Single-trabecula building block for
large-scale finite element models of
cancellous bone
D. Dagan
M. Be’ery
A. Gefen
Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Israel
Abstract—Recent development of high-resolution imaging of cancellous bone allows
finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress=strain analyses can include effects of
anatomical variations and local damage that can bias the interpretation of the
results from individual specimens with respect to large populations. This study
developed a standard (generic) ‘building-block’ of a trabecula for large-scale FE
models. Being parametric and based on statistics of dimensions of ovine trabeculae,
this building block can be scaled for trabecular thickness and length and be used in
commercial or custom-made FE codes to construct generic, large-scale FE models of
bone, using less computer power than that currently required to reproduce the
accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with
this building block, after it was scaled to trabeculae of the human proximal femur,
provided apparent elastic moduli of 150 MPa, in good agreement with experimental
data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner,
osteoporotic-like trabeculae could predict a reduction of 30% in the apparent elastic
modulus, as reported in experimental studies of osteoporotic femora. Based on these
comparisons, it is concluded that the single-trabecula element developed in the
present study is well-suited for representing cancellous bone in large-scale generic
FE simulations.
Keywords—Spongy bone, Trabecular tissue stiffness, Apparent elastic modulus,
Constitutive properties, Osteoporosis
Med. Biol. Eng. Comput., 2004, 42, 549––556
1 Introduction
TRABECULAR BONE consists of delicate plates and struts of bone
tissue, trabeculae, that branch and intersect to form a sponge-like
lattice. Individual trabeculae are the load-bearing elements of
cancellous (spongy) bone. The overall architecture of trabecular
lattices aligns with the principal load-transfer pathways in bone
under physiological loading. This makes the epiphysis in long
bones, which consist mainly of trabecular bone, an efficient
structure in distributing concentrated loads from the joint
surfaces to the diaphysis.
Little is known about the distribution of mechanical stresses
and strains in the individual trabeculae of bone under physiological loading. As direct measurements of stresses and strains in
individual trabeculae are not feasible, finite element (FE) models
of the micro-architecture of bone have been used for such
studies. Traditionally, to simplify the calculations, these
Correspondence should be addressed to Dr Amit Gefen;
email: gefen@eng.tau.ac.il
Paper received 17 November 2003 and in final form 13 April 2004
MBEC online number: 20043907
# IFMBE: 2004
Medical & Biological Engineering & Computing 2004, Vol. 42
models have represented trabecular bone as a continuum, and
so only average tissue stresses and strains could be predicted.
The recent development of high-resolution imaging of bone
(serial sectioning, micro-CT and micro-MRI scanning) opened a
new field of study in bone mechanics: FE analysis of realistic
trabecular architectures. With these techniques, the detailed
three-dimensional (3D) architecture of trabecular bone samples
can be digitised and converted to large-scale FE models from
which tissue stresses, displacements and strains in individual
trabeculae can be obtained (VAN RIETBERGEN et al., 1995; 1999;
2003).
Such models can be validated experimentally using the
texture correlation technique, which extracts displacement
patterns from digitised contact radiographs of the samples
under load (BAY et al., 1999). However, if the specific bone
specimens subjected to the stress=strain analysis contain some
anatomical variations or local damage, conclusions regarding
large populations can be biased. This calls for the development
of a complementary generic trabecular bone model that can be
used where it is desired to study the mechanics of a ‘typical’,
rather than specific, bone.
Moreover, epiphyses of human long bones contain thousands
of trabeculae, each with irregular and unique geometry.
Accordingly, meshing of these complex lattices in the FE
method produces vast databases that currently require a
549
supercomputer or a cluster of computers for analysis
(VAN RIETBERGEN et al., 1999). Although, with the constantly
growing power of computers, it is expected that this would be
less of a problem in the future, in many cases, the complexity of
the modelling and, mainly, of the FE meshing would be
substantially reduced if the jagged and irregular geometries of
individual trabeculae were approximated to smoother and
simpler standard elements. It has also been suggested that
smoother surfaces of trabeculae in FE models reduce solution
artifacts (GULDBERG et al., 1998).
Several generic models of repeated cellular solid structures
were developed to study the mechanical behaviour of trabecular
bone using different geometrical descriptions for the unit cell
(GIBSON, 1985; WERNER et al., 1996; ANDERSON and CARMAN,
2000; KIM and AL-HASSANI, 2002; KOWALCZYK, 2003). The
more recent contributions accounted for the curved geometry of
individual trabeculae rather than treating them as beams with
uniform (circular or rectangular) cross-sections. Specifically,
KIM and AL-HASSANI (2002) considered differences between
the base and central thicknesses of trabeculae and used linear
regression equations for relating thickness and separation of
trabeculae to the age of bone. Most recently, KOWALCZYK
(2003) described the shape of unit cells using Bézier curves,
which made it possible to demonstrate a wide variety of
microstructural patterns. However, none of the published
generic models employed real architectural statistical data to
define the unit cell geometry.
The goal of the present paper was to present and characterise a
standard ‘building block’ of a trabecula for large-scale FE
models. Being parametric and based on statistics of dimensions
of mammalian trabeculae, this building block can be scaled for
trabecular thickness and length and used in commercial or
custom-made FE codes to construct generic large-scale FE
models of bone that can serve as a ‘gold standard’ in basic
studies of bone mechanics, as well as during the design and
performance evaluation of orthopaedic implants. This paper also
provides basic statistical information on the geometrical variations between individual trabeculae.
2 Methods
2.1 Geometric model of a single trabecula
Sheep became a common orthopaedic model because, in
addition to being relatively inexpensive, their bones are large
enough for the insertion of implants and for the conducting of
mechanical property studies (AN and FRIEDMAN, 1999).
Accordingly, we developed a single-trabecula geometric
model based on statistical analysis of the dimensions of 200
rod-like trabeculae from the epiphyseal parts of six ovine
femora. Six specimens were transversely cut from the upperthird of the epiphysis of each femur, with an electrically powered
saw, after the bones had been dried at 85 C for 4.5 h. The dried
samples were kept at 18 C and defrosted to room temperature
before measurement of the trabecular dimensions.
Under digital optical microscopy* (magnification x30), we
measured the length L, base thickness tmax (at the junctions of the
lattice) and minimum thickness tmin (at the centre of the strut) of
each trabecula (Figs. 1 and 2) from a transverse view, using
designated software for microscopic measurements.{ The base
thickness tmax at each edge of a trabecula was determined by
containing the respective trabecular junction within a circle and
measuring the distance between points common to the profiles of
the trabecula and the junction circle, as demonstrated in Fig. 1b.
*Axiolab A, ZEISS Co.,
{
MGI photosuite 3.0SE
550
This uniquely defines the base thickness tmax values for each
trabecula (Fig. 1b). The value of tmin was measured at the centre
of the trabecula, halfway between the two locations of its tmax
boundaries. We found significant linear correlation (R2 ¼ 0.71,
p50.05) between the base and minimum thickness dimensions
of individual trabeculae (tmax ¼ atmin þ b, where a ¼ 1.3736 and
b ¼ 40.9 mm; see Fig. 1c).
By means of cross-correlation of digitised trabecular profiles,
we also found high degrees of symmetry of the curvature of
individual trabeculae (Fig. 1a) around their longitudinal (z) and
radial (r) axes (R2 ¼ 0.97 0.99), which made it possible to fit
cosinusoidal curves to the upper and lower trabecular profiles
r
2z 1 1
b
3
cos
3a
¼ cos
(1)
tmin
L
2
tmin
2
Because tmin and tmax are linearly related, (1) can also be
formulated in terms of tmax. It is also possible to write both
tmin and tmax as functions of the average thickness of a trabecula t
(where t ¼ (tmin þ tmax)=2) and of the constants a, b. This made it
possible to simplify the representation of trabecular profiles in
(1) so that only two parameters, the characteristic length L and
average thickness t, are incorporated
2tb
r¼
1þa
2z 1 1
b (1 þ a)
3
cos
3a
6 cos
L
2
2tb
2
(2)
Utilising our microscopy measurements, which yielded that the
range of thickness of trabeculae was between 0.3 times and 2.86
times the mean thickness (215 mm, see Fig. 2a), (2) allows
representation of the complete spectrum of potential trabecular
profiles in sheep.
The volume bounded within the surface of revolution derived
from (2) (i.e. the surface generated by rotating the positive curve
of (2) 360 about the z-axis) provides an estimate for the volume
V of a trabecula with given nominal thickness t and length L
2t b
L sin g 3L
V ¼p
(3)
1þa
g
2
where
1
b(1 þ a)
3a
g ¼ cos
2
2t b
1
t, L40
Equation (3) thus approximates the distribution of volumes of
trabeculae in sheep (Fig. 2c).
Bone morphology studies across species suggest that the
shape of individual trabeculae is common to all mammals,
although dimensions of trabeculae and their structural arrangement do differ between species (FAJARDO and MULLER, 2001).
Accordingly, to represent a single, normal rod-type trabecula of
the human proximal femur with mean dimensions, we scaled the
parameters of (2) and (3), so that L ¼ 1 mm and t ¼ 283 mm
(PUZAS, 1996). To represent further the spectrum of potential
trabecular profiles in a normal human femoral epiphysis, we
assumed that the extent of biological variation in trabecular
thickness found in normal sheep (Fig. 2a) applies to normal
humans, i.e. that the ratios of maximum-to-mean and minimumto-mean thicknesses are similar in normal sheep and normal
human cancellous bone. This assumption allowed us to plot the
spectrum of potential geometric profiles of human trabeculae
(Fig. 3). The 3D reconstruction ((2) and (3)) of a rod-type human
trabecula of the femoral neck with mean thickness and length
(t ¼ 283 mm; L ¼ 1) is shown in Fig. 4a.
Medical & Biological Engineering & Computing 2004, Vol. 42
a
b
800
t max = at min + b
a = 1.3736, b = 40.932 mm
700
R 2 = 0.71
600
t max, mm
500
400
300
200
100
0
0
100
200
300
400
500
t min, mm
c
Fig. 1 (a) Basic geometric dimensions of rod-like trabecula: base thickness (tmax) and minimum thickness at the centre (tmin); (b) method of
determination of base of trabeculae shown for junction between 3 trabeculae marked i, j and k, with corresponding base thickness values
timax, tjmax and tkmax; (c) base and minimum thickness of individual trabeculae were found to be linearly correlated (p50.05).
tmax ¼ atmin þ b; a ¼ 1.3736; B ¼ 40.9 mm; R2 ¼ 0.71 (Micrograph magnifications: 630)
2.2 Characterisation of the elastic properties of orthogonal
trabecular lattices
Equations (2) and (3) describe a parametric geometric
building block of a trabecula for constructing large-scale FE
models. To test whether FE models constructed with these
elements present apparent elastic properties that are typical of
trabecular bone structures, we constructed computer models of
six orthogonal lattices{ and performed computational FE experiments of uni-axial compression of these cubic lattices. Each
lattice comprised 144 trabecular building blocks (Fig. 4a) of the
same geometry, connected at 64 junctions. The mean thickness t
values used for trabeculae in the six lattices were 86 (lower limit
{
using SolidWorks 2001
Medical & Biological Engineering & Computing 2004, Vol. 42
of the thickness range; see Fig. 3), 100, 130, 150, 186 and
283 mm (mean thickness of trabeculae at the normal human
proximal femur). Cancellous bone specimens containing trabeculae with mean thickness lower than 120 mm are considered
osteoporotic (WERNER et al., 1996), and therefore the lattices
comprising trabeculae with thicknesses of 86 and 100 mm
represent osteoporotic bone quality.
To connect adjacent trabeculae by a junction to construct 3D
lattices, we developed a junction element (Fig. 4b). The six
connection ports on a junction element (Fig. 4b) have the same
diameter as the base diameter of the attached trabeculae (tmax),
and the fillet radii between connection ports were set as tmax=3.
Fig. 4c shows a lattice constructed from trabecular building
blocks with thickness of 283 mm. As the compressive loads
applied to a face of the orthogonal lattice cube align with the
551
Fig. 2 Histograms showing distributions of trabecular (a) mean thickness, (b) length and (c) volume (estimated from (3)) in femoral epiphyses of
sheep. N ¼ 200
orientation of trabeculae, the orthogonal architecture provides
maximum structural resistance to uni-axial loading, and the
resulting structural properties should be considered ideal.
The geometries of the six lattices were transferred to an FE
software package** for analysis of structural (apparent) properties. The lattice geometries (e.g. Fig. 4c) were meshed with fournode tetrahedral elements, and the density of the meshes was
optimised by decreasing the size of elements until stable
solutions of the stress distribution under compression were
**NASTRAN 2001
552
obtained. For a model containing trabeculae with thickness of
283 mm, this was achieved when each trabecula (with tissue
volume of 0.05 mm3; see (3)) was meshed into 276 elements. It
was assumed that the tissue contained in each trabecula building
block was a homogenous, isotropic and linear elastic material,
with elastic modulus of 10 GPa and Poisson’s ratio of 0.3
(TOWNSEND et al., 1975; RHO et al., 1993; WERNER et al., 1996).
Gradually increasing compressive loads were applied quasistatically at the junctions on one face of the cube, and the
junctions on the opposite face were constrained for displacements in the direction of loading (unconfined compression).
Medical & Biological Engineering & Computing 2004, Vol. 42
r
averaged
thickness
z
The compressive loads ranged from zero to a maximum of 1.3 N
and were uniformly distributed over the joints at the loaded face,
generating a maximum pressure of 500 KPa. These pressures
caused small axial strains, of up to 0.3%. Within this stress–
strain range, all lattices behaved linearly, with a constant
proportion between the (applied) compressive load and (calculated) structural strain. This constant of proportion, the apparent
elastic modulus of the trabecular lattice, was calculated for each
thickness case.
To estimate the degradation of the apparent elastic properties of lattices when the structural arrangement is not ideal (e.g.
as a result of fracture of a trabecula or resorption of a trabecula
in osteoporotic bone), we repeated the above simulations after
mm
810
650
510
370
280
230
85
0
Fig. 3 Potential surface profiles of rod-like trabeculae in proximal
femora of humans, predicted from (2) after setting of average
thickness t and length L as 283 mm and 1000 mm, respectively
a
b
c
d
e
Fig. 4 Characterisation of elastic properties of lattices built with trabecular building block (2) and (3): (a) Volume of revolution representing
idealised geometry of trabecula with average thickness of 283 mm (mean thickness of rod-like trabeculae in human femoral neck). (b)
Junction element designed for building ideally organised lattices from building block shown in (a). (c) Ideally organised orthogonal
lattice of trabecular building blocks comprising 144 trabeculae (64 junctions). (d) Example for testing effect of disconnecting trabecula
on apparent elastic modulus of lattice. (e) Stress concentrations due to bending of trabeculae under compression in vicinity of missing
trabecula in (d). Peak stresses in circled region are 1.8 times stress value at same site, in corresponding intact lattice
Medical & Biological Engineering & Computing 2004, Vol. 42
553
4 Discussion
Fig. 5 Apparent elastic moduli Ea of ideally organised orthogonal
lattice (144 trabeculae, 64 junctions) against average thickness t of trabeculae in lattice. Ea ¼ 36.4 t0.256 (for t40);
R2 ¼ 0.98
removing a centre trabecula aligned parallel with the
direction of load (Figs 4d and e) or perpendicular to the
direction of load.
3 Results
For the lattice containing trabeculae with thickness characteristic of normal human proximal femora (283 mm), we found an
apparent elastic modulus of 151.9 MPa. We also found that a
reduction in the thickness t of trabeculae had a substantially
deteriorating effect on the apparent modulus Ea (Fig. 5). A lattice
constructed with trabeculae of the minimum thickness considered in this study, 86 mm (corresponding to our geometric and
statistical analyses of trabecular profile shapes (Fig. 3)),
produced an apparent modulus of 111 MPa (27% reduction
from the ‘normal’ condition). Overall, the reduction in moduli
with reduction in trabecular thickness could be described with a
power law (R2 ¼ 0.98)
Ea ¼ mt n
(t40)
(4)
where the constants are m ¼ 36.4 MPa and n ¼ 0.256.
When a central trabecula was removed from a lattice structure
and the lattice was loaded in the direction of the missing
trabecula, bending-related stress concentrations appeared at the
‘necks’ of neighbouring trabeculae (Fig. 4e). These focal
stresses were typically 1.8 times greater than stresses at the
same site in the intact lattice. This bending phenomenon
consistently reduced the apparent elastic moduli, by 8–9%
(Table 1). However, when a trabecula perpendicular to the
loading direction was removed from the centre of the lattice,
the apparent moduli were nearly unaffected (decreased by 1%
or less).
This study described the geometric and mechanical characteristics of an idealised trabecula element that was developed based
on empirical observations of anatomical variations in individual
ovine trabeculae. Based on experimental studies of the trabecular architecture in mammals (FAJARDO and MULLER, 2001),
we assumed that trabeculae from human and ovine proximal
femora share a similar shape.
The distributions of thickness and length of ovine trabeculae
from the femoral epiphysis (Figs 2a and b) are right-skewed
(log-normal distributions), demonstrating a large range of
intraspecimen variation in the shape and size of trabeculae.
Importantly, this statistical characterisation allowed development of an anatomically and physiologically based geometric
characterisation of the single trabecula building block ((2) and
(3) and Fig. 3). Designed for large-scale FE studies of cancellous
bone, this trabecula model ((2) and (3)) is parametric for length
and thickness and can therefore represent trabeculae in different
anatomical sites and account for the distribution of anatomical
variations in shape and size of trabeculae. The idealisations in
this model also allow large-scale generic FE analyses of
trabecular microstructures.
Constantly improving computer technology should be able to
provide the computational power for routine, patient-specific,
large-scale FE models in the future. An important advantage of
patient-specific, large-scale models is their utility in computing
patient-specific structural properties of trabecular bone (e.g.
stiffness and strength). This allows for many new, clinically
important evaluations in the diagnosis and prognosis of patients,
such as assessment of the risk of suffering an osteoporosisrelated fracture, or monitoring of the effect of a drug on the
mechanical performance of individual bones. However,
specimen-specific properties of bone may bias the conclusions
regarding large populations, because of anatomical variations or
local damage that may be included in the specific specimen.
Thus, to complement the patient-specific, large-scale type of
model, there is also a need for generic FE models of trabecular
bone.
The advantage of a generic bone model is its utility where it is
necessary to study the mechanics of a ‘typical’, rather than
specific, bone. For example, reconstruction of the trabecular
architecture of the femur using the generic trabecula element
described herein, by assembling building block trabeculae on the
trabecular paths of the femur, can provide an enhanced ‘standardised femur’ model that, unlike the existing one (VICECONTI
et al., 2003), accounts for bone architecture at the micro-scale.
Such standardised generic models are useful for preliminary
implant design, where the effect of the geometry and material
properties of the implant on the bone micro-architecture can be
simulated systematically to minimise subsequent animal studies
and clinical tests. Importantly, evaluation and improvement of
implant performances through the design process cannot be
Table 1 Apparent elastic moduli Ea of trabecular lattices (each containing 144 trabeculae) against
average trabecular thickness t. Moduli are calculated for intact lattice structures and for lattices missing
centre trabecula (Fig. 4d) parallel to direction of load or perpendicular to direction of load
554
t, mm
Ea of intact lattice, MPa
100
118.1
150
132.4
186
138.5
Direction of missing trabecula
with respect to loading
parallel
perpendicular
parallel
perpendicular
parallel
perpendicular
Ea of lattice with missing
trabecula, MPa
107.5
118.1
122.4
132
125.4
137
Medical & Biological Engineering & Computing 2004, Vol. 42
carried out using individual, subject-specific, large-scale FE
models: individual anatomy or the presence of local defects in
the specimen can lead to misinterpretation of the analysis of
mechanical performances of the bone-implant system with
regard to a population of patients. This illustrates the need for
both generic and specimen-specific bone models for practical
purposes, even when computer resources for routine, large-scale
FE modelling become available.
A literature review of experimental data reported for the
apparent elastic moduli of adult human trabecular bone from
the proximal femur (BANSE et al., 1996; LI and ASPDEN, 1997;
AUGAT et al., 1998; BROWN et al., 2002; HOMMINGA et al.,
2002; KOHLES and ROBERTS, 2002; MORGAN et al., 2003)
demonstrates that the reported properties vary by as much as
an order of magnitude. Minimum reported values are around
100 MPa, and maximal ones are in the order of 4000 MPa. Even
within individual specimens, large ranges and high standard
deviations were reported (KRISCHAK et al., 1999). This substantial variability has been attributed mainly to the inhomogeneous
trabecular bone structure (KRISCHAK et al., 1999), but discrepancies may also relate to differences in testing protocols (e.g.
specimen shape and size, specimen preparation, strain magnitudes, strain rate etc.). Nevertheless, several experimental
studies of the proximal femur (LI and ASPDEN, 1997; AUGAT
et al., 1998; BROWN et al., 2002) reported apparent elastic
moduli in the range of 100–200 MPa, which overlap the apparent
elastic modulus of our computational lattice (150 MPa) with
femoral trabeculae of normal, average thickness (283 mm).
We further compared our computed apparent modulus
(150 MPa) with values provided by other structural models.
The volume fraction Vf in our model (bone tissue volume
calculated using (3) and divided by a total lattice volume of
27 mm3) is Vf ¼ 0.267 (for trabeculae that are 283 mm thick),
which is comparable with the study of VAN RIETBERGEN et al.
(1995), who conducted FE analyses of real trabecular microarchitecture from the human tibial plateau (Vf ¼ 0.20–0.33). The
apparent moduli calculated by VAN RIETBERGEN et al. (1995)
varied between 80 and 102 MPa, which is in good agreement
with the present findings.
In contrast, for comparable Vf, our model predictions disagree
with the apparent moduli (of over 500 MPa) predicted by
WERNER et al. (1996), who used two truncated pyramids
facing each other to represent a single trabecula. Apparently,
for comparable Vf, a lattice made of truncated pyramids
(WERNER et al., 1996) is stiffer than a lattice that is constructed
with the present building blocks, which are based on real
architecture. This stresses the importance of using real trabecular
architecture in generic bone models.
Considering the results from the above experimental and
structural modelling studies together, we conclude that our
building block trabeculae are suitable for representing the
apparent elasticity of trabecular bone.
The computational lattices containing thin, osteoporotic-like
femoral trabeculae with thicknesses of 100 mm and 86 mm
provided apparent moduli that were 22% (118.1 MPa) and
27% (111 MPa) lower, respectively. This prediction is in
excellent agreement with experimental data showing a 30%
reduction in the apparent elastic modulus of osteoporotic
cancellous bone from the proximal femur with respect to
normal controls (LI and ASPDEN, 1997).
Based on these comparisons, we conclude that the singletrabecula generic element developed in the present study is well
suited for representing cancellous bone in FE simulations
of osteoporotic changes. The latter results also support
previous studies that suggested that the main cause of the loss
of mechanical quality of trabecular bone in osteoporosis is loss
of structure, rather than degradation of the properties of the
trabeculae tissue material (WERNER et al., 1996).
Medical & Biological Engineering & Computing 2004, Vol. 42
In conclusion, we have presented a new, standard, parametric
building block that is useful for large-scale FE studies of
cancellous bone. Being idealised and smooth, but also being
based on anatomical and physiological statistical data, this
trabecula model is useful for reconstructions and FE analyses
of large-scale bone models that represent ‘typical’, rather than
subject-specific bones. Orthogonal lattices built using this
building block showed structural stiffness behaviour that is
very similar to that of real cancellous bone tested with small
strains.
Studies are currently being performed by our group to develop
FE models of the trabecular structures of the calcaneus (for which
we characterised the trabecular micro-architecture in detail
(GEFEN and SELIKTAR, 2004) using this new trabecula model
as a building block. The trabecula building block will be
duplicated along polynoms that were previously fitted to the
dominant trabecular paths in the calcaneus (GEFEN and
SELIKTAR, 2004), to form two- and three-dimensional lattices
of ‘typical’ trabecular bone volumes in the calcaneus. These
generic models of regions of interest in the calcaneus will be
employed in FE studies of stresses and strains in the trabecular
micro-architecture of the calcaneus during physiological loadbearing.
Acknowledgments—This study was supported by the Ela
Kodesz Institute for Medical Engineering and Physical
Sciences and by the Internal Fund of Tel Aviv University, Israel.
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Author’s biography
AMIT GEFEN is a Lecturer in the Department of Biomedical Engineering at the Faculty of Engineering of Tel Aviv University, Israel. He
received his BSc in mechanical engineering in 1994, his MSc in 1997,
and PhD in biomedical engineering (2001) from Tel Aviv University.
During 2002–3, Dr Gefen was a post-doctoral fellow at the Injury
Biomechanics Laboratory of the Bioengineering Department at the
University of Pennsylvania. His research interests are in the study of
normal and pathological effects of mechanical factors on the structure
and function of human tissues, with an emphasis on the musculoskeletal system.
Medical & Biological Engineering & Computing 2004, Vol. 42