Department of Electrical & Computer Engineering

MSc. Biomedical Engineering

Master Thesis

Ultrasound propagation through trabecular

structures – Influence of structure and material

Anastasia K. Manta

Mathematician

Laboratory of Biomechanics and Biomedical Engineering,

Department of Mechanical Engineering & Aeronautics

Patras 2021

Department of Electrical & Computer Engineering

MSc. Biomedical Engineering

Master Thesis

Ultrasound propagation through trabecular

structures – Influence of structure and material.

Anastasia K. Manta

Three-member Advisory Committee

Deligianni Despina, Professor Supervisor

Polyzos Dimosthenis, Professor Academic staff member

Mavrilas Dimosthenis, Peer Professor Academic staff member

Laboratory of Biomechanics and Biomedical Engineering,

Department of Mechanical Engineering & Aeronautics

University of Patras Department of Electrical & Computer Engineering

Anastasia K. Manta ©2021-All rights reserved

Acknowledgements

I would like to thank my supervisor professor Mrs. Deligianni Despina for

the opportunity she offered to me to conduct my master thesis in the Laboratory

of Biomechanics and Biomedical Engineering of University of Patras, as well as

for her guidance in achieving this goal.

Also, I would like to thank Dr. Apostolopoulos Konstantinos for his support

and for the knowledge and the advices he provided to me, in order to improve

myself both as a person and as a scientist.

In addition, I would like to thank professor Mr. Polyzos Dimosthenis and

peer professor Mr. Mavrilas Dimosthenis for their contribution as members of

the three-member advisory committee.

Anastasia K. Manta

Patras, 2021

i

Contents

Abstract .................................................................................................................... iii

Περίληψη ................................................................................................................... v

List of figures ......................................................................................................... vii

List of tables ........................................................................................................... ix

1. Chapter 1: Introduction .................................................................................. 1

1.1. Applications of ultrasonic waves ................................................................ 1

1.2. Object of master thesis ................................................................................ 2

1.3. Outline .......................................................................................................... 2

Bibliography ............................................................................................................ 3

2. Chapter 2: Literature review .......................................................................... 5

2.1. Review on ultrasound propagation through trabecular bone .................. 5

2.2. Bone structure-Physical properties of trabecular bone ........................... 9

2.3. Wave characteristics-Physics of ultrasound ............................................ 13

2.4. Characteristics of probes-transducers ..................................................... 16

2.5. Interaction of ultrasound with trabecular bone ..................................... 18

2.6. Modeling of differential scattering cross section of ultrasound ........... 20

2.7. 3D-printing technology ............................................................................ 24

2.8. Research on 3D-printed trabecular bone ................................................. 27

Bibliography ......................................................................................................... 28

3. Chapter 3: Materials ....................................................................................... 37

3.1. Polylactic Acid (PLA) ................................................................................ 37

3.2. Thermoplastic Polyurethane (TPU) ......................................................... 38

3.3. Polypropylene (PP) .................................................................................... 39

Bibliography ......................................................................................................... 40

4. Chapter 4: Experimental Procedure ........................................................... 41

4.1. Fabrication of bone specimens ................................................................. 41

4.1.1. 3D-printing with transparent PLA material ........................................ 42

4.1.2. 3D-printing with white TPU 95A material .......................................... 42

4.1.3. 3D-printing with transparent PP material ........................................... 43

4.2. Measurements of ultrasound acoustic properties ................................... 45

ii

Bibliography ......................................................................................................... 48

5. Chapter 5: Results ......................................................................................... 49

5.1. Relationship between speed of sound and apparent density ................ 49

5.2. Influence of material properties on ultrasound propagation ................ 51

5.3. Simulation of osteoporosis ....................................................................... 52

Bibliography ......................................................................................................... 56

6. Chapter 6: Conclusions ................................................................................. 57

Bibliography ......................................................................................................... 59

iii

Abstract

Ultrasound is used broadly in research, such as the field of biomechanics,

where osteoporosis is studied by mechanisms of interaction of ultrasound with

trabecular bone. The present study concerns the influence of trabecular bone

architecture and material on ultrasound characteristics, speed of sound and

backscatter coefficient, using 3D-printed trabecular bone models.

3D-printing is an innovative technology used for the creation of 3D objects.

Its applications concern industry, healthcare and medical industry. This

technology applied to this study, because it offers the opportunity of

constructing identical trabecular bone structures for each single sample in order

to quantify structural degradation. The main purpose was to construct trabecular

bone replicas with as much accurate structure as possible, following the same

printing methods for all the specimens in order to ensure that the results and

conclusions concern only the material influence on ultrasound properties.

First, replicas of bovine cancellous bones, with different structures and

materials, were fabricated by a 3D-printer. Polylactic acid (PLA), thermoplastic

polyurethane (TPU) and polypropylene (PP) were used for the fabrication of the

specimens. Then, ultrasound propagation experiments were conducted and the

backscattered signals were studied in order to make conclusions about the

parameters of trabecular bone replicas (material properties, structure) that

influence the ultrasound propagation.

The ultrasound measurements indicated that speed of sound has a perfect

linear relationship with apparent density and that material properties, such as

density and stiffness, influence the magnitude of the backscatter spectrum,

whereas the shape of backscatter coefficient as a function of frequency depends

on the bone structure.

These outcomes most likely cannot be associated with the original

trabecular bone; especially, in case of osteoporotic one. Nevertheless, significant

conclusions are presented related to the origins of backscatter and ultrasound

properties alteration due to structural degradation, which is a result of the ageing

process and extent research may contribute to the formulation of osteoporosis

diagnostic devices.

iv

v

Περίληψη

Ο υπέρηχος χρησιμοποιείται ευρέως στην έρευνα, όπως στο πεδίο της εμβιομηχανικής, όπου η οστεοπόρωση μελετάται μέσω μηχανισμών αλληλεπίδρασης υπερήχων με δοκιδωτό οστό. Η παρούσα μελέτη αφορά την επίδραση της αρχιτεκτονικής και του υλικού του σπογγώδους οστού στα χαρακτηριστικά των υπερήχων, ταχύτητα του ήχου και συντελεστής οπισθοσκέδασης, χρησιμοποιώντας μοντέλα σπογγώδους οστού τρισδιάστατης εκτύπωσης.

Η τρισδιάστατη εκτύπωση είναι μια καινοτόμος τεχνολογία που χρησιμοποιείται για τη δημιουργία τρισδιάστατων αντικειμένων. Οι εφαρμογές της αφορούν την βιομηχανία, την υγειονομική περίθαλψη και την ιατρική. Η τεχνολογία της τρισδιάστατης εκτύπωσης εφαρμόστηκε στην παρούσα μελέτη, επειδή προσφέρει την ευκαιρία κατασκευής πανομοιότυπων δομών σπογγώδους οστού για κάθε μεμονωμένο δείγμα προκειμένου να ποσοτικοποιηθεί η οστική αποδόμηση. Ο κύριος σκοπός ήταν η κατασκευή αντιγράφων δοκιδωτού οστού με όσο το δυνατόν ακριβέστερη δομή, ακολουθώντας τις ίδιες μεθόδους εκτύπωσης για όλα τα δοκίμια, προκειμένου να διασφαλιστεί ότι τα αποτελέσματα και τα συμπεράσματα αφορούν μόνο την επίδραση του υλικού στις ιδιότητες των υπερήχων.

Αρχικά, αντίγραφα από δοκιδωτά οστά βοοειδών, με διαφορετικές δομές και υλικά, κατασκευάστηκαν από έναν 3D-εκτυπωτή. Τα υλικά: πολυγαλακτικό οξύ (PLA), θερμοπλαστική πολυουρεθάνη (TPU) και πολυπροπυλένιο (PP) χρησιμοποιήθηκαν για την κατασκευή των δοκιμίων. Στη συνέχεια, πραγματοποιήθηκαν πειράματα διάδοσης υπερήχων και τα σήματα οπισθοσκέδασης μελετήθηκαν προκειμένου να εξαχθούν συμπεράσματα σχετικά με τις παραμέτρους των αντιγράφων των δοκιδωτών οστών (ιδιότητες υλικού, δομή) που επηρεάζουν τη διάδοση των υπερήχων.

Οι μετρήσεις υπερήχων έδειξαν ότι η ταχύτητα του ήχου έχει εξαιρετική γραμμική σχέση με την φαινόμενη πυκνότητα και ότι οι ιδιότητες του υλικού, όπως η πυκνότητα και η ακαμψία, επηρεάζουν το μέγεθος του φάσματος οπισθοσκέδασης, ενώ η μορφή του συντελεστή οπισθοσκέδασης ως συνάρτηση της συχνότητας εξαρτάται από την δομή του.

Τα παραπάνω αποτελέσματα, πιθανότατα δεν μπορούν να συσχετιστούν με το αρχικό δοκιδωτό οστό, ειδικά σε περίπτωση οστεοπορωτικού οστού. Παρ 'όλα αυτά, παρουσιάζονται σημαντικά συμπεράσματα σχετικά με την προέλευση της μεταβολής του συντελεστή οπισθοσκέδασης και των ιδιοτήτων των υπερήχων, που προκύπτουν από την οστική αποδόμηση, η οποία είναι αποτέλεσμα της διαδικασίας γήρανσης. Επομένως, η εκτενής έρευνα μπορεί να συμβάλει στη διαμόρφωση διαγνωστικών συσκευών της οστεοπόρωσης.

vi

vii

List of figures

Figure 1: Application of Ultrasound in Medicine (a) Ultrasound in a transplanted

kidney artery, (b) Display of the fetus in uterus ...................................................... 1

Figure 2: Ultrasound measurement techniques ...................................................... 1

Figure 3: Light micrographs of bones. Osteoblasts (Ob) and bone lining cells

(BLC) are on bone surface. Osteocytes (Ot) are observed entrapped in the bone

matrix. B: bony trabecula. BV: blood vessels [56]. ................................................ 10

Figure 4: Organization of osteons and lamellae in compact bone. The orientation

of collagen fibers in adjacent lamellae of an osteon. ............................................ 10

Figure 5: Compact and trabecular bone representation. ....................................... 11

Figure 6: Light micrograph of compact and trabecular bone. .............................. 11

Figure 7: Direction of oscillation and propagation of ultrasound waves. (a)

Longitudinal wave, (b) Transverse wave. ............................................................... 15

Figure 8: (a) Transducer beam characteristics, (b) Immersion transducers. ...... 17

Figure 9: (a) Prediction of differential scattering cross section in spongy bone

with 70% porosity for different sizes of scatterers, (b) Prediction of attenuation.

Dense Populate [7]. .................................................................................................. 22

Figure 10:(a) Prediction of differential scattering cross section in spongy bone

with 70% porosity for different sizes of scatterers, (b) Prediction of attenuation.

Fluid spherical distribution [7]. .............................................................................. 23

Figure 11: A 3D-printing machine. .......................................................................... 24

Figure 12: Two cardiac 3D-printed models opened at the level of the four-

chamber view, for healthcare teaching [113]. ........................................................ 26

Figure 13: (a) Ultimaker 3D-printer, (b) 3D-printing process of a bone replica. 41

Figure 14:3D-printed PLA replicas of trabecular bone. (a) BV/TV=40%, (b)

BV/TV=34%. ............................................................................................................ 42

Figure 15: 3D-printed TPU replicas of trabecular bone. (a) BV/TV=40%, (b)

BV/TV=34%. ............................................................................................................. 43

Figure 16: 3D-printed PP replicas of trabecular bone. (a) BV/TV=55%, (b)

BV/TV=40%. ............................................................................................................. 43

Figure 17: 3D-printed PP replicas of trabecular bone. (a) BV/TV=34%, (b)

BV/TV=21%. ............................................................................................................. 44

Figure 18: (a) The degassing of specimens, (b) Through-transmission ultrasound

measurements layout. .............................................................................................. 45

Figure 19: The area characterized as the interface refers to the surface between

the water and the bone specimen with a depth of about 3mm, due to the nature

of the bone. The area of 7mm delimits the volume of interest of which the

differential scattering cross section 1800 is measured and follows the interface.

The length z is measured from the beginning of the specimen to its middle

volume of which the differential scattering cross section 1800 is measured. ..... 47

viii

Figure 20:(a) Linear relationship between SOS and apparent density for three 3D-

printed trabecular bone specimens with different bone volume fractions,

constructed from PLA, in the three directions, (b) Graph data and analysis. ... 50

Figure 21: (a) Linear relationship between SOS and apparent density for three 3D-

printed trabecular bone specimens with different bone volume fractions,

constructed from PP, in the three directions, (b) Graph data and analysis. ....... 51

Figure 22: Backscatter coefficient as a function of frequency of two 3D-printed

trabecular bone specimens with the same bone volume fraction, constructed

from PLA and TPU in the (a) X direction, (b) Y direction and (c) Z direction. .. 52

Figure 23: Backscatter coefficient as a function of frequency of two 3D-printed

trabecular bone specimens with different bone volume fractions, constructed

from PLA. (a) X direction, (b) Y direction and (c) Z direction. ............................ 54

Figure 24: Backscatter coefficient as a function of frequency of 3D-printed

trabecular bone specimens with different bone volume fractions, constructed

from PP. (a) X direction, (b) Y direction and (c) Z direction. ............................. 56

ix

List of tables

Table 1: The most important quantities of ultrasound physics. ........................... 16

Table 2: Thermal properties of transparent PLA material. ................................... 37

Table 3: Mechanical properties of 3D-printing transparent PLA material. ......... 38

Table 4: Thermal properties of TPU 95A white material. ..................................... 38

Table 5: Mechanical properties of 3D-printing TPU 95A white material. ........... 39

Table 6:Thermal properties of PP material. ........................................................... 39

Table 7: Mechanical properties of 3D-printing PP material. ............................... 40

Table 8: Physical quantities of 3D-printed replicas. ............................................. 44

x

Introduction

1

1. Chapter 1:

Introduction 1.1. Applications of ultrasonic waves

Ultrasound is sound waves with a frequency above human hearing (20,000

hertz or 20 kilohertz). Ultrasonic waves have many different applications.

Ultrasonic devices are used for object detection and distance measurements. In

medicine, ultrasound is used for diagnostic or therapeutic purposes. Ultrasound

imaging or sonography is a technique applied in order to create an image of

internal body structures such as blood vessels, and internal organs, either to

determine the source of a disease or to exclude pathology [1][2], as it is shown in

figure 1. Soft tissue and bone injuries treatment, cancer therapy and focused

ultrasound surgery are some of ultrasound therapeutic applications [3-5].

(a)

(b)

Figure 1: Application of Ultrasound in Medicine (a) Ultrasound in a transplanted kidney artery, (b) Display of the fetus in uterus

In industry, it is used for cleaning and accelerating chemical processes

[6][7]. Also, ultrasonic waves are applied in food technology, contributing to the

analysis, processing and quality control of food [8-10]. Finally, ultrasound is used

broadly in research (Figure 2), such as the field of biomechanics, where

osteoporosis is studied by mechanisms of interaction of ultrasound with

trabecular bone [11].

Figure 2: Ultrasound measurement techniques

Introduction

2

Regarding the ultrasound effects and safety, there is no evidence that

ultrasound exposure could cause hearing loss. However, exposing subjects to

frequencies of 18kHz at 150dB has caused concerns to scientific community.

Also, studies have shown that symptoms of nausea, fatigue, and headaches could

be triggered from airborne ultrasound. Health Canada recommend a

conservative standard according to which, sound pressure levels should be less

than 110dB beyond 25kHz, regardless of the exposure duration [12][13].

1.2. Object of master thesis

The present master thesis concerns the influence of 3D-printed trabecular

bone models’ architecture and material on ultrasound propagation. First,

replicas of bovine cancellous bones were fabricated by a 3D-printer. 3D-printed

specimens were constructed with different structures and materials. Polylactic

acid (PLA), thermoplastic polyurethane (TPU) and polypropylene (PP) were used

for the fabrication of the specimens. Then, ultrasound propagation experiments

were conducted and the backscattered signals were studied in order to make

conclusions about the parameters of trabecular bone replicas (material

properties, structure) that influence the ultrasound propagation. The results

indicated that the material properties affect the magnitude of backscatter

coefficient and that the trabecular structure is related to the characteristic

backscatter coefficient patterns which correspond to the thickness of trabeculae.

1.3. Outline

Chapter 1: Applications of ultrasonic waves are presented and an introduction to the object of the master thesis is given.

Chapter 2: First, a review on ultrasound propagation through trabecular bone is conducted and bone structure, physics of ultrasound and characteristics of probes-transducers are presented. Then, the interaction of ultrasound with trabecular bone and the modeling of differential scattering cross section of ultrasound are described. Finally, 3D-printing technology and research on 3D-printed trabecular bone are introduced.

Chapter 3: The characteristics and properties of the materials, that were used in this study, are described. The materials were polylactic acid (PLA), thermoplastic polyurethane (TPU) and polypropylene (PP).

Chapter 4: The experimental procedure is described. In particular, the fabrication of bone specimens and the measurements of ultrasound acoustic properties are presented.

Chapter 5: The results of the current study, which are related to the influence of material properties and bone structure on ultrasound propagation, are presented and analyzed.

Introduction

3

Chapter 6: The conclusions of this study are quoted and the advantages and limitations are presented.

Bibliography

[1]. Wells, P. N. (2006). Ultrasound imaging. Physics in Medicine & Biology,

51(13), R83.

[2]. Carovac, A., Smajlovic, F., & Junuzovic, D. (2011). Application of ultrasound

in medicine. Acta Informatica Medica, 19(3), 168.

[3]. Ter Haar, G. (1999). Therapeutic ultrasound. European Journal of ultrasound, 9(1), 3-9.

[4]. Miller, D. L., Smith, N. B., Bailey, M. R., Czarnota, G. J., Hynynen, K., Makin, I. R. S., & Bioeffects Committee of the American Institute of Ultrasound in Medicine. (2012). Overview of therapeutic ultrasound applications and safety considerations. Journal of ultrasound in medicine, 31(4), 623-634.

[5]. Robertson, V. J., & Baker, K. G. (2001). A review of therapeutic ultrasound: effectiveness studies. Physical therapy, 81(7), 1339-1350.

[6]. Harvey, G., Gachagan, A., & Mutasa, T. (2014). Review of high-power ultrasound-industrial applications and measurement methods. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 61(3), 481-495.

[7]. Payne, P. A. (1985). Medical and industrial applications of high resolution ultrasound. Journal of Physics E: Scientific Instruments, 18(6), 465.

[8]. Awad, T. S., Moharram, H. A., Shaltout, O. E., Asker, D. Y. M. M., & Youssef, M. M. (2012). Applications of ultrasound in analysis, processing and quality control of food: A review. Food research international, 48(2), 410-427.

[9]. Dolatowski, Z. J., Stadnik, J., & Stasiak, D. (2007). Applications of ultrasound in food technology. Acta Scientiarum Polonorum Technologia Alimentaria, 6(3), 88-99.

[10]. Mason, T. J., Riera, E., Vercet, A., & Lopez-Buesa, P. (2005). Application of ultrasound. In Emerging technologies for food processing (pp. 323-351). Academic Press.

[11]. Wear, K. A. (2019). Mechanisms of interaction of ultrasound with cancellous bone: A review. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 67(3), 454-482.

[12]. Howard, C. Q., Hansen, C. H., & Zander, A. C. (2005). A review of current ultrasound exposure limits. The Journal of Occupational Health and Safety of Australia and New Zealand, 21(3), 253-257.

[13]. Health Protection Branch Health Canada, Environmental Health Directorate. Guidelines for the safe use of ultrasound: Part II - Industrial and commercial applications - safety code 24. Technical report, Published by authority of the Minister of National Health and Welfare, 1991. URL http://www.hc-sc.gc.ca/ hecs-sesc/ccrpb/pdf/safety code24.pdf. EHD-TR-158, Catalogue No. H46- 2/90-158E, ISBN 0-660-13741-0

Introduction

4

Literature review

5

2. Chapter 2:

Literature review 2.1. Review on ultrasound propagation through trabecular bone

Trabecular bone is a composite material with two phases, large porosity and

complex architectural structure [1]. Its inhomogeneity and anisotropy make its

characterization very difficult, both in vivo and in vitro.

Studies about ultrasound propagation in the trabecular bone has found a

great response in recent years [2][3]. Ultrasound is able to provide information

for both the bone density, as well as for the geometry of the trabeculae within

the spongy bone. By this method, both factors, that determine the mechanics

properties of bones, can be determined [4].

The main methodologies, that have been developed for the diagnosis of

osteoporosis with the use of ultrasound, concern the change of group velocity

and phase velocity, the calculation and change of fast and slow wave, that occur

during wave propagation, as well as the correlations of velocity and attenuation

with the density [5][6].

Also, the determination of bone mass may be achieved with similar

techniques that have been developed. These techniques are:

Magnetic resonance imaging (MRI), Radiographic absorptiometry (RA), Dual X-

ray absorptiometry (DXA), Peripheral Quantitative computed tomography

(pQCT), Quantitative computed tomography (QCT), Peripheral Dual X-ray

absorptiometry (pDXA), Single-photon absorptiometry (SPA), Dual-photon

absorptiometry (DPA), Single X-ray absorptiometry (SXA), and Quantitative

ultrasound (QUS) [7-9].

The advantages that ultrasound has, compared to the previous techniques

that have been developed are:

• Non-invasive diagnostic tests on the human body

One of the important applications of ultrasound is the diagnosis of diseases in

human organism. The well-known ultrasound is used in order to make diagnoses

of diseases related to the liver, pancreas, thyroid, breast, etc. Also, it could give

information on movements of internal organs of the human body such as parts

of the heart.

• Non-destructive ultrasound testing.

Literature review

6

Sound is a phenomenon that does not cause any permanent change in the

medium in which it propagates, although its presence is easily observed. This is

the reason why, the application of sound is appropriate to the non-destructive

testing, where the aim is to diagnose accurate information about the condition

of the specimen that is examined, without changing its state. For this purpose, a

method, which produces a distinct reaction with the specimen, but does not

change its state, is required. That's why, the advantage of sound to be passive,

makes it appropriate for testing materials [10].

Sound waves are mechanical waves and therefore they require a medium,

through which they will propagate. Condition of any medium, either solid, liquid

or gas, could be assessed through the interaction of sound waves with it. The

basis of ultrasonic testing is the way in which the waves are affected by their

propagation through the medium examined. During the wave propagation,

changes, that occur, could be measured. According to these changes, the state of

the material examined, could be assessed [11][12]. The evaluation of material

properties could be done indirectly, by using models and empirical relations that

connect changes in the sound signal with a specific state of the material or the

existence of discontinuities. The assessment of the quality of the material always

depends on its reliability method we use and from the proper interpretation of

the signal that we receive.

• The accuracy of osteoporosis evaluation

Osteoporosis is recognized as a silent epidemic disease with an ever-increasing

need for its diagnosis and treatment. The technique of ultrasound is widely used

to evaluate osteoporosis [13] and relies mainly on Broadband Ultrasound

Attenuation (BUA) and Speed of Sound (SOS) [14]. In general, ultrasound

provides valuable density-related information (Bone Mineral Density) that are

associated with information we get through methods like DXA, in various areas

of body such as the thigh, vertebrae, hip, etc. In some cases, ultrasound gives

more accurate information than other techniques [15-19].

Speed of sound (SOS) and attenuation of the ultrasonic signal (BUA), are

the two properties of ultrasound that have been studied mainly in trabecular

bone [20-22].

Studies that have been conducted regarding the speed of sound have led to

the following conclusions:

• There is a very good correlation (R2> 0.85) between the density of the

specimens and the speeds, as well as the speeds with modulus of elasticity

in the three dimensions of space [18][23].

Literature review

7

• There is a linear relationship between the modulus of elasticity determined

with ultrasound and the modulus of elasticity measured by mechanical

tests (R2 = 0.935) [23].

Modulus of elasticity of the trabecular bone depends on both its density

and its architectural structure. By the fact that modulus of elasticity is well

correlated with density [24], it is concluded that probably density is a factor of

primary importance for the elasticity of material. However, different values of

modulus of elasticity occur from measurements in the three directions, while the

density is constant [25].

Langton (1984) developed a technique known as Broadband Ultrasound

Attenuation (BUA). The correlation coefficient of ultrasound attenuation with

the density of spongy bone in vitro, is around 0.5 [20]. The effects of attenuation

during ultrasound propagation through the cancellous bone are due to on the

one hand the absorption, on the other hand the scattering. Absorption depends

on the density of spongy bone, the viscosity of the bone marrow, and the

frequency of ultrasonic wave. Scattering depends on the structure of the bone

[26]. The BUA parameter is directly related to the 3D architecture of spongy bone

as it is associated with ultrasound scattering effects.

The relation between attenuation and physical-mechanical properties of

trabecular bone is not easy to be determined. Research studies on bones, that

conducted in vitro, led to the following conclusions:

• The BUA parameter is not related to modulus of elasticity in the three

dimensions of space [18].

• Attenuation of ultrasonic signal (BUA) in human bones in vitro, is linearly

related to density as well as modulus of elasticity [27-29].

In most researches, an attempt is made in order to correlate the ultrasound

properties, mainly with the density and modulus of elasticity of the sponge bone,

without essentially taking into account the “architectural structure” factor.

However, the above remarks led to the conclusion that a further study on the

effect of bone architectural structure on both ultrasound propagation, and in

general to the mechanical properties of the spongy bone it is necessary [30-33].

Currently, various 3D techniques have been developed for the trabecular

bone imaging. Some of the most common imaging techniques are [34]:

• X-ray tomographic methods

• Serial sectioning

• Nuclear Magnetic Resonance (NMR)-Magnetic Resonance Imaging (MRI)

Literature review

8

Applying the above methods, images from the inside of the trabecular bone could

be stored in the computer. Then, if the images get composed with the aid of

suitable software, a digital representation of the architectural structure of bone

could occur [35].

Having represented the structure of trabecular bone, the next step is its

quantification, i.e., the application of methods that will give us information on

the density, porosity, and orientation of trabeculae. A method used is Mean

Intercept Length (MIL). Similar methods have been developed such as volume

orientation, star volume distribution, star length distribution, which are referred

to as alternative versions of MIL method [34]. Also, Quantitative Computed

Tomography (QCT) is a very well-known method, which provides information

for both density and structure [36]. Finally, in recent years the characterization

of structure with fractals is implemented [37-40] and emphasis is given to three-

dimensional analysis by the finite element method, which could be used in

combination with one of the above quantification methods of the architectural

structure of bone [41][42].

Despite the fact that a large number of measurements, that have carried

out, about ultrasound speed propagation and attenuation, the range of values

mentioned in the literature is wide. The authors’ opinions differ in the extent to

which these quantities are related to other physical and mechanical parameters

of normal spongy bone or pathological specimens [14][43][44]. In order to

systematically examine the individual contribution of density and structure to

attenuation, various researchers have proposed the introduction of new

directions in the characterization of bone with ultrasound, such as

measurements with the pulse-echo technique [45].

Finally, the need of processing new parameters that describe the structure

of bone tissue as important information for predicting fracture risk has been

recognized and an international effort in this direction is made [1][46].

In addition, except for speed and attenuation, scattering is another

property that can provide information on osteoporosis. Studies of wave

scattering from various biological tissues have been conducted [47-49], with

results of good correlation with density [50]. The size of the scatterers is

estimated according to the autocorrelation functions of Dense Populate and

Fluid Sphere distribution. From experimental calculation of a differential

scattering cross section of 180° in a representative bovine spongy specimen, using

ultrasound, peaks appear at specific frequency values corresponding to dominant

groups of trabeculae. These peaks correspond to the aforementioned

autocorrelation functions to beams of specific dimensions.

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The differential scattering cross section 180° that the ultrasound undergoes

during its propagation to the cancellous bone, is particularly sensitive to

microstructure changes associated with osteoporosis, as opposed to speed and

attenuation [19]. Also, there has been a strong correlation between the three

acoustic parameters of ultrasound during the propagation to trabecular bone

[14]. The remarks performed in the above parameters concern experiments on

human spongy bones, and especially osteoporotic, thus limiting the results to a

small range of densities.

2.2. Bone structure-Physical properties of trabecular bone

Bones have a remarkable and extremely complex structure [51-55]. They have two main functions:

• They form the skeleton that supports mechanically and protects the body.

• They maintain the homeostasis of minerals components in the body by

regulating the concentration of electrolytes in the blood.

Bones are neither morphologically nor mechanically homogeneous, but their

heterogeneity not only does not prevent their functional adaptation, but on the

contrary contributes to it. The adaptation to the mechanical function concerns

the shape, the axial shape, the distribution of the material along their length and

cross section, and their internal structure.

Bones could be distinguished at three levels of structural organization:

• Molecular level

• Microscopic level

• Macroscopic level

At the lower level of organization bone can be considered as a composite

material consisting of a fibrous protein, collagen (basic binding protein tissue),

and calcium phosphate. The other components are water, amorphous

polysaccharides and proteins, living cells and blood vessels. The tiny crystals

hydroxyapatite, that are formed by calcium and phosphorus, are found along the

collagen fibrils. Collagen microfibers have a diameter of 50-70 nm and their

pattern direction is not random but defined. Bone tissue consists of three types

of bone cells; osteocytes, osteoblasts and osteoclasts. Among them there is the

intercellular substance. Osteocytes occupy, completely the bone lumen during

their lifetime. From osteocytes begin numerous delicate offshoots that enter the

bone tubes where they come in contact with offshoots of neighboring osteocytes.

In the developed bone tissue, the osteocytes are osteoblasts, which are

surrounded by bone tissue they produce themselves (Figure 3). They remain

active cells that they have a role in the maintenance of bone substance and the

mobilization of calcium from bone tissue into the blood. Osteoblasts produce

the organic elements of bone substance; collagen, polysaccharides. Osteoclasts

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are agile giant multinucleated cells with a diameter of 20-100 μm containing 5-

50 nuclei. They are where bone tissue is absorbed and they usually are into the

scaphoid lumens of the free surface of the bone substance [51-55].

(a)

(b)

Figure 3: Light micrographs of bones. Osteoblasts (Ob) and bone lining cells (BLC) are on bone surface. Osteocytes (Ot) are observed entrapped in the bone matrix. B: bony trabecula. BV: blood

vessels [56].

At the microscopic level, in mammals, there are two types of bone [57][58].

In the laminar tissue, the collagen and the hydroxyapatite form layers called

lamellae, which have a thickness about 5μm. Collagen fibrils are located at the

level of bony lamella and tend to be oriented in one direction within that level.

Some researchers claim that all collagen fibrils have the same direction within a

lamella [59][60]. But it is more likely that fibrils with a specific orientation

occupy small areas. Within an area the orientation of the fibrils is not constant,

but varies from area to area on the same lamella. Although, all the fibrils in a

lamella do not have the same direction, it seems that going from one lamella to

the other, the direction changes. The second type of bone consists of osteons or

Haversian systems formed as the bone around a blood vessel is absorbed by

osteoclasts. In this way a lumen about 100 μm in diameter is formed (Haversian

canals). The walls of the lumen are smooth and the bone is located at the inner

surface in concentric layers. The central lumen contains one or two blood vessels.

Figure 4: Organization of osteons and lamellae in compact bone. The orientation of collagen fibers in adjacent lamellae of an osteon.

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At the macroscopic level of organization, there is an extremely important,

in terms of mechanics, distinction between compact and spongy bone, called

trabecular or cancellous bone (Figure 5 & 6). In compact bone the only pores,

that exist, are those occupied by osteocytes, bone canals (canaliculi), vessels and

areas of erosion. On the contrary, spongy bone has pores that occupy a large

percentage of its volume. The bone tissue from which the trabecular bone is

composed, is usually primary lamellar tissue or parts of Haversian systems.

Spongy bone is an anisotropic material. Both in terms of the tissue that makes it

up, but also its structure macroscopically. Singh (1978) [61] described in detail

the morphology of trabecular bone based on the microscopic studies of

Whitehouse and others [62][63]. The study of the cancellous bone from various

parts of human skeleton reveals a great architectural variety. Trabecular bone

architectural structure could be classified into types I, II a, II b, II c, III a, III b

and III c.

Figure 5: Compact and trabecular bone representation.

Figure 6: Light micrograph of compact and trabecular bone.

In addition, inside bones there is a soft tissue called bone marrow. Bone

marrow is rich in vessels and it is found not only between the trabeculae of the

cancellous bone, but also in their medullary lumen of long bones and in the

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larger tubes of the Haversian canals. Its composition varies in different bones

and it depends on age. Bone marrow occurs in two forms, pale or fatty and red

marrow.

The hue of fatty marrow occurs due to the presence of numerous fat cells,

which are its main component. The marrow consists of a thin layer of free blood

cells and vessels that fill the interstices. Adipocytes disperse individually into the

interstices of its reticular layer whose reticular cells are derived from perivascular

cells (mesenchymal cells). The wall of the capillaries of marrow allows the

passage of free cells of the tissue in the blood. Between these capillaries and

trabeculae of reticular layer exist all forms of platelets at various stages of

development; erythrocytes, granular leukocytes, lymphocytes, monocytes and

platelets [64].

Characterization of bone structure is necessary in order to study further its

properties. The structural and architectural approach of a tissue is called

histomorphometry. Histomorphometry studies and quantifies the relation

between various parameters that characterize the structure of a tissue. The most

important parameters that describe the structure of the trabecular bone are the

following [65-71]:

• BV/TV (Relative bone volume), is the relative amount of bone per unit of

volume. It is a dimensionless quantity and is measured in % or in unit

fractions.

• BS/BV (Bone surface to volume ratio), is the relative area of bone per unit

of volume, and describes the complexity of the structure. This parameter

occurs from 3D μCT, and is measured in mm-1.

• Tb.Th. (Trabecular thickness), refers to the thickness of the trabeculae.

This parameter is calculated by measurements in the plane (2D),

considering two models of trabeculae; the model of parallel plate and the

cylinder rod model.

• Tr.Sp. (Trabecular separation), refers to the average width of the pores

perpendicular to trabecula direction. It is measured in mm or μm, for both

models.

• Tr.N. (Trabecular number), refers to the average distance of the trabeculae,

from ridge to ridge, and is measured in mm for both models.

• D.A. (Degree of anisotropy). A material is characterized as anisotropic

when its properties change in different directions. Trabecular bone is

generally an anisotropic material with great complexity in its structure.

The most important techniques that determine and quantify anisotropy are

Mean Intercept Length (MIL), Star Volume Orientation (SVD) and Star Length

Distribution (SLD), whose algorithmic applications in 3D are well correlated [72].

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Bone physical properties are related to bone density, bone mineral density

and porosity [73]. Density is defined as a scalar quantity that expressed by

quotient of the mass of an object, to the volume of the object. In the spongy bone

the density is expressed in the same way, but complex problems occur in terms

of both mass estimation and volume estimation. Mass calculation concerns the

presence or absence of marrow. The calculation of volume that occurs from the

porosity leads to two solutions. The first calculation concerns the volume as a

whole, including pores that are filled with marrow and is called total volume. The

second calculation refers to the volume without the marrow and is called matrix

volume [74]. Therefore, the density of the trabecular bone is expressed as either

real density or as apparent density:

• Real density is defined as the quotient of wet mass-weight of the specimen

to the actual volume of the tissue.

• Apparent density is defined as the quotient of the mass of solid matrix), to

the corresponding total volume of the specimen.

Other expressions of density occur depending on the state of the mass, such as

dry mass-weight 100°C or ash mass-weight 500°C.

The porosity in porous materials, is what makes them have different and

complex physical properties, in relation to non-porous ones. The complexity of

their properties may be increased if the pores of materials include liquids, even

in a very small percentage [75]. The ratio of the volume of the interstices to the

total volume of the object is called porous and is relatively easy to be determined

and be measured. Nevertheless, it is much more difficult and complicated to have

a geometric description of the pores, because in most cases the pores have a

complex geometry. Finally, only a few specific cases can be described

quantitatively for instance, when the pores are spheres of the same diameter.

2.3. Wave characteristics-Physics of ultrasound

Wave is one of the ways in which energy travels without mass transfer with

main feature the periodicity in space and in time [76]. The process by which

energy is transmitted from one area to another is called propagation.

Useful definitions [76-79]:

• An isophasic surface is the locus of the points that have the same period

and phase.

• Plane, spherical, cylindrical wave, is the wave that has a plane, spherical

and cylindrical isophasic surface respectively.

• A stationary wave is that whose isophasic or nodal surfaces do not travel in

space.

• Node is the point with a null distance for any time t.

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• Wavenumber is the measure of the direction vector of the wave. Its

notation is k and is defined as k = 2π / λ (1 / m).

• Phase velocity is the one at which the phase of wave travels. It is given by

the formula: c = λ / Τ = ω / k.

• Intensity of wave is the energy of the incident wave per second and per unit

area.

• Wave front is the first surface of the wave that comes in contact with non-

disrupted space. The geometry of the wave front may be plane, spherical,

cylindrical and so on.

• Wave attenuation is the degression of the wave amplitude.

• Dispersion is the gradual change of the wave shape due to the property of

the medium to propagate the various harmonics waves that compose the

wave, with different phase velocities, depending on ω.

• Dissipation is the natural mechanism that creates the attenuation effects.

The energy loss because of distance is due to conversion of mechanical

energy or any other form of energy into heat or in the diversion of energy

from the main propagation direction.

• Scattering effect happens when the propagation path of a wave is

interrupted by any inhomogeneity of compressibility or density. Scattering

may be seen as a change of the amplitude, frequency, phase velocity or

direction of the wave propagation as a result of inhomogeneity of the

medium within which it propagates [80]. This is due to the finite size of the

scatterers, compared to the wavelength and is measured in Sr-1cm-1. Should

be noted that a sound wave is not scattered when the acoustic properties

of the medium in which the wave propagates are not differentiated

(density, compressibility).

• Backscattering: The differential scattering cross section 1800, expresses the

percentage of power of the wave scattered at 1800 to intensity of the

incident wave.

• Attenuation coefficient expresses the loss of energy to any direction.

• Attenuation due to scattering expresses the loss of ultrasound energy due

to scattering.

• Nepers (Np) is a dimensionless unit that expresses the ratio of two similar

quantities logarithmically. The number 2.71878 is the basis of the Np unit

in contrast to the dB unit that has the number 10 as a basis (1 Neper-8,686

decibels).

The physical principles governing ultrasound [81][82] are the same as those

of sound in the auditory field, with the difference that the oscillation evolves so

rapidly that it cannot be perceived by the human ear. While the limit of audibility

is at about 0.02 MHz in ultrasound experiments frequencies are used between

0.5 MHz and 20 MHz. The property of ultrasound of not being perceived has the

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advantage that it may be used during experiments, such a high sound volume

that if it were in the auditory field would be unbearable.

Any medium, either solid, liquid or gas is able to oscillate. If the oscillation

evolves so rapidly that it cannot be perceived by the human ear is referred to as

ultrasound. In fact, there are small particles of the medium that oscillate like

being connected in elastic way. The type of oscillation is determined by the

elastic properties of the medium and by the shape of the pulse that causes the

oscillation. The oscillation propagates in the medium at a sound velocity c. The

sound oscillation may be described as a motion of the medium particles, for

example as a displacement of the particles as a function of their position and time

δ = f (z, t), or as the change in sound pressure as a function of position and time

p = f (z, t). The sound pressure or the change in pressure because of oscillation is

very important because the electric potential created by a piezoelectric crystal

U = f (z, t) is directly proportional to the sound wave generated and vice versa.

Figure 7a shows the propagation of sound in gases, solids and liquids. The

particles of the medium oscillate in the direction of sound propagation. This type

of oscillation is called longitudinal wave. At the points where particles are close

to each other, there is little displacement but the speed and pressure of sound is

high. If shear forces may be developed the particles can also oscillate in a

direction perpendicular to the wave propagation (It mainly happens in solids).

This oscillation is called a transverse wave (Figure 7b).

(a)

(b)

Figure 7: Direction of oscillation and propagation of ultrasound waves. (a) Longitudinal wave, (b) Transverse wave.

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However, the above applies only in ideal cases and for infinitely long media.

If, during the experiment, there is a reflection from the outer surfaces of the

specimens that are slightly apart, entangled waveforms are developed (plate

waves). The equations that apply to purely longitudinal and transverse waves do

not apply to this type of waves. All these types of waves may coexist in the testing

of a specimen, making the interpretation of corresponding effects very difficult.

The most important quantities concerning the physics of ultrasound and

its propagation in specimens are given in the table below.

Table 1: The most important quantities of ultrasound physics.

Quantities Formula Units

of measurement

Angular velocity ω = 2πf rad/s

Frequency f 1/s or Hertz (Hz)

Speed of sound c m/s

Wavelength λ = c / f m

Particle displacement δ m

Particle velocity ν m/s

Density ρ Kg/m3

Force F Kgm/s2 or Newton (N)

Difference of sound pressure p Kg /ms2 or Pascal (Pa)

Poisson's ratio μ , m -

Modulus of elasticity E Kg/ms2

Shear modulus G Kg/ms2

Acoustic impedance Z = ρc Kg /m2s

Sound power P Watt (W)

Sound intensity I W/m2

2.4. Characteristics of probes-transducers

Probe or transducer is a conversion mechanism of mechanical energy to

electrical, or electrical to mechanical. Sound waves can be generated in many

ways such as electromagnetic mechanisms (Electromagnetic Acoustic

Transducers-EMATS), special sheets of semi-crystalline plastic material

(Polyvinylidene fluoride PVDF) or even using a laser [83][84]. Nevertheless, the

most common technique is electrical excitation of piezocrystals [85].

Piezocrystals are made of either natural crystals such as quartz and

tourmaline or of ceramic materials. Characteristic of piezocrystals is that the

application of electric field in their end-points cause a change in their physical

dimensions. The interaction between the material within the limits of the crystal

lattice and the electric field, causes mechanical stresses and deformations which

in turn create the ultrasound wave. In the reverse process, ultrasound waves

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cause mechanical stresses which in turn are converted to potential difference in

the end-points of the piezocrystal.

Crystal transmitters-receivers are devices that perform at the maximum

level when the piezocrystal they contain be excited near its resonance frequency.

In this case, the pressure produced is proportional to the excitation voltage.

Usually, the piezocrystals are in the form of a thin disk and they have electrodes

placed on each side of them. The resonance frequency f of the transmitter-

receiver is determined by the thickness of the disk. A common dimension is λ /

2, where λ = c / f. On its outer side is placed a protective layer of suitable

absorbent material, depending on the environment in which it operates, with a

thickness equal to λ / 4. Also, thin layers are placed on the back of the crystal in

order to absorb the reflections from the outer cover of the transmitter. In this

way, the back sheets play the role of the damper. When the damping is small the

pulse is of large duration (Narrow band). On the contrary, high damping leads

to short pulses (Broad band), which are commonly used to measure thickness

and generally for accurately definition of the duration of events.

The entire construction of the transmitter-receiver can be such that it

transmits or receives waves perpendicular to the testing object (normal beam

probes) or at an angle (angle beam probes). There is a case of two crystals

existence in the same cover where one is used as a transmitter and the other as a

receiver. In addition, if the excitation of the piezocrystal was continuous there

would be a great difficulty in isolation of signals that occur from reflections.

That’s why, the excitation of the piezocrystal is made with pulses of a specific

duration.

(a) (b) Figure 8: (a) Transducer beam characteristics, (b) Immersion transducers.

The most important technical characteristics of the probes are:

• The Sound Field is the set of pressure values at each point of space and it is

divided into two zones. In the near field zone and the far field zone [86].

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• Near Field Length is the distance of the probe surface from the position

where the beam develops the maximum pressure value.

• Far Field is the corresponding position behind the NFL, where the pressure

distribution is zero, after first decreasing gradually, (Figure 8a).

• Beam shape is the "theoretical" shape of the sound field, that is defined by

the set of pressure values. In circular cross section probes, the beam has a

conical shape where its cross-section is being reduced to NFL and then it is

being increasing.

• Element size D or axb: The transducers have a circular or rectangular cross

section. The size of the cross section greatly affects the form of the

transmitted sound.

• Central frequency is the peak of the probe response curve.

• Focus and unfocus transducers focus the ultrasound beam on a small

(focus) or a larger part of the material (unfocus), thus giving corresponding

information about these areas, as it is shown in figure 8b.

2.5. Interaction of ultrasound with trabecular bone

As it has been mentioned, the research about the characteristics and

properties of trabecular bone, using ultrasound, is achieved by studying the

changes in ultrasound propagation and its physical properties. Below, they will

be introduced the corresponding mechanisms [87] that constitute the basis of

this study; SOS, attenuation coefficient and backscatter coefficient.

The through-transmission method is used in order to measure the Speed of

Sound (SOS) and attenuation of ultrasound (BUA). Two transducers are used in

the through-transmission process. The first transducer is applied for a

broadband pulse transmission into the trabecular bone. The second transducer

is opposite co-axially-aligned positioned and it operates as a receiver of the

attenuated signal that passed through the bone.

SOS is often computed from the following formula:

𝑆𝑂𝑆 =𝑐𝑤

1 +𝑐𝑤𝛥𝑡

𝑑

where cw is the acoustic velocity in water. Δt is the difference between the times

of transmission of the two pulses, and d is the thickness of the specimen. Unit of

measurement is m/sec [88].

Attenuation coefficient is a material property which depends on frequency

and describes loss of energy due to absorption and scattering. If f is frequency,

X(f) is the amplitude spectrum of calibration (with water) and Y(f) is the

amplitude spectrum of the signal that is propagated through the trabecular bone,

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the formula according to which the attenuation coefficient is calculated, is the

following:

20 log|𝑋(𝑓)|

|𝑌(𝑓)|

where the attenuation in water is neglected [89]. The slope of a linear part of

20log[X(f)/Y(f)] vs. f over the functional frequency band of the ultrasound

measurement system is known as broadband ultrasound attenuation (BUA).

Normalized BUA (nBUA) is BUA divided by the thickness d of the specimen [90].

Units of measurement for BUA and nBUA are dB/MHz and dB/cmMHz

respectively.

For in vitro experiments, the surfaces of trabecular bone specimens are

fabricated to be approximately planar. That’s why, the dependence of frequency

on transmission coefficients could be neglected over the experimental frequency

band. According to this assumption, the slope of the attenuation coefficient

occurs from nBUA.

As it has been mentioned above, the loss of energy that occurs during the

propagation of ultrasound in the biological tissues (hard and soft), is mainly

because of two factors: absorption and scattering. Absorption occurs from the

conversion of acoustic energy into thermal energy while scattering takes place

by transmitting acoustic waves, with properties different from those of the

incident wave, when they come in contact with a point of the medium that has

different acoustic properties (scatterer).

So, if a plane wave Pinc(f) is incident upon a scatterer with backscattering

amplitude Φb(f), then the scattered wave Pscat(f) that is measured in distance r

away from the scatterer could be described by the following formula [87][91][92]:

𝑃𝑠𝑐𝑎𝑡(𝑟, 𝑓) = 𝑃𝑖𝑛𝑐(𝑓)𝛷𝑏(𝑓)𝑒𝑖𝑘𝑟

𝑟

If kr >> 1, kas << 1, and as is the scatterer radius. The backscatter coefficient η(f)

occurs from the following formula [87][93]:

𝜂(𝑓) = 𝑛0|𝛷𝑏(𝑓)|2

where n0 is the number of scatterers per unit volume.

Backscatter coefficient is an intrinsic material property and it provides

useful information about the size and distribution of scatterers. Backscatter

measurements take place using pulse-echo method. In this method, one

transducer is applied that operates as a transmitter and receiver of the signal,

simultaneously. In addition, constructive and destructive interference from

waves scattered by randomly-positioned scatterers make backscatter

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measurements noisier than sound of speed and attenuation measurements

[3][93] and backscatter coefficient is difficult to be determined by in vivo

measurements.

2.6. Modeling of differential scattering cross section of ultrasound

The scattering that ultrasound undergoes when it propagates into spongy

bovine bone, has recently begun to be studied and has been approached with

two models. The first is proposed by Wear [94-96] who uses the detailed Faran

models, which they provide an analytical solution for the differential scattering

cross section from a spherical or a cylindrical elastic solid body. The

measurements of the differential scattering cross section are in good agreement

with theoretical predictions at low frequencies. In addition, Chaffai and his

colleagues [97] found well correlations between experimental data of Faran’s

cylindrical and spherical models. The second model [12][98] is based on one

Chernov’s proof that scattering is proportional to the fluctuation of

compressibility, and to the autocorrelation function that concerns the body. In

this model, the medium is considered as a continuous random fluid and this

modeling was successful in soft tissues. Scatterers are described as sources of

disturbance in the wave transmitted to the surrounding fluid. This approach

presupposes weak scattering.

Strelitski and Nicholson [99] presented a scattering model, using the

variation of velocity in a two-phase object and an exponential autocorrelation

function to describe statistical properties of the medium, but without being

compared with experimental results.

Jenson [100] used various autocorrelation functions (Gaussian, exponential

and dense populate) to calculate the differential scattering cross section and

found well correlations between the theoretical predictions and experimental

data. The best prediction was achieved with the Gaussian autocorrelation

function, although no large differences in results were observed comparing to

these that occurred from the use of other autocorrelation functions. Significant

correlations emerged between the predicted values for the trabeculae of spongy

bone that occurred from the models and those that calculated from the

experimental results.

All of the above models have studied scattering in human spongy bone and especially in osteoporotic calcaneus, characterized by low density and small scattering. Healthy or younger human bones, or even most animal bones, are much denser and they have larger trabeculae, resulting in a different scattering behavior. Between human and bovine spongy bone, there are differences in structure and composition. The dimensions of the trabeculae for the bovine spongy bone are from 90 up to 400 μm while for human one the range is from 50 to 230μm [101][102]. The dense and complex structure of bovine spongy bone is a

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limiting factor for modeling spongy bone trabeculae with cylinders. Bovine spongy bone structure does not consist of trabeculae-scatterers with little fluctuation in thickness as it happens in the osteoporotic human spongy bone, but from one set of trabeculae with large thickness variation.

As it has been mentioned, the existence of the scatterers is due to different

density or compressibility. Also, they may have a random position or a random

population into the medium, thus characterizing it inhomogeneous. This is

observed to a very large extent in biological tissues and especially in the hard

ones. In a homogeneous medium with no absorption, an acoustic wave can

propagate unchanged. Nevertheless, in biological tissues neither density nor

compressibility are constant, but both values fluctuate due to differences in

tissue structure. These fluctuations create the scattering of the acoustic wave and

consequently the possibility to be diagnosed through ultrasound.

For the modeling of a medium with random continuous inhomogeneity, as

it happens with the spongy bone, two different autocorrelation functions are

applied. The most important assumptions of the theory for the modeling of

differential scattering cross section 1800 of ultrasound as it propagates through

the cancellous bone, are the following:

• The assumption that the specimen is statistically homogeneous and

isotropic.

• There are no multiple scattering effects. This would happen in the bovine

spongy bone if only the trabeculae were of a size comparable to wavelength

[103][104].

• The assumption of weak scattering. Weak scattering is a result of small

changes in compressibility and density fluctuations, and is valid only when

the logarithm of the range of the attenuation coefficient in the direction of

the propagation of ultrasound is between 0.2-0.5 [11]. The range of the

attenuation coefficient on a heterogeneous random medium in the model

of dense populate, is given by the formula:

𝜎𝜒2 = ⟨𝛾2⟩

2

3√2𝑎𝑘2𝐿√𝜋

where: L is the distance that ultrasound travels in the specimens. The

attenuation coefficient is a function of the quantity αk2, because L and γ2

are constants. According to the above relation for the maximum variation

value of the refraction index γ2 which is 0.4, (it occurs for porosity over

65%), the range variation can be assessed as a weak one for frequencies

above 600 kHz and for scatterer size less than 300μm [7]. Thus, the

experimental data fall within the limits of weak scattering.

• An additional limitation of the propagation theory in continuous media

with random inhomogeneities, is that it takes into account only

longitudinal waves of propagation, and a possible case of conversion into

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shear waves at the interfaces solid and fluid is considered negligible.

Finally, although the theory of propagation in continuous media with

random inhomogeneities is suitable for soft tissues, hard tissues are

described quite well.

• The phasic speed of sound is obtained constant in the whole range of

frequencies.

Below, the two autocorrelation functions used for the description of the

dense spongy bone are presented; dense populate, fluid sphere distribution [7].

Autocorrelation function of dense populate.

In bovine spongy bone the trabeculae are densely distributed. Therefore,

the mean values of density ρ0 and compressibility κ0 do not only come from those

of the fluid that surrounds the trabeculae (marrow), but also from the

corresponding ones of trabeculae-scatterers. Thus, cancellous bone can be

considered as a densely populated medium where ρf <ρ0 and κf <κ0. With other

words cancellous bone is a medium where each of its inhomogeneities is more

uncompressed and denser than the surrounding medium. Τhe differential

scattering cross section σb and the attenuation αsc (Figure 9) have been proven

to be determined by the following formulas:

𝜎𝑏 =1

6√

2

𝜋𝛾2𝑘6𝑎5𝑒−2𝑎2𝑘2

𝑎𝑠𝑐 = √𝜋

2

𝑘2𝜇2

6𝑎𝑒−

9𝑘2𝛼2

2 (−2 − 9𝑎2𝑘2 + 𝑒4𝑎2𝑘2(2 + 𝑎2𝑘2))

where α is the size of scatterer, μ2 is the variation of speed and k= 2π /λ.

(a) (b) Figure 9: (a) Prediction of differential scattering cross section in spongy bone with 70% porosity

for different sizes of scatterers, (b) Prediction of attenuation. Dense Populate [7].

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Autocorrelation function of fluid sphere distribution.

Suppose a random medium in which there are spheres of the same radius

randomly distributed, of different density and compressibility from this

medium. The autocorrelation function of this medium (spherical

distribution function) has been determined by the autocorrelation of a

sphere in three dimensions [78]. The differential scattering cross section σb

and the attenuation αsc (Figure 10) have been proven to be determined by the

following formulas:

𝜎𝑏 =𝑘4𝑉𝑆

2�̅�𝛾02

16𝜋2(

3

2𝑘𝑎𝐽1(2𝑘𝑎))

where: J1 is of first degree and first type of the spherical function Bessel, Vs is the

total volume of spherical scatterers with a radius α, n is the average of scatterers

per unit volume in the medium, γ0 is the average square variation per scatterer

and k= 2π /λ.

𝑎𝑠𝑐 =𝑘2𝜇2

2[10 − 9 cos 2𝑎𝑘 − cos 6𝑎𝑘

36𝑎𝑘2+

1

𝑎3𝑘4(

41

108+

3(−2 + 4𝑎2𝑘2) cos 2𝑎𝑘

16+

+(−2 + 36𝑎2𝑘2) cos 6𝑎𝑘

432) +

3 sin 2𝑎𝑘 + sin 6𝑎𝑘

6𝑘+

1

8𝑎2𝑘3((−6 + 4𝑎2𝑘2) sin 2𝑎𝑘 +

+1

81(−6 + 36𝑎2𝑘2) sin 6𝑎𝑘)]

where μ2 is the variation of speed.

(a) (b) Figure 10:(a) Prediction of differential scattering cross section in spongy bone with 70% porosity for different sizes of scatterers, (b) Prediction of attenuation. Fluid spherical distribution [7].

Literature review

24

2.7. 3D-printing technology

Three-dimensional (3D) printing is a method used for the fabrication of

objects. A 3D-printer is a progressive machine that is able to fuse or deposit

materials in layers in order to create a 3D object. The materials applied may be

plastic, metals, ceramics, powders, liquids, or even living cells. The 3D-printing

procedure is also referred to as rapid prototyping (RP), additive manufacturing

(AM), or solid free-form technology (SFF) and it is expected to dominate

medicine and other fields.

Figure 11: A 3D-printing machine.

There are a lot of 3D-printing processes that differ from each other, they

are applied to distinct fields and their printer technologies, speeds, resolutions,

and materials vary. The 3D object could be constructed in almost any shape

imaginable as defined in a computer-aided design (CAD). The 3D-printer follows

the instructions programmed by the computer in order to build the base of the

object, moving the printhead along the x–y plane. Then, it continues moving the

printhead along the z-axis to build the object vertically layer by layer [105-109].

Last but not least, it is remarkable the fact that two-dimensional (2D)

radiographic images can be converted into digital 3D-print files, thus giving the

opportunity of complex, customized anatomical and medical structures

fabrication. Radiographic images may come from magnetic resonance imaging

(MRI), computerized tomography (CT) or x-rays scans.

In the early 1980s, Charles Hull invented 3D-printing, which he called

“stereolithography”. He was working at the company Ultra Violet Products in

California, making objects from photopolymers. Stereolithography uses an .stl

file format that contains instructions about the shape, the color, the texture and

the thickness of the 3D-printing object. This .stl file is applied for the

Literature review

25

interpretation of the data in a CAD file, allowing this to be communicated

electronically to the 3D-printer.

Later, Hull founded the company 3D Systems, which developed

“stereolithography apparatus” the first 3D-printer. In 1988, 3D Systems

introduced the 3D-printer SLA-250, which was the first commercially available,

while many other companies followed suit and developed 3D-printers for

commercial applications [108].

As it was mentioned before, there are many distinct 3D-printing processes

according to the fields that these are applied. The types of 3D-printing are

[110][111]:

• Binder jetting

• Directed energy deposition

• Materials extrusion

• Materials jetting

• Powder bed fusion

• Sheet lamination

• Vat Photopolymerization

Materials that are used for 3D-printing technology in manufacturing

industry are [105][110][111]:

• Metals

• Polymers

• Ceramics

• Composites

• Smart materials

• Special material, such as food, lunar dust and textile.

The applications of 3D-printing in manufacturing technology concern the industries of aerospace, automotive, food, architecture and building, fabric and fashion, electric and electronic and finally healthcare and medical industry [105][110]. Regarding the applications of 3D-printing in medicine there are four levels [112][113].

• Organ models are constructed in order to help in preoperative planning

and surgical treatment analysis.

3D-printed organ and medical models aid doctors in the preparation of a surgery

but they also can provide a medium of communication between doctors and

engineers, thus assisting in surgical analysis and diagnosis. Applications that

include in vitro equipment, medical models, testing standards and prosthesis

design do not require the biocompatibility of materials, because these 3D objects

will not enter the body.

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26

• Permanent non-bioactive implants.

In dentistry and orthopedics are used permanent medical implants

manufactured by non-degradable biomaterials. Permanent medical implants

provide good biocompatibility after the surgical operation and compared with

traditional fabricated implants, 3D-printing ones with any complex structure can

be personalized real-time manufactured with high dimensional accuracy.

• Fabricating bioactive and biodegradable scaffolds.

Fabrication of tissues and organs could be achieved by two possible ways. The

first method concern the tissue engineering and it is known as indirect cell

assembly, which includes the construction of a 3D scaffold and then the seeding

of cells. The biomimetic tissue-like microarchitecture structures could be created

by biocompatible materials, growth factors, and physical factors. This could be

achieved either only with these factors or combined with living cells [114]. The

second method creates both cells and materials into a composite structure and

it is known as direct cell assembly.

• Directly printing tissue and organs.

Cell and organ printing represents the origin of modern 3D bioprinting

technology. Various materials and ‘‘biological ink” containing seed cells, growth

factors, and nutritional components are printed layer by layer, thus forming

tissue structures. Then, by the process of culturing, tissues or organs with

physiological functions can be formed.

Figure 12: Two cardiac 3D-printed models opened at the level of the four-chamber view, for healthcare teaching [113].

3D-printing has become an innovative tool that has plenty of distinct

application fields, including medicine and it is a constantly developing

technology [108], as printer performance, resolution, and available materials are

increased. The medical advances that 3D-printing has offered, are significant and

Literature review

27

exciting. However, scientists continue to improve the existing medical

applications of 3D-printing technology, such as organ printing.

2.8. Research on 3D-printed trabecular bone

3D-printing technology is used for trabecular bone replicas fabrication in

order to simulate the same bone structure with distinct parameters. It is difficult

to have the same sample in different states and thus, compare the characteristics

and mechanical properties. Thus, 3D-printing technology gives the opportunity

to overcome these issues and study the bone properties with different ways that

lead to quantified results easily [115][116].

C.M. Langton (1997) used the method of stereolithography in order to

manufacture a model, thus simulating the trabecular bone of the human

calcaneus [31]. In this way, perforation and thinning of trabecular bone related

to osteoporosis was simulated and the dependence of ultrasound and mechanical

parameters on the cancellous bone structure was assessed. Also, in 2006, C.M.

Langton and C.A. Dobson applied stereolithography in order to construct models

of trabecular bone structures [117]. The 3D-printed models were mechanically

tested and the results regarding to bone stiffness were compared with that

predicted by finite element analysis. After this comparison a strong correlation

between the predicted and calculated stiffnesses of the structures occurred, thus

showing that the method of stereolithography is promising. After a few years,

Haydar Aygün (2010) applied ultrasound propagation through stereolithography

bone replicas that were 13 times larger than the original bone samples [118]. The

measurements of pulses, that were centered on 100 kHz and 1 MHz and

transmitted through the bone replicas, were compared with predictions of a

modified anisotropic Biot–Allard theory.

V. Kuhn (2014) studied the quality and difference of microCT-based

trabecular bone structures and the biomechanical properties of 3D-printed

trabecular bone specimens, having used high-end 3D-printers enabling

resolutions up to 16μm [119]. Y.J. Yoon (2015) applied the 3D-printing technology

and the compression test in order to investigate the mechanical properties of

engineered trabecular bone and honeycomb structures [120]. The structures

designed were manufactured using the fused deposition modeling (FDM) with

acrylonitrile butadiene styrene (ABS) as a material.

The following year, F. Meziere carried out ultrasound measurements of 1:1

scale 3D-printed trabecular bone specimens [121]. The ultrasound through

transmission experiments were performed through a highly anisotropic version

of the bone structure, and both the fast and slow waves were observed. In this

study the potential of stereolithography is underlined and the relevance of such

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28

bone models for the study of ultrasound propagation in bone indicates the

upcoming progress of science and research.

D. Wu (2020) assessed the possibilities of using fused deposition modeling

(FDM) regarding to the cancellous bone simulation [122]. A composite of

degradable polymer, polylactic acid (PLA), and hydroxyapatite (HA) was used for

better mimic real bone, both in terms of mechanical properties and

biodegradability. Micro-computed tomography, compression and screw pull out

tests were conducted in order to be evaluated the morphometric and mechanical

properties of the 3D-printed models. The reproduction of the trabecular bone

structures by 3D-printed PLA/HA composites occurs to be a promising strategy

for synthetic bone models, when high printed resolution can be achieved. The

same year, R.M. Carew evaluated the surface quality of 3D- printed bone models

[123]. He manufactured models of nine human bones using selective laser

sintering (SLS). The results indicated that the 3D-printed specimens were

accurate to within 2.0 mm of the original dry bone.

The most recent study published in terms of ultrasonic wave propagation

through a 3D-printed replica model of trabecular bone conducted by A.

Tsirigotis, D. Deligianni and K. Apostolopoulos (2021) [124]. First, the fact that

the 3D-printer is able to produce precisely and repeatedly “bone replica models”

of different size and density was verified by compressive tests. Then, replicas of

the original trabecular bone specimens were constructed with two different

polymers and thinned trabeculae models were used for the assessment of the

influence of material properties on ultrasound characteristics. The results

indicated that only the magnitude of the backscatter coefficient is influenced,

whereas the characteristics of ultrasonic wave propagation is associated with the

trabecular structure.

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[93]. Wear, K. A. (2001). Fundamental precision limitations for measurements of frequency dependence of backscatter: Applications in tissue-mimicking phantoms and trabecular bone. The Journal of the Acoustical Society of America, 110(6), 3275-3282.

[94]. Wear, K. A. (1999). Frequency dependence of ultrasonic backscatter from human trabecular bone: Theory and experiment. The Journal of the Acoustical Society of America, 106(6), 3659-3664.

[95]. Wear, K. A., & Laib, A. (2003). The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: Theoretical and experimental results. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 50(8), 979-986.

[96]. Wear, K. A. (2004). Measurement of dependence of backscatter coefficient from cylinders on frequency and diameter using focused transducers—with applications in trabecular bone. The Journal of the Acoustical Society of America, 115(1), 66-72.

[97]. Chaffaı, S., Roberjot, V., Peyrin, F., Berger, G., & Laugier, P. (2000). Frequency dependence of ultrasonic backscattering in cancellous bone: Autocorrelation model and experimental results. The journal of the Acoustical Society of America, 108(5), 2403-2411.

[98]. Morse, P. M., & Ingard, K. U. (1986). Theoretical acoustics. Princeton university press.

[99]. Nicholson, P. H. F., Strelitzki, R., Cleveland, R. O., & Bouxsein, M. L. (2000). Scattering of ultrasound in cancellous bone: predictions from a theoretical model. Journal of biomechanics, 33(4), 503-506.

[100]. rédéric Jenson, F., rédéric Padilla, F., & Laugier, P. (2003). Prediction of frequency-dependent ultrasonic backscatter in cancellous bone using

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statistical weak scattering model. Ultrasound in medicine & biology, 29(3), 455-464.

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[102]. Thomsen, J. S., Ebbesen, E. N., & Mosekilde, L. I. (2002). Static histomorphometry of human iliac crest and vertebral trabecular bone: a comparative study. Bone, 30(1), 267-274.

[103]. Tourin, A., Derode, A., Peyre, A., & Fink, M. (2000). Transport parameters for an ultrasonic pulsed wave propagating in a multiple scattering medium. The Journal of the Acoustical Society of America, 108(2), 503-512.

[104]. Page, J. H., Sheng, P., Schriemer, H. P., Jones, I., Jing, X., & Weitz, D. A. (1996). Group velocity in strongly scattering media. Science, 271(5249), 634-637.

[105]. Ventola, C. L. (2014). Medical applications for 3D-printing: current and projected uses. Pharmacy and Therapeutics, 39(10), 704.

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[116]. Barak, M. M., & Black, M. A. (2018). A novel use of 3D-printing model demonstrates the effects of deteriorated trabecular bone structure on bone

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stiffness and strength. Journal of the mechanical behavior of biomedical materials, 78, 455-464.

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[118]. Aygün, H., Attenborough, K., Lauriks, W., & Langton, C. M. (2010). Ultrasonic wave propagation in stereo-lithographical bone replicas. The Journal of the Acoustical Society of America, 127(6), 3781-3789.

[119]. Kuhn, V., Ivanovic, N., & Recheis, W. (2014). High resolution 3D-printing of trabecular bone based on micro-CT data. Journal of Orthopaedic Translation, 4(2), 238.

[120]. Yoon, Y. J., Moon, S. K., & Hwang, J. (2014). 3D-printing as an efficient way for comparative study of biomimetic structures—trabecular bone and honeycomb. Journal of Mechanical Science and Technology, 28(11), 4635-4640.

[121]. Meziere, F., Juskova, P., Woittequand, J., Muller, M., Bossy, E., Boistel, R., ... & Derode, A. (2016). Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms. The Journal of the Acoustical Society of America, 139(2), EL13-EL18.

[122]. Wu, D., Spanou, A., Diez-Escudero, A., & Persson, C. (2020). 3D-printed PLA/HA composite structures as synthetic trabecular bone: A feasibility study using fused deposition modeling. Journal of the mechanical behavior of biomedical materials, 103, 103608.

[123]. Carew, R. M., Morgan, R. M., & Rando, C. (2020). Experimental assessment of the surface quality of 3D-printed bones. Australian Journal of Forensic Sciences, 1-18.

[124]. Athanasios, T., Konstantinos, A., & Despoina, D. (2021). Three-dimensional-printed replica models of bone for experimentally decoupling trabecular bone properties contribution to ultrasound propagation parameters. The Journal of the Acoustical Society of America, 149(1), 296-306.

Materials

37

3. Chapter 3:

Materials

In the present study, they were manufactured 3D-printed replicas of bovine

trabecular bone, using three different materials in order to evaluate the influence

of material properties in ultrasound propagation through the bone structures.

First, Polylactic Acid (PLA) and Thermoplastic Polyurethane (TPU) were used

for the fabrication of trabecular bone specimens of BV/TV=40% and

BV/TV=34%. Then, Polypropylene (PP) has a density close to that of the human

bones. Thus, it was used for trabecular bone specimens of BV/TV=55%,

BV/TV=40% and for osteoporotic ones (BV/TV=34% and BV/TV=21%) in order

to simulate the real conditions and make useful conclusions in terms of

osteoporosis. In total, they were manufactured eight specimens.

3.1. Polylactic Acid (PLA)

Polylactic acid is a biodegradable and renewable aliphatic polyester that is

extensively researched and utilized. It has proven that PLA is able to replace

petrochemical-based polymers used for industrial applications and be a leading

biomaterial for various applications in medicine [1]. Some of its applications in

medicine concern:

• Wound management and stent applications

• Drug delivery system-based PLA

• Orthopedic and fixation devices

• Tissue engineering and regenerative medicine

PLA is a thermoplastic, high-strength and high-modulus polymer that can

be derived from annually renewable resources to produce distinct components

either for industrial usage or for the biocompatible/bioabsorbable medical device

construction. It can be easily processed on standard plastic for the fabrication of

fibers, film or molded parts. Also, PLA is widely used for 3D-printing, where it is

not suitable for food contact and in-vivo applications.

Below, technical data [2] of transparent PLA used for 3D-printing are

presented (Table 2&3):

Table 2: Thermal properties of transparent PLA material.

Transparent PLA

Thermal Properties Typical Value

Melt mass-flow rate (MFR) 6.09 g/10min

Glass transition ~60 ̊C

Melting temperature 145-160 C̊

Materials

38

Table 3: Mechanical properties of 3D-printing transparent PLA material.

Transparent PLA-3D-printing

Property Typical Value

Density 1.24 g/cm3

Me

cha

nic

al

Pro

pe

rtie

s Tensile modulus 2346.5 MPa

Tensile stress at yield 49.5 MPa

Tensile stress at break 45.6 MPa

Elongation at yield 3.3 %

Elongation at break 5.2 %

Flexural strength 103.0 MPa

Flexural modulus 3150.0 MPa

Izod impact strength, notched (at 23 ̊C)

5.1 kJ/m2

3.2. Thermoplastic Polyurethane (TPU)

Thermoplastic polyurethane (TPU) is synthesized via the reaction of a

polyol with a diisocyanate. TPU is extensively used because of its useful

properties. Characteristic properties of TPU are the mechanical strength,

elasticity, flexibility, good wear resistance, and transparency [3]. According to the

type of polyol used for synthesis of TPU, this material may present typical

properties of either soft elastomers or hard plastics.

TPU is widely used in healthcare, aerospace and many industries for

coatings, components and customer goods, because of its good properties and

compound versatility. Also, it is used for 3D-printing, where it is not suitable for

food contact and in-vivo applications.

Below, technical data [4] of TPU 95A White used for 3D-printing are

presented (Table 4&5):

Table 4: Thermal properties of TPU 95A white material.

TPU 95A White

Thermal Properties Typical Value

Melt mass-flow rate (MFR) 15.9 g/10min

Heat deflection (HDT) at 0.455 MPa 74 ˚C

Heat deflection (HDT) at 1.82 MPa 49 ˚C

Glass transition -24 ˚C

Coefficient of thermal expansion 100·10-6 ˚C-1

Melting temperature 220 ˚C

Materials

39

Table 5: Mechanical properties of 3D-printing TPU 95A white material.

TPU 95A White -3D-printing

Property Typical Value

Density 1.21 g/cm3

Me

cha

nic

al

Pro

pe

rtie

s Tensile modulus 26.0 MPa

Tensile stress at yield 8.6 MPa

Tensile stress at break 39.0 MPa

Elongation at yield 55.0 %

Elongation at break 580.0 %

Flexural strength 4.3 MPa

Flexural modulus 78.7 MPa

Izod impact strength, notched (at 23 ̊C)

34.4 kJ/m2

3.3. Polypropylene (PP)

Polypropylene (PP) is a thermoplastic material which has a rigid and

crystalline structure [5]. Its applications concern the construction of everyday

objects like household products, battery cases, packaging trays, and medical

devices. Also, polypropylene is one of the most important industrial

petrochemical building blocks used to produce various chemical derivatives.

Polypropylene is a leading material among polyolefins because of its

favorable properties. It is a low-density material with high melting temperature,

chemical inertness and low-cost production. Also, structural designs and

mechanical properties diversity may be achieved because of its high versatility.

Finally, the usage of fillers or reinforcing agents and blending PP with other

polymers can lead to the fabrication of distinct morphological structures of PP,

thus achieving superior characteristics.

In addition, polypropylene is extensively used as a 3D-printing material,

which is not suitable for food contact and in vivo applications. Below, technical

data [6] of PP used for 3D-printing are presented (Table 6&7):

Table 6:Thermal properties of PP material.

Polypropylene (PP)

Thermal Properties Typical Value

Melt mass-flow rate (MFR) 20 g/10min

Vicat softening temperature at 5N 115°C

Melting temperature 130 °C

Materials

40

Table 7: Mechanical properties of 3D-printing PP material.

PP-3D-printing

Property Typical Value

Density 0.89 g/cm3

Me

cha

nic

al

Pro

pe

rtie

s Tensile modulus 220MPa

Tensile stress at yield 8.7MPa

Tensile stress at break No break within testing range

Elongation at yield 18%

Elongation at break >300%

Flexural strength 13MPa

Flexural modulus 305MPa

Izod impact strength, notched (at 23 ̊C)

27.1kJ/m2

Bibliography

[1]. Farah, S., Anderson, D. G., & Langer, R. (2016). Physical and mechanical properties of PLA, and their functions in widespread applications—A comprehensive review. Advanced drug delivery reviews, 107, 367-392.

[2]. Technical data sheet PLA, Published by Ultimaker Company, 2017. URL https://ultimaker.com/materials/pla

[3]. Datta, J., & Kasprzyk, P. (2018). Thermoplastic polyurethanes derived from petrochemical or renewable resources: A comprehensive review. Polymer Engineering & Science, 58(S1), E14-E35.

[4]. Technical data sheet TPU 95A, Published by Ultimaker Company, 2017. URL https://ultimaker.com/materials/tpu-95a

[5]. Maddah, H. A. (2016). Polypropylene as a promising plastic: A review. Am. J. Polym. Sci, 6(1), 1-11.

[6]. Technical data sheet PP, Published by Ultimaker Company, 2018. URL https://ultimaker.com/materials/pp

Experimental procedure

41

4. Chapter 4:

Experimental Procedure 4.1. Fabrication of bone specimens

In the present study, they were manufactured eight 3D-printed replicas of

trabecular bone from bovine femur. The specimens were of BV/TV=55%,

BV/TV=40%, BV/TV=34% and BV/TV=21% (Figures 14-17, Table 8).

First of all, microfocus X-ray computed tomography was performed on the

original specimens, using a X-CUBE CT Scanner [1]. The bone marrow had been

removed before this procedure. Then, the projections were reconstructed into a

3D volume into X-CUBE software and using a 3D filter back-projection

algorithm. After the image construction process [1], the differentiation of bone

from non-bone pixels followed. For this study, a cube of size 6 mm (110 x 110 x 110

voxels) was the selected volume of interest (VOI). Finally, a 3D surface model of

the trabecular bone specimen was reconstructed by the import of the stack with

the differentiated images into InVesalius 3.1.1 software [1][2] and the 3D surface

model saved as “stl” file.

The fabrication of 3D-printed trabecular bone replicas was achieved using

an Ultimaker 2+ 3D-printer. First, the “stl files” mentioned before, are imported

into a software called Ultimaker Cura in order to process the characteristics of

models and define the 3D-printer appropriate settings. Then, slicing of the

models and their conversion into g-code, follows. G-code is a readable file type

by the 3Dprinter. Ultimaker 2+ follows a procedure called Fused Filament

Fabrication (FFF), which has a great accuracy for complex engineering

structures.

(a)

(b)

Figure 13: (a) Ultimaker 3D-printer, (b) 3D-printing process of a bone replica.

Experimental procedure

42

In the present study, three different materials were used in order to

evaluate the influence of material properties in ultrasound propagation through

the bone structures. Pure polylactic acid (PLA) and thermoplastic polyurethane

(TPU 95A) were used for the fabrication of bone specimens of BV/TV=40% and

BV/TV=34% (a total of four specimens) in order to compare the ultrasound

properties. These materials were chosen because of their different mechanical

properties, except density which is similar. Also, polypropylene (PP) was used for

trabecular bone specimens of BV/TV=55%, BV/TV=40% and for osteoporotic

ones -BV/TV=34% and BV/TV=21%- because of its density which is similar to that

of the human bones. Should be noted that all the materials used for the 3D-

printing process were obtained directly from the “Ultimaker” company.

4.1.1. 3D-printing with transparent PLA material As it was mentioned before, “stl” files of the 3D models were imported into

a software called Ultimaker Cura. The dimensions of the 3D bone models of

BV/TV=40% and BV/TV=34% determined to be about 18mm with uniform

scaling and the 3D-printer settings were defined by the default standard of

“Ultimaker” company. G-code files, that was occurred after slicing, were saved at

3D-printer SD card, which then was inserted the printer.

Then, according to the instructions of “Ultimaker” company, a nozzle of

0.25mm diameter was installed, whereas the nozzle temperature and the build

plate temperature were set to be at 210 0C and 60 0C, correspondingly. After

calibrating the 3D-printer, the printing process started with a set print speed of

30 mm / s. Should be noted that each trabecular bone specimen was

manufactured separately. The 3D-printed bone replicas are shown in figure 14.

(a)

(b)

Figure 14:3D-printed PLA replicas of trabecular bone. (a) BV/TV=40%, (b) BV/TV=34%.

4.1.2. 3D-printing with white TPU 95A material “Stl” files of the 3D models were imported into Ultimaker Cura software.

The dimensions of the 3D bone models of BV/TV=40% and BV/TV=34% were

determined to be about 18mm with uniform scaling and the 3D-printer settings

were defined by the default standard of “Ultimaker” company. G-code files, that

Experimental procedure

43

was occurred after slicing, were saved at 3D-printer SD card, which then was

inserted the printer.

Then, according to the instructions of “Ultimaker” company, a nozzle of

0.25mm diameter was installed, whereas the nozzle temperature and the build

plate temperature were set to be at 235 0C and 70 0C, correspondingly. After

calibrating the 3D-printer, the printing process started with a set print speed of

40 mm / s. Should be noted that each trabecular bone specimen was

manufactured separately. The 3D-printed bone replicas are shown in figure 15.

(a)

(b)

Figure 15: 3D-printed TPU replicas of trabecular bone. (a) BV/TV=40%, (b) BV/TV=34%.

4.1.3. 3D-printing with transparent PP material “Stl” files of the 3D models were imported into Ultimaker Cura software.

The dimensions of the 3D bone models of BV/TV=55%, BV/TV=40%,

BV/TV=34%, and BV/TV=21% were determined to be about 18mm with uniform

scaling and the 3D-printer settings were defined by the default standard of

“Ultimaker” company. G-code files, that was occurred after slicing, were saved at

3D-printer SD card, which then was inserted the printer.

(a)

(b)

Figure 16: 3D-printed PP replicas of trabecular bone. (a) BV/TV=55%, (b) BV/TV=40%.

Then, according to the instructions of “Ultimaker” company, a nozzle of

0.4mm diameter was installed, whereas the nozzle temperature and the build

plate temperature were set to be at 220 0C and 100 0C, correspondingly. Because

Experimental procedure

44

of PP susceptibility to warping, an adhesion sheet was applied to the glass plate,

as it was recommended by the company. Also, due to the same reason, a provided

front enclosure was used in order to remove possible air draft and keep the

temperature inside the 3D-printer at around 45 °C. These environment

conditions provide a higher print success rate, better quality and performance of

the printed bone replicas. After calibrating the 3D-printer, the printing process

started with a set print speed of 25 mm / s. Should be noted that each trabecular

bone specimen was manufactured separately. The 3D-printed bone replicas are

shown in figures 16&17.

(a)

(b)

Figure 17: 3D-printed PP replicas of trabecular bone. (a) BV/TV=34%, (b) BV/TV=21%.

Below, are presented the physical quantities of 3D-printed bone replicas

that were measured at room temperature 25 0C, after their fabrication. Their

mass was measured using a digital scale and their volume was determined by

measuring the external dimensions of the cubes with a caliper.

Table 8: Physical quantities of 3D-printed replicas.

Material PLA TPU PP

BV/TV 40% 34% 40% 34% 55% 40% 34% 21%

Dim

ensi

on

s

(mm

)

X 18.5 18.2 18.5 18.2 18.3 18.0 18.0 18.0

Y 18.3 18.2 18.3 18.2 18.0 19.4 18.0 18.0

Z 18.3 18.5 18.3 18.5 18.1 18.0 18.1 18.2

Mass (gr)

2.894 2.611 2.851 2.552 2.421 2.139 1.863 0.999

Volume (cm3)

6.195 6.128 6.195 6.128 5.962 6.286 5.864 5.897

Density (gr/cm3)

0.467 0.426 0.460 0.416 0.406 0.340 0.318 0.169

Experimental procedure

45

4.2. Measurements of ultrasound acoustic properties

In a number of eight 3D-printed trabecular bone specimens, measurements

were conducted in three directions perpendicular to each other. In the axial (Y)

direction, the anterior-posterior (X), and lateral (Z). The ultrasonic

measurements were performed in distilled water at room temperature [3]. The

specimens were degassed in a vacuum flask to remove air bubbles. In order to

position the specimen in the ultrasound beam a custom holder was used.

(a)

(b)

Figure 18: (a) The degassing of specimens, (b) Through-transmission ultrasound measurements layout.

Unfocused immersion transducers (Panametrics, V303, d =1.27cm (0.5in),

center frequency 1MHz, and focal length F = 23mm) were used in this study

connected to an ultrasonic pulse receiver (USD 10NF, Krautkraemer, Germany).

Ultrasonic pulse receiver can operate in two ways:

• With two coaxially aligned transducers (transmitter and receiver), and the

specimen between them (through-transmission method).

• With a transducer which is both a transmitter and receiver (pulse-echo

method).

RF digital signals were received with frequency sampling 35 MHz. The

-20dB frequency bandwidth corresponds to frequency from 0.38 to 1.18 MHz for

unfocused transducers.

The through-transmission method was used to measure ultrasound speed

(SOS) and attenuation (BUA) that occurs when propagating through water or

the specimen. The attenuation coefficient has the dB as a unit and it is calculated

as the decimal logarithm of the ratio of the spectrum ranges of wave power

propagated through the specimen and water respectively. The attenuation as a

function of frequency shows a linear region in a frequency range from 200 to 900

kHz. The slope of attenuation linear area as a function of frequency determines

Experimental procedure

46

the value of broadband ultrasound attenuation (BUA). The speed of ultrasonic

wave propagation through the 3D-printed cancellous bone specimens is based

on the determination of the ultrasound pulse time of flight [4] from the

transducer-transmitter to the transducer-receiver (Section 2.5). Errors generated

during the diffraction of sound when this propagates from water into the

specimen, were calculated and eliminated [5].

The measurements of the differential scattering cross section were

conducted applying the pulse-echo method. The differential scattering cross

section 1800 as a function of frequency was calculated by the method described

by Roberjot and Chaffai [6][7]. The RF signals from 3D-printed bone specimens

were received in 1 mm steps, in a 2D scan of their cross section. The cross section

of ultrasound beam occurs by the ratio 2.44λF / d = 6.75mm [8] for a transducer

of frequency 1MHz, where λ is the wavelength, F is the focal length and d is the

diameter of the transducer. From the time series of the signal corresponding to

the entire length of the specimen a range of 7 mm was selected in which the

differential scattering cross section 1800 was calculated. This calculation includes

a correction at the edges of signal with Hamming window, and three correction

factors which are related to errors due to signal attenuation in bone specimens

[9], to the frequency dependence on the testing volume, and to the refraction [5]

that occurs in sound when it meets water-bone interface.

The power spectrum of the 7mm area of the specimen, that occurs from the

transition from the time domain to the frequency domain with the Fourier

transform, is divided by the corresponding power spectrum of a steel plate

considered as a reference. The surface of the plate is as far away from the

transducer as the distance of the transducer from the middle of the selected 7mm

area of the specimen. In this way, occurs the apparent scattering coefficient with

the following formula:

�̂�𝛣(𝑓) =⟨𝑆𝐵(𝑓)⟩

⟨𝑆0(𝑓)⟩

where <SB(f)> is the average of the power spectrum values obtained in different

positions and they correspond to the area of the specimen, that is tested, and

<S0(f)> is the average of the power spectrum values of the reference steel plate.

The use of the average rather than just one measurement for spectrum

determination is necessary, because in this way, the statistical errors of the

reflected signal, that occur due to the random phase of the fundamental reflected

waves, are removed. The apparent scattering coefficient must be corrected due

to the sufficient sources of error, including signal loss caused by reflection on the

surface of the specimen, the attenuation of the signal through the specimen, and

the frequency dependence on the volume being measured. Has been proved that

Experimental procedure

47

99% of the incident energy is transferred longitudinally. This fact interprets the

reflection effect at the interface.

Thus, the losses that concern the attenuation may be compensated by the

through-transmission data. The scattering cross section 1800 is calculated by the

following formula:

𝜇𝐵(𝑓) = �̂�𝐵(𝑓)𝐴𝑑(𝑓)𝐶(𝑓)𝐹𝑎𝑐𝑡𝑜𝑟𝑠(𝑓)

where C(f) is the correction coefficient due to attenuation, Αd(f) is the correction

coefficient due to refraction and is equal to 0.99, and Factors(f) is the correction

coefficient that depends on the frequency in the volume of sub examination area

of the specimen. The coefficient C(f) is given by the equation:

𝐶(𝑓) = 𝑒4�̂�(𝑓)𝑧4�̂�(𝑓)𝑑

𝑒2�̂�(𝑓)𝑑 − 𝑒−2�̂�(𝑓)𝑑

And the coefficient Factors(f) is given by the equation:

𝐹𝑎𝑐𝑡𝑜𝑟𝑠(𝑓) =1

0.632

𝑘2𝑎2

8𝜋𝑑 [1 + (𝑘𝑎2

4𝐹 )]

where (1/0.63)2 is the correction factor for the Hamming gate function, �̂�(f) is the

frequency dependent attenuation coefficient in measurement unit Nepers / MHz

/ cm, d is the length of the testing area, z is the distance from the beginning of

the specimen up to the middle of the testing area, k = 2π/λ is the wave number,

α is the radius of the transducer and F is the focal length. 0 and 3.11 show the sizes

d, z and N respectively.

Figure 19: The area characterized as the interface refers to the surface between the water and the bone specimen with a depth of about 3mm, due to the nature of the bone. The area of 7mm

delimits the volume of interest of which the differential scattering cross section 1800 is measured and follows the interface. The length z is measured from the beginning of the specimen to its

middle volume of which the differential scattering cross section 1800 is measured.

Experimental procedure

48

Bibliography

[1]. Athanasios, T., Konstantinos, A., & Despoina, D. (2021). Three-dimensional-printed replica models of bone for experimentally decoupling trabecular bone properties contribution to ultrasound propagation parameters. The Journal of the Acoustical Society of America, 149(1), 296-306.

[2]. Amorim, P., Moraes, T., Silva, J., & Pedrini, H. (2015, December). InVesalius: An interactive rendering framework for health care support. In International symposium on visual computing (pp. 45-54). Springer, Cham.

[3]. Deligianni, D. D., & Apostolopoulos, K. N. (2007). Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models. The Journal of the Acoustical Society of America, 122(2), 1180-1190.

[4]. Njeh, C. F., Boivin, C. M., & Langton, C. M. (1997). The role of ultrasound in the assessment of osteoporosis: a review. Osteoporosis international, 7(1), 7-22.

[5]. Xu, W., & Kaufman, J. J. (1993). Diffraction correction methods for insertion ultrasound attenuation estimation. IEEE transactions on Biomedical Engineering, 40(6), 563-570.

[6]. Roberjot, V., Laugier, P., Droin, P., Giat, P., & Berger, G. (1996, November). Measurement of integrated backscatter coefficient of trabecular bone. In 1996 IEEE Ultrasonics Symposium. Proceedings (Vol. 2, pp. 1123-1126). IEEE.

[7]. Chaffaı, S., Peyrin, F., Nuzzo, S., Porcher, R., Berger, G., & Laugier, P. (2002). Ultrasonic characterization of human cancellous bone using transmission and backscatter measurements: relationships to density and microstructure. Bone, 30(1), 229-237.

[8]. Wear, K. A. (2001). Fundamental precision limitations for measurements of frequency dependence of backscatter: Applications in tissue-mimicking phantoms and trabecular bone. The Journal of the Acoustical Society of America, 110(6), 3275-3282.

[9]. O’Donnell, M., & Miller, J. G. (1981). Quantitative broadband ultrasonic backscatter: An approach to nondestructive evaluation in acoustically inhomogeneous materials. Journal of Applied Physics, 52(2), 1056-1065.

Results

49

5. Chapter 5:

Results

The aim of this study was to investigate and decompose the influence of

trabecular bone architecture and material on ultrasound characteristics,

speed of sound and backscatter coefficient, using 3D-printed trabecular

bone models. It was very significant to fabricate trabecular bone replicas with as

much accurate structure as possible, following the same printing methods for all

the specimens in order to ensure that the results and conclusions concern only

the material influence on ultrasound properties and characteristics since the

bone samples are the same.

5.1. Relationship between speed of sound and apparent density

A strong linear dependence of speed of sound (SOS) with the density of 3D-

printed trabecular bone specimens occurred from ultrasound propagation

measurements. Especially, a correlation coefficient of 𝑅2 = 0.97 − 1.00 was

occurred in all three directions of the specimens, taking into consideration a PLA

bone replica with BV/TV=21% [1]. In figure 20, the correlation between the

density of the specimens and SOS is presented. The replicas were fabricated

using the same material (PLA). Thus, they have the same Young’s modulus. This

is the reason why SOS and apparent density have a strong linear relationship.

Finally, the difference in trabecular bone structure in each direction becomes

obvious by the slopes of the three lines that correspond to 𝑋, 𝑌, 𝑍 directions.

(a)

Results

50

(b)

Figure 20:(a) Linear relationship between SOS and apparent density for three 3D-printed trabecular bone specimens with different bone volume fractions, constructed from PLA, in the

three directions, (b) Graph data and analysis.

Also, a linear dependence of speed of sound (SOS) with the density of 3D-

printed trabecular bone specimens occurred from ultrasound propagation

measurements. Especially, a correlation coefficient of 𝑅2 = 0.93 − 1.00 was

occurred in all three directions of the specimens. In figure 21, the correlation

between the density of the specimens and SOS is presented. The replicas were

fabricated using the same material (PP). Thus, they have the same Young’s

modulus. This is the reason why SOS and apparent density have a strong linear

relationship. Finally, the difference in trabecular bone structure in each direction

becomes obvious by the slopes of the three lines that correspond to 𝑋, 𝑌, 𝑍

directions.

(a)

Results

51

(b) Figure 21: (a) Linear relationship between SOS and apparent density for three 3D-printed

trabecular bone specimens with different bone volume fractions, constructed from PP, in the three directions, (b) Graph data and analysis.

5.2. Influence of material properties on ultrasound propagation

The backscatter coefficient of two 3D-printed replicas of the same

trabecular bone sample fabricated using two different materials -PLA and TPU

95A- is presented in figure 22 as a function of frequency. In each direction is

observed a significant similarity between the two backscatter coefficient

patterns. It is obvious that the corresponding backscatter spectra are different.

The 3D-printed specimen fabricated from a material with higher modulus of

elasticity has a higher backscatter coefficient magnitude. Also, it is remarkable

that the partial peaks correspond to certain frequencies and they are identical in

all directions for PLA and TPU materials. An interesting conclusion is that the

magnitude of the backscatter coefficient depends on the modulus of elasticity of

the corresponding material and that its pattern is influenced by the structure of

trabecular bone.

(a)

Results

52

(b)

(c)

Figure 22: Backscatter coefficient as a function of frequency of two 3D-printed trabecular bone specimens with the same bone volume fraction, constructed from PLA and TPU in the (a) X

direction, (b) Y direction and (c) Z direction.

5.3. Simulation of osteoporosis

The backscatter coefficient of two different 3D-printed replicas -

BV/TV=40%, BV/TV=34%- constructed from PLA is shown in figure 23 as a

function of frequency. In a previous study [2], was applied a weak scattering

model for the ultrasound backscatter in dense bovine trabecular bone as a

Results

53

function of frequency. In particular, two autocorrelation functions were used for

the description of the medium and the study indicated that the maximum value

of the backscatter coefficient corresponds to a certain frequency, whereas reflects

a scatterer of a certain size. Based on this study, it was assumed that the partial

peaks of the backscatter coefficient correlate to a certain scatterer size. In this

way, the scatterers size of the trabecular bone with BV/TV=34% were estimated.

In particular, the above scattering model indicated that the thickness of

trabeculae is reduced at 15% compared to the bone specimen with BV/TV=40%

[1][2].

(a)

Results

54

(b)

(c)

Figure 23: Backscatter coefficient as a function of frequency of two 3D-printed trabecular bone specimens with different bone volume fractions, constructed from PLA. (a) X direction, (b) Y

direction and (c) Z direction.

The backscatter coefficient of 3D-printed trabecular bone replicas

constructed from PP is shown in figure 24 as a function of frequency. The integral

of the backscatter coefficient as a function of frequency tends to be proportional

to the density of the bone specimens. In particular, in most cases it has lower

values in lower density bone specimens. However, this relationship has not been

determined. Finally, as it was mentioned before, the maximum value of the

backscatter coefficient corresponds to a certain frequency, whereas reflects a

scatterer of a certain size [2].

Results

55

(a)

(b)

Results

56

(c) Figure 24: Backscatter coefficient as a function of frequency of 3D-printed trabecular bone specimens with different bone volume fractions, constructed from PP. (a) X direction, (b) Y

direction and (c) Z direction.

Bibliography

[1]. Athanasios, T., Konstantinos, A., & Despoina, D. (2021). Three-dimensional-printed replica models of bone for experimentally decoupling trabecular bone properties contribution to ultrasound propagation parameters. The Journal of the Acoustical Society of America, 149(1), 296-306.

[2]. Deligianni, D. D., & Apostolopoulos, K. N. (2007). Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models. The Journal of the Acoustical Society of America, 122(2), 1180-1190.

Conclusions

57

6. Chapter 6:

Conclusions

The purpose of this study was to investigate the influence of trabecular

bone structure and material on ultrasound properties and characteristics. In

total, three materials were used for the construction of trabecular bone

specimens by a 3D-printer. These were PLA, TPU that have similar density but

different mechanical properties and PP that has lower density, close to that of

the human bones. In total, eight trabecular bone specimens were constructed

with different bone volume fractions by a 3D-printer and measurements of

ultrasound propagation through the specimens were conducted.

3D-printing offers the opportunity of constructing identical trabecular

bone structures for each single sample in order to quantify structural

degradation. The main purpose was to construct trabecular bone replicas with as

much accurate structure as possible, following the same printing methods for all

the specimens in order to ensure that the results and conclusions concern only

the material influence on ultrasound properties.

It is known that the backscatter signals may be sensitive to small

displacements of the transducer because of the phase-sensitivity of the

ultrasound propagation measurements. However, a perfect conformity of the

backscatter signals pattern was achieved, concerning two identical 3D-printed

trabecular bone specimens, constructed from two different materials (Figure 22).

The ultrasound measurements indicate that material properties, such as

density and stiffness, influence the magnitude of the backscatter spectrum,

whereas the shape of backscatter coefficient as a function of frequency depends

on the bone structure (Figure 22). The fact that the material properties influence

the magnitude of the backscatter spectrum is verified by the results occurred

from bone replicas with the same material but different density (Figure 23 & 24).

Also, an interesting observation is that the integral of the backscatter coefficient

as a function of frequency seems to be proportional to the density of the bone

specimens. In particular, it has lower values in lower density bone specimens.

However, this relationship has not been determined.

In addition, based on a weak scattering model and combination of two

autocorrelation functions [1], the thinning of the trabeculae was estimated by

measuring the shift of the partial peaks of the backscatter coefficient as a

function of frequency. In particular, the thickness of bone specimen trabeculae

with BV/TV=34% is reduced at 15% compared to the bone specimen with

BV/TV=40% [2].

Conclusions

58

Also, a remarkable result occurred from this study; speed of sound has a

perfect linear relationship with apparent density. The dependence of SOS on

apparent density presents a correlation coefficient of 𝑅2 = 0.97 − 1.00 and of

𝑅2 = 0.93 − 1.00 for PLA and PP, respectively (Figure 20 & 21). This means that

SOS indicates the quantity of material present in the direction of ultrasound

propagation. Should be noted that SOS is different along the three orientation

axes because of bone specimens’ different structural modulus. However, the

values of SOS in three directions of the constructed trabecular bone replicas did

not show high anisotropy of specimens. In case of ultrasound propagation

parallel to the main orientation of trabeculae, through specimens with high

anisotropy, two waves -fast and slow- are observed. As a result, there will be

different relationships between SOS and apparent density. Finally, the

construction of trabecular bone replicas from the same material, which means

that they have the same matrix material Young’s modulus and density, led to the

observation of SOS and mechanical properties decrease in a perfectly linear way

as a function of apparent density, when the structure degrades because of bone

loss.

3D-printing technology offers the opportunity of studying the mechanical

and ultrasound properties alteration due to structural degradation for a single

sample because it is feasible the manufacture of the same sample in both intact

and degraded state. The fact that the printed trabecular bone specimens have

larger dimensions than that of the original ones and that their matrix material

have different density comparing to that of bones were the limitations of this

research.

The purpose of this study and the corresponding ones, was the

investigation of the qualitative features of ultrasound propagation through the

3D-printed specimens. The outcomes, that occurred from the research on

ultrasound propagation through the 3D-printed bone specimens, most likely

cannot be associated with the original trabecular bone; especially, in case of

osteoporotic one. Nevertheless, significant conclusions are presented related to

the origins of backscatter and ultrasound properties alteration due to structural

degradation, which is a result of the ageing process. Also, 3D-printing technology

has progressed to the point that the idea of reconstructing structural tissues

using inorganic materials is feasible. Finally, as micro-CT and manufacturing

technologies advance, specimens with morphometric characteristics and

properties close to these of diseased bones can be developed. The extent research

on these phantoms may contribute to the formulation of osteoporosis diagnostic

devices.

Conclusions

59

Bibliography

[1]. Deligianni, D. D., & Apostolopoulos, K. N. (2007). Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models. The Journal of the Acoustical Society of America, 122(2), 1180-1190.

[2]. Athanasios, T., Konstantinos, A., & Despoina, D. (2021). Three-dimensional-printed replica models of bone for experimentally decoupling trabecular bone properties contribution to ultrasound propagation parameters. The Journal of the Acoustical Society of America, 149(1), 296-306.