Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/jmbbm
j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 1 4 ( 2 0 1 2 ) 1 8 6 – 1 9 1
1751-6161/$ - see frohttp://dx.doi.org/10
nCorresponding autE-mail address:
Technical Note
Full-field optical deformation measurement inbiomechanics: Digital speckle pattern interferometryand 3D digital image correlation applied to bird beaks
Joris Soonsa,n, Pascal Lavab, Dimitri Debruyneb,c, Joris Dirckxa
aLaboratory of Biomedical Physics, University of Antwerp, Groenenborgerlaan 171, B2020 Antwerpen, BelgiumbDepartment of Mechanical Engineering, Catholic University College Ghent, Gebroeders Desmetstraat 1, B9000 Gent, BelgiumcDepartment MTM, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, 3001 Leuven, Belgium
a r t i c l e i n f o
Article history:
Received 15 March 2012
Received in revised form
2 May 2012
Accepted 6 May 2012
Available online 18 May 2012
Keywords:
Digital image correlation (DIC)
Digital speckle pattern
interferometry (DSPI)
Finite element modeling
Validation experiment
Beak
nt matter & 2012 Elsevie.1016/j.jmbbm.2012.05.00
hor. Tel.: þ32 32653438; [email protected] (J. S
a b s t r a c t
In this paper two easy-to-use optical setups for the validation of biomechanical finite
element (FE) models are presented. First, we show an easy-to-build Michelson digital
speckle pattern interferometer (DSPI) setup, yielding the out-of-plane displacement. We
also introduce three-dimensional digital image correlation (3D-DIC), a stereo photogram-
metric technique. Both techniques are non-contact and full field, but they differ in nature
and have different magnitudes of sensitivity. In this paper we successfully apply both
techniques to validate a multi-layered FE model of a small bird beak, a strong but very light
biological composite. DSPI can measure very small deformations, with potentially high
signal-to-noise ratios. Its high sensitivity, however, results in high stability requirements
and makes it hard to use it outside an optical laboratory and on living samples. In addition,
large loads have to be divided into small incremental load steps to avoid phase unwrapping
errors and speckle de-correlation. 3D-DIC needs much larger displacements, but auto-
matically yields the strains. It is more flexible, does not have stability requirements, and
can easily be used as an optical strain gage.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
The beaks of granivorous birds have to withstand large forces
during the crushing of seeds. The large ground finch (Geospiza
magnirostris), for instance, only weighs 30 g but can generate a
50 N bite force (pers. obs.). These birds are also constrained
by their flying lifestyle. As a result, beaks are expected to be
highly optimized, making them interesting from both a
biological and a mechanical point of view. The multi-layered
beak consists of trabecular bone in the center, surrounded by
compact bone and the keratinous rhamphotheca. Previous
r Ltd. All rights reserved4
x: þ32 32653318.oons).
studies on the java finch include morphology, ontogenesis,
material characterization and finite element (FE) modeling
(Soons et al., 2010, 2012a, in press; Genbrugge et al., 2012).
Finite element modeling has proven to be an important tool in
biomechanics (Dumont et al., 2005; Degrange et al., 2010; Groning
et al., 2009; Bright and Groning, 2012; Ross et al., 2011; Kupczik
et al., 2007). It allows us to understand complex problems. An
important step in a good FE analysis is a relevant validation
measurement. Strain gauging is a well-known and straightfor-
ward validation technique (Ross et al., 2011; Kupczik et al., 2007),
but it has some major disadvantages. Strain gauges are attached
.
Fig. 1 – Experimental setup. Top left: schematic drawing of
the digital speckle pattern interferometry (DSPI) setup.
Bottom left: schematic drawing of the digital image
correlation (DIC) setup. Inset: the skull and jawbones of a
java finch are constrained in a sample holder, filled with
polyester resin. The seed reaction force is simulated by an
indentation at the tip of the upper beak.
j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 1 4 ( 2 0 1 2 ) 1 8 6 – 1 9 1 187
to the sample, which may influence the measurement. The
installation is also time-consuming and difficult, especially on
small and complex structures such as the beak of finches.
Moreover, the strains can only be obtained on a small number
of measurement locations. These issues can be overcome by
using optical techniques. In this paper, we will show two easy-
to-build full field methods: out-of-plane digital speckle pattern
interferometry (DSPI), also known as electronic speckle pattern
interferometry (ESPI), and digital image correlation (DIC). The
main goal of this paper is to test their applicability in validating
FE analysis derived results. Both techniques will be assessed by
measuring the bending of the java finch’s upper beak and by
comparing it with FE model results. The presented techniques,
however, are applicable in a wide range of biomechanical
problems.
Both techniques rely on speckles. The nature of the speck-
les is, however, completely different. In DSPI a speckled
image is obtained by diffuse reflections of coherent light
on a rough surface. The reflected light will have the same
frequency, but different phases and amplitudes caused by the
random microscopic height variations. When added together,
the resultant amplitude, and therefore intensity, will vary
randomly. As a result, a speckled pattern is observed.
DSPI is an interferometric setup. If the speckle pattern from
an object is combined with a reference beam, a complex
interference pattern is obtained. After the deformation of the
object, phase differences are introduced in this complex
interference pattern. These phase differences can be linked
to the displacement. If the displacement is measured in three
different directions, and the surface shape is known, one can
calculate the surface strains. The very high sensitivity (sub-
wave length resolution) makes it a valuable tool for non-
destructive testing. The sensitivity is independent of the pixel
size. The pixel size determines the number of phases that can
be resolved and as such the maximum permissible displace-
ment. The high sensitivity requires sub-wavelength stability
and makes it difficult to apply this technique outside the
optical lab or in vivo. Recently, DSPI has been introduced in
biomechanics. Some examples are found in literature, includ-
ing the displacement of the tympanic membrane (Del Socorro
Hernandez-Montes et al., 2009), the strains on human and
macaque tooth (Zaslansky et al., 2005, 2006; Barak et al.,
2009a, 2009b; Chattah et al., 2011) on human bones (Barak
et al., 2009a, 2009b), the mouse femur (Yang et al., 2007), the
ovine callus (Bottlang et al., 2008), the human mandible
(Groning et al., 2009) and zygomatic arch of the pig (Bright
and Groning, 2012).
DIC, on the other hand, is a photogrammetric setup. The
speckled pattern is physically applied to the object. Coordi-
nates of points, labeled by the randomly applied stochastic
(speckled) pattern are captured with a camera and identified
with a computing intensive image correlation. These points
are followed when the object is deformed and displacements
are acquired with sub-pixel resolution. Three-dimensional
surface results can be acquired using a stereo camera system.
The optical setup is straightforward and there are no inter-
ferometric stability requirements, making this technique
easy-to-use, scalable, highly usable for applications outside
the lab and for measurements in biomechanics. Increasing
computer power has made the technique more popular
(Schmidt et al., 2003) and has recently resulted in biomecha-
nical applications: including strain measurements on human
bone and tendon (Tyson et al., 2002), on mouse arteries
(Sutton et al., 2008) and on mouse bone (Sztefek et al., 2010).
2. Material and methods
2.1. Bending experiment
It is difficult to constrain the bite position and to apply the
(muscle) forces to the tiny jaw bones of the java finch’s upper
beak, especially if interferometric stability is required. Hence we
work the other way around and propose a bending experiment
to mimic tip biting on a seed (inset in Fig. 1). In this experiment
the jaw bones and the skull are constrained in a sample holder
filled with cured polyester resin (VIAPAL 223BS/65). A seed
reaction force is introduced with a stepper motor (steps of
16 nm per motor step, range 2 mm, PI M-235.2DG) at the tip of
the beak and the precise force is measured with a loadcell
(Sensotec 31, 5 N and 50 N range). Two java finches were used
for the bending experiment: one for DIC and one for DSPI.
Those beaks were approximately 15 mm in length and the
difference in length and width were smaller than 10%. Lower
j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 1 4 ( 2 0 1 2 ) 1 8 6 – 1 9 1188
beak, feathers, muscles and brains were removed. The resin
was allowed to cure for a minimal time of 48 h. The study was
performed according to the regulations of the Ethical Commit-
tee for Animal Experiments of the University of Antwerp. More
information about this bending experiment and the sample
preparation can be found in Soons et al. (2012a, in press).
2.2. Finite element model
A third java finch was imaged at the European Synchrotron
Radiation Facility (ESRF, Grenoble) (image matrix of 2 kpx�
2 kpx with a resolution of 45 mm). Bone and keratin were
segmented semi-automatically (Amira 4.1; 64-bit version, TGS
systems) and a multi-layered volumetric grid, consisting of a
bony core surrounded by a keratin layer, was established (as
described in Soons et al., in press). This FE mesh of the beak
was subsequently scaled to the same dimension as the upper
beaks used in the bending experiments. Boundary conditions
were chosen in order to simulate the mechanical loading: a
loading force in the z-direction, depending on the measured
reaction force, was applied at the bite position, and the
embedding in polyester resin (Fig. 1) was simulated by con-
straining elements of the jaw bones and the beginning of the
skull. The Poisson’s ratio for bone and keratin was chosen to
be 0.4 (Franck et al., 2006, Wroe, 2008). The Young’s modulus
for avian bone and dry keratin are 7.3 GPa and 3.1 GPa,
respectively (Soons et al., 2012a). All FE analyses were con-
ducted in FEBio, a FE program designed for the mechanical
analysis of biological structure (Maas and Weiss, 2008).
2.3. Digital speckle pattern interferometry
A He–Ne laser (l¼632.8 nm) was expanded with a telescopic
lens with spatial filter (Fig. 1, top). Next, a Michelson setup,
placed on a vibration-isolated table, was used to illuminate
the top of the upper beak in the bending experiment and a
reference plate. Interference patterns of both were combined
and captured with a telecentric camera (AVT pike F-505,
2048�2452 pixels, resulting in a 8 mm pixelsize). A displace-
ment of 5 mm was introduced with the stepper motor. Corre-
lation between the undeformed and deformed interference
pattern gave the full field out-of-plane displacement (w).
With the beak in undeformed state, four phase-shifted inter-
ferograms were recorded by translating the reference plate in
subsequent steps of an eighth of the light wavelength. From
these four undeformed interferograms and one interfero-
gram recorded in the deformed state, the object deformation
can be calculated with high precision (720 nm). The deriva-
tive of the out-of-plane displacement (z) was calculated. For
the characterization of bending, this value seems to be more
useful than just the out-of-plane displacement. Indeed, the
derivative of a rigid body movement, which is not interesting
from a mechanical point-of-view, yields a constant and can
be easily neglected (Leendertz and Butters, 1973). The corre-
sponding FE model boundary conditions are estimated based
on photos of the experimental setup. More information about
this technique can be found in Soons and Dirckx (2010) and
Soons et al. (2012a).
The coefficient of determination (R-squared) is calculated to
compare DSPI with FE modeling results (Soons et al., 2012a, in
press). For this comparison, the derivative of the out-of-plane
displacement along the x-direction is considered for all visible
points, except for the bending area and some noisy parts. If the
experiment and model results coincide, an R-squared of 1
is obtained. R-squared values smaller than 0 indicate that
the model prediction is less accurate than the mean of the
experimental data.
2.4. Digital image correlation
A Stereo system with two cameras (AVT pike F-505, 2048�2452
pixels, Smc Pentax bellows lens 1:4 100 mm, f/32, resulting in
a 7 mm pixelsize and a field of view of 14�17 mm2) with an
opening angle of approximately 301 is used (Fig. 1, bottom).
Polarized light is used to illuminate the sample. As a conse-
quence, polarizers in front of the camera can be used to reduce
specular reflections. Automatic system calibration was con-
ducted before and after the actual measurements using various
images of a translated and rotated regular grid pattern within a
bundle adjustment technique (Triggs et al., 2000). As a result,
intrinsic (focal lengths, distortions and image plane center
location) and extrinsic (rotation and translation) camera para-
meters were obtained.
Four stereo images were taken, two before and two after the
125 mm displacement. In the first step, the initial undeformed
shape was reconstructed by finding the corresponding speckles
in the images captured by camera 1 and camera 2 and via a
triangulation method invoking the determined stereo camera
parameters (Lava et al., 2011). Next, a similar procedure was
applied to the images of the deformed state. Finally, a direct
comparison of the deformed (x,y,z) and the undeformed
(x0,y0,z0) shape yields the 3D deformation coordinates (u,v,w).
These contain all the information needed to determine the in-
plane normal and shear strain components (ex,ey,exy).
The following settings were used in the displacement deter-
mination: a subset size of 21 pixels, a step size of 10 pixels,
correlation algorithm, bicubic interpolation and affine shape
functions. Strains were calculated in the Green–Lagrange con-
vention and a strain window of 50�50 pixels2 and a bilinear
interpolation was taken. Results are transformed into the
coordinate system of camera 1 (Fig. 3), which is aligned parallel
to the direction of the punch force. Accordingly, the correspond-
ing FE model can be easily transformed to the same coordinate
system. DIC requires the presence of a random pattern on the
specimen. This is applied by air brushing on top of the upper
beak (pattern can be seen in Figs. 2 and 3). The influence of this
pattern is expected to be minimal due to the stiff keratin and
bone. All calibration and correlation are executed in the
MatchID software package (in-house developed: http://www.
matchid.org/).
3. Results
The full-field out-of-plane displacements (w) obtained with
DIC and DSPI are shown in Fig. 2 (left). The results presented in
this paper are from a single measurement. Repetition of the
experiment shows a very small variation for the displacement
measurement of both DSPI and DIC. The variation for the
derivatives (and strains) was larger due to the induced noise.
Fig. 2 – Left: out-of-plane displacement (w) for DIC (top) and DSPI (bottom). Notice the different magnitude in displacement:
80 lm for DIC (reaction force¼5.5 N) and 3 lm for DSPI (reaction force¼0.21 N). Right: derivative of the out-of-plane
displacement (w) along the x-direction (longitudinal cross-section indicated at the left), normalized to the reaction force for
DIC (top) and DSPI (bottom), compared to FE results.
Fig. 3 – Strains (ex: 1st row, ey: 2nd row, exy: 3rd row) measured with DIC (1st column) and calculated from FE model (2nd
column). Cross-sectional results are shown in the 3rd (longitudinal, dashed line in 2nd column) and 4th column (transversal,
dotted line in 2nd column). DIC results are presented with the continuous lines, FE results with the dashed lines.
j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 1 4 ( 2 0 1 2 ) 1 8 6 – 1 9 1 189
Multiple measurements will improve the signal-to-noise ratio
(Soons et al., in press). We did not combine measurements to
show the capability of both techniques. The precision and
accuracy are described by comparing the experiments with the
FE results. For DSPI, the measured displacement at the tip of
beak was approximately 3 mm and a reaction force of 0.21 N
was obtained. In contrast, for DIC a 25 times larger displace-
ment (80 mm at the tip) and reaction force (5.5 N) were
obtained. The sub-wavelength sensitivity of DSPI is approxi-
mately 20 nm, independent of the pixel size used. On the other
hand, the sensitivity for DIC is highly scalable. For our setup,
an out-of-plane displacement precision of approximately 1 mm
and an in-plane of 0.5 mm was found.
Next, the derivative of this out-of-plane displacement (w)
along the x-direction was taken. The longitudinal cross-sections
obtained with DSPI and DIC, normalized to the reaction force, are
presented in Fig. 2 (right) and compared with the corresponding
FE models. A full field R-squared of 0.89 between DSPI and FE
was calculated on the entire visible surface, except for some
noisy locations (Soons et al., in press). For DIC, the results were
noisier, so a larger window was used to calculate the derivatives
and a lower R-squared of 0.52 was obtained.
Besides the displacement in the z-direction, DIC also yields
the coordinates (x,y,z) of the surface and the displacement
(u,v,w) at every (visible) point. As a result, we can obtain the
strains (ex, ey, exy) over this surface. The full field results of the
j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 1 4 ( 2 0 1 2 ) 1 8 6 – 1 9 1190
strain, compared with their corresponding FE results, are
presented in Fig. 3. A qualitative examination indicates a fairly
good correspondence between model and experiment, except
for a noisy part at the left side of the upper beak.
A quantitative comparison for the longitudinal and transversal
(Fig. 3) cross-sections shows a good correspondence. Maximal
strains in both experiment and model are approximately 3000
microstrain. A good correspondence is found for ex. The quite
uniformly negative values for ex indicate an almost uniform
compression at the top of the beak of approximately 1000
microstrain. For in vivo bite forces, which are expected to be
approximately 2 times larger, strains about 2000 microstrain are
expected. This compression is a result of the bending. More
towards the edge of the beak, the bending becomes smaller and
so do the ex value (Fig. 3, 1st row, 4th column). For x-values
smaller than 2, a larger deviation is observed (Fig. 3, 1st row, 3rd
column). We believe that this deviation is a local error, caused by
the modeling approach of the bending zone. The results for eyshow positive strains, thus an extension in the y-direction, on
top of the upper beak. A deviation, probably due to noise,
between experiment and model is observed for y smaller than
3 mm. The shear strain exy shows, except for the same noisy
part, good correspondence in the transversal direction (Fig. 3, 3rd
row, 4th column). The longitudinal results (Fig. 3, 3rd row, 3rd
column), however, show some offset towards the tip of the beak.
This deviation is, in our opinion, due to the use of two different
samples, resulting in a misalignment.
4. Discussion
The two optical techniques, digital speckle pattern interfero-
metry (DSPI) and digital image correlation (DIC), were achieved
with an easy experimental setup (Figs. 2 and 3). The results for
DIC, DSPI and FE were obtained on three different specimens.
As a result, intra-specific variation between the specimens is
neglected and a direct comparison is difficult. Nevertheless, a
qualitative comparison between the experimental techniques
and the modeling outcome shows good correspondence.
DIC requires the presence of a random pattern on the
specimen. This coating can influence the results on compli-
ant materials or if one is interested in dynamical behavior.
DSPI only needs a coating if the reflection is low or to avoid
specular reflections. On macroscopic irregular surfaces one
needs to avoid ‘shadow’ artifacts. For 3D-DIC, this means that
every point has to visible by both cameras. In out-of-plane
DSPI, shadow artifacts are easily avoided by the perpendicu-
lar laser illumination and viewing direction. Nevertheless, if
one wants to obtain in-plane displacements with DSPI, one
also needs to take these shadow artifacts into account.
The derivative of the out-of-plane displacement along x,
normalized to the reaction force (d(w/F)/dx) was shown to be a
good parameter to describe the bending (Leendertz and Butters,
1973). Indeed, a rigid body movement will introduce a constant
factor. This additional factor is neglected in our analysis because
an offset is expected due to an approximation near the bending
zone. The normalization to the force, allows us to compare the
two experimental techniques. The reaction force and the
induced displacement of DSPI are 25 times smaller than DIC.
This large difference is caused by the different sensitivities of
both optical techniques. Indeed, large displacements for DSPI
will cause phase unwrapping and de-correlation errors, while for
DIC, too small displacements cannot be captured on camera.
The normalization requires a linear behavior of the sample. This
assumption is reasonable, because the reaction forces of 0.21 N
for DSPI and 5.5 N for DIC are below the natural maximum bite
force of 9.0 N (Soons et al., in press). A good correspondence is
found between the FE model and the DSPI results (R2¼0.89). As a
consequence, this measurement can be used in an inverse
analysis to obtain values for the elastic modulus of bone and
keratin (Soons et al., 2012a). It should be noted that the signal-to-
noise ratio, and thus the R-squared, will drop drastically if the
interferometric stability is not met. Some important require-
ments for a good stability are the use of an optical table and
dehydrated samples. The dehydrated state is easily obtained
during the 48 h curing of the resin. After this curing period, the
deformation did not change significantly. The lower coefficient of
determination between DIC and FE modeling (R2¼0.52) is caused
by a noisier result, but, as can be seen in Fig. 2, a reasonable
correspondence was obtained. DIC does not need high stability
requirements and can be used without an optical table and on
fresh samples. In future research, we plan to use it in vivo.
Another major advantage of DIC over DSPI, besides its robust-
ness, is the possibility to acquire full 3D coordinates and
displacements in one single measurement. Hence, surface
strains (ex,ey,exy) can be calculated. It should be mentioned that
one could combine three or more DSPI measurements so one
could also obtain 3D displacements (e.g. Yang et al., 2007; Bright
and Groning, 2012). The strains, measured with DIC and calcu-
lated with FE, are shown in Fig. 3. A good qualitative agreement,
and a reasonable quantitative agreement is observed for all the
strains and DIC can be a simple alternative for strain gauges. We
plan to make a full quantitative comparison, by calculating
R-squared values between DIC and FE strains. In this way, an
inverse analysis should be possible (Soons et al., 2012a).
5. Conclusions
In this paper we presented two easy-to-use optical setups for the
validation of FE models. DSPI is a very sensitive (20 nm) inter-
ferometric setup that makes it possible to measure very small
deformations (sub-micron). As a result it can be used for non-
destructive testing. Its high sensitivity, however, makes it difficult
to use outside the lab and for in vivo experiments. DIC is less
sensitive (1/10 of the pixelsize), but much more robust, so it
allows us to do in vivo experiments and it can easily be used for
full 3D displacement measurements. In addition, the technique
is highly scalable. One just needs to apply a speckle pattern on
the surface and capture the deformation with two cameras. As a
result, we suggest that DIC is the preferred technique to measure
the deformation on bird beaks and by extension in a lot of other
biological structures. In future, we plan in vivo measurements.
Acknowledgments
Financial support to this project is given by the Research
Foundation–Flanders (FWO). We thank F. Wiese for his tech-
nical assistance and J. Peacock for English proofreading.
j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 1 4 ( 2 0 1 2 ) 1 8 6 – 1 9 1 191
r e f e r e n c e s
Barak, M.M., Geiger, S., Chattah, N.L.-T., Shahar, R., Weiner, S.,2009a. Enamel dictates whole tooth deformation: a finiteelement model study validated by a metrology method.Journal of Structural Biology 168 (3), 511–520.
Barak, M.M., Sharir, A., Shahar, R., 2009b. Optical metrologymethods for mechanical testing of whole bones. VeterinaryJournal 180 (1), 7–14 (London, England, 1997).
Bottlang, M., Mohr, M., Simon, U., Claes, L., 2008. Acquisition offull-field strain distributions on ovine fracture callus cross-sections with electronic speckle pattern interferometry. Jour-nal of Biomechanics 41 (3), 701–705.
Bright, J.A., Groning, F., 2012. Strain accommodation in thezygomatic arch of the pig. A validation study using digitalspeckle pattern interferometry and finite element analysis.Journal of Morphology (published online).
Chattah, N.L.-T., Kupczik, K., Shahar, R., Hublin, J.-J., Weiner, S.,2011. Structure–function relations of primate lower incisors: astudy of the deformation of Macaca mulatta dentition usingelectronic speckle pattern interferometry (ESPI). Journal ofAnatomy 218 (1), 87–95.
Degrange, F.J., Tambussi, C.P., Moreno, K., Witmer, L.M., Wroe, S.,2010. Mechanical analysis of feeding behavior in the extinct‘terror bird’ Andalgalornis steulleti (Gruiformes: Phorusrhacidae).PloS ONE 5 (8), e11856.
Del Socorro Hernandez-Montes, M., Furlong, C., Rosowski, J.J.,Hulli, N., Harrington, E., Cheng, J.T., Ravicz, M.E., Santoyom,F.M., 2009. Optoelectronic holographic otoscope for measure-ment of nano-displacements in tympanic membranes. Jour-nal of Biomedical Optics 14 (3), 034023.
Dumont, E.R., Piccirillo, J., Grosse, I.R., 2005. Finite-element ana-lysis of biting behavior and bone stress in the facial skeletonsof bats. The Anatomical Record Part A: Discoveries in Mole-cular, Cellular, and Evolutionary Biology 283 (2), 319–330.
Franck, A., Cocquyt, G., Simoens, P., De Belie, N., 2006. Biomecha-nical properties of bovine claw horn. Biosystems Engineering93 (4), 459–467.
Genbrugge, A., Herrel, A., Boone, M., Van Hoorebeke, L., Podos, J.,Dirckx, J., Aerts, P., Adriaens, D., 2012. The head of the finch: theanatomy of the feeding system in two species of finches (Geospizafortis and Padda oryzivora). Journal of Anatomy. http://dxdoi.org/10.1111/j.1469-7580.2011.01437.x (published online).
Groning, F., Liu, J., Fagan, M.J., O’Higgins, P., 2009. Validating avoxel-based finite element model of a human mandible usingdigital speckle pattern interferometry. Journal of Biomecha-nics 42 (9), 1224–1229.
Kupczik, K., Dobson, C.a., Fagan, M.J., Crompton, R.H., Oxnard, C.E.,O’Higgins, P., 2007. Assessing mechanical function of the zygo-matic region in macaques: validation and sensitivity testing offinite element models. Journal of Anatomy 210 (1), 41–53.
Lava, P., Coppieters, S., Wang, Y., Van Houtte, P., Debruyne, D.,2011. Error estimation in measuring strain fields with DIC onplanar sheet metal specimens with a non-perpendicularcamera alignment. Optics and Lasers in Engineering 49, 57–65.
Leendertz, J., Butters, J.N., 1973. An image-shearing speckle-pattern interferometer for measuring bending moments. Journalof Physics E—Scientific Instruments 6, 1107–1110.
Maas, S., Weiss, J.A., 2008. FEBio: Finite Elements for Biomecha-nics, User’s Manual, version 1.0. Online Publication /http://mrl.sci.utah.edu/software/febioS.
Ross, C.F., Berthaume, M.A., Dechow, P.C., Iriarte-Diaz, J., Porro,L.B., Richmond, B.G., Spencer, M., Strait, D., 2011. In vivo bonestrain and finite-element modeling of the craniofacial haft incatarrhine primates. Journal of Anatomy 218 (1), 112–141.
Schmidt, T., Tyson, J., Galanulis, K., 2003. Full-field dynamicdisplacement and strain measurement using advanced 3d imagecorrelation photogrammetry: part 1. Experimental Techniques 27(3), 47–50.
Sztefek, P., Vanleene, M., Olsson, R., Collinson, R., Pitsillides, A.A.,Shefelbine, S., 2010. Using digital image correlation todetermine bone surface strains during loading and afteradaptation of the mouse tibia. Journal of Biomechanics 43(4), 599–605.
Soons, J., Dirckx, J.J.J., 2010. Full field displacement and strainmeasurement of small complex bony structures with digitalspeckle pattern interferometry and shearography. In: Proceed-ings of the SPIE—The International Society for Optical Engi-neering, 2010, pp. 73870C (10 pp).
Soons, J., Herrel, A., Aerts, P., Dirckx, J.J.J., 2012a. Determination andvalidation of the elastic moduli of small and complex biologicalsamples: bone and keratin in bird beaks. Journal of the RoyalSociety Interface 9 (71), 1381–1388.
Soons, J., Herrel, A., Genbrugge, A., Adriaens, D., Aerts, P., Dirckx, J.J.J.Multi layered bird beaks: a finite-element approach towards therole of keratin in stress dissipation. Journal of the Royal SocietyInterface, http://dx.doi.org/10.1098/rsif.2011.0910, in press.
Sutton, M.A., Ke, X., Lessner, S.M., Goldbach, M., Yost, M., Zhao, F.,Schreier, H.W., 2008. Strain field measurements on mousecarotid arteries using microscopic three-dimensional digitalimage correlation. Journal of Biomedical Materials Research.Part A 84 (1), 178–190.
Triggs, B., Mclauchlan, P., Hartley, R., Fitzgibbon, A., 2000. Bundleadjustment—a modern synthesis. In: Triggs Bill, ZissermanAndrew, Szeliski Richard (Eds.), Vision Algorithms.Springer, Berlin.
Tyson, J., Schmidt, T., Galanulis, K., 2002. Biomechanics deforma-tion and strain measurements with 3d image correlationphotogrammetry. Experimental Techniques 26 (5), 39–42.
Wroe, S., 2008. Cranial mechanics compared in extinct marsupialand extant African lions using a finite element approach.Journal of Zoology 274, 332–339.
Yang, L., Zhang, P., Liu, S., Samala, P.R., Su, M., Yokota, H., 2007.Measurement of strain distributions in mouse femora with3D-digital speckle pattern interferometry. Optics and Lasers inEngineering 45 (8), 843–851.
Zaslansky, P., Shahar, R., Friesem, A.A., Weiner, S., 2006.Relations between shape, materials properties, and function inbiological materials using laser speckle interferometry: in situtooth deformation. Advanced Functional Materials 16 (15),1925–1936.
Zaslansky, P., Currey, J.D., Friesem, A.A., Weiner, S., 2005. Phaseshifting speckle interferometry for determination of strainand Young’s modulus of mineralized biological materials:a study of tooth dentin compression in water. Journal ofBiomedical Optics 10 (2), 024020.