant and Eo is the

dielectric constant of free space.

b) The current source model

Figure I-7. Current source model. A piezoelectric stack generator modeled as a current source in parallel with a capacitance.

The equation for the current source (Ip) is:

dtdFnd

dtdFgEnEI orp 3333 ==

Eq. I-15

Where, dF/dt is the derivative of the force. The piezoelectric constant (g33) is related to

the charge constant (d33) through the following equation:

3333 gEEd or=

Eq. I-16

38

The capacitance (Cp) is given by the equation:

tAEnEC or

p =

Eq. I-17

c) Equivalence of the two models

When the force in Figure I-8 is continuously applied to the piezoelectric stack, the

resulting voltage across RL is shown in Figure I-9. The output voltage is the same whether

the voltage source or current source circuit is used, demonstrating that they are

equivalent.

Figure I-8. Force applied continuously to the piezoelectric stack and the derivative of the force.

39

Figure I-9. Simulation results from application of the force in Figure I-8 to the piezoelectric stack. The top trace uses the voltage source circuit. The bottom trace uses the current source trace. The resulting output voltage is the same for both circuits, demonstrating that they are equivalent.

40

II. DESIGN CONSIDERATIONS

This chapter will provide more detail on the concept and design of the generator. This

chapter has been published as a journal article, with the following citation:

Lewandowski BE, Kilgore KL, Gustafson KJ, Design considerations for an implantable,

muscle powered piezoelectric system for generating electrical power. Ann Biomed Eng,

35(4), 2007, pp. 631-641.

A. ABSTRACT

A totally implantable piezoelectric generator system able to harness power from

electrically activated muscle would augment the power systems of implanted functional

electrical stimulation devices by reducing the number of battery replacement surgeries or

by allowing periods of untethered functionality. The generator design contains no moving

parts and uses a portion of the generated power for system operation. A software model

of the system was developed and simulations performed to predict the output power as

the system parameters were varied within their constraints. Mechanical forces that mimic

muscle forces were experimentally applied to a piezoelectric generator to verify the

accuracy of the simulations and to explore losses due to mechanical coupling. Depending

on the selection of system parameters, software simulations predict that this generator

concept can generate up to 690 µW of power, which is greater than the power necessary

to drive the generator, conservatively estimated to be 46 μW. These results suggest that

this concept has the potential to be an implantable, self-replenishing power source and

warrants further investigation.

41

Key words: Power generation; electrical stimulation; power conversion.

B. INTRODUCTION

Implanted functional electrical stimulation (FES) devices provide beneficial

therapies and functional assistance for patients with severe paralysis. These devices are

powered by batteries implanted along with the device or by transcutaneous power

sources. Replacement of depleted implanted batteries requires frequent, costly surgeries

with increased risk of complications [8]. Transcutaneuos power sources have external

equipment that can be damaged, burdensome to carry, cosmetically unappealing and

cannot be used in a wet environment. Misalignment of the external and internal coils can

cause power interruptions [10;11] and the heat generated by the inherent resistance of the

coils has the potential to cause tissue necrosis or an inflammatory reaction [10]. The use

of stimulated muscle power to drive a self-replenishable, totally implantable power

source could augment the power systems that are currently used. It could extend the

lifetime of implanted batteries, reducing or possibly eliminating the number of required

replacement surgeries. Or, it could augment transcutaneous power sources by allowing

periods of untethered FES device functionality during which a shower or other types of

daily activities could be performed independently.

The fundamental concept of our implanted generator is to place a piezoelectric

stack generator in series with a muscle-tendon unit as illustrated in Figure II-1. The

generator is attached between the muscle-tendon unit and bone such that isometric

muscle contractions result from stimulation of the nerve innervating the muscle. A

42

mechanical device is used to hold the piezoelectric generator in place and to convert the

tensile force produced by stimulated muscle contractions into a compressive force that is

applied to the piezoelectric material. Repetitive stimulation of the motor nerve results in

muscle contractions that exert a repetitive force on the piezoelectric material. Due to the

electromechanical properties of the piezoelectric material, charge will develop when it is

strained from the applied compressive forces. A portion of the resulting charge will be

used to power the nerve stimulations and the remaining charge will be available to power

the targeted application.

Figure II-1. The generator concept. A piezoelectric stack generator in a mechanical holder is surgically attached in series with a muscle-tendon unit. Stimulation of motor nerve causes sustained isometric muscle contractions, repetitively exerting force on the piezoelectric material. The charge developed in the strained piezoelectric material is stored and utilized in a circuit. A portion of the generated power is used to power the stimulator and the rest is used to power an application such as a neural prosthesis.

43

Others have evaluated the use of piezoelectric generators to harness the energy

associated with various physiological processes. A variety of prototypes have been

developed, using different types of piezoelectric material with different loading

strategies, producing a range of power generation results. Elvin et al. used a single piece

of polyvinylidene fluoride (PVDF) piezoelectric material mounted on a simply supported

beam as a bone strain sensor and telemeter, which produced approximately 0.1 μW of

power [43]. Hausler et al. rolled PVDF piezoelectric material into a tube and connected it

between two ribs in a canine. The rib displacement during breathing produced a strain on

the piezoelectric material, which produced 17 μW of power [44]. Ko placed a mass on the

end of a single piezoelectric cantilever beam ceramic wafer (2 cm x 5 cm x 1 cm) and

packaged it in a box for attachment to the heart. When 80 bpm mechanical pulses shook

the box, the piezoelectric material was vibrated at 6.5 Hz, resulting in 160 μW of power

[45;46]. When chronically driven by actual canine heart contractions, the efficiency of

the generator was reduced to a sustained output power of 30 μW [46]. The reduction in

efficiency was due to the reaction of the tissue to wall-off the generator thus minimizing

force transfer to the generator.

Our generator is less invasive than these previous designs, it has a more natural

attachment in series with the muscle tendon unit and it operates with essentially with no

moving parts. Attempts at chronically implanting power generating devices that require

movement for operation have resulted in reductions in the efficiency of the generator due

to fibrous growth. For example, after 12 weeks of operation a 65% reduction in output

pressure was found with a device used to convert muscle power to pneumatic pressure for

cardiac assist [63]. Fibrous growth around our generator will be tolerable because the

44

displacement of the piezoelectric stack is only in the micrometer range, a movement that

should be undetectable by the surrounding tissue. This minimal excursion of the

piezoelectric material dictates that isometric muscle contractions be used. While

shortening contractions and long excursions of a power generating device might initially

appear to be more advantageous, in the long term the efficiency of such a device will

decrease. In contrast, the efficiency of our conversion device should not decrease due to

our unique design features.

Our design incorporates the use of electrically-stimulated muscle contractions,

which is a well established method for restoring function in spinal cord injury patients

[3]. A portion of the power produced by the piezoelectric generator will be used to

operate the electrical stimulator, which will produce the regular pulses that activate the

muscle driving the piezoelectric generator. Theoretically, the output power of the

generator will be greater than the power required to activate the driving stimulator since

skeletal muscle is an autologous power source. The mechanical output power of a muscle

is substantially greater than the electrical power necessary for artificial stimulation of the

motor nerve. A conservative estimate of the sustained output power of stimulated,

conditioned muscle producing isotonic tetanic contractions is 1 mW/g [49;61;62]. The

human latissimus dorsi is approximately 150 g [59;60], corresponding to an output power

of 150 mW. An estimate of the electrical power needed for stimulations to produce this

amount of muscle output power is 0.5 μW, calculated from the stimulation parameters

[49]. Simply comparing the electrical stimulation input power to the muscle output

power, muscle is a power conversion system with a multi-order gain (five orders of

magnitude of gain in this simplified example). The gain is achieved through the chemical

45

energy obtained from nutrients. In addition, as the size of the muscle increases the output

power increases. However, the stimulus amplitude required to fully activate the nerve of

different sized muscles is essentially the same relative to the differences in output power.

Therefore, the gain available between the input power necessary to stimulate a muscle

and the mechanical output power of the muscle increases as the size of the muscle

increases. Three potential muscles are examined to represent the range of potential power

sources. Therefore, the muscle requirements for novel applications may be determined.

Electrically-stimulated power generation has some significant advantages over

power scavenging schemes when considering a power source for neuroprosthetic

applications. We hypothesize that more power can be obtained from a stimulated muscle

than from scavenging power from intermittent processes such as the strain experienced

by bone or by naturally occurring muscle contractions, even though the stimulation

utilizes some of the power generated by the system. Since our targeted applications are

for individuals with extensive paralysis, such as spinal cord injury, naturally occurring

muscle contractions are significantly reduced. However, a paralyzed muscle could be

used to run the generator to provide power for restoration of other functions. The system

parameters dependent on frequency can be easily tuned for optimal performance if a

consistent pattern of operation is used. For these reasons, we have incorporated into our

design the use of stimulated-muscle contractions to drive our implanted generator.

This study was performed to determine the feasibility of a stimulated muscle

powered piezoelectric generator. The theoretical output power of such a generator was

compared to the power necessary for motor nerve stimulation. The output power of the

generator was estimated with simulations of a software circuit model developed to

46

represent the system. The model included the input force from the muscle, the

piezoelectric material and the load circuit. The constraints of the system parameters were

identified and simulations were performed to evaluate how changes to the system

parameters within those constraints affect the output power. Force that mimics the force

produced by muscles during contraction was applied mechanically to a non-optimized

prototype system. Compressive force was applied directly to a piezoelectric generator and

tensile force to a mechanical device built as a holder and connector for the piezoelectric

generator. The results were used to determine the accuracy of the software model and to

determine power losses due to mechanical coupling.

C. METHODS

1. SOFTWARE MODEL

a) Software model circuit representation

The circuit representation of our system concept is shown in Figure II-2. The

equations introduced in the following paragraphs describe the circuit components. The

piezoelectric stack generator was electrically represented as a voltage source (Vp) in

series with a capacitor (Cp). Vp depends upon the applied input force, the piezoelectric

constant and the shape and the dimensions of the material:

FA

tgVp33=

Eq. II-1

47

The piezoelectric constant (g33) is the electromechanical property of the material, t

is the thickness of one layer of the stack, A is the cross-sectional area of the generator and

F is input force, which results from muscle contractions for our application [65;67].

Triangle pulses with a pulse width of 250 msec were used to represent the force of a

muscle contraction. In the software simulations a piece-wise linear data file of the force

waveform was used.

Figure II-2. Circuit representation of the generator system. The piezoelectric generator is electrically represented as a voltage source (Vp) in series with a capacitor (Cp). Vp is proportional to the applied force. A diode bridge and filter capacitor were used to obtain a DC load voltage (VL). VL was recorded across the load resistor (RL) and used to calculate the system output power.

The layers of stack generators are electrically connected in parallel, so the total

capacitance of the stack is the capacitance of one layer multiplied by the number of layers

in the stack. The dependence of the capacitance upon the shape and dimensions of the

material and on the material’s dielectric constant is given by:

tAEnEC or

p =

Eq. II-2

48

The number of layers equals n, Er is the relative dielectric constant and Eo is the

dielectric of free space (8.9x10-12 Fm-1) [65;67].

A diode bridge and filter capacitor (CL) were used to convert the piezoelectric

voltage to an approximately DC voltage source across a load resistor (RL). A small

decrease in the steady state output voltage during each cycle (voltage ripple) is present

due to the leakage current of the circuit. Increasing the size of CL reduces the ripple,

however, it also increase the time it takes the generator to reach its steady state voltage.

The amount of ripple that can be tolerated will depend on the load connected to the

generator, dictating the size of CL and the charging time of the generator. For this study

CL was chosen to be 100 times greater than Cp.

The output power of the system (Pout) is the power dissipated through the load

resistance. It can be calculated as:

L

ssLout R

VP2

=

Eq. II-3

RL is the load resistor and VLss is the steady state voltage across the load resistor.

The maximum output power of the generator occurs when the load impedance matches

the impedance of the piezoelectric generator [66]:

49

pL fC

R 1=

Eq. II-4

The frequency of force application is f. When the impedances are matched, the

steady state output voltage will equal one half of the peak piezoelectric voltage,

neglecting the voltage drop in the diodes:

mmp

ssL FV

V2A

tg 2

33==

Eq. II-5

Fm is the peak amplitude of the input force pulse and Vpm is the peak piezoelectric

voltage. Substituting Eq. II-2 into Eq. II-4 and Eq. II-4 and Eq. II-5 into Eq. II-3 results in

Eq. II-6 for the average optimal output power (Pout opt):

AfEtnEFgfCV

P ormpmpoptout 44

2233

2

==

Eq. II-6

b) Software simulations within parameter constraints

Through inspection of Eq. II-6 the relationship between the system parameters

and output power can be determined. The output power increases as the piezoelectric and

dielectric constants increase. However, these parameters are not independent.

50

Piezoelectric material that has a high piezoelectric constant typically has a low dielectric

constant. This results in stacks with either a high output voltage but low capacitance or a

low output voltage but high capacitance. In Figure II-3, the relationship between the

dielectric constant (Er) versus the piezoelectric constant (g33) is shown for several

different commercially available piezoceramic materials, as specified in commercial data

sheets. For these particular materials, a decaying exponential relationship was fitted

between Er and g33 with an r2 value of 0.91:

334.64572,11 gr eE −=

Eq. II-7

Figure II-3. Relationship between piezoelectric and dielectric constants. The piezoelectric (g33) and dielectric constants (Er) for several commercially available piezoelectric materials were plotted to identify the relationship between the two constants. The data points were obtained from the manufacturer’s data sheets. The fitted relationship was

51

334.64572,11 gr eE −= , R2 = 0.91. The g33, Er pair that results in maximum power was g33 =

0.0325 VmN-1, Er = 1427, determined through software simulations.

To increase the output power of the stack generator for this application, the length

of the generator (the thickness of one layer times the number of layers) should be

increased and the cross-sectional area should be decreased. Therefore, a long, slim stack

is the best shape for the stack generator. This shape lends itself to a serial connection

between tendon and bone, as proposed in our design. The limit on the overall length of

the generator depends on the space available for implantation. Since the generator will

essentially replace the tendon, the generator length can be designed to be approximately

the length of the tendon. The generator length used in the simulations was chosen based

on the tendon lengths. We assume that muscle length will not be significantly increased

by the incorporation of the generator and artificial tendon connection into (or replacing)

the natural tendon. The tendon lengths of skeletal muscles can range from 50 mm for the

brachioradialis muscle in the forearm to 200 mm for the gastrocnemius in the leg [60].

There is a lower limit to the cross sectional area of piezoelectric material that can be

machined and if the cross sectional area of the stack is made too small there is a risk of

breaking the generator as force is applied.

The output power of the generator will increase as the amplitude and frequency of

the input muscle force increases. Muscle force increases as the cross-sectional area of the

muscle increases and will depend upon what muscle is chosen to run the generator.

Estimates of the maximum contraction forces can be found by multiplying the muscle’s

physiological cross sectional area by a conversion factor of 35 Ncm-2 [47]. For sustained

52

operation of the generator it will be necessary to use submaximal muscle contractions.

The cross-sectional area of small forearm muscle such as the brachioradialis has been

reported to be between 1.5 and 4.7 cm2 [59;60]. It is 7.5 to 25 cm2 for a midsized muscle

such as the latissimus dorsi [58;60] and 25 to 60 cm2 for a large muscle such as the

gastrocnemius [57;60]. Based on these cross-sectional areas and a conservative

submaximal force level of 10 – 30 % of maximum, an estimate of the range of possible

input muscle forces was determined to be 25 – 250 N. The upper limit of the sustained

frequency of the input force will be dictated by the rate at which the muscle can sustain

contractions without fatigue. Table II-1 summarizes the system parameter constraints.

Table II-1. Summary of system parameter constraints

Parameter Symbol Physical or physiological constraint

Range of values

Piezoelectric constant g33 Material properties 0.014 – 0.054 VmN-1

Dielectric constant Er Material properties 400 – 5800

Number of layers N Space for implantation 25 – 1500

Thickness of one layer T Manufacturing processes 0.13 – 2 mm

Length L Space for implantation 50 – 200 mm

Area A Manufacturing processes 0.06 – 4 cm2

Input force frequency F Muscle fatigue 0.5 – 2 Hz

Peak input force Fm Size of muscle and stimulation parameters

10 – 250 N

Note: For maximum output power, all parameters should be maximized except for area, which should be minimized. There is an inverse relationship between g33 and Er. A proper ratio must be maintained between the length (L = nt) and the area. The number of layers and the thickness of one layer can be used to set the output voltage of the generator. There is an inverse relationship between Fm and f.

53

Simulations were performed with SPICE software (EMA Design Automation,

Inc., Rochester, NY) to predict the theoretical output power of the generator as the

system parameters were varied within the constraints imposed by the properties of the

piezoelectric material and by the physiological constraints. The output power was

calculated using Eq. II-3, using the simulated steady state output voltage across the load

resistor (RL). Once the parameters that result in maximum output power were identified,

the predicted output power for three scenarios was found. Scenario 1) is a 2.5 cm long

generator with an input force of 50 N, such as would be appropriate if the generator was

developed for use with a brachioradialis muscle. Scenario 2) is a 4 cm long generator

with a 100 N force, for use with a muscle such as the latissimus dorsi. Scenario 3) is an 8

cm long generator, with an input force of 250 N, such as for use with a gastrocnemius

muscle. The rest of the parameters were held constant across the three scenarios at values

corresponding to those found in the parameter simulations to result in maximum output

power within the constraints of the system.

c) Muscle stimulation power requirements (Input Power)

Some of the generated power will be used to electrically stimulate the muscle

which drives the generator. This will be referred to as input power. The amount of

required input power consists of two parts, stimulation power and controller power. The

amount of stimulation power required depends upon the pulse width and amplitude of the

stimulating current pulse, the frequency and duration of the stimulus and the rate of

stimulation, resulting in a range of possible stimulation power requirements. At the high

end of this range, is the estimate of 6 μW of power necessary for tetanic contractions.

54

This is based on 500 μs pulses of 1 mA, applied at 50 Hz for 250 ms per contraction at a

rate of 1 contraction per second, assuming a 1 kΩ impedance. The low end of the range is

an estimate of 50 nW, for the power necessary for 1 Hz muscle twitches. This is based on

single current pulse of 500 μA for 200μs through a resistance of 1kΩ, operating at 1 Hz.

In addition to the power necessary for stimulation, power will also be needed for a

stimulator controller. A controller for a single channel stimulator continuously consumes

an average power of approximately 40 μW when the device is on [68]. Therefore, a

conservative estimate of the required stimulation power for our design is the controller

power plus the stimulation power, or approximately 46 μW. However, it is likely that this

amount could be reduced by using a simpler controller.

2. EXPERIMENTAL METHODS

Force was applied to a non-optimized prototype system with a material testing

system (MTS) machine (MTS Systems Corporation, Eden Prairie, MN) to verify the

accuracy of the software simulations and to explore possible sources of power loss within

the system. A lead zirconate titanate (PZT) piezoelectric stack generator (part number

T18-H5-104, Piezo Systems, Inc. Cambridge, MA), with a volume of 0.5 cm3 (5 mm x 5

mm x 18 mm), was used in the experimental trials. The piezoelectric material of the stack

had a piezoelectric constant of 0.013 VmN-1 and a relative dielectric constant of 5400.

The thickness of each layer was 0.11 mm and the stack contained approximately 164

layers. These values were specified by the manufacturer.

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The piezoelectric generator was connected to the circuit shown in Figure II-2. A

100 µF filter capacitor (CL) was chosen to balance between charging time and voltage

ripple. Cp was measured to be 1.86 μF, so a 540 kΩ load resistor (RL) was used, which

was calculated using Eq. II-4. The MTS machine was used to apply compressive force

directly to the piezoelectric stack. The applied force consisted of 250 ms triangle force

pulses at 1 Hz with peak values of 25, 50, 100, 150, 200 and 250 N. For each trial, the

pulses were applied for 240 seconds while the voltage was recorded across RL. The output

power of the system was calculated with Eq. II-3 using the resulting steady state voltages

from the six trials. The parameters values of the piezoelectric stack and load circuit used

in the mechanical experiments were entered into the circuit model and software

simulations were performed using the same force values as used in the mechanical

experiments. The experimental output power was compared to the software simulations

in order to verify the accuracy of the model.

A mechanical device was built as a holder and connector for the piezoelectric

generator. A picture of the mechanical holder is shown in Figure II-4. Since the muscle-

tendon unit will always be producing tension, the mechanical device was designed to

convert the tensile force produced by the muscle into a compressive force applied to the

stack. The MTS machine was also used to apply tensile force to the mechanical device

containing the piezoelectric generator. The applied tensile force consisted of 250 ms

triangle force pulses at 1 Hz with peak values of 25, 50, 100, 150, 200 and 250 N. The

pulses were applied for 240 seconds and the recorded steady state voltages across RL

were used to calculate the output power. The differences in output power between force

56

applied directly to the stack and force applied to the piezoelectric stack in a mechanical

device was compared to determine losses due to the mechanical coupling.

Figure II-4. Photo of the mechanical holder. A mechanical device was built to hold the piezoelectric stack and convert the tensile force of muscle into a compressive force applied to the piezoelectric stack. When tensile force is applied between the two attachment sites a compressive force results between the top and bottom plates of the holder. The piezoelectric stack experiences the compressive force since it is held in place between the top and bottom plates.

D. RESULTS

1. MODEL RESULTS

Figure II-5 contains the results of the SPICE simulations that were performed to

predict the output power of the system as the system parameters were varied within their

constraints. Using the relationship found between g33 and Er, the maximum output power

occurs when g33 is approximately 0.0325 VmN-1 and Er is 1427 (Figure II-5 (A)). The

output power increases with increasing length (L) (the thickness of one layer times the

number of layers) and decreases with increasing cross sectional area (Figure II-5 (B)).

The output voltage can be increased by increasing the thickness of the individual layers,

while keeping the overall length constant. This will not increase the output power since

57

the number of layers will decrease. However, by changing the thickness of the layers the

output voltage of the system can be controlled and appropriately matched to the load

connected to the generator. Figure II-5(C) illustrates how the output power increases as

the rate of the applied input force increases. However, muscle fatigue will likely occur at

higher frequencies. The output power increases quadratically as the amplitude of the

input force increases, as shown in Figure II-5(D). Example of muscles that can produce

force in the three highlighted ranges is also given. The values used for the parameters

when they were not varied were, g33 = 0.0325 VmN-1, Fm = 50 N, L = 0.018 m, Er =

1427, f = 1 Hz, A = 5 mm x 5 mm.

Figure II-5. Predicted output power as a function of system parameters. A. Output power vs. the piezoelectric constant (g33) using the relationship between Er and g33 found in Fig. 3. The g33, Er pair that results in maximum power is g33 = 0.0325 VmN-1, Er = 1427. B. The length (L) (the thickness of one layer times the number of layers) is varied from 0 to 10 cm for three different cross sectional areas. The output power increases with increasing length and decreases with increasing cross sectional area. C. The output power increases as the

58

rate of the applied input force increases. The higher the frequency, the more likely muscle fatigue will occur. D. The output power increases quadratically as the amplitude of the input force increases. An example of a muscle that can produce the force in the three highlighted ranges is given. The values used for the parameters when they were not varied were, g33 = 0.0325 VmN-1, Fm = 50 N, L = 0.018 m, Er = 1427, f = 1 Hz, A = 5 mm x 5 mm.

The results of the simulations performed to predict the output power of the three

generator scenarios is shown in Figure II-6. The predicted output power for the three

generator scenarios was: 1) 8 μW for a 2.5 cm generator with 50 N peak input force; 2)

54 μW for a 4 cm generator with 100 N peak input force; 3) 690 μW for an 8 cm

generator with 250 N peak input force. The power required for a stimulator controller and

for the range of possible stimulation power requirements is also shown in Figure II-6 for

comparison.

Figure II-6. Predicted output power for three generator scenarios. SPICE simulations were performed to predict the output power for three generator scenarios: 1) A 2.5 cm long generator with 50 N peak input force, which would be appropriate if the generator was

59

connected to the brachioradialis muscle. This scenario resulted in 8 μW of power; 2) A 4 cm long generator with 100 N peak input force, resulting in 54 μW. An example of a muscle for this scenario is the latissimus dorsi; 3) An 8 cm long generator with 250 N input force could be used with a muscle such as the gastrocnemius, resulting in 690 μW. All other parameters were constant for the three scenarios and were: g33 = 0.0325 VmN-1, Er = 1427, f = 1 Hz, A = 5 mm x 5 mm. These parameter values correspond to those found in the parameter simulations to result in maximum output power, within system constraints. The range of power required for motor nerve stimulation and the power required for a single channel stimulator controller are shown for comparison.

2. EXPERIMENTAL RESULTS

The output voltage resulting from direct repetitive compression of the

piezoelectric stack with the MTS machine is shown in Figure II-7. The voltage across RL

increases from zero to a steady state value. The output voltage is proportional to the

applied force and increases as the force increases. The steady state voltage ranged from

0.33 V when 25 N force pulses are applied to 6.1 V when 250 N force pulses are applied.

The steady state voltages were used with Eq. II-3 to determine the output power of the

generator system when it was subjected to direct compression. The output power was also

calculated from the steady state voltages resulting from repetitive tensile force applied to

the mechanical holder containing the piezoelectric stack. These experimental output

power values were compared to the simulated output power results in Figure II-8.

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Figure II-7. Output voltage resulting from repetitive force application. Triangle force pulses with a 250 ms pulse width were mechanically applied with a MTS machine at 1 Hz for 240 s with six different peak force values, 25, 50, 100, 150, 200 and 250 N, to a non-optimized piezoelectric generator connected to the circuit shown in Figure II-2. The output voltage was proportional to the applied force and increased as the force was increased. The steady state voltage when 25 N force pulses are applied was 0.33 V. It was 1.26, 2.23, 3.52, 4.85 and 6.1 V for 50, 100, 150, 200 and 250 N force pulses respectively. The steady state voltages were used with Eq. II-3 to determine the output power of the generator system.

The output power results obtained in the simulations matched the output power

resulting from direct compression of the piezoelectric stack. An average difference of 4

µW was observed over the range of input forces, from 25 to 250 N (Figure II-8). When

the output power resulting from direct compression of the stack is compared to the output

power resulting from tensile force applied to the mechanical device, the output power

was essentially the same over the range of 25 to 250 N (Figure II-8). The average

difference was 0.08 µW.

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Figure II-8. Simulation and experimental output power comparison. The simulated output power over a range of input force from 25 to 250 N is compared to the experimental output power resulting from mechanical force applied directly to the piezoelectric stack and to the stack in the mechanical holder. The experimental output power was calculated using Eq. II-3 with the steady state voltage levels measured across the load resistor. The simulated output power corresponds well with the experimental output power, demonstrating the accuracy of the software model. There is essentially no difference between the output power when force is applied in compression directly to the stack and when it is applied in tension to the mechanical holder. This demonstrates that the mechanical holder can be used without significant mechanical coupling losses.

E. DISCUSSION

Our results provide evidence that a stimulated muscle powered piezoelectric

generator system may be feasible for extending the life of, or possibly eliminating, the

batteries of implanted electronic devices. It also may be possible to use the generator to

allow for periods of untethered FES device functionality. Simulations of the software

model of our system were used to identify parameter values which maximize the output

power of the system, within the system constraints. Our simulations predict that with an 8

cm long generator and 250 N input force pulses, 690 μW of power may be achieved by

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an implanted, muscle powered piezoelectric generator. This is greater than the

conservative estimate of the necessary input power of 46 μW, which includes the power

requirements of a stimulator controller and for motor nerve stimulation. It is predicted

that a 4 cm long generator with 100 N input force pulses will produce 54 μW of output

power, also in excess of the stimulation power required to drive the generator. For a 2.5

cm long generator with 50 N input force pulses, a lower power stimulator will need to be

developed in order for the generator to produce more output power than required

stimulation power.

It may be possible to reduce the amount of required stimulation input power by

using a simpler controller. If the stimulation pattern is continuous and unchanging and no

sensing is needed, it should be possible to reduce the controller’s power requirements.

Another possible way to reduce the input power requirements is to design one controller

that combines the control functions needed for both the stimulations to drive the

generator and another functional electrical stimulation application. Additionally, current

research may lead to reductions in the power requirements of stimulator controllers. For

example, Wong et al. developed a pacemaker that combined the sensing, controlling and

stimulation delivery into a single, very-low-power integrated circuit that consumed only 8

μW of power [69]. The theoretical output power of our generator was based on

continuous operation. The power requirements of targeted applications may require large

bursts of power during short periods of time. Thus, electrical circuitry will be needed to

match these different duty cycles and may cause increased power losses within the

system.

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The two key parameters in our design will be the selection of the muscle used to

drive the generator and the rate of muscle contraction. A large muscle will produce more

force and output power than a small muscle. However, implementation may be easier

with a small muscle and the use of a redundant muscle is attractive in order to minimize

the effect of the loss of functionality of the muscle used to run the generator. The

presented analysis may be used to determine the required muscle sizes for novel

applications. The force produced by muscles also varies depending on the stimulation

frequency. Low frequency single pulse stimulations will require less stimulation power,

but will result in low force muscle twitches. High frequency stimulation pulse trains will

produce maximal tetanic force, but will require greater input stimulation power.

Additionally, the rate at which muscle contraction can be sustained depends on the

fatigability of the muscle. Studies have shown that 500 ms tetanic contractions can be

sustained without fatigue at a rate of 40 contractions per minute in conditioned muscle

[49]. Since twitch contractions are less fatiguing then tetanic contractions, it may be

possible to sustain twitch contractions a higher rate, however, studies have shown that

twitch contractions repeated at 2 Hz in conditioned muscle produced fatigue after 116

minutes [70]. Clearly, the trade-offs between amplitude and rate of force production,

input power, and fatigue will be critical when specifying the motor nerve stimulation

patterns.

We expect that the muscle contractions produced as part of the muscle-powered

piezoelectric generator will be tolerable to the users. This is based on the experience of

spinal cord injured individuals who utilize implanted neuroprostheses for hand function

[6]. In order to build and maintain muscle bulk and fatigue resistance, these individual’s

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muscles are exercised through electrical stimulation for eight hours a day. This repetitive

stimulation of the paralyzed muscle is usually performed at night while the individual is

sleeping and discomfort as a result of the stimulations has not been reported [6].

There was good agreement between the simulated and experimental results

demonstrating that the software model accurately represents the piezoelectric generator

system and can be used to evaluate system performance. The software model electrically

represented a piezoelectric generator operating at low frequency, similar to the methods

used elsewhere to model piezoelectric generators [43;45;65;67]. The software model

developed for this study, along with data from the literature, will be used to investigate

the major trade-offs of the system and will be used to identify the stimulation patterns

that result in maximum output power. In addition, the software model will be used to

develop and assess design changes in an effort to improve system performance.

Our results demonstrate that a mechanical device can be used to hold the

piezoelectric stack and convert tensile force into a compressive force applied to the stack,

without significant mechanical coupling losses. However, strategies for in vivo

attachment between the tendon and the mechanical device and between the device and

the bone need to be developed further. The sharp corners of the current holder were

convenient to machine, but will need to be rounded in future implantable versions. The

tendon attachment strategy will likely use artificial tendon. Artificial tendon is a

commercially available product (for example, CardioEnergetics, Inc., Cincinnati, OH)

that has been used for other purposes. For example, Trumble et al., found that connecting

their ventricular assist device to artificial tendon made of polyester fibers and

incorporating it into the natural tendon was more stable than connecting the device

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directly to natural tendon [71]. Additionally, it is likely that existing bone attachment

strategies developed for orthopedic prosthetics can be used to attach our generator to a

bone in close proximity to the tendon. Ideally, the muscle-tendon-generator system will

be attached across the length of a single long bone so that no limb movement is produced

during electrical stimulation of the muscle. The next step of development towards a

tangible implantable generator requires demonstration of closed-loop operation of a

prototype system in an ex vivo or in vivo animal model. A prototype system should

include a low power consuming stimulator and electrical circuitry which allows closed-

loop operation and storage of excess power.

F. CONCLUSION

The results of this study provide evidence that a stimulated muscle powered

piezoelectric generator system may be feasible for extending the life of the batteries of

implanted electronic devices or for allowing periods of FES device use untethered from

external power sources. Simulations performed in this study predict that approximately

690 μW of power can be achieved by a muscle powered implanted piezoelectric

generator that is 8 cm long and to which peak force pulses of 250N are applied. This is

greater than the necessary input power, conservatively estimated to be 46 μW. These

results suggest that this concept has the potential to be an implantable, self-replenishing

power source and should be investigated further.

G. ACKNOWLEDGEMENTS

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This project is funded by NASA Glenn Research Center’s Alternate Energy

Foundational Technologies Project, which is part of the NASA Vehicle System Program

of the Aeronautics Research Enterprise, NIH HD40298 and The State of Ohio BRTT 03-

10. The NASA Glenn Research Center's Mechanics and Lifing Branch of the Structures

Division is acknowledged for their generous support of this project by conducting the

mechanical test in their Fatigue Lab. William Brown (Sierra Lobo) is particularly

recognized for conducting the mechanical tests. Katie Hallahan (Case Western Reserve

University Biomedical Engineering student) is acknowledged for her contribution to the

design of the mechanical holder and to the experimental design of the mechanical tests.

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III. IN-VIVO DEMONSTRATION OF GENERATOR CONCEPT

This chapter describes the in-vivo experiments performed to demonstrate feasibility of the

generator concept. This chapter will be submitted as a journal article to Annals of

Biomedical Engineering.

A. ABSTRACT

An implantable, stimulated-muscle-powered piezoelectric active energy

harvesting generator was previously designed to exploit the fact that the mechanical

output power of muscle is substantially greater than the electrical power necessary to

stimulate the muscle’s motor nerve. We reduced to practice the concept by building a

prototype generator and stimulator. We demonstrated its feasibility in-vivo, using rabbit

quadriceps to drive the generator. The generated power was sufficient for self-sustaining

operation of the stimulator and additional harnessed power was dissipated through a load

resistor. The prototype generator was developed and the power generating capabilities

were tested with a mechanical muscle analog. In-vivo generated power matched the

mechanical muscle analog, verifying its usefulness as a test-bed for generator

development. Generator output power was dependent on the muscle stimulation

parameters. Simulations and in-vivo testing demonstrated that for a fixed number of

stimuli/minute, two stimuli applied at a high frequency generated greater power than

single stimuli or tetanic contractions. Larger muscles and circuitry improvements are

expected to increase available power. An implanted, self-replenishing power source has

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the potential to augment implanted battery or transcutaneously powered electronic

medical devices.

Key words: Piezoelectric energy conversion, mechanical muscle power, electrical

stimulation, rabbit

B. INTRODUCTION

Implanted electronic medical devices, such as pacemakers, deep brain stimulators,

neurostimulators and intramuscular stimulators, are commonly used to provide beneficial

therapies and increase quality of life [2-6]. However, power management of these devices

remains a technical challenge. Power consuming devices such as neurostimulators use

batteries implanted along with the device and require replacement surgeries when the

batteries are depleted. Each surgery is costly and carries the common risks of surgical

procedures [7-9]. Applications such as intramuscular stimulation have greater power

requirements and may use transcutaneous power sources to provide high levels of energy

transfer between external and internal coils or wires. The disadvantage of transcutaneous

systems is the need for external equipment, which can be damaged, is burdensome to

carry, is cosmetically unappealing and cannot be used in a wet environment [10;11]. A

totally implantable electrical power source that is replenished by conversion of an energy

source within the human body may be an advantageous alternative or augmentation to

implanted batteries or transcutaneous power sources. The number of required battery

replacement surgeries could be reduced or possibly eliminated. Periods of intramuscular

69

device functionality untethered from external equipment could be possible, during which

a shower or water therapy could be performed independently.

The concept of converting both external and internal human energy sources into

electrical power has been studied for a variety of applications. For example, the thermal

energy from surface body heat has been converted to electrical energy for powering wrist

watches [72]. Human powered generators that convert mechanical energy to electricity

include hand cranks for powering radios, shake generators for flashlights, cycle driven

portable generators [39], heel strike generators for lessening the weight burden that

soldiers carry [41], inductive and piezoelectric generators incorporated into hiking

backpacks for powering mobile communication devices [38;40] and a regenerative brake

located at the knee joint that operates using the negative work of locomotion for

powering prosthetic limbs [37]. Research and development of implanted generators has

included thermoelectric generators driven by body heat [42] and piezoelectric generators

driven by bone strain [43;73], acceleration during locomotion [74], the motion of

respiration [44] and heart contractions [45;46]. The power generated from these

generators have been in the μW or sub-μW range and the potential applications have been

small power consuming devices, such as telemetry of sensor data, drug pump delivery

systems and pacemakers.

We have been developing a unique, implantable, active energy harvesting

generator driven by stimulated skeletal muscle contractions. An advantage of skeletal

muscle is that it contains a significant amount of potential chemical energy. A

conservative estimate of the sustained mechanical output power of stimulated,

conditioned skeletal muscle producing isotonic contractions is 1 mW/g [49;61;62]. The

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mass of human limb and trunk muscles range from 10 - 1000 g [60] and therefore the

mechanical power available for conversion could be as great as 1 W. Active energy

harvesting uses a small portion of the generated power to control the system in order to

increase overall power transfer [36]. Our generator takes advantage of the fact that the

μW’s of electrical power necessary to stimulate a motor nerve is orders of magnitude less

than the mW’s of mechanical power available from muscle contractions or that can be

harvested with piezoelectrics [75]. Motor nerve stimulation is used drive muscle

contractions to occur in a constant and consistent pattern. We have chosen to use a

piezoelectric stack to convert the mechanical power of the stimulated muscle into

electrical power. The advantage of a piezoelectric stack is its small displacement, in the

μm range. That limits the decrease in efficiency due to fibrous growth encapsulation and

increases reliability by having no moving mechanical parts that could break.

The concept for the implantable, stimulated-muscle-powered piezoelectric

generator is shown in Figure III-1. A piezoelectric stack generator in a mechanical holder

is surgically attached between a bone and a muscle-tendon unit. A muscle that is

paralyzed for which restoration of function is not anticipated or a redundant muscle

whose function can be sacrificed are the types of muscles that are targeted to drive the

generator. The motor nerve of the muscle is electrically stimulated to produce isometric

muscle contractions, which repetitively exert force on the piezoelectric generator. As

force is applied, the piezoelectric material is strained causing charge to develop, which is

stored in electrical circuitry. A portion of the generated power is used to stimulate the

motor nerve and the rest is available to power an implanted medical device application.

Further details about the generator design have been previously reported in [75;76].

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Figure III-1. The implantable, stimulated-muscle-powered piezoelectric energy generator concept. A piezoelectric stack generator in a mechanical holder is surgically attached between a bone and muscle-tendon unit. Stimulation of the motor nerve causes isometric muscle contractions, repetitively exerting force on the piezoelectric generator. The charge developed by the strained piezoelectric material is stored in electrical circuitry. A portion of the generated power is used to power the stimulator and the rest is available to power an implanted medical device application.

Muscle force is the system parameter that has the largest effect on generator

output power. The output power increases quadratically with increases in amplitude and

linearly with increases in the frequency of the muscle force [75]. The amplitude of

muscle force is dependent on the size of the muscle and the stimulation pattern (number

of pulses, frequency and repetition rate) applied to the motor nerve [48;50-55]. Both

muscle amplitude and frequency should be as large as possible for maximum output

power. However, for sustained muscle activity without fatigue, there is a trade-off

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between smaller force muscle twitches repeated at a faster rate and larger force tetanic

contractions repeated at a slower rate.

An additional condition for maximum power transfer is that the impedance of the

load circuit needs to match the impedance of the generator. The impedance of the

generator depends on the frequency of the muscle force. For un-fused contractions two

frequencies are present, the un-fused stimulation frequency and the burst repetition rate.

It is important to determine the frequency to which the load circuit should be tuned for

maximum power transfer if multi-peak force bursts are used to drive the generator.

The goal of this study was to reduce to practice our concept of an implantable,

self-sustaining stimulated-muscle-powered piezoelectric active energy harvesting

generator that exploits the fact that the mechanical output power of a muscle is

substantially greater than the electrical power necessary to stimulate the motor nerve. The

study objectives were to 1) build a mechanical muscle analog to use as a test bed for

generator development; 2) build a generator prototype consisting of a piezoelectric stack

generator, storage circuitry, a motor nerve stimulator and a load resistor; 3) demonstrate

continuous, self-sustaining operation of the stimulator and dissipation of additional power

through the load resistor, in-vivo, using rabbit quadriceps to drive the generator system;

4) verify the accuracy of the mechanical muscle analog by comparing data obtained with

it to data obtained from in-vivo trials; 5) determine the combination of stimulation

parameters that results in maximum output power and determine the fundamental

frequency to which the load circuit should be tuned.

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C. METHODS

1. MECHANICAL MUSCLE ANALOG

A mechanical muscle analog test bed (Figure III-2) was built for generator

prototype development and to reduce the number of required animal experiments. It was

designed to produce tension with a magnitude and profile similar to that of a muscle

twitch. This was achieved by using a linear motor controlled with an H-bridge circuit

(TPIC0107B, Texas Instruments, Dallas, TX) to stretch and relax a spring. The spring

was attached to the mechanical holder that housed the piezoelectric stack and converted

tensile force to the compressive force needed for generator operation. The other end of

the holder was anchored to the test stand. Tension (10 to 50 N) was controlled by the

motor power supply voltage. Frequency (0.125 - 2 Hz) was controlled by the clock of the

H-bridge circuit. Force was measured with a load cell (LC703-50, Omega Engineering,

Inc., Stamford, CT).

Figure III-2. Schematic of the mechanical muscle analog test bed. The mechanical muscle analog was used to develop and test the generator system prior to in-vivo trials, reducing the number of animal experiments. The linear motor, controlled with an H-bridge circuit, stretched and relaxed a spring to produce tension with a magnitude and profile similar to that of a muscle twitch. The available force (10 to 50 N) was controlled with the motor power supply voltage. The clock of the H-bridge circuit was used to control the frequency of the force pulses.

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The output power capabilities of the generator were assessed with the mechanical

muscle analog. A 7 x 7 x 44 mm, modified lead zirconate titanate piezoelectric stack

(TRS Technologies, State College, PA) with a piezoelectric constant of 0.035 VmN-1 and

a capacitance of 323 nF was connected to the power analysis circuit (Figure III-3). The

power analysis circuit consisted of a half diode bridge, a 1000 μF tantalum storage

capacitor (CL) and a 3 MΩ load resistor (RPA), sized to match the impedance of the

piezoelectric stack. The mechanical muscle analog was used to apply force ranging from

10 – 50 N to the piezoelectric stack in eighteen trials until the voltage across RPA reached

a steady state (VLss). Data acquisition equipment (DAQPad 6052E & Labview Software,

National Instruments, Austin, TX) was used to acquire force and voltage data. The output

power (P) was calculated with Eq. III-1 and plotted vs. input force.

PA

Lss

RV

P2

=

Eq. III-1

Figure III-3. Power analysis circuit schematic. The electrical schematic of the system used to measure the power generating capabilities of the implantable, stimulated-muscle-powered piezoelectric generator concept. The storage circuit consisted of a half diode bridge

75

and a 1000 μF capacitor (CL). The load resistor (RPA) was matched to the impedance of the piezoelectric generator. Voltage (VL) was recorded across the load resistor and power was calculated using Eq. III-1.

2. PREPARATION FOR IN-VIVO DEMONSTRATION

A prototype generator system was specifically built for the in-vivo demonstration.

The prototype generator system consisted of the piezoelectric stack generator connected

to a half diode bridge, a 1000 μF tantalum storage capacitor (CL) a stimulator circuit and

a load resistor (RL) (Figure III-4). The load resistor RL represented a target application

and was used to measure the output power generated in addition to that needed for motor

nerve stimulation. The simplified nerve stimulator was built from a CMOS Schmitt

trigger circuit, producing a biphasic current pulse (using C2 = 0.2 µF) that was applied to

the motor nerve through a custom fabricated tripolar spiral nerve cuff electrode.

Potentiometer R1 (100 kΩ potentiometer set at 5.6 kΩ) and capacitor C1 (0.1 µF)

controlled the pulse width of the stimulus, which could be adjusted to be between 10 and

2000 µs, and R2 (100 MΩ) and C1 (0.1 µF) controlled the inter pulse interval, which was

set to approximately 1 s.

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Figure III-4. Generator system circuit schematic. The electrical schematic of the system built to demonstrate the implantable, stimulated-muscle-powered piezoelectric generator concept. Stimulated muscle contractions applied force to the piezoelectric generator which powered both the stimulator and a load. The stimulator delivered a current pulse to the motor nerve which produced muscle contractions.

We chose to use the rabbit quadriceps muscle to drive the generator during the in-

vivo demonstration since simulations and mechanical testing of expected forces

suggesting this muscle would be sufficient. Estimates of output power expected from the

generator when driven by rabbit quadriceps were compared to estimates of the power

requirements of the stimulator to determine if there was adequate power for sustained

operation of the stimulator. The rabbit quadriceps can produce 30 – 50 N of twitch force

[77-80], corresponding to 2 – 8 μW of output power, predicted from the simulation

results of previous studies [75]. It was not possible to directly measure the stimulator

power requirements since the measurement process changed the characteristics of the

circuit, so an estimate was determined indirectly using the mechanical muscle analog. A

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40 N force was applied with the mechanical muscle analog to the piezoelectric stack

connected to the power analysis circuit (Figure III-3). A 2.4 V steady state voltage (VLss)

resulted across RPA (3 MΩ), corresponding to an output power of 1.9 μW, calculated with

Eq. III-1. The piezoelectric stack was then connected to the circuitry shown in Figure

III-4, with the electrode-nerve impedance approximated with a 1 kΩ resistor. A 40 N

force was applied with the mechanical muscle analog to the piezoelectric stack and load

resistor RL was adjusted until the steady state voltage was equal to the steady state voltage

from the power analysis circuit trial (2.4V). This occurred when RL equaled 5 MΩ. The

power requirement of the stimulator (PStim) was estimated to be 0.8 µW (Eq. III-2), which

is less than the predicted output power of the generator. The current pulse produced by

the stimulator across the 1 kΩ resistor was a 700 µA, 200 µs pulse, a value that should be

adequate for stimulating a motor nerve. These estimates provided confidence in the

ability to demonstrate our generator in-vivo using a rabbit quadriceps to drive the

generator.

−=

LPALssStun RR

VP 112

Eq. III-2

3. IN-VIVO EXPERIMENTAL PROTOCOL

Five New Zealand White rabbits (3.9 ± 0.4 kg, n = 5) were used in the study. The

experimental protocol was approved by the Case Western Reserve University

Institutional Animal Care and Use Committee. Anesthesia was initiated with (50 mg/kg)

Ketamine and (5 mg/kg) Xylazine and maintained throughout the experiment with 1-3%

78

Isoflurane. A surgical procedure was performed to mechanically connect the piezoelectric

generator to the rabbit quadriceps. The patellar tendon was detached from the tibia,

keeping the muscle attachment to the tendon intact. A hole was drilled through the patella

and connected to the piezoelectric holder with stainless steel wire. The other end of the

piezoelectric holder was anchored to the test stand and the rabbit’s ankle and knee joints

were secured to prevent movement. A tripolar spiral nerve cuff electrode was placed on

the femoral nerve. Stimulus parameters for maximal muscle activation were determined.

The experimentation performed included 1) in-vivo, self-sustaining demonstration of the

generator concept; 2) in-vivo power generation data collection for comparison to the

mechanical muscle analog; 3) collection of in-vivo force data for use in software

simulations for the stimulation parameter study; and 4) in-vivo power generation data

collection for comparison to the software simulation results. The rabbits were euthanized

at the conclusion of the experiment and the quadriceps muscles were dissected and

weighed (63.8 ± 10 g, n = 5).

a) In-vivo self-sustaining demonstration of generator concept

feasibility

We demonstrated in one rabbit experiment that the mechanical power of muscle

can be converted to electrical power in amounts greater than is needed for stimulation of

the motor nerve. The ability of the generator to maintain a steady state or increase the

output voltage during the in-vivo trials demonstrated that our active energy harvesting

generator concept was feasible. The capacitor CL was pre-charged and resistor RL was set

to maintain a steady state voltage. Connection of the piezoelectric stack to the system

79

circuit (Figure III-4) and connection of the nerve electrode to the stimulator initiated

generator operation. The system was allowed to run for 120 s. The power generated in

addition to that needed to power the stimulator was calculated with Eq. III-1, using the

value of RL and the steady state voltage of the system.

b) Comparison of in-vivo data to mechanical analog data

In-vivo results were compared to results obtained with the mechanical muscle

analog to verify its accuracy. The output power capability of the generator when driven

by muscle was assessed in two in-vivo experiments. The piezoelectric generator was

mechanically connected to the muscle and electrically connected to the power analysis

circuit (Figure III-3). Muscle length was adjusted to where maximum twitch force

resulted and the minimum current level for producing maximum twitch forces was found.

The femoral nerve was stimulated at 1 Hz (Pulsar Stimulators, FHC Inc., Bowdoinham,

ME) until the voltage across the load resistor (VL) reached a steady state. Capacitor (CL)

was pre-charged to decrease the time necessary for VL to reach its steady state. The output

power of the generator was calculated using Eq. III-1 and the in-vivo output power results

were compared to the mechanical muscle analog output power data.

c) In-vivo collection of force data for the evaluation of stimulus

parameters

A stimulation parameter study was performed to determine the combination of

stimulation parameters that results in maximum output power and to determine whether

80

the load circuit should be tuned to the stimulation frequency or the repetition rate

frequency. The force of the rabbit quadriceps, resulting from the application of various

stimulation patterns to the femoral nerve (Pulsar Stimulator, FHC Inc., Bowdoinham,

ME), was recorded in three rabbit experiments. The stimulation patterns for a fixed

aggregate rate of 1 stimuli/s were 1 pulse repeated at 1 Hz and trains of 2, 4, and 8 pulses

at repetition rates of 0.5, 0.25 and 0.125, respectively. Stimulation frequencies for each of

the trains of multiple pulses included 20, 40, 50 and 100 Hz. Three contractions were

obtained during each trial of a stimulation pattern combination and the force was

averaged over those three contractions. At least two trials of each stimulation pattern

were obtained.

Evaluation of stimulus parameters using software simulations

In-vivo muscle force data were used as input to software simulations which

predicted the generator output power resulting from sustained application of each force

waveform. The software simulation methods are described in detail in [75]. The SPICE

circuit (EMA Design Automation, Inc., Rochester, NY) used in the simulations included

a voltage source and capacitance to represent the piezoelectric stack, and a half diode

bridge, storage capacitor and a load resistor. The piezoelectric voltage was calculated by

multiplying the input force by a scalar, determined from the piezoelectric constant and

dimensions of the piezoelectric stack. The output of the simulations was the steady state

voltage (VLss) across the load resistor (RL) and the predicted output power of the generator

was calculated using Eq. III-1.

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For each input force trace, the output power was predicted over a range of load

resistors (RL = 10 kΩ to1000 MΩ). The load resistor (RLopt) resulting in the greatest

output power (Popt) was determined. RLopt is related to the input impedance of the

generator. Frequency (fsim) was calculated with Eq. III-3 using RLopt found in the software

simulations and Cp = 323 nF. fsim was compared to the stimulation frequency and the

repetition rate of the stimulus to determine the frequency to which the load circuit should

be tuned for maximum power transfer. Average peak force was defined as the peak force

for twitches and the average of the peaks for un-fused contractions. The stimulation

parameter combination (number of pulses in the train and stimulation frequency of the

train) resulting in the greatest predicted output power was identified.

Loptpsim RC

f 1=

Eq. III-3

d) In-vivo data collection for comparison with software simulation

predictions

A comparison of the output power of the generator using two different stimulation

parameter combinations was performed during one rabbit experiment. The two

stimulation parameter combinations were 1) single pulses repeated at 1 Hz; 2) the

stimulation parameter combination predicted from the software simulations to result in

the greatest output power. The piezoelectric generator was mechanically connected as

described above and was electrically connected to the power analysis circuit, shown in

Figure III-3. The load resistor (RPA) was tuned according to the repetition rate. The two

82

different stimulation parameters were applied (Pulsar Stimulator, FHC Inc.,

Bowdoinham, ME) until the voltage across the load resistor (VL) reached a steady state.

Capacitor CL was pre-charged to decrease the time necessary for VL to reach its steady

state. The output power of the generator was calculated with Eq. III-1 and compared for

the two stimulation parameter combinations.

D. RESULTS

1. OUTPUT POWER CAPABILITIES OF THE GENERATOR

The output power (P) of the generator as a function of applied force (F) with the

mechanical muscle analog is shown in Figure III-5. The equation of the curve fitted

through the data points was:

91.00031.0001.0

2

2

=

−=

RFFP

Eq. III-4

A second order polynomial fit was chosen because the output power of the generator

theoretically increases quadratically with the input force [75]. The shape of the fit

through the mechanical analog data matches the shape of a fit through theoretical

predictions performed with software simulations [75]. The output power results from the

mechanical analog experiments where a factor of 10 less than the theoretical output

power predictions. The 90% confidence interval was the range between P ± 2E, where

83

(E) is the error in the fit due to measurement error. The variation in force produced by the

mechanical muscle analog within each trial was 2.1 ± 0.7 N (1.2 to 4.0 N).

Figure III-5. In-vivo power generation matched the mechanical muscle analog. The output power of the generator is shown as a function of input force applied with both the mechanical muscle analog (white squares) and the two in-vivo experiments (black circles). The variation in force within each trial is contained within the markers. The solid line is a polynomial curve fitted through the mechanical analog data points. The dashed lines show the 90% confidence interval of the mechanical muscle analog data points.

2. IN-VIVO DEMONSTRATION OF GENERATOR CONCEPT

In an in-vivo experiment we demonstrated that the mechanical power of muscle

can be converted to electrical power in amounts greater than is needed for stimulation of

84

the motor nerve. Once the piezoelectric stack was mechanically connected to the rabbit

quadriceps, operation of the generator system was initiated by connecting the

piezoelectric stack to the system circuit and the femoral nerve electrode to the stimulator

(Figure III-4). RL was set at 100 MΩ and CL was pre-charged to 1.65 V.

Figure III-6. Example stimulus pulse, twitch force and step increases in output voltage during the in-vivo demonstration. Application of the stimulating pulses (A & B) to the rabbit femoral nerve resulted in quadriceps twitch force (C & D). The twitch force was applied to the piezoelectric stack resulting in a step increase in generator output voltage (VL) (E & F). Continuous application of the stimulus pulses and resulting force bursts resulted in the self-sustaining generator operating voltage charging shown in Figure III-7.

The width of the current pulse generated by our stimulator during the in-vivo

demonstration was 1400 μs and the repetition rate was 0.6 Hz (Figure III-6A & B). A 500

μA, 200 μs pulse produced the same 30 N twitch with an external stimulator, therefore

we estimate the current pulse amplitude from our stimulator to be 200 μA. Twitch force

decreased over the 2 min run from 30 N to 13 N (Figure III-6C & D). We estimated for

85

these force levels that the total power generated was between 0.1 and 1 μW (Figure III-5).

Initial maximum twitch force was 35 N, thus the generator was operating at 37 – 86 % of

maximum twitch force. Each force pulse applied to the piezoelectric stack resulted in a

step increase in the output voltage of the system (Figure III-6E & F) Over 120 s of

continuous operation the output voltage increased to a steady state value of 1.7 V (Figure

III-7), during which the generator produced continuous power for stimulator operation

and an additional 30 nW of power through the 100 MΩ load resistor, demonstrating

concept feasibility.

86

Figure III-7. Self-sustaining, in-vivo power generation. This is the recorded output voltage (VL) when the rabbit quadriceps was driving the generator system shown in Figure III-4. The generator charges CL to a steady state voltage producing continuous power in an amount sufficient to run the stimulator and to dissipate 30 nW of additional power through a 100 MΩ load resistor. The ability of the generator to increase the output voltage of the system and to maintain a steady state demonstrates the feasibility of our generator concept.

3. COMPARISON OF IN-VIVO DATA TO MECHANICAL ANALOG

DATA

The output power generated during two in-vivo trials matched the mechanical

analog power results and were within 4% of the mechanical analog curve fit (Figure

III-5). During one in-vivo trial an average force of 11 N was produced by the quadriceps,

the steady state voltage was 0.6 V and the output power was 0.12 µW. Non-maximal

force was obtained in this experiment. The other in-vivo trial produced force in the

87

expected range, 31 N, resulting in a steady state voltage of 1.7 V and an output power of

1 µW.

4. STIMULATION PARAMETER EVALUATION

When a multi-pulse stimulation pattern is applied to the motor nerve the resulting

muscle force waveform can contain two frequencies, the stimulation frequency and the

repetition rate. Generator output power increases with increases in frequency, however,

tuning the circuit to the higher stimulation frequency did not result in a higher output

power. The tuning frequency (Table III-1) for each of the stimulation parameter

combinations was calculated with Eq. III-3 using RLopt found from the software

simulations. Two cases were observed. In the first case the tuning frequency matched the

repetition rate. This occurred for stimulation patterns that approached single force bursts:

1Hz single pulses and multi-pulse trains with high stimulation frequencies (50 and 100

Hz and sometimes 40 Hz). In the second case, the tuning frequency was greater than the

repetition rate but much less than the stimulation frequency. This occurred for stimulation

patterns of un-fused multi-pulse trains with a stimulation frequency of 20 Hz and

sometimes 40 Hz. No advantage was obtained by tuning to the higher stimulation

frequency; therefore the system should be tuned to the repetition rate to maximize power

output.

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Table III-1. The load circuit tuning frequency for stimulation pattern combinations

Case 1: Tuning frequency matched repetition rate Number

of pulses

Stimulation Frequency

(Hz)

Repetition Rate (Hz)

Tuning frequency Mean ± SD

(Hz) 1 N/A 1 1.0 ± 0.0 2 40 0.5 0.5 ± 0.0 2 50 0.5 0.5 ± 0.0 2 100 0.5 0.5 ± 0.0 4 50 0.25 0.25 ± 0.0 4 100 0.25 0.25 ± 0.0 8 50 0.125 0.2 ± 0.1 8 100 0.125 0.125 ± 0.0

Case 2: Tuning frequency did not match repetition rate or stimulation frequency Number

of pulses

Stimulation Frequency

(Hz)

Repetition Rate (Hz)

Tuning frequency Mean ± SD

(Hz) 2 20 0.5 1.0 ± 0.0 4 20 0.25 0.7 ± 0.1 4 40 0.25 0.6 ± 0.25 8 20 0.125 1.0 ± 0.0 8 40 0.125 0.7 ± 0.5

Note: For single pulses of force the tuning frequency matched the repetition rate. For un-fused multi-pulse force bursts, the tuning frequency was greater than the repetition rate and substantially lower than the stimulation frequency. Therefore the system should be tuned to the repetition rate to maximize power output.

The greatest predicted output power occurred when 2 stimulation pulses were

applied with a stimulation frequency of 100 Hz and a repetition rate of 0.5 Hz (Table

III-2). The predicted output power was 4 times greater than the power obtained from

muscle twitches. The variation in output power within a stimulus pattern group was due

to pooled data from three rabbits. Since the repetition rate was chosen so that the power

necessary for the stimulations was kept constant (a fixed number of 1 stimuli/s), the most

advantageous stimulation pattern was the one with the greatest predicted output power.

89

In the in-vivo trial the output power for 2 stimulation pulses at 100 Hz and a

repetition rate of 0.5 Hz was 2.7 greater than the output power for 1 stimulus pulse

repeated at 1 Hz. The 2 pulse stimulation pattern resulted in an average peak force of 83

N, a steady state voltage of 4V and a continuous generator output power of 2.7 µW. The

1 pulse stimulation pattern resulted in an average peak force of 31 N, a steady state

voltage of 1.7 V and a continuous generator output power of 1.0 µW.

Table III-2. Predicted output power for different stimulation patterns

Power (µW) Mean ± Std

Force (N) Mean ± Std

Number of pulses

Stimulation frequency (Hz)

Repetition rate (Hz)

44.12 ± 8.97 77.86 ± 7.86 2 100 0.5 35.24 ± 6.84 54.74 ± 5.09 2 50 0.5 24.6 ± 8.27 81 ± 14.72 4 100 0.25 20.78 ± 0.76 44.01 ± 4.1 2 40 0.5 18.1 ± 1.57 54.97 ± 5.03 4 50 0.25 16.11 ± 0.61 93.61 ± 2.7 8 100 0.125 15.69 ± 0.43 38.54 ± 1.82 8 20 0.125 14.98 ± 5.97 33.22 ± 5.83 2 20 0.5 14.27 ± 3.92 56.47 ± 8.04 8 40 0.125 13.68 ± 7.92 34.69 ± 5.55 4 20 0.25 13.65 ± 7.03 44.5 ± 10.3 4 40 0.25 11.16 ± 10.7 24.95 ± 13.02 1 N/A 1

10 ± 2.28 56.68 ± 4.15 8 50 0.125 Note: The patterns consisted of different combinations of the number of stimulus pulses, the stimulation frequency and the repetition rate. For a fixed number of 1 stimuli/s, two stimuli applied at a high frequency generated greater power than single twitches or tetanic contractions.

E. DISCUSSION

We demonstrated in an acute animal model that the mechanical power available

from an electrically stimulated muscle can be converted into electrical power in excess of

that needed to power the motor nerve stimulator. To our knowledge this has not been

demonstrated before. This approach takes advantage of the power amplification

90

characteristics of muscle, where the mechanical output power of the muscle is much

greater than the electrical power necessary to stimulate the motor nerve. In previous work

we introduced the concept of a stimulated-muscle-powered piezoelectric generator [75].

In this study we reduced to practice our concept by building a generator and stimulator

prototype and demonstrating its feasibility in-vivo, using rabbit quadriceps to drive the

generator. The generated power was sufficient for continuous self-sustaining operation of

the stimulator and a small amount of additional power was dissipated through a load

resistor (Figure III-7). This demonstration is the first step towards realizing a stimulated-

muscle-powered generator that can be implanted within the human body and used as a

power source for implanted medical devices.

The use of a larger muscle will have the largest impact towards increasing the

output power of future generator prototypes. We used the smallest animal muscle

possible for our in-vivo demonstration resulting in μW’s of total generated power and

only 30 nW of power in excess of that needed to power the stimulator. An estimate of the

range of twitch forces available from human muscle is 1 to 800 N [57-60], assuming a

conversion factor of 50 Ncm-2 [81] and twitch force to be 10 to 30% of the maximal

contractive force. The upper range of this twitch force is approximately 30 times greater

than the twitch force of the rabbit (~30 N), increasing the expected output power of the

generator by a factor of nearly 103, since output power increases quadratically with input

force. This puts the output power of the generator in the mW range when using large

human muscles, rather than in the μW range seen in these experiments. Since the input

muscle stimulation power requirements remains essentially constant as muscle size

increases, the generated power will increase as the size of the muscle increases.

91

Gains in generator output power may also be possible by using muscle shortening

to optimize the muscle’s mechanical power production if efficiency decreases due to

fibrous growth interference can be overcome. Our generator system used a piezoelectric

generator with no moving parts and µm displacements for reasons of reliability and

efficiency. The mechanical power associated with a 23 μm displacement of a

piezoelectric stack, using a 100 N, 0.25 s, 1Hz triangular force pulses is 0.3 mW. A 60 N

peak force and 2 cm displacement can produce a mechanical power of 0.15 W [82],

which is an increase of a factor of approximately 500. Therefore, it is worth exploring

mechanical to electrical conversion devices that would operate with optimal muscle force

and stroke. However, implanted devices that have relied on larger displacement to

convert muscle power have experienced decreases in efficiency during chronic studies

due to the interference of fibrous growth with generator motion [45;46], so methods for

minimizing the failure of moving parts and the reduced efficiency due to fibrous growth

are critical aspects of the design.

Future versions of the generator should incorporate voltage regulation to optimize

the power transfer between the piezoelectric generator and the load circuitry and to

ensure that the stimulating pulse is the minimum pulse needed produce maximum twitch

force. The current amplitude produced by our simplified low power stimulator was

dependent on the operating voltage of the generator, which is not optimal. A long pulse

width kept the current amplitude low, but used approximately three times more charge

per pulse than needed for muscle activation. The steady state voltage that our system

operated at produced a current pulse which generated 37 - 83% of maximal twitch force.

A fixed input voltage for the stimulator would result in a constant stimulus current and

92

would prevent wasted energy. This could be achieved by adding a DC-DC converter

commonly used with piezoelectric generators [73;83;84] to the system to regulate the

voltages of the stimulator and the load. Additionally, emerging technologies should be

incorporated [85] into the design of the stimulator and the electrical circuitry should be

customized to further reduce power costs.

This study took the first steps towards identifying the muscle stimulation

parameters that are the most advantageous for generating output power for this

application. The output power of the piezoelectric generator increases as both the

magnitude and frequency of the applied force increase. However, the muscle force

dynamics are complicated by the trade-off between force amplitude and contraction rate.

The data demonstrate that repetition rate was the dominate frequency for tuning the

system to maximize power output (Table III-1) and that no advantage could be achieved

by tuning the circuit to the stimulation frequency seen in non-fused contractions. When

using repetition rates that keep the stimulating power requirements constant, the use of

two high frequency stimulus pulses out performed the use of single pulses and of 4 and 8

pulse trains by generating three to four times as much output power (Table III-2 and in-

vivo results). Two pulses per burst can optimize the force per pulse [48;50-55]. The force

produced by the two pulses was much greater than the force produced by twitches and

only slightly less than the force produced with 4 and 8 pulses. However, the two pulse

stimulus trains can be applied at a higher repetition rate than 4 or 8 pulse trains.

Additional studies are necessary to fully understand the potential benefit of the

use of two high frequency stimulus pulses. To implement the use of multi-pulse stimulus

trains an additional timer would be required, adding power costs to the stimulator circuit.

93

Chronic low frequency stimulation conditions muscle, resulting in a slower, fatigue

resistant fiber type population [86], which produces less maximal force than fast twitch

type fiber [87]. Therefore, the potential gain in power could be used up in additional

stimulator power costs and the effectiveness of a two pulse, high frequency stimulus train

may be reduced in slower muscles. The simulation tools developed in this study can aid

investigations of this type that weigh the benefits with the disadvantages.

A mechanical muscle analog was built to aid in the development of the prototype

generator built for this study. Comparison of mechanical muscle analog data and in-vivo

data from this study verified its accuracy (Figure III-5). The mechanical muscle analog is

a tool that can be used during the development of future generator prototypes. Chronic

animal studies are needed to study attachment strategies [71], biocompatibility and

demonstrate chronic device performance.

F. CONCLUSION

This study demonstrated that the mechanical power from muscle contractions can

be converted to electrical power in excess of that needed to stimulate the motor nerve of

the muscle. We reduced to practice our concept by building a generator and stimulator

prototype and demonstrating its feasibility in-vivo, using a rabbit quadriceps to drive the

generator. The generated power was sufficient for continuous operation of the stimulator

and a small amount of additional power was dissipated through a load resistor. In

addition, a mechanical muscle analog was built and its usefulness as a test-bed for future

generator developments was verified. More complex stimulation patterns that may

94

increase the output power capabilities in future versions of the generator were identified.

An implantable, stimulated-muscle-powered generator system has the potential to be a

power source for implanted electronic medical devices.

G. ACKNOWLEDGEMENTS

This project was funded by NASA Glenn Research Center’s Human Health and

Performance Project, The State of Ohio BRTT 03-10, the Department of Veterans Affairs

RR&D B367R, the NIH DK077089 and supported by the Cleveland Functional Electrical

Stimulation Center. We would like to acknowledge the contribution of Narendra Bhadra,

CWRU, who designed the nerve cuff electrodes used in the animal experiments. We

would like to acknowledge the contributions of Fred Montague, CWRU, who designed

the low power stimulator and Steve Garverick, CWRU, who provided design advice on

the load circuitry used in our system.

95

IV. DISCUSSION

A. DISSERTATION IMPACT

A review of existing energy harvesting technology research is located in part C.

EXISTING RESEARCH ON ENERGY HARVESTING TECHNOLOGY, of section I.

INTRODUCTION. During the development of our concept we reviewed the energy

harvesting research being conducted for biological and non-biological applications and

the various methods available for energy conversion and energy storage. In our judgment

we adapted the most relevant aspects of the previous research into our design and

advanced the field of implantable power generators with our key design feature. Our most

significant design feature was that we used a portion of the generated power to drive the

generator, instead of simply scavenging power. This allows the generator to operate

continuously and consistently, ensuring appropriate impedance matching during

generator operation. Additional design decisions included selecting skeletal muscle to

drive the generator, since it is a source of significant amounts of potential power. We

chose the type of piezoelectric material and the configuration that was best suited to

match with the slow, large force of muscle, in contrast to the high frequency applications

and we simplified the stimulating and storage circuit used in our demonstration to keep

the power requirements as small as possible.

Once the concept for an implanted, stimulated muscle powered piezoelectric

generator was created, we further developed the design and demonstrated feasibility in an

acute animal model with a prototype generator. To aid in the design we built design tools

including a software simulation model and a mechanical muscle analog test bed. We

developed a SPICE circuit to represent our system and performed computer simulations

96

in order to understand the effect of changes to the system parameters on output power

and to predict the output power resulting from the force produced from muscle

contractions. The simulations provided evidence that that our concept was feasible, since

we predicted that we could generate more electrical power with a piezoelectric generator

driven by stimulated muscle contractions then was needed to power the stimulations. To

further demonstrate feasibility, we built a prototype generator system consisting of a

piezoelectric generator, an electrical storage circuit, a motor nerve stimulator and a load.

We built a bench top mechanical muscle analog to aid in the development and testing of

the prototype system. The force produced by the mechanical muscle analog was similar

the force produced from a physiological muscle twitch. Comparison of results from

animal experiments to results from the mechanical muscle analog to verified the

usefulness of the mechanical muscle as a test bed for generator development. Testing

with the mechanical muscle analog allowed us to reduce the number of animal

experiments that were necessary for demonstrating our concept.

Once the system was operating with the mechanical muscle, we successfully

demonstrated generator operation with an acute animal muscle model. As expected we

observed that the electrical power necessary for motor nerve stimulation was less than the

resulting mechanical muscle power. The force produce by the muscle contractions was

great enough to produce continuous power for operation of the stimulator and a small

amount of additional power through a load resistor. The current pulse produced by the

stimulator was of sufficient amplitude and pulse width for activation of the motor nerve

to cause the muscle contractions. The ability of the generator to increase the output

voltage of the system and to maintain a steady state demonstrated the feasibility of our

97

generator concept. Our demonstration that it is possible to convert the mechanical power

resulting from muscle contractions initiated through artificial electrical stimulation into

electrical power in amounts greater than the power required for the muscle stimulations

has not been demonstrated before, to our knowledge, and is the first step towards

realizing an implanted, stimulated muscle powered piezoelectric generator for implanted

medical applications.

B. SIMPLIFIED ESTIMATE OF SYSTEM PARAMETERS

As a check we can make a simplified calculation on the expected steady state

voltage of the generator system when a 13 N force is driving the generator, with a load

consisting of the stimulator and a load resistor. The piezoelectric coupling between the

force and the piezoelectric voltage is given by:

FA

tgVp33=

Eq. IV-1

For our stack:

2

33

000049.0000621.0

035.0

mAmtN

Vmg

=

=

=

Making the voltage to force ratio:

98

NV

FVp 44.0=

Eq. IV-2

For a 13 N force, the expected piezoelectric voltage is:

VVp 8.5)13)(44.0( ==

Eq. IV-3

The for maximum power transfer, the output voltage is:

VV

V pL 9.2

28.5

2===

Eq. IV-4

There is a loss through the diodes of 0.7 V, so the expected steady state voltage is 2.2 V.

Our steady state voltage was 1.7 V which is close to the expected. Two sources of loss

are: 1) imprecise mechanical coupling and 2) use of a non-optimized electrical circuit

(i.e. the impedance of the load may not have exactly matched the impedance of the

piezoelectric stack).

C. NEXT STEPS TO FURTHER ADVANCE THE TECHNOLOGY

With successful demonstration of the concept in an acute animal experiment, the

next step in reducing our generator concept to clinical practice is chronic animal studies.

Sustained generator operation in an awake, fully functioning animal would allow us to

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begin to answer questions about generator attachment stability, biocompatibility, long

term efficiency and longevity. While we are unaware of stimulated muscle power being

converted to electrical power, there is a body of research on the conversion of stimulated

muscle power into hydraulic power in an effort to assist with circulatory pumping in

patients with compromised heart function [71]. It would be our intention to collaborate

with this research group in order to minimize the preparation effort necessary for chronic

experiments of our generator system. Trumble et al. reported that the pull force produced

by the canine Latissimus Dorsi was 60 N with a 2 cm stroke [82]. We estimate that the

isometric force would be at least 100N and our previous studies have shown that this is

ample force for operation of our generator [75]. Therefore our next step would be to

chronically test our generator with a canine latissimus dorsi driving the generator. The

general goals of the chronic experiments would be to 1) develop stable attachment sites;

2) study the biocompatibility of the generator; 3) determine the effect of encapsulation on

the power generation capabilities; 4) improve the electrical circuit of the generator; and

5) develop a measurement system to use during the chronic tests to measure system

performance. Specific objectives of the study will be driven by the unique aspects of the

identified target application.

1. ATTACHMENT SITES

Stable attachment sites are important for maintaining generator efficiency and for

minimizing the risk of an adverse foreign body reaction. In our generator concept we

require a bone attachment strategy and a tendon attachment strategy. Trumble et al.

attached their MEC between the rib cage and the tendon of the latissimus dorsi muscle in

100

dogs during their chronic studies [71]. The MEC was anchored to the rib cage using a

perforated stainless steel anchor plate, the smooth surfaces of which were sandblasted to

increase total surface area, to promote adhesion with fibrous tissue in growth. The mesh

plate was secured to the ribs using stainless steel surgical wire and ultraviolet adhesives

to seal the edges. The latissimus dorsi tendon was replaced with an artificial tendon,

comprised of polyester fibers that were separated into eight individual bundles and sewn

into the humeral insertion. The bundles came together to form a single braided cord that

was clamped to the piston head of the MEC. Use of these strategies in chronic studies,

lasting up to 10 weeks, resulted in stable attachment sites for the MEC [71].

2. BIOCOMPATIBILITY

To avoid an adverse foreign body reaction, the implanted generator must be

biocompatible. One strategy for obtaining biocompatibility is to identify a biocompatible

piezoelectric material which is safe for direct contact with the body. Barium titanate

(BaTiO3) is a material that can be made to have piezoelectric properties and studies have

provided evidence that it is biocompatible. It was implanted subcutaneously in the backs

of rabbits for 20 weeks and into the canine femurs for up to 99 days. In both cases the

histology results showed no evidence of inflammation or foreign body reactions and only

a thin fibrous capsule surrounded the implant [88;89]. The purpose of the studies was to

assess the feasibility of using BaTiO3 as a material at bone implant interfaces since its

piezoelectric properties could be utilized in the bone implant healing process. Further

studies showed tissue growth into the cylinders of porous BaTiO3 implanted into canine

femurs after 16 days and a mature, healthy bone implant interface after 86 days [90].

101

Polarized BaTiO3 was also implanted into the jaw bone of dogs for up to 12 weeks and

showed an improvement in osteogenesis over non-polarized ceramic implants [91].

Two key properties of piezoelectric material are the piezoelectric constant and the

dielectric constant. During the design of our generator we determined that both of these

parameters should be a large as possible for maximizing generator output power. Values

for the piezoelectric and dielectric constant of BaTiO3, obtained from manufacturer’s

specifications, are 0.013 VmN-1 and 1250, respectively. These values for the modified

lead zirconate titanate (PZT) piezoelectric material used throughout our experiments,

were 0.035 VmN-1 and 6500. Clearly, the modified PZT has superior properties over

BaTiO3 and the biocompatibility advantage of BaTiO3 would need to be weighed against

its inferior power generation capabilities. Others researching the use of biocompatible

piezoelectric material as an electrode for stimulation or sensing in pacemakers have also

found that existing biocompatible piezoelectric materials have less attractive piezoelectric

properties than non-biocompatible piezoelectric materials. This has sparked research into

the development of biocompatible piezoelectric materials with improved piezoelectric

properties using different combinations of Na, K and NbO3 [92]. As these materials are

developed, future comparisons of their power generating capabilities to those of modified

PZT can be made.

3. ENCAPSULATION

An alternative method for achieving biocompatibility is to encapsulate the

piezoelectric generator in a biocompatible material such as silicone or titanium. The

102

advantage of silicone is its flexibility and while it has the ability to repel water, it cannot

be used to form a hermitic seal and water may leak in over time. A hermetic seal can be

formed with titanium and it is a durable encapsulate. The disadvantage of titanium is that

it is a hard, inflexible material. The key design consideration is to ensure that there is

minimal loss of force transmission between the tendon and the piezoelectric generator

due to encapsulation. From testing with an MTS machine we found the displacement of a

5x5x18 mm piezoelectric stack to be 23 µm when 100 N of force was applied in

compression. This corresponds to a strain of 0.0013 and a modulus of elasticity of 3.1

GPa. Keeping the strain constant, the amount of force absorbed by a block of silastic with

a modulus of elasticity of 2.7 MPa was calculated to be 0.09 N, an insignificant amount

compared to the 100 N applied to the piezoelectric stack. In contrast, the modulus of

elasticity of titanium is 115 GPa, two orders of magnitude greater than the piezoelectric

stack. Thus, titanium encapsulation could potentially absorb a significant portion of the

force applied by the muscle unless a configuration, such as a box with very thin walls or a

foil wrapper, is used that is effective in forming a biocompatible barrier with insignificant

force absorption.

The effect of encapsulation of the piezoelectric stack in silicone on the voltage

and power generating capabilities of the piezoelectric stack was experimentally tested

using the mechanical muscle analog. The peak voltage across a 10 MΩ load resistor,

connected directly to a PZT stack with dimensions of 5x5x18 mm, was recorded as the

mechanical muscle analog applied a peak force of 50 N. The voltage across the load

resistor was the same, 0.83 V, for both the coated and uncoated cases. Similarly, when a

peak force of 50 N was applied to the stack when it was connected to a diode bridge,

103

1000 µF capacitor and 550 kΩ load resistor, the steady state voltage for both the coated

and uncoated cases was 0.12 V, corresponding to 0.026 µW. In these simplified

experiments there was not a reduction in force due to encapsulation of the piezoelectric

material in silicone.

4. IMPROVEMENTS TO THE ELECTRICAL CIRCUIT

We were able to simplify the electrical circuitry of the system when using the

small rabbit quadriceps muscle to demonstrate our generator concept. The current pulse

produced by the stimulator was dependent on the operating voltage of the generator and

the steady state operating voltage was near the voltage where the current pulse of the

stimulator produced a maximal twitch force. However, voltage regulation will need to be

added to the electrical circuit in order to keep the amplitude of the stimulating pulse at a

constant level where a maximal twitch force is produced as the system is tested with

larger muscles. The use of voltage regulators with piezoelectric generators is common.

For example, Platt et al. and Tan et al. used linear regulators in their piezoelectric energy

harvesting applications [73;84] and Kim et al. used a switching regulator [83].

The use of a voltage regulator may add some power cost to the stimulator, but it is

anticipated that the power requirements of the stimulator will not increase significantly as

there is opportunity to decrease the power requirements of the stimulator circuitry over

what was used in this experiment. Our stimulator was made out of commercially

available parts and improvements may be possible if a custom made circuit is designed

using only the components necessary for this application. The Schmitt trigger IC was

104

utilized in our design to regulate the timing of the stimulus pulses. Lin et al. reported the

development of a timer circuit with a sub-pW power cost that could possibly replace the

Schmitt trigger and significantly reduce the power consumption of the stimulator [85].

5. MEASUREMENT OF SYSTEM PERFORMANCE DURING CHRONIC

STUDIES

During the chronic studies it will be necessary to include measurement

capabilities in order to monitor the operation of the generator. Potentially, a force

transducer would be used to measure the force produced by the muscle and the operating

voltage of the generator system would be monitored. A battery powered telemeter system

would be used to transmit the force measurement and the operating voltage level. In

addition, it is desirable to have a remote method for periodically discharging the electrical

energy that is generated and stored in order to have a method for quantifying the

generator’s power generating capabilities and efficiency. There are examples within the

literature where in vivo telemetry systems are under development [93] and commercially

available telemetry systems are available (for example, Data Sciences International, St.

Paul, MN). These existing technologies will serve as a starting point for the development

of a measurement system for use in chronic studies of our stimulated muscle powered

generator.

105

D. THE EFFECT OF OPTIMIZATION OF EACH PART OF THE SYSTEM

ON GENERATOR OUTPUT POWER

The goal of our demonstration was to show that it is possible to convert

stimulated muscle power to electrical power in amounts greater than that needed for the

stimulation. Our goal was not optimization of all the parts of the system. Therefore,

improvement in generator output power is expected through optimization of the

individual parts and the interfaces between the parts. Areas for improvement include: 1)

muscle size 2) optimization of the mechanical power of the muscle; 3) stimulator power

requirements; 4) mechanical coupling; and 5) stimulation parameters. The following

paragraphs provide detail on these improvements and the estimated gain in output power

that may be possible is summarized in Table IV-1.

1. MUSCLE SIZE

We have shown that the output power of the generator increases quadratically as

the input force increases. Therefore, use of larger muscles will significantly increase the

output power. We used a small rabbit quadriceps muscle which produced approximately

30 N. The force production of human muscle is much greater. Force production of human

muscle is dependent on the cross-sectional area of the muscle. The physiological cross-

sectional area is multiplied by the specific tension of muscle to obtain the maximum force

the muscle can produce. There is a wide range of specific tension values used within the

biomechanical research community. A very conservative estimate is 35 N/cm2 [47], but

values of 50 N/cm2 to 65 N/cm2 [81] have been used in biomechanical models. As an

106

example, an average value for the physiological cross-sectional area of the latissimus

dorsi is 8.16 cm2 [94]. This equates to range of estimated maximum force production

between 290 and 530 N. Twitch force is 10 – 30% of the maximum force produced, or 30

– 180 N for the latissimus dorsi. An estimate of the twitch force of a large leg muscle,

such as the vastus medialis with a cross-sectional area of 47 cm2 [60] is between 165 –

1000 N. The high end of this range is factor of 34 increase over our 30 N rabbit muscle.

Since the output power increases quadratically with power, this equates to a factor of

1000 increase in output power, putting the estimate for a generator driven by a large

human muscle in the miliwatt range rather than the microwatt range observed in our

experiments.

2. OPTIMAL MECHANICAL POWER OF MUSCLE

We designed our generator system with no moving parts and we used isometric

muscle contractions to drive the generator. The reasons for this design decision were

reliability and maintaining efficiency. With no moving parts the risk of mechanical

failure was reduced, thus increasing reliability. Others who have designed implantable

piezoelectric generators that relied on larger displacements experienced a significant

reduction in generator output power during chronic studies due to the interference of

fibrous growth with generator motion. During the MTS experiments a triangular force

pulse, with a pulse width of 0.25 s and a peak force of 100 N, was applied to the

piezoelectric stack, displacing it 23 μm. When repeated at 1 Hz, this equates to 0.3 mW.

Trumble et al, used a displacement of 2 cm for power generation using the a canine

latissimus dorsi, which was generating a pull force of 60 N [82]. Assuming a similar

107

force profile, this equates to 0.15 W, or a factor of approximately 500 greater than that

which is generated using small displacements and nearly isometric contractions. Since the

potential gain in output power is large, it is worth exploring mechanical to electrical

conversion devices that would operate with an optimal force and stroke. However, ways

to minimize the failure of moving parts and the reduced efficiency due to fibrous growth

must be a critical aspect of the design. Some work in this area already exists, as Trumble

et al, has used a layer of Seprafilm bioresorbable membrane over the muscle insertion

and piston head to act as an adhesion barrier to successfully preserve free piston motion

[71].

3. STIMULATOR POWER REQUIREMENTS

We have calculated the low end of the power necessary for motor nerve

stimulation to be 50 nW [75]. This is a factor of 20 less than the 1 μW of power

consumed by the stimulator built for our demonstration. The ideal stimulator for the

generator system would be one where the power consumed was essentially only the

power necessary for the stimulations. The power necessary for the controlling circuitry

would be an insignificant portion. This has the potential to be realized by using circuit

components that utilize leakage current for operation in the sub-pW range [85]. A non-

damaging, low impedance connection between the stimulating electrodes and the nerve is

important for keeping the required stimulation power in the nW range. In addition, it is

necessary to ensure that the entire electrical circuitry used in the generator system is

matched to the impedance of the piezoelectric generator for maximum power transfer.

108

4. MECHANICAL COUPLING

The mechanical coupling of the piezoelectric generator between the muscle and

bone and the direction of the force application are significant factors. The stability of the

attachment points is important, since any movement of the generator housing will waste

muscle force and cause a decrease in generator output power. The direction of force

application should be exactly perpendicular to the piezoelectric stack for maximum

output power. If the force is applied at an angle other than a right angle to the stack, the

electromechanical coupling between the resultant parallel force vector and the stack will

produce a voltage opposite in sign to that which develops from force applied

perpendicularly. The sum of the two voltages added together is less than the voltage that

is possible from force applied at right angles, thus lowering the output power of the

generator. In our experimentation we applied force to piezoelectric stacks using a

Material Testing System (MTS) and a mechanical muscle analog, which used a linear

motor and spring to apply force. In the MTS experiments we had the ability to precisely

apply perpendicular force and our results showed very little difference between the

experimental trials and predicted values from simulations. However, the mechanical

coupling when the mechanical muscle analog was used was not precise and we saw that

the experimental values were approximately a factor of 10 less than simulation

predictions.

109

5. STIMULATION PATTERNS

The force generated by the muscle is also dependent on the stimulation pattern

used to stimulate the motor nerve. We have seen an approximately 3 fold increase in

output power when comparing twitch force repeated at 1Hz to a train of two pulses

applied at 100 Hz, with a repetition rate of 0.5 Hz.

Table IV-1. Estimated increase in output power resulting from system improvements

System part Improvement Estimated factor of increase in power

Muscle size Use a larger muscle 1000 Optimal mechanical power of muscle

Use a generator with a displacement that corresponds to optimal mechanical power generation of the muscle

500

Stimulator power requirements

Reduce power consumption of stimulator to be essentially only the power necessary for stimulation

20

Mechanical coupling

Ensure force is applied perpendicular to the stack

10

Stimulation parameters

Use a train of two pulses at 100 Hz, repeated at 0.5 Hz.

3

E. PRACTICALITY OF REALIZING THE TECHNOLOGY IN A HUMAN

APPLICATION

The next step to realizing this technology in a human is to identify a specific

location for the generator. Due to the need to sacrifice a muscle for implementation of

the generator, it is unlikely that the advantages of this technology would outweigh the

advantages of battery technology that is currently used with medical device that only

requires a small amount of power, such as a pacemaker. Therefore, the application that is

targeted for further development is one that requires larger amounts of power, such as

functional electrical stimulation for motor function restoration. Two possible muscles that

110

could be used that would only minimally impact movement are the palmaris longus and

the latissimus dorsi. Other muscles in the arm are available for movement of the wrist and

other back muscles can maintain posture. The palmaris longus is a small muscle and may

not generate enough force for driving a generator that powers medical devices. The

latissimus dorsi is a good candidate since it is a large muscle and it has successfully been

used to power ventrical assist devices. However, a large leg muscle such as the

quadriceps would be optimal for power generation. Loss of function of this muscle may

not be acceptable, except in the case of paralysis. A leg muscle that is paralyzed and for

which restoration of function is not anticipated is the muscle that should be targeted for

driving the generator.

For this case, implantation at the knee could be explored [95]. Platt et al,

incorporated a piezoelectric generator inside a knee replacement orthotic [73]. A similar

type of vessel for housing the generator is attractive, and attachment to the distal femur

should be explored in order to prevent flexion of the lower leg during generator

operation. The tendon and bone attachment strategies listed above should be the starting

point for the orthopedic design of a generator for use in a human.

In order for our generator to be realized as an alternative power source to

currently used implanted power sources, the long term efficiency of the generator must be

quantified. The majority of spinal cord injuries occur in young adults between the age of

16 and 30 [1]. Therefore, the timeframe over which the FES device is needed can be quite

long, potentially 50 years or longer, as life expectancy for SCI patients with less severe

injuries are only slightly less than people without SCI [1]. If the generator operates

continuously (24 hours a day/7 days a week) at 1Hz for 50 years, 1.6 billion cycles will

111

be necessary. The points within the system that could fail within this time period include:

1) fatigue of the piezoelectric system; 2) the tendon and bone attachment sites; 3) the

electronics; and 4) failure of the encapsulation’s hermetic seal. A system for clinical use

would need to account for these risks.

Studies have quantified the reduction in output power due to piezoelectric

material fatigue as a function of the number of cycles of strain experienced by the

material. For example, Platt et al. experienced a 7.5% reduction in output power between

the first cycle and the 106 cycle [73]. This reduction in efficiency would need to be taken

into account. The tendon and bone attachment sites must be stable without any

movement. If the attachment loosens over time, the efficiency of the generator will be

reduced and most likely tissue necrosis will result. Integrated circuit reliability is an

important factor for all electronics applications. Therefore, methods exist for the

estimation of integrated circuit reliability that can be used to estimate the lifetime of the

electronics needed for the generator system [96-98]. Loss of the hermetic seal would

result in body fluids coming in contact with the generator system’s electronics. This

could cause a short circuit malfunction of the electronics.

In addition to addressing the above issues, a thorough review of the concept by

clinicians is necessary for identifying further issues and for defining what level of

evidence would be required before there would be significant interest in the concept.

While we have made the first step towards demonstrating feasibility, such a review would

identify other hurdles that will need to be overcome prior to realizing this technology in a

clinical application. The next generation prototype design must incorporate the methods

listed above that can be used to advance the output power of the generator to the mW to

112

W range. If these design requirements can be realized in the next generation prototype

generator, then our concept may have a future as an implantable power source for

medical devices.

113

V. CONCLUSION

In this work we demonstrated that the mechanical power from muscle

contractions can be converted to electrical power in excess of that needed to stimulate the

motor nerve of the muscle. To our knowledge this has not been demonstrated before. An

implantable, stimulated-muscle-powered generator system that takes advantage of this

phenomenon has the potential to be a power source for implanted electronic medical

devices.

114

APPENDIX A. REQUIREMENTS AND DESIGN SELECTION

PROCESS

The initial steps of this study were to identify the sources of energy that exist

within the human body and technologies that might be used to harvest energy from those

sources. The energy sources within the human body include: chemical energy in the form

of carbohydrates and fatty acids; thermal energy from the heat generated from burning

calories; hydraulic energy from blood flow; and mechanical energy from muscle

contractions. Possible methods of harnessing this energy were identified, and are listed in

Table A-1.

To evaluate each method of energy harvesting, the method was rated against the

requirements identified for the generator. The requirements included the ability to

produce large amounts of power. An example power requirement of potential application

was 0.12 W for 2 hours/day for restoration of hand grasp [99]. Since the space available

for implantation is limited, the output power/device volume must be maximized. The

system must produce power in amounts greater than is necessary to start, sustain, and

control the system, with plenty of additional power for applications. The system must be

completely implantable. Replacement or maintenance surgeries must be unnecessary. The

system has long term durability. It doesn’t break, run out of charge, it doesn’t leak, etc. If

the device is used 24 hours a day at 1 Hz for 50 years it would need to perform ~ 1.6

billion cycles. The design and implementation contain unknowns that have a high

likelihood of being solved. We gave a rating of 0 - 4 in each requirement category for the

different method. A 4 was given to a design that would likely meet the criteria and a 0

was given to a design that could not meet the criteria.

115

Table A-1. Evaluation of ideas for scavenging power from the body

Method/Feature Completely implantable

Low unknowns

High power produced

Long term durability

Total

Piezoelectric 4 3 3 3 13 Linear

electromagnetic induction

4 3 3 3 13

RF transmission 0 4 4 4 12 Flywheel 4 3 3 2 12 Toro ring 0 3 4 4 11

Muscle pump 4 3 1 3 11 Electrodes on

muscle 4 2 2 3 11

Ratchet and gear 4 3 3 1 11 Crankshaft 4 3 3 1 11

Bicycle generator

0 3 3 4 10

Blood flow meter

4 1 2 3 10

Glucose fuel cells

4 0 3 3 10

Piezoelectric bone

4 1 1 3 9

Heel strike generator

0 3 3 3 9

Vibrating MEMS device

4 1 2 2 9

Muscle fibers to MEMS

4 1 2 2 9

Infrared photosensors

4 1 2 2 9

pH 4 1 2 2 9 Harness Krebs

cycle 4 0 3 2 9

Bloodflow generator

4 1 2 1 8

Nuclear battery 4 0 4 0 8 Implanted batteries

0 4 4 0 8

Thermoelectric 0 2 2 3 7 Hydrogen fuel

cells 0 2 4 0 6

4 = Able to meet requirement 0 = Not able to meet requirement

116

The ratings for each method were added together and the top two methods were a

piezoelectric generator and linear electromagnetic induction. Further analysis was

conducted on these two methods.

A. LINEAR ELECTROMAGNETIC INDUCTION

1. THE THEORETICAL ANALYSIS OF THE MAGNET AND COIL

SYSTEM

F = Fmsinωt (N) (Force produced by muscle)

Fm = 20 (N)

B = 2 (N/m/s) (Damping effect of the muscle)

Mg = 0.00872 (kg) (Mass of a 10mm diameter, 15mm length NdFeB magnet)

Ki = 1300 (N/m) (Spring constant of implanted spring)

N = 10 (Number of turns in the coil)

F

B Ki

Muscle Magnet, coil & springBone Bone

Mg

NF

B Ki

Muscle Magnet, coil & springBone Bone

MgMg

N

117

ig

ig

m

KMwhenisP

wKMB

FP

1__||

)1(||

max

22

2

=

−+=

ω

ω

|Pmax| depends on Ki and w

Electrical circuit:

VL(t) = Voltage in the inductor (magnet & coil)

L = 3.82 (μH) (Inductance of the magnet & coil)

RL = 0.008 + 9.992 (Ω) (Resistance of the magnet & coil + extra resistance to match

capacitor resistance)

RC = 10 (Ω) (Resistance of the capacitor)

C = 5.6 (F) Capacitor

i(t) = Current in the circuit

Force, displacement and velocity of magnet at 10 Hz:

VL(t)

L RL

RC

C+

VC-

i(t)VL(t)

L RL

RC

C+

VC-

i(t)

118

Flux density vs. time in coils at 10 Hz:

119

Voltage in coils:

Power in capacitor C:

Five of these waveforms occur per twitch for a total of 66x10-9J of energy.

2. MAGNET AND COIL EXPERIMENTAL RESULTS

In these experiments a magnet is oscillated by a motor driving a spring.

120

This approximates the open circuit voltage of the magnet and coil generator. The force

applied to the magnet was applied at 4 Hz.

The voltage after 60 s is 0.03 V.

The energy in CL after 60s:

ECL = 0.5*CL*VL2 = 1.5e-6 J

The power of the stack:

P = ECL/60s = 2.5e-8 W

The energy the stack can produce per day:

E/day = P*3600s/hr*24hr/day = 2.2e-3 J/day

121

B. PIEZOELECTRIC GENERATOR

1. THEORETICAL ANALYSIS OF THE PIEZOELECTRIC GENERATOR

The model of thin film piezoelectric material connected to a parallel circuit

c

LL

pCRt

CRt

LLL

CRt

p

pc

ViP

VCRtV

eV

eR

VCRte

RV

i

LL

LLLL

=

+=

−

+=

−

−−

)0(

)0(1

+Vp-

Cp

CLip+V-

Rp

RL

+ Vcp -

ic ir

Piezoelectric material

+Vp-

Cp

CLip+V-

Rp

RL

+ Vcp -

ic ir

Piezoelectric material

122

Positive portion of the power curve is estimated as a parabola. The area under the curve is

found to be: 0.036 μJ (The output power was multiplied by the coupling factor in this

calculation)

2. PIEZOELECTRIC GENERATOR EXPERIMENTAL RESULTS

Force is applied by hand to piezoelectric material:

123

Force application is approximately a rectified sinusoidal pulse with an average maximum

magnitude of 17 N, an average pulse width of 0.7 s and an average frequency of 0.9 Hz

The voltage across CL after 60s is 0.15 V. The energy in CL after 60s:

ECL = 0.5*CL*VL2 = 6.2e-6 J

The power of the stack:

P = ECL/60s = 0.1e-6 W

The energy the stack can produce per day:

E/day = P*3600s/hr*24hr/day = 0.009 J/day

C. SUMMARY OF THE TWO OPTIONS

Theoretical Estimates:

Power conversion idea

Estimated input power needed to run system

Best first guess on output power obtained from system

Total power if system runs 24 hours/day

Output power per volume

Piezoelectric material

1x10-9 W 36x10-9 W 0.003 J/day 1.38 W/m3

124

Linear electromagnetic generator

1x10-9 W 66x10-9 W 0.0057 J/day 0.014 W/m3

Experimental estimates:

Requirements/ Concepts

Mechanically simulated experimental output power

Small Volume

Power per volume

Moving parts Biocompatible

Piezoelectric generator 2.6 µW 0.45

cm3 5.8 W/m3 NO

Encapsulation probably needed

Electromagnetic generator 0.025 µW 30 cm3 0.00083

W/m3 YES Encapsulation probably needed

Based on these early analyses, the piezoelectric generator was selected as the power

conversion method for our system.

125

APPENDIX B. SIMULATION MODEL

A Spice model was used to perform analyses of the generator system, as shown in

Figure B-1.

Figure B-1. Software simulation schematic. The schematic of the piezoelectric generator and electrical circuitry used in the software simulations.

The piezoelectric generator was represented by V1, E1 and C1. V1 was defined

by a comma separated value data file containing the force waveform. E1 represents the

electromechanical conversion from input force to piezoelectric voltage. C1 represents the

capacitance of the piezoelectric stack. Diodes D1 and D2 are used to rectify the force

pulses, charge is stored in capacitor C2 and the load is represented by R1. R1 is defined

as a parameter so that a parameter sweep can be performed, where the voltage across R1

126

is calculated for several values of R1. The V probe can be used to plot the calculated

voltage across R1 resulting from the input force and is shown in Figure B-2.

Figure B-2. Example output of the software simulations.

127

APPENDIX C. MECHANICAL MUSCLE ANALOG

Figure C-1. Schematic of the mechanical muscle analog control system.

The mechanical muscle analog consisted of a linear motor (FA-150-S-12-3,

Firgelli Automations, Ferndale, WA), motor control and a spring. The linear motor

applied periodic tension to the spring, which applied force to the piezoelectric stack in a

manner in which mimicked the twitch force of a muscle. The force level ranged from 10

to 50 N and was adjusted by varying the motor power supply between 4 and 6 V and by

using two springs with different spring constants. A spring with a spring constant of

10,000 N/m was used for force levels of 10-20 N. A spring with a spring constant of

13,500 N/m was used for force levels of 30 – 50. Force was measured with a load cell

128

(LC703-50, Omega Engineering, Inc., Stamford, CT). Data was acquired with a data

acquisition board and data collection software (DAQPad 6052E & Labview Software,

National Instruments, Austin, TX). The motor control consisted of a 20-pin H-bridge

circuit (TPIC0107B, Texas Instruments, Dallas, TX). The following pin assignments

were used:

Pin 1: Ground

Pin 2: 4-6 V from a DC power supply for the motor power supply (this voltage was used

to control the force level)

Pin 3: Input from A/D board counter (DAQPad 6052E & Measurement & Automation

Explorer, National Instruments, Austin, TX). The clock was set at 1 Hz, with a 0.475

duty cycle between high and low output.

Pin 5: - Motor

Pin 8: 6 V Control voltage

Pin 15: + Motor

The periodic high/low input from the A/D board counter switched the voltage to the

motor from positive to negative, allowing the motor shaft to cycle back and forth. This

motion pulled and relaxed the spring causing cyclical tension on the piezoelectric stack

holder. Tension on the piezoelectric stack holder (Figure II-4) caused a compressive force

to be applied to the piezoelectric stack. A 7 x 7 x 44 mm piezoelectric stack of modified

lead zirconate titanate (PZT) material (TRS Technologies, State College, PA) with a

piezoelectric constant of 0.035 VmN-1 and a capacitance of 323 nF was used in this

129

study. The power analysis circuit (Figure III-3) and the generator system circuit (Figure

III-4) were the two circuits connected to the piezoelectric generator and used in the

development and testing of the system.

130

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