Methodology to Produce Specimen-Specific Models of Vertebrae: Application to Different Species
Methodology to Produce Specimen-Specific Models of Vertebrae: Application to Different Species
FERNANDO Y. ZAPATA-CORNELIO 0 1
GAVIN A. DAY 0 1
RUTH H. COE 0 1
SEBASTIEN N. F. SIKORA 0 1
VITHANAGE N. WIJAYATHUNGA 0 1
SAMI M. TARSUSLUGIL 0 1
MARLE` NE MENGONI 0 1
RUTH K. WILCOX 0 1
0 School of Mechanical Engineering, Institute of Medical and Biological Engineering, University of Leeds , Leeds LS2 9JT , UK. Electronic mail:
1 School of Mechanical Engineering, Institute of Medical and Biological Engineering, University of Leeds , Leeds LS2 9JT , UK
-Image-based continuum-level finite element models have been used for bones to evaluate fracture risk and the biomechanical effects of diseases and therapies, capturing both the geometry and tissue mechanical properties. Although models of vertebrae of various species have been developed, an inter-species comparison has not yet been investigated. The purpose of this study was to derive speciesspecific modelling methods and compare the accuracy of image-based finite element models of vertebrae across species. Vertebral specimens were harvested from porcine (N = 12), ovine (N = 13) and bovine (N = 14) spines. The specimens were experimentally loaded to failure and apparent stiffness values were derived. Image-based finite element models were generated reproducing the experimental protocol. A linear relationship between the element grayscale and elastic modulus was calibrated for each species matching in vitro and in silico stiffness values, and validated on independent sets of models. The accuracy of these relationships were compared across species. Experimental stiffness values were significantly different across species and specimen-specific models required species-specific linear relationship between image grayscale and elastic modulus. A good agreement between in vitro and in silico values was achieved for all species, reinforcing the generality of the developed methodology.
Bone elastic modulus; Image-based model; Sensitivity analysis; Finite element analysis; In silico models
Over the last decade, the use of specimen- and
subject- specific finite element models of spinal
vertebrae has become more widespread to evaluate fracture
risk14 and the biomechanical effects of diseases and
therapies.21,27,45 These models are usually based on
computed tomography (CT) or micro-CT data,
enabling both geometrical and material property
information to be derived from the images. In many cases,
the elastic modulus is derived on an
element-by-element basis using the image data within each element
For continuum-level models, where the element
sizes are larger than the individual trabeculae, a number
of approaches have been adopted to determine the
elastic modulus and other material properties from the
image data.30 In some cases, an average grayscale is
determined from the voxels within the element volume
and the elastic modulus is derived by assuming a
relationship to this grayscale value (i.e. by assuming
that the modulus is related to the bone density and the
density related to the grayscale).6,9,18,23,44,48 In other
cases, the trabecular architecture and bone volume
fraction within each element volume are used to derive
the elastic behaviour, which may include anisotropic
effects based on the fabric tensor.5,35 Regardless of the
method used, the relationships between the image
information and the material parameters need to be
derived. Many of these relationships originate from
experimental tests on bone samples, whilst some have
also been determined by reverse engineering sets of
vertebral finite element models to fit corresponding sets
of experimental test data.20 A number of different
forms of equation have been proposed, but for
vertebral bone under physiological loads, linear
relationships have been shown to be as accurate as non-linear
relationships,48 provided the associated constants have
been optimally adjusted.
Experimentally, a wide range of animal models are
used in bone research to investigate disease progression
or the effect of interventions including (but not limited
2017 The Author(s). This article is an open access publication
to) rodents (mouse and rat3,38,42,46), rabbits,2,15,16,43
dogs,8,19,22,25 pigs,37,41,47 sheep12,26,33,49 and goats.7,24,51
Peric et al.36 summarised the similarity of animal models
to human bone based on macro- and micro-structure,
composition and remodelling, and placed the pig model
as the closest animal (non-primate) model to human
bone, followed by dogs and sheep. Rodents and rabbits
on the other hand, scored low in similarities related to
the macrostructure and composition, which is not
surprising as both species lack a Haversian system, have
permanently open growth plates and their size and
shape differ from human bones.36 Similar animal
models have been reported in the use of spinal
research,11 with bovine, ovine and porcine being
amongst the commonest models used.1
Specimen-specific finite element models have
therefore been based on a number of different species, to
allow direct comparison with experimental data and to
assess variability or the potential for remodelling.
Because of the variation in bone mineral density across
species, and the differing ages of animal used, it is
likely that the material properties for bone derived
from CT images require calibration for each different
species. Although finite element studies of different
species have been developed, there has yet to be a
comparison across multiple species to evaluate how
these relationships differ.
The aim of this study was therefore to derive
species-specific modelling methods and compare the
accuracy of image-based finite element models of
vertebrae across species.
Combined experimental and computational
approaches previously described44,45,48 were used to
develop specimen-specific finite element models of
bovine, ovine and porcine vertebrae. The models of
each species were divided into calibration and
validation sets and the calibration sets used to derive a linear
relationship between the element grayscale and elastic
modulus. The parameter values and accuracy of the
relationships were then compared across species.
MATERIALS AND METHODS
Specimen Preparation, Imaging and Mechanical Testing
Mature ovine (3–5 years old), juvenile porcine (24–
26 weeks old) and sub-adult bovine (2–2.5 years old)
spines obtained from a local abattoir were used in this
study. The specimens were harvested to isolate the
bone from other tissues, yielding the following:
thirteen ovine vertebrae coming from the cervical (N = 4)
and thoracic regions (N = 9), twelve porcine vertebrae
from the thoracic (N = 7) and lumbar (N = 5) regions
and fourteen bovine vertebrae from the coccygeal
region (N = 14).
The samples were mounted in PMMA cement
endcaps to enable flat surfaces on which to apply
load.45 A delrin fiducial marker was incorporated in
the endcap to locate the position of the applied load.
The ovine and porcine specimens were imaged using a
lCT scanner (lCT, Scanco Medical AG, Switzerland)
at an isotropic voxel size of 73.6 lm, energy settings
114 lA, 70 kVp and 300 ms exposure time. Bovine
specimens were imaged using a HR-pQCT (XtremeCT,
Scanco Medical AG, Switzerland) at an isotropic voxel
size of 82 lm, energy settings 900 lA, 60 kVp and
300 ms exposure time. Each specimen was axially
compressed in a material testing machine (Instron 3365
with a 10kN load cell, Instron, UK). The load was
applied to the specimens via a stainless steel ball and
loading plate, enabling the upper endplate to rotate. A
pre-load of 50 N was initially applied, followed by
cyclic loading with a maximum load of 300 N. The
specimens were then loaded at rate of 1 mm/min and
compressed until failure or reaching the safety limit of
the load cell (9.8 kN). Load–displacement data was
used to derive the maximal experimental stiffness of
each specimen, calculated as the largest slope over a
moving average of 0.6 mm aperture.
Finite Element Modelling
All specimens were modelled with a
specimenspecific approach. The geometry of each specimen was
built from the 3D scan data. The CT images were
truncated to remove any negative values, and the result
was consistently normalised to a 0–255 grayscale
(8bit) using a bespoke script
(MATLAB R2014b, The
MathWorks, Inc., Natick, MA, US)
. Images obtained
from the HR-pQCT were converted to lCT equivalent
images (see Appendix). The images were
down-sampled to an isotropic 1 mm resolution, using a partial
volume effect algorithm, and segmented to isolate the
bone from the cement endcaps in Simpleware ScanIP
v7.0 (Synopsys, Mountain View, USA).
Morphological operations were used to produce continuum-level
masks. The segmented images were meshed with a mix
of linear tetrahedral and hexahedral elements of
uniform size matching the down-sampled voxel size,
yielding models with 79–515 thousands elements. The
bone tissue was modelled with Hooke elasticity, using
element-specific elasticity moduli (Eele) dependent of
the average grayscale value for the element (GSele):
Eele ¼ aGSeleðGPaÞ
where a is a conversion factor determined separately
for each species.44,45,48 A Poisson’s ratio of 0.3 was
used. The cement was modelled with Hooke elasticity
with a modulus of 2.45 GPa and Poisson’s ratio of
Boundary conditions replicating the experimental
tests were applied: the bottom surface of the lower
endcap was clamped and a rigid plane tied to the upper
surface of the upper endcap was defined to model the
loading plate. A 1 mm translation in the axial direction
was applied to the rigid plane centred on the location
of the load application marker; translations in the
other directions were restricted and rotations were kept
free to replicate the experiment.
Within each species, the specimens were arbitrarily
divided into two groups. The first group was used for
calibration of a for each species (porcine and ovine
N = 6; bovine N = 8 specimens), the second group for
validation (porcine and bovine N = 6; ovine N = 7
specimens). A golden section search scalar
optimisation process using the Brent method4 was used to
derive the conversion factor a on the calibration group.
The opti4Abq toolbox28,29 using the Brent method
implementation in SciPy (Python Software
Foundation, v2.7, www.python.org) was used in this work.
The objective function was the root mean square
normalised difference (RMSE) between experimental
specimen stiffness and the corresponding finite element
stiffness. The optimisation process was terminated
when the objective function or its variation reached a
threshold set at 0.1. All finite element analyses were
Non-Linear quasi-static and run in parallel with
Abaqus 6.14 (Simulia, Dassault Syste` me, London,
UK). Models were run on a standard desktop
computer and each model solved under 5 min.
The degree of anisotropy (DA), trabecular
orientation and bone volume fraction (BV/TV) were
calculated for six specimens of each species using BoneJ
1.4.210 together with Fiji/ImageJ 1.51 g.39 A region of
interest (ROI) was selected by fitting the largest
possible cylinder within the trabecular bone between the
two endplates, with its axis parallel to the superior/
inferior axis. Trabecular orientation was calculated as
the deviation (in degrees) of the MIL fabric tensor17
principal eigenvector with respect to the
After testing for normality and outliers with a
Shapiro–Wilk test, the experimental stiffness values,
degree of anisotropy, trabecular orientation and BV/
TV values were compared between species using a
Kruskal–Wallis test and post hoc Wilcoxon
signedrank test. The agreement between the in silico predicted
stiffness values and the in vitro measured stiffness
values was assessed using concordance correlation
coefficients (CCC). All statistical analysis were
performed using statistical software R.3.2.3 (R foundation
for statistical computing, Vienna, Austria).
The data associated with this paper (lCT images,
mechanical testing results, model input files, and all
processed outputs) are openly available from the
University of Leeds Data Repository.50
A statistically significant difference in in vitro
stiffness values was observed between species (p =
6.38 9 1026), for all paired test (porcine vs. bovine,
p = 0.046; porcine vs ovine, p = 2.57 9 1025; bovine
vs ovine, p = 1.19 9 1026). The lowest in vitro stiffness
observed was for the bovine specimens (mean 5.3 kN/
mm, st.d. 0.7 kN/mm), followed by porcine (mean 5.8
kN/mm, st.d. 0.42 kN/mm) and ovine (mean 8.4 kN/
mm, st.d. 1.34 kN/mm) specimens; see Fig. 1. The
load–displacement curves for typical specimens are
shown in Fig. 2. Porcine specimens showed a clear
non-linear behaviour with a marked toe-region while
bovine specimens exhibited relatively linear behaviour
For the imaging conditions and computational
methodology presented, the optimisation yielded
converged conversion factor a values of 0.00726 GPa for the
bovine tissue, 0.00904 GPa for porcine and 0.00971 GPa
for ovine. The stiffness RMSE was below 16% for each
calibration group (Table 1), with the highest local
relative error (one ovine specimen) being 25.9% (see Fig. 3).
Using each of the species-specific conversion factors on
the corresponding validation sets yielded a RMSE
below 22% for all groups, with the highest relative error for
an individual specimen (ovine) being 37.5%.
Good agreement between in vitro and in silico
stiffness values was achieved for bovine specimens
(CCC = 0.6193), while it was lower for ovine
(CCC = 0.2356) and porcine (CCC = 0.3902)
The results of the morphology analysis are presented
in Table 2, with significant variation between species in
the DA (Kruskal–Wallis test, p = 4.18 9 1025; porcine
vs. bovine, p = 1.55 9 1024; porcine vs. ovine,
p = 1.55 9 1024; bovine vs. ovine, p = 3.10 9 1024),
and the ovine vertebrae showing the highest anisotropy.
There was a significant difference between species in the
BV/TV values (Kruskal–Wallis test, p = 0.0066). The
post hoc test revealed that this difference was observed
only for the porcine vs. bovine pair (Wilcoxon test,
p = 0.0029).
For all specimens, the trabecular orientation was
mainly aligned with the superior/inferior axis, (mean
deviation of 2.2 , st.d 1.1 for ovine; mean 3.6 , st.d
1.6 for bovine; mean 8.4 , st.d 10.8 for porcine).
There was a significant difference between species in
the trabecular orientation results (Kruskal–Wallis test,
p = 0.01231) and the post hoc test revealed that this
difference was observed only for the porcine vs. ovine
pair (Wilcoxon test, p = 0.004662) and the ovine vs.
bovine pair (Wilcoxon test, p = 0.04988). Table 2
shows examples of the bone plugs analysed in 2D and
A previously developed methodology was used for
the generation of specimen-specific finite element
models of vertebrae from lCT data, and for the
determination of the grayscale to Young’s modulus
conversion factors for each species. The models were
validated against corresponding experimental
compression tests for porcine, ovine and bovine tissue.
Results showed significant differences between each of
the tested species, in their experimental behaviour, in
the assessment of their morphology, and in the
conversion factor needed to produce finite element models
with good agreement.
The low error on the stiffness values for the
validation sets was of the same order of magnitude as for
the calibration sets, it is thus fair to conclude that, for
the tested conditions and in silico methodology, this is
a valid modelling approach to represent the vertebral
apparent stiffness in axial compression.
All tested groups showed a good agreement between
in silico and in vitro stiffness values, however a varying
degree of concordance was observed. This may be a
reflection of the variation and spread of the stiffness
values seen within each of the different groups, where
the ovine specimens have the largest range of values
and the largest RMSE.
Of the many factors that could explain the
difference seen between the conversion factors for different
species, most can be grouped around properties either
not captured in lCT scans or not present within the
finite element models. Of the first type, the lCT does
not allow for any distinction in the type of interstitial
marrow or other tissues. It is likely that the
preparation protocol, from the moment of slaughter in the
abattoir to the testing of the specimen in the
laboratory, generates different states of these tissues, with
more or less clotted blood within the samples, and
more or less marrow content depending on the species.
Other tissues include the growth plate, a cartilaginous
tissue softer than bone, of which the size depends on
the maturity level of the specimens used. The
interstitial tissue and growth plates, however, are averaged
either in the trabecular or cortical space grayscale
value and its stiffness variation is not at all accounted for
in the computational models. Finally, the ovine
specimens showed the largest error and also presented with
the largest range of stiffness values in the experimental
data. This is mainly due to the difference in size
between the cervical (N = 4) and thoracic (N = 9)
vertebrae, for which the cervical vertebrae exhibited a
lower stiffness. It is possible that considering different
conversion factors for different vertebral level to
account for differences in the underlying tissue
properties would improve the error.
Regarding the properties not included in the
computational models, some of the details relating to the
internal geometry of the vertebrae are lost when
downsampling the images. Information such as the
trabecular direction, the ratio of cortical bone to trabecular
bone (the cortical shell thickness), and to some extent
the bone volume fraction (BV/TV) and level of
mineralisation, is all merged into the grayscale of the image
underlying each element. Interspecies variation in these
properties may be a factor in the variation of the
conversion factor across species. In particular, the
degree of anisotropy (DA) varied significantly between
species, with the porcine bone containing the most
isotropic trabecular structure and the ovine tissue
containing the most anisotropic trabeculae. This
increased trabecular orientation, with more trabeculae
aligned axially, gives an increased stiffness in axial
compression for the ovine vertebral bodies, which also
shows a higher conversion factor. However, given the
lack of correlation between the DA and the conversion
factor, other properties may explain the variation
across species, such as BV/TV. For instance, the
reduced bone volume fraction for bovine vertebrae is due
to areas devoid of trabeculae within the vertebral body
which possibly explains its low value for the conversion
factor, despite the relative alignment of its trabecular
network with the loading direction.
The conversion factor a calculated for each species
is valid only when used with 8-bit grayscale images
generated from the lCT 100 and the scanning settings
described in the specimen preparation section, thus
making the value of a dependent on the equipment and
settings used to scan the specimen. A calibration
method was developed to enable the conversion of
8bit images generated from HR-pQCT to lCT
equivalent images, with an acceptable degree of accuracy (see
Appendix). This provides a framework to reuse our
method to develop in silico vertebrae tests regardless of
the equipment or scanner settings (i.e. resolution) when
used within reasonable limits.
LIMITATIONS AND CHALLENGES
The finite element models were built using linear
material models and non-linear geometrical effects.
Using such material models allows only a
representation of the linear part of any load–displacement
behaviour. Within human vertebrae however, the linear
portion of the in vitro load–displacement curve
correThe ROI was selected by fitting the largest possible cylinder within the trabecular bone between the two endplates.
sponds to the physiologically relevant loading
regime.31,32,34,40 The material models does not allow us
to represent the full non-linear experimental behaviour
observed for all species in this study. There is no clear
indication whether the non-linearity at low
displacements is mainly a material non-linearity or whether it is
linked to the experimental setup and the interactions
between different components.
The results of this study suggest that there is not a
universal conversion factor that can be applied to
derive vertebral bone elastic modulus from the image
grayscale. Across species tested, the conversion factor
increased with increasing vertebral stiffness, but the
relationship was not linear and the number of species is
not enough to draw a concrete conclusion. Higher
levels of accuracy in the FE predictions could be
achieved by further narrowing the specimen choice
(e.g. to a particular spinal region), but would clearly
then limit the application of the derived conversion
factor. The values presented here are valid only for
ovine tissue from mature animals, porcine tissue from
juvenile animals and bovine tissues from sub-adult
animals, and for vertebral bone submitted to axial
compression, and imaged and meshed following a
prescribed methodology. In particular, the tissue
preparation will affect the results, as will the image
resolution and imaging method. These will change how
the bone density is represented in the images that the
models are built from. Moreover, the type and size of
mesh elements in the computational models will
influence the results. The methodology however can be
extended to other tissue preparation and model
development steps with appropriate calibration
This study showed that the methodology for
generating specimen-specific vertebral finite element
models previously developed for a given species can be
translated to other species, but without a universal
value of grayscale to elasticity modulus conversion.
This single parameter includes a large range of
properties and varies from species to species. However,
when care is taken to ensure specimen preparation
reproducibility, and phantoms are used to convert
image data from one lCT system to another, then
there is no reason why the conversion factor
established in a given in vitro and in silico environment
should not be re-used for other tests. In particular, in
the present case of vertebral bone or models that
incorporate several vertebral joints can use the
conversion factors derived in this work.
APPENDIX: IMAGE CONVERSION:
It is known that the range of grayscale values of an
image generated from CT equipment is machine
dependent.13 For this study, a calibration methodology
was generated for the conversion of the images
generated from a HR-pQCT (XTremeCT, Scanco
Medical, Switzerland) to images that could be comparable
to a set of images from a lCT system (microCT100,
Scanco Medical, Switzerland).
A lCT phantom with five known density zones (0–
800 mg HA/cm3) was scanned in both machines and
the images were converted to 0–255 grayscale
following the methodology described in this work. Each
density zone was segmented for both sets of images
and an average grayscale value for each density was
calculated in an image processing package (Simpleware
ScanIP v7.0, Synopsys, Mountain View, USA). A
linear relation between average grayscale values and the
densities was derived for each imaging facility. From
this, a linear relation between the original HR-pQCT
image and the equivalent lCT one was derived,
enabling the conversion of HR-pQCT images to lCT
images (lCT equivalent or lCT-E images). Pearson’s
coefficients were calculated to verify the linearity of the
In order to validate this methodology, three bovine
vertebrae from the coccygeal region were scanned in
both CT machines and the HR-pQCT images were
converted to lCT-E images using the described
methodology. Finite element models were generated
from both lCT and lCT-E set of images keeping all
other parameters constant. The stiffness results were
compared between lCT and lCT-E models.
The grayscale values varied almost perfectly linearly
with the known density values of the phantom in both
imaging facilities (Fig. 4a). There was a perfect linear
correlation between grayscale values of both scanning
machines (Fig. 4b).
The computational stiffness from the models
obtained using lCT-E were over-estimated by about
5% when compared to model generated from lCT
images (Table 3).
For the equipment used in this study, it was found
that a linear relationship could be used to create lCT
equivalent images from the HR-pQCT modality
provided it was calibrated using the same phantoms.
The error in stiffness values calculated from
computer model using lCT-E images were acceptable and
the methodology can thus be used to convert lCT
equivalent images and FE models based on these
This work was Funded through EPSRC Grants EP/
K020757/1, EP/G012172/1, EP/L014823/1 and EP/
F010575/1 and ERC Grant StG-2012-306615.
CONFLICT OF INTEREST
There is no conflict of interest in this study.
This article is distributed under the terms of the
Creative Commons Attribution 4.0 International
which permits unrestricted use, distribution, and
reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons license, and
indicate if changes were made.
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