PHYSIOLOGICAL AND BIOMECHANICAL APPROACH FOR HUMAN FINGER MOVEMENT: MODELING, SIMULATION AND...

PHYSIOLOGICAL AND BIOMECHANICAL APPROACH

FOR HUMAN FINGER MOVEMENT: MODELING,

SIMULATION AND EXPERIMENTAL VALIDATION

SAMAR ALLOUCH*,†,‡, RAFIC YOUN�ES*,§,

SOFIANE BOUDAOUD†,¶ and MOHAMAD KHALIL*

*EDST- AZM Centre for Biotechnology Research, Lebanese University, France

†University of Technology of Compi�egne, UMR 7338 BMBI, France‡[email protected]§[email protected]

¶[email protected]

Received 13 October 2013

Revised 12 August 2013

Accepted 17 November 2013

Published

The work presented in this paper deals with the description of an analytic modeling of the

neuromusculoskeletal system responsible for the finger movement. This simulation task is

complex due to the interacting processes (physiological and biomechanical) represented by

muscles, joints and bones. In this study, we focused on the presentation of a complete model for

the finger motion decomposed in quasi-static positions. In fact, this model can be considered as

a preliminary step before dynamic modeling. The proposed model is composed of several

compartments: biomechanical finger model, mechanical muscle model and muscle/neural

activation model. The main objective of this study is to estimate, by inverse procedure, the

muscle forces, muscle activations and neural activations that are responsible for generating a

given finger movement decomposed in successive quasi-static positions. The anatomical model

contains six muscles which control the decomposed movement of the three joints of the system.

To estimate the model unknowns, an optimization technique is proposed for improving

robustness to initial conditions and physiological reliability. After, an experimental protocol

for recording surface electromyogram (sEMG) data, from three extrinsic muscles, according to

specific finger positions is applied on five subjects to evaluate the model reliability.

From analysis of the obtained results, both in simulation and experiment, the presented

model seems to be able to mimic, in a realistic way, the finger movement decomposed in quasi-

static positions. Finally, results, model limitations and further developments are discussed.

Keywords:

Nomenclature

ai:Muscle activation of muscle i.

ui:Neural activation of muscle i

December 10, 2013 3:30:17pm WSPC/170-JMMB 1450040 ISSN: 0219-5194Page Proof

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Journal of Mechanics in Medicine and Biology

Vol. 14, No. 3 (2014) 1450040 (19 pages)

°c World Scientific Publishing Company

DOI: 10.1142/S0219519414500407

1450040-1

http://dx.doi.org/10.1142/S0219519414500407

Administrator

Text Box

AQ: Please provide keywords.

"i:Muscle deformation of muscle i.

Fi:Muscle force of muscle i.

eðtÞ:Post processed EMG.

Pi:Phalanx i

DIP:Distal interphalangeal joint.

PIP:Proximal interphalangeal joint.

MCP:Metacarpophalangeal joint.

FDS:Flexor digitorum superficialis muscle.

FDP:Flexor digitorum profundus muscle.

EDC:Extensor digitorum communis muscle.

LU:Lumbricalis muscle.

RI:Dorsal interossei muscle located on the radial side of the finger.

UI:Dorsal interossei muscle.

�i:Force distribution coefficient of muscle i or muscular bound i.

Mext1:external moment applied on the system in Fig. 3.



�1:Flexion angle of DIP joint.

�2:Flexion angle of PIP joint.

�3:Flexion angle of MCP joint.

Fmaxi :Maximal force contraction (MVC) of muscle i.

1. Introduction

Since the beginning of the 20th century, man has tried to understand, analyze and

model body motions that he carries out, like walking, waving and grasping with

applications including surgery, functional rehabilitation, diagnosis and prevention.1

The hand is a particularly complex and necessary functional part that performs

various daily activities,2,3 and that increases the need for a realistic hand model

based on its physiology.4 Due to its importance, a lot of studies, which model human

hand, were done.2,3,5,6 A recent study, which gave inspiration to the proposed work,

for predicting muscular force in the hand and forearm system was presented by

Chalfoun.7,8 The estimation of muscular force, activation and deformation during

the simulation of static positions of the hand were the general framework of his

work. He studied the hand’s kinematics; the system that he considered was linear

because he did not take into account the variations of the extensor mechanism of the

fingers at different positions of the land. According to the human movement theory,

the extensor mechanism is defined as the magnitude of the tension transmitted in

different bands. For finger movement, it is necessary to improve the modeling

procedure in terms of anatomical issues and this will increase the complexity and

nonlinear behavior as depicted in the recent following studies9–12 correlated to the

proposed study.


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S. Allouch et al.

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Indeed, Vigouroux et al.9 worked recently on the biomechanical modeling of the

human hand. Its model aimed to deduce muscle forces from movement. He took into

account, in his model, the torque of nonmuscle and passive structures (ligaments).

In addition, he used surface electromyogram (sEMG) information in the optimiz-

ation procedure. Buchanan et al.10 presented an overview of dynamic neuro-

musculoskeletal modeling for the upper limb. The aim of such models is to estimate

or predict muscle forces, joint moments, and/or joint kinematics from neural intent

extracted from sEMG signals. This work is similar to what is proposed in this study,

but in the reverse direction.

Qi Shao et al.11 presented an sEMG driven musculoskeletal model to estimate

muscle forces and joint moments using joint kinematics and sEMG as inputs. In the

proposed study, we incorporated the anatomical model, described in this study, as a

part of our model. Paclet et al.12 have focused their research efforts on the study of

biomechanics of the upper limb tendon transfers, including consideration of co-

contraction activity estimated from sEMG recording on extensor and finger flexor

muscles. The biomechanical model of the hand is further developed by including

muscle length, and the wrist joint in his model. This work is limited to the deduction

of muscular forces.

The presented work consists of the proposition of a realistic neuromusculoske-

letal model of human middle finger in quasi-static conditions. This model contains

three important submodels as depicted in Fig. 1. The first submodel is the finger

biomechanical model. It deals with the finger anatomy and the phalanx positions as

input and provides us with estimated involved muscle forces, by inverse optimiz-

ation procedure. The second submodel is the mechanical muscle model. This model

links the provided muscle force with the muscle deformation (length modification)

and the muscle activation (correlated to the number of active Motor Units in the

muscle). We propose in this study, an inverse optimization procedure that incor-

porates the two depicted submodels, and allows the estimation of muscle activations

from the phalanx positions. Finally, the third submodel, namely the neural muscle

activation, permits the modeling of the relation linking the neural intent, estimated

Fig. 1. Schematic view of the model structure and the validation procedure.


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Physiological and Biomechanical Approach for Human Finger Movement

1450040-3

from the sEMG data, and the muscle activation. It represents the neural part of the

presented neuromusculoskeletal model. We used the same term, namely the neural

activation, introduced by Buchanan et al.10 to describe the intermediate stage

between the recorded sEMG signal and muscle activation.

Using this complete model, the aim is to deduce the neural intent from finger

data position as shown in Fig. 1. Validation of the proposed model is performed by

comparing neural activations, estimated by the model, and neural activations

deduced from sEMG recorded on three extrinsic muscles, involved in the finger

decomposed movement, following a specific experimental protocol.

In other words, the proposed model uses the three angles of finger joints and the

three external joint moments as inputs to estimate the individual muscle forces,

muscle activation and neural activation. Each submodel is explained and detailed

by imposing some hypotheses and simplifications that are necessary to reduce model

complexity. The innovation of the proposed model is the coupling between bio-

mechanical and neurophysiological aspects using physical models to simulate the

complete inverse finger motion (decomposed in quasi-static positions) chain from

the finger phalanx position to the neural intent.

The proposed study will be decomposed as follows. In Sec. 2, we present and

detail the finger biomechanical model. Then, the mechanical muscle model is

described in Sec. 3. Later, we present the used neural/muscle activation model in

Sec. 4. In Sec. 5, the methodology to estimate the models unknowns, by a new suited

optimization procedure, is described and an example of application is presented to

enhance clarity. Some simulated data, from the proposed model, are presented in

Sec. 6 and compared to the experimental data obtained by a specific protocol in

Sec. 7. Finally, we conclude the obtained results and propose further possible

improvements for the model and the validation methodology.

2. Finger Biomechanical Model

In this work, we focused on the biomechanical modeling of the third finger, namely

the middle finger. To obtain a realistic modeling, we included physiological aspects

concerning the knowledge on bones, joints and muscles constituting this finger. In

addition, the extensor mechanism and the biomechanics used are detailed.

2.1. Bones and joints

Middle finger is composed of a metacarpal bone P4 (ossa metacarpalia) and three

phalanges (see Fig. 2), the proximal phalanx P1, the media phalanx P2 and the

distalis phalanx P3. These four bones are mobilized around three joints. The

metacarpophalangeal articulation (MCP) binds metacarpal bone to the first pha-

lanx through a joint \asymmetrical condylar". The proximal interphalangeal joint

(PIP) and distal interphalangeal joint (DIP) bind the first, second and third pha-

lanx. These joints are of type \trochlea".13


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2.2. Muscles

The three joints are mobilized by six muscles shown in Fig. 3. Three muscles are

classified as \extrinsic" in hand. These muscles are located in the forearm and act on

the hand through long tendons14:

. Flexor digitorum profundus muscle (FDP) which flexes the wrist, MCP, PIP and

DIP.

. Flexor digitorum superficialis muscle (FDS) flexes the elbow joint, wrist, MCP

and PIP.

. Extensor digitorum communis muscle (EDC) attaches to the epicondyle of the

humerus and mobilizes the four fingers through the tendons that attach to the

proximal phalanx and the extensor mechanism (see Sec. 2.3) of the fingers.

Through this mechanism it extends the DIP and PIP joints. Three other muscles

are classified as \intrinsic" to the hand. Their muscular bodies are located in the

hand and act on the three MCP, PIP and DIP joints.

. The muscle lumbricalis (LU).

Fig. 3. Muscles and tendons mobilizing middle finger. The top schematic represents tendon insertions

and strips of the extensor mechanism.9

Fig. 2. The phalanges and joints of human major finger.


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1450040-5

. The dorsal interossei muscle located on the radial side of the finger (RI).

. The dorsal interossei muscle located on the ulnar side of the finger (UI).

LU, RI and UI muscles are flexors of MCP joint. LU and RI muscles are adductors of

the MCP joint while the abductor muscle is UI.2 The intrinsic muscles of the hand

have the distinction of having some of their insertions located on the finger extensor

mechanism.8 These muscles therefore have an action extension at PIP and DIP

joints.

2.3. Extensor mechanism

The symmetrical model8,15 is used to describe this mechanism (Fig. 3). To model the

action of muscles on DIP and PIP joints through the extensor mechanism, it is

necessary to assess the magnitude of the tension transmitted in different bands. Chao

et al.13measured the angle of bands and tendons at each node on the hands of cadavers.

From these angles, authors estimated the value of the coefficient of stress distribution

in the bands of extensor mechanism.

Those coefficient values were measured at a position where all the joints are zero

degrees of flexion. But the extensor mechanism has the distinction of being

deformable by finger posture. The angles of the nodes and the lengths of the bands

change according to flexion of DIP and PIP joints.16 To resolve this problem,

Brook17 has proposed to add variables (�), which change with angles flexion and

illustrate the distribution of tensions (forces) transmitted in different bands, and

then they obtained the following equations:

FTE ¼ 0:992ðFRBÞ þ 0:995ðFUBÞ;FRB ¼ �EDCFEDC þ �LUFLU þ �RIFRI;

FUB ¼ �EDCFEDC þ �UIFUI;

FES ¼ ð1� �UIÞFUI þ ð1� �LUÞFLU þ ð1� 2�EDCÞFEDC;

ð1Þ

where FEDC, FUI and FLU are the tensions of EDC, UI and LU, FTE, FRB, FUB and

FES are the tensions in the bands TE, RB, UB and ES.

The coefficients �EDC, �UI, �LU and �RI are unknown coefficients reflecting the

transmission of forces in the extensor mechanism according to the posture of the

finger. They are determined in accordance with the following inequalities:

1 � 2 � �EDC � 0;

1 � �UI � 0;

1 � �RI � 0;

1 � �LU � 0:

ð2Þ

2.4. Biomechanical model

The model presented here is inspired from the work done by Paclet12 in 2010 where,

bones are modeled as four nondeformable solids. There is only one degree of freedom


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for DIP and PIP. There are two degrees of freedom for MCP. To simplify our model,

we have considered only a single degree of freedom for each joint.

When applying an external force, the finger is considered in static mechanical

equilibrium. In all movement equation we will take every system as static. This

simplification is necessary, in a first step, to evaluate the proposed neuro-

musculoskeletal model. To apply the fundamental principles of static mechanics

to the particular case of the finger, we will consider successively the follow-

ing three systems in equilibrium: P3 system rotating around DIP (Fig. 4(a)), (P3

þ P2) system around PIP (Fig. 4(b)) and (P3 þ P2 þ P1) system around MCP

(Fig. 4(c)).

By developing the equations resulting of application of fundamental principle of

static mechanics on the three previous phalangeal systems, we arrive at a system of

three equations that have 10 unknowns (six muscle forces and four distribution beta

coefficients):

m11 � � � m16

: � � � :m31 � � � m36

24

35�

FFDP

FFDS

FLU

FRI

FUI

FEDC

266666664

377777775þ

Mext1

Mext2

Mext3

24

35 ¼ 0; ð3Þ

where Mext1, Mext2 and Mext3 , which will be considered as inputs to the model, are

respectively the external moment applied on the three previous systems (Fig. 4),

they represent the external moments caused by the weight of three systems, we have

taken its values as constants. The coefficientsmij obtained from the system have the

expressions displayed on Table 1.

In Table 1, MA(a/b) represents the moment arm for muscle or muscular bound

\a" at joint \b". For an extensor muscle the moment arm is considered as constant9

(a) (b) (c)

Fig. 4. (a) Forces applied on the (P3) system, (b) forces applied on the (P3þ P2) system, (c) forces

applied on the (P3þ P2þ P1) system.9


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1450040-7

Fig. 5(a), and for an flexor muscle MA is geometrically calculated using the model

presented in Fig. 5(b).

3. Mechanical Muscle Model

In this section, the mechanical model linking the muscle force to muscle deformation

(length) and muscle activation related to the number of active motor units is

described. The model is of hill type with no pennation angle hypothesis (the muscle

fibers are aligned with the tendons). This last simplification has reduced effects in

anisometric context as in our study.18,19

The muscle tendon unit was modeled as a contractile element (Ec) in serial with

a passive element (Es) and in parallel with a passive element (Ep).20 The total

muscle force FM is the sum of a passive force and an active force. Since the simu-

lated movements are decomposed on static positions, the velocity of the contraction

was not taken into account. Only a force–length relationship was established. The

forces were normalized to the maximum isometric force for each muscle. The general

form of the equation of the force produced by the muscle-tendon unit is given by

Audu.21

FM ¼ FT ¼ Fmax½aðtÞfð"Þ þ fpð"Þ�; ð4Þ

Table 1. The coefficient of biomechanical model presented in Eq. (3).

m11 ¼ MA(FDP/DIP) m21 ¼ MA(FDP/PIP) m31 ¼ MA(FDP/MCP)

m12 ¼ 0 m22 ¼ MA(FDS/PIP) m32 ¼ MA(FDS/MCP)

m13 ¼ �0:992�MAðTE=DIPÞ � �LU m23 ¼ �MAðRB=PIPÞ � �LU �MAðES=PIPÞ � ð1� �LUÞ

m33 ¼ �MAðLU=MCPÞ

m14 ¼ �0:992�MAðTE=DIPÞ � �RI m24 ¼ ��RI �MAðRB=PIPÞ m34 ¼ �MAðRI=MCPÞm15 ¼ �0:995�MAðTE=DIPÞ � �UI m25 ¼ �MAðUB=PIPÞ � �UI �

MAðES=PIPÞ � ð1� �UIÞm35 ¼ �MAðUI=MCPÞ

m16 ¼ �1:987�MAðTE=DIPÞ � �EDC m26 ¼ �MAðUB=PIPÞ � �EDC �MAðRB=PIPÞ � �EDC �MAðES=PIPÞ � ð1� 2�EDCÞ

m36 ¼ �MAðEDC=MCPÞ

(a) (b)

Fig. 5. (a) Moment arm for extensor muscle,9 (b) moment arm for flexor muscle.9


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where aðtÞ is the activation at time t, " ¼ ðl� l0Þ=l0 is the muscle deformation, l is

the muscle fiber length at time t, l0 is the optimal fiber length at which maximum

muscle force could be obtained, the numerical value of l0 can be found in Refs. 22

and 23. The parallel passive elastic muscle force fpð"Þ and fð"Þ is the force-length

relationship in the contractile element and it is given by Maurel24:

fð"Þ ¼ e� ð"þ1Þ0:96343� 1� 1

iað Þ�1

0:35327�ð1�iaÞ

� �2

ia < 1;

fð"Þ ¼ e�½2:727277�lnð"þ1Þ�2 ia ¼ 1;

ð5Þ

where ia (anatomy index) represents the ratio between the fiber length and the

muscle length. The ratio of the muscles is given by Maurel.24 The parallel passive

elastic muscle force fpð"Þ was obtained from an exponential relationship used by

Maurel,24 and has the following form:

fpð"Þ ¼ b1 � eb2�" � b1; ð6Þ

where b1 and b2 are muscle constants determined experimentally by Hill.25

These constants are taken to be 0.03 and 7, respectively. It has been proven22

that the effective operating range of muscle begins at roughly 0.5 l0 and ends at

1.5 l0. A muscle cannot generate active force beyond these lengths. This will

give us a displacement range of �0:5 < " < 0:5. In addition, when muscle is

stretched to lengths greater than 1.2 l0, it generates a significant amount of

passive force.24

4. Neural Activation-Muscle Activation Model

In this section, we present a relationship model between neural activation uðtÞ andmuscle activation aðtÞ from the work of Manal and Buchanan.26 The model is tuned

by one parameter A. The value for A defines the curvature (nonlinearity) of the

relationship, which can range from a linear curve to a family of nonlinear curves that

fit the data from the biceps brachii muscle and given by Woods and Bigland-

Ritchie27 as depicted on Fig. 6. The coordinates of the node point (P) reported on

Fig. 6, were approximately fixed to u0 ¼ 0:222 and a0 ¼ 0:395.

The degree of curvature and location of the node point for each curve in this

family of piecewise curves is related to the distance from point O along the A-line in

the direction of point P. Point O (0.3085, 0.3085) lies at the perpendicular inter-

section of a ¼ u and the A-line.26

The relationship between parameter A and the (u; a) coordinates of the node

point (u0; a0) are given by

u0 ¼ 0:3085� A cos 45�;

a0 ¼ 0:3085� A sin 45�:

ð7Þ


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1450040-9

The curvilinear portion of the piecewise curve was modeled using the following

equations.

a ¼ � lnð�uþ 1Þ ð0 � u � u0Þa ¼ muþ c ðu0 � u � 1Þ ð8Þ

Here �, �, m and c are constants that all can be determined from the single par-

ameter \A" (for details, see Ref. 26). According to the following model we should

deduce the constant A for each muscle resolving a tuning problem. The physical

meaning of A is nothing more than the path length from point O to P, which is used

to characterize the degree of nonlinearity between neural activation and muscle

activation. We searched values of the parameter \A" in the literature26 and used the

following values in our study and respecting physiological limits (0:0 < A � 0:12)

for the six studied muscles: AFDP ¼ 0:1, AFDS ¼ 0:015, ALU ¼ 0:004, ARI ¼ 0:002,

AUI ¼ 0:01, AEDC ¼ 0:0058.

5. Estimation Procedure

In this section, the estimation of the model unknowns by means of optimization

procedure is described in detail. In fact, a new optimization function is proposed for

estimating the muscle forces, deformations, and activations using the equation

Fig. 6. Nonlinearization of neural activation, uðtÞ; to muscle activation, aðtÞ: The open circles represent

data for the biceps reported by Woods and Bigland-Ritchie (1983).26


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system in Eq. (3) and the muscle mechanical model defined in the last section. The

problem to optimize respects the following equations:

MinX

ðFið"i; aiÞ=F 2maxi þ a2

i þ "i="2maxÞ

m11 � � � m16

: � � � :m31 � � � m36

24

35�

FFDP

:

Fið"i; aiÞ:

FEDC

266664

377775þ

Mext1

Mext2

Mext3

24

35 ¼ 0

lb <

"iai�j

24

35 < ub

8>>>>>>>>>>>>>><>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>>=>>>>>>>>>>>>>>;

; ð9Þ

where Fi represents the force value of each muscle finger and Fmaxi is the corre-

sponding max force value. In this optimization cost function, the forces Fi are not

directly estimated since we put its expression, using the Hill model, in terms of

deformation and activation Fi ¼ Fmaxi ½aiðtÞfið"iÞ þ fið"iÞ�. In this way we obtain a

system of 3 equations with 16 variables "i; ai and �j.

The resolution of such system corresponds to search results by optimizing

deformation and activation of each muscle without finding the values of muscular

forces. It should be noted that the function to be minimized isP

Fið"i; aiÞ=Fmaxi2,

where Fið"i; aiÞ is an expression of muscular force as a function of "i and ai. By

minimizing the cost function f ¼ P ðFið"i; aiÞ=Fmaxi2 þ a2

i þ "i="max2Þ with respect

to lower lb and upper bounds ub of variables, the system unknowns are estimated

using suitable initial conditions. Estimated forces are obtained by using the esti-

mated "i and ai and the Hill model equation. This new optimization cost function

prevents from numerical instability and aberrant estimating parameters compared

to classical ones based on the minimization of the quadratic sum of normalized

muscle forces.8,9

5.1. Estimation methodology

In this subsection, an example, to illustrate the estimation process, is provided. As

described before, the estimation methodology consists of resolving one optimization

problem Eq. (9) for estimating muscle activation ai and muscle deformation "i for

each finger muscle in addition to the coefficient distribution �i.

As a first step, we introduce external moments applied on the finger (Mext1,

Mext2, Mext3Þ and the finger position, which is represented by the three joint angles

(�1, �2, �3), to our model as input to obtain after optimization the muscle acti-

vation, muscle deformation of each finger muscle and the distribution coefficient

introduced in extensor mechanism depicted in Fig. 7. The values that we have used

as input and the result are presented in the Table 2.

For numerical implementation, we used the optimization toolbox in Matlab.

After estimating muscle activations and deformations, we calculate muscle forces


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from the Hill model in Eq. (4). We obtain six following values: FFDP ¼ 0:1113N;

FFDS ¼ 0:5098N; FLU ¼ 0:0061N; FRI ¼ 0:0105N; FUI ¼ 0:6557N; FEDC ¼0:2094N. We searched neural activation from the model presented in Eq. (12) which

relies on muscle activation. We obtained the following neural activation values

normalized of each finger muscle: uFDP ¼ 0; uFDS ¼ 0:0028; uLU ¼ 0:0007; uRI ¼ 0;

uUI ¼ 0:0070; uEDC ¼ 0:0030.

6. Simulation Results

We simulated the finger motion (finger closing and opening), depicted in Fig. 8, by

decomposing it into 300 static positions. At each position corresponding to a specific

joint angle triplet (�1i, �2i, �3i) with reduced external moments (no hand load),

we estimated muscle forces, activation, muscle deformations and neural activations.

We considered the hand in closing and opening movement with slow velocity. As can

be seen in the Fig. 8 in the order 1 ! 6, our finger system is dynamic and not static,

Fig. 7. Estimation methodology.

Fig. 8. Simulated finger motion.8

Table 2. Inputs and estimated outputs of the finger

biomechanical model at a specific position.

Model inputs Estimated model outputs

Mext1 ¼ 0:50N.m �EDC ¼ 0:5; �LU ¼ 1:0

Mext2 ¼ 0:35N.m �UI ¼ 1:0; �RI ¼ 0:0001

Mext3 ¼ 0:15N.m aFDP ¼ 0; "FDP ¼ �0:0037m

�1 ¼ 2:0735 rd aFDS ¼ 0:0034; "FDS ¼ 0:0004m

�2 ¼ 2:0735 rd aLU ¼ 0:0008; "LU ¼ 0:0002m

�3 ¼ 2:0735 rd aRI ¼ 0; "RI ¼ �0:0005m

aUI ¼ 0:0083; "UI ¼ 0:0009m

aEDC ¼ 0:0035; "EDC ¼ 0:0003m


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so our methodology consists of taking several successive positions of the finger, hand

opening and then hand closing. In this case we divided the finger movement, by the

desired accuracy, into static positions to allow the estimation procedure depicted in

Sec. 4.

Then, we obtained the following curves presented in Fig. 9 that represents force,

deformation, activation and neural activation for each of the six muscles obtained

after optimization procedure.

The position 1 corresponds to the full extension of the finger and the position 150

corresponds to the full flexion. From the position 1 to 150, this part represents the

hand closing and the second part which is from the position 150 to 300 is about hand

opening. Observing the curve shape of FDP and FDS muscle forces, we notice that

they havemaximumvalues at the full flexion and extension, and aminimumvalues at

the position where the hand is relaxing (from the position 15 to 135). Those results are

convincing because the two muscles FDP and FDS are responsible for hand flexion.

The deformation has the same curve shape as muscle force for the six muscles,

but the deformations have values that are between �0.004m and 0.008m which are

acceptable. About muscle activation, it also has the same curve shapes as muscle

force with obtained values between 0 and 0.05 is also acceptable.

0 50 100 150 200 250 300-5

0

5

10

15

20

positions

Fro

ces

[N]

Forces

FDPFDSLURIUIEDC

0 50 100 150 200 250 300-0.05

0

0.05

0.1

0.15

Positions

Nor

mal

ised

Act

ivat

ion

Muscle Activation

FDPFDS

LU

RI

UIEDC

0 50 100 150 200 250 300-5

0

5

10

15x 10

-3

positions

Def

orm

atio

n [m

]

Muscle Deformation

FDPFDSLURIUIEDC

0 50 100 150 200 250 300-0.05

0

0.05

0.1

0.15

Positions

Nor

mal

ised

Act

ivat

ion

Neuronal Activation

FDPFDSLURIUIEDC

Fig. 9. Estimated muscle force, activation, deformation and neural activation curves for the six studied

muscles.


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As we can see on Fig. 9, the obtained neuronal activation and muscle activation

curves are relatively similar. This is due to the linearity between the two functions

since the highest possible muscle activation is 0.04 and is inside the linear part

(0 < A < 0:04) of the neural activation/muscle activation relationship function.

7. Evaluation with Experimental Data

To validate the simulation results, we conducted experiments to measure sEMG

signals of accessible muscles during several positions of the same motion (the

opening and closing of the hand) depicted in Sec. 6. To compare experimental with

simulated results, we can compare neural activations estimated by simulation with

that computed from experiment using a neural activation/sEMG model which

allows deducing neural activation from sEMG signal. For this operation, we have

used the model presented by Buchanan et al. in 2004,10 which is represented by the

following equation:

uðtÞ ¼ �eðt� dÞ � �1uðt� 1Þ � �2uðt� 2Þ; ð10Þwhere d is the electromechanical delay and �, �1 and �2 are the coefficients that

define the second-order dynamics. These parameters (d, �, �1 and �2Þ map the

EMG values, eðtÞ, to the neural activation values, uðtÞ. In this study, these par-

ameters are fixed according to the study presented by Barrett et al.28

The sEMG signals were recorded from the FDP, FDS and EDC, using bipolar

electrodes, as presented in Fig. 10. Those muscles were identified by palpating the

skin during appropriate finger movements of the studied subjects.

Bipolar electrodes (disposable surface electrodes (Al/AgCl) with 10mm diam-

eter) were located on the skin overlying each muscle with a 2 cm inter-electrode

distance. Before the electrode application, the skin was cleaned for reducing skin

impedance (< 10 k�). The EMG signals were measured by portable transmitter

system (TeleMyo 2400T G2 transmitter, Noraxon) combined with the receptor

(TeleMyo 2400R G2 receiver, Noraxon). Signals are band pass filtered (10–500Hz),

digitized (1000 samples/s) and saved on the hard disk of a personal computer.

We made the measurements on five persons, aged 25� 2 years, 180 cm size and

weight close to 80� 3 kg. The proposed protocol is in accordance with the

Declaration of Helsinki and after association of the local ethic comity. None of the

Fig. 10. Bipolar electrodes placements for FDP, FDS and EDC muscles.


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volunteers were regular exercise practitioners. They did not present any symptoms

of neuromuscular or ligament disorders, and were not using anti-inflammatory

medication or muscle relaxants during the experimental sessions. Written informed

consent had been given by all subjects prior to the sessions.

We took seven critical hand positions (that belong to the simulated position

vector). In fact, each subject was asked to put his arm on a horizontal plane to

ensure immobility of the wrist. Right besides the hand, the seven positions are

plotted on a vertical plane where the subject tries to respect by visual checking. The

subject must fix his hand at each position for 10 s, and then he should move his hand

slowly to reach the next position avoiding fast transition from one position to

another to reduce the risk of getting sEMG peak value due to dynamic behavior.

The sEMG signals are then recorded for each subject, normalized and rectified. For

each subject we have repeated the measurement five times. Then, we did the

average of those measurements to obtain finally representative sEMG data from

FDP, FDS and EDC at the same 13 positions between hand opening, closing and

opening again. Where we have 10 s for each position, the values thus obtained are

used as inputs for the EMG-neuronal activation model depicted in Eq. (10) to get

the neural activation corresponding values. To have accurate neural activation

value for each position, the calculus was done on 10 s duration and then averaged.

By this way, we obtained 13 pairs of neural activation values and positions.

In Fig. 11, we represented the neural activation curves (green and blue) of

respectively FD, FDS and EDC muscles looked by experiment for two subjects (the

same curves have been observed on the other subjects). Those curves represent the

Subject 1

Subject 2

0 50 100 150 200 250 300-0.01

0

0.01

0.02

0.03

0.04

Positions

Neu

ral A

ctiv

atio

n

FDP Neural Activation

Simulation

Experimentation

0 50 100 150 200 250 3000

0.02

0.04

0.06

0.08

0.1

0.12

Positions

Neu

ral A

ctiv

atio

n

FDS Neural Activation

Simulation

Experimentation

0 50 100 150 200 250 3000

1

2

3

4

5x 10

-3 EDC Neural Activation

Positions

Neu

ral A

ctiv

atio

n

0 50 100 150 200 250 300-0.01

0

0.01

0.02

0.03

0.04

Positions

Neu

ral A

ctiv

atio

n

FDP Neural Activation

Simulation

Experimentation

0 50 100 150 200 250 3000

0.02

0.04

0.06

0.08

0.1

0.12

Positions

Neu

ral A

ctiv

atio

n

FDS Neural Activation

Simulation

Experimentation

0 50 100 150 200 250 3000

2

4

6

8x 10

-3 EDC Neural Activation

Positions

Neu

ral A

ctiv

atio

n

Fig. 11. (Color online) Neural activations of FDS, FDP and EDC muscles estimated by simulation and

experiment for two subjects.


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neural activation calculated from sEMG data measured at the 13 static positions of

the hand closing and opening slow motion. We also represented the simulated curves

(blue) obtained (Sec. 6).

We observe, in Fig. 11, that the simulation curves are in agreement with the

experimental result in the shape of the curve during the closing and opening of the

hand. In fact, the curves corresponding to the neural activations of FDP and FDS

flexor muscles fit the simulated curves during both hand extension, with a plateau

near zero, and the hand flexion (total closure), with maximum values.

It is important to notice here that we normalized both experimental and simu-

lation curves in order to compare tendencies. In fact, it is clear that many par-

ameters in the model are taken without any calibration when comparing to

experimental data. Another difference between experiment and simulation is the

high obtained values for FDP and FDS neural activations at the position 0, 150 and

300 in the simulation. This simulated result should be explained by numerical

instability in the optimization procedure at those positions due to the supposed zero

values of the three finger joint angles.

As we can also see on Fig. 11, we do not have a similarity but inversion between

the EDC muscle curves in experiment and simulation. This should be explained by

biased estimation due to simplifications applied in the proposed biomechanical

model. In fact, the obtained experimental result is relevant due to the maximum

value of the neural activation for EDC muscle at the full hand extension, and also

the small contribution of this muscle at full hand flexing observed for both subjects

(especially for subject 1).

8. Discussions and Conclusion

The presented work concerned the proposition of a system of models including

biomechanical and electrophysiological aspects of the finger movement. The model

contained six muscles and one degree of freedom representing the free movements of

the three joints of the finger system. In fact, an optimization procedure has been

proposed to estimate muscle forces, muscle activations, muscle deformations and

neural activations during quasi-static positions of the finger. This optimization

procedure has been improved to guarantee both initialization stability and ana-

tomical realism.

To assess the model reliability, a validation procedure was proposed using

experimental sEMG recordings. In fact, for three important and accessible extrinsic

muscles (FDP, FDS and EDC) activations calculated by optimization have been

compared to those coming from the sEMG signals measured by surface electrodes.

According to the obtained results, a similarity between patterns of the normalized

simulated and experimental results has been found for FDP and FDS muscles. For

these muscles, the proposed model seems to qualitatively mimic experimental

observations. However, differences still remain for EDC muscle data. These differ-

ences are due to hypotheses and simplifications supposed in the several used models.


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In fact, information from real muscle and neural activations should be incorporated

in future optimization procedure to increase physiological realism.

The novelty in our work first appears in taking into account the nonlinearity in

the finger system by adding the force distribution coefficient between muscles and

muscle bands as additional variables to the six muscle forces. This is an

improvement in the optimization procedure and biomechanical study of the

system compared to the study done by Chalfoun in 2005.8 Another important and

novel idea in this study is the optimization function which depends not only on

forces but also on muscle activations and muscle deformations. This type of

optimization function ensures a unique solution for different initial values. After a

simulation of the system, experiments were carried out on five adult males, it is a

novelty compared to studies done by Chalfoun, Vigouroux and Paclet8,9,12 who

have not made experimental measurements on several subjects and even for more

muscles.

By comparing experimental results with those of Chalfoun,8 the curves we

obtained in simulation and experimentation are acceptable, especially during the

total closure of the hand. In this study we sought neural activations in addition to

muscle forces and muscle deformations from the kinematic data that is an additional

step compared to similar studies that are on hand and finger biomechanical mod-

eling and using kinematic data as inputs.

Futures works will include the improvement of the anatomical modeling by

taking into account forces of tendons in the biomechanical model. In addition, the

system will be studied in dynamic i.e., joint speeds will be considered nonzero and

the biomechanical model will be supplemented with kinematic parameters. For this

purpose, a new validation protocol should be proposed that incorporates both

kinematic data (joint moments) estimated by motion analysis methods coupled to

sEMG data recording to evaluate the model efficiency.

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PHYSIOLOGICAL AND BIOMECHANICAL APPROACH FOR HUMAN FINGER MOVEMENT: MODELING, SIMULATION AND...

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