MEASURING SOFT TISSUE PROPERTIES USING DIGITAL IMAGE
CORRELATION AND FINITE ELEMENT MODELLING
S. L. Evans and C. A. Holt
School of Engineering, Cardiff University
The Parade, Cardiff CF24 3AA, UK
H. Ozturk and K. Saidi
Université de Franche- Comté, Besançon, France
N. G. Shrive
University of Calgary
ABSTRACT
An understanding of the mechanical properties of soft tissues such as skin, muscle and tendon is important in many
applications, such as the design of orthopaedic implants, the planning of surgical procedures or the evaluation of cosmetic
products or drugs. However, the behaviour of soft tissues is complex, highly nonlinear and poorly understood, and so the
measurement of their mechanical properties presents many difficulties. This study focuses on the measurement of the
properties of skin, which has the advantage that it can conveniently be tested in situ in a living human subject.
In many published studies simple tensile tests have been used, but these require samples to be cut from the tissue and can
only characterize the uniaxial tensile properties, whereas in vivo biaxial tension, in- plane compression and shear are also very
important. In other studies, tabs have been attached to the skin and loaded in plane, in torsion or by indentation, but the
measurements of the resulting deformation have been limited and the boundary conditions are poorly defined, so that it is
difficult to properly characterize the resulting state of strain.
Full field optical measurements offer the possibility of characterizing the full strain distribution under complex loading, and
accurately measuring the displacement boundary conditions, so that the deformation of the skin can be properly characterized.
The aim of this study was to use digital image correlation (DIC) in conjunction with a finite element model, using an ArrudaBoyce constitutive law, to identify the properties of the skin in situ in a living human subject.
It was found that although the Arruda- Boyce model can represent the uniaxial behaviour of the skin with reasonable accuracy,
the strain distribution under more complex loading was very different from that measured using DIC. In particular, the
compressive stiffness of the skin is much lower than the Arruda- Boyce model predicts due to wrinkling. A more sophisticated
constitutive model that incorporates progressive wrinkling under in- plane compression and correctly represents the shear
behaviour of the skin is needed.
The DIC technique was highly effective in measuring the deformation of the skin, and the full field strain measurements
provided valuable insights into the behaviour of the skin. This technique has great potential for characterizing the properties of
the skin and for developing better constitutive models.
Introduction
There are many possible reasons why it might be useful to model the mechanical behaviour of skin, including simulation of
impacts and injuries, modeling of equipment such as seating or razors that must interact with the skin, understanding the
development of diseases such as pressure sores and predicting the effects of treatments such as wound closure or cosmetic
surgery. In addition, it is currently very difficult to measure the mechanical properties of skin because without a satisfactory
constitutive model it is not clear which parameters should be measured, and so a constitutive model would be very useful in
measuring changes in the properties of the skin as a result of cosmetics or drug treatments, diseases or scar formation.
Despite these numerous practical applications, there have been few attempts to model the mechanical behaviour of skin,
probably due to the considerable mathematical difficulty of the problem. The mechanical properties of skin are complex and
very highly nonlinear, making it one of the m ost challenging materials to represent in a conventional mathematical framework.
The stiffness of skin varies greatly with strain, becoming much stiffer at large tensile strains, and in compression wrinkling
occurs. Large deformations occur, causing computational problems, and it is also anisotropic and viscoelastic. The properties
are highly dependent on the environment and should ideally be measured in situ in a living subject. Because of these
problems, conventional test methods are rarely appropriate or adequate in testing soft tissues, and new techniques are
required.
The general problem in characterising the properties of a material is to find a function f which relates the stresses and strains
at a point within the material:-
{σ } = f ({ε })
(1)
When testing homogenous, linearly elastic materials such as metals, the form of the function f is well known and provides a
linear relationship between the stress and strain. It is then possible to separate the calculation of the applied stresses from the
measurement of the resulting strains, and also to calculate properties such as the modulus from the average deformation over
an area of the specimen, since the deformation may be assumed to be homogenous. When testing materials which obey
more complex, as yet unknown constitutive functions, this approach is not possible. Instead it is necessary to assume an
approximate form of the constitutive function f, to measure the strain under some known load, and to use a numerical model in
which the various constitutive parameters are iteratively optimized until the numerical results match as closely as possible the
results of the experiment. Alternatively, in some cases other numerical procedures such as the virtual fields method may be
used [1], but this is difficult for soft tissues because of the very complex and highly nonlinear constitutive models that are
required.
Various experimental designs have been used, such as indentation testing [2,3], torsion testing [4], suction testing [5] and in
plane tensile loading [6]. Typically a load is applied and the resulting displacement at the loading point is measured. This
provides only a limited amount of data and it is necessary to use the whole load- displacement curve to find parameters that
correctly predict the nonlinear elastic behaviour of the material. However, the acquisition of the load- displacement curve
takes some time, during which some viscoelastic deformation occurs, and so it is difficult to separate the nonlinear elastic and
viscoelastic behaviour of the material. Additionally, some material parameters may have little effect on the overall
displacement at the load point and so cannot be accurately optimized.
The use of full field displacement measurements offers some sig nificant advantages in this type of testing. Non- contact
techniques such as digital image correlation are well suited to in vivo measurements in living subjects, and the measurement
of the whole strain field provides a wealth of information which allows much more accurate determination of the material
parameters. When the displacement at a single point is measured, it is necessary to use the whole load- displacement curve
to investigate nonlinear elastic behaviour, but if the full strain field is measured, information is available for a range of stresses
and strains for a single load point. The additional information from different points on the load- displacement curve can then be
used to determine the viscoelastic properties of the material. Another advantage of particular importance is that it is no longer
necessary to control the boundary conditions, as the displacements around the boundary of the test area can be measured
directly. This is invaluable when testing in vivo.
In this preliminary study, data was acquired for several human subjects, using in- plane loading of the skin of the forearm. A
two- dimensional finite element model was developed, using displacement data from the DIC measurements to provide
boundary conditions, and the results were compared with those of the DIC tests. In- plane loading is a useful test because it
generates tensile, compressive and shear strains in different areas around the loading point, and this allows the model to be
optimised under a variety of states of stres s. For a material such as skin, this is much more informative than simply using
tensile test data.
Experimental
Experimental data was acquired using a Vic3D (Limess GmbH, Pforzheim, Germany) digital image correlation system. Two
cameras were used, with 28 mm lenses, positioned about 0.5m from the area of measurement and giving a field of view of
about 100mm as shown in Fig. 1. Measurements were carried out on the inner forearm of healthy adult volunteers (Fig. 1); an
additional speckle pattern was applied using non- toxic paint to improve contrast and registration by the DIC system.
The skin was loaded using a fine wire attached to the skin in the middle of the field of view using adhesive tape. A 5N
precision load cell (Interface Force Measurements, Crowthorne, UK) was used to apply a load to the wire in various directions
and the load was recorded by the DIC system. Images were recorded at a frame rate of 5Hz and the load was increased and
decreased over a period of approximately five seconds.
The images were then processed using Vic3D software and selected frames were used for further analysis. The data were
exported to Matlab (The Mathworks, Inc., Natick, Massachusetts, USA) where they were cropped and interpolated to give data
for a rectangular region with the loading point on one edge. Missing data points were filled by interpolation from the
surrounding pixels.
A finite element model was used to simulate the experiment and to identify the material parameters. This model was written in
Matlab; a two- dimensional model was used in which the skin was assumed to lie in a single plane. An unaligned mesh of
identical square four node linear elements was used, together with a total Lagrangian formulation, and this allows a very
efficient solution since the B matrices which relate the nodal displacements to the strains at the Gauss points are identical for
all elements and all iterations. A single generic set of matrices can be calculated at the beginning, instead of recalculating
them for each Gauss point at each iteration. Using a regular square mesh also makes it easy to compare the results with the
DIC data. A geometrically nonlinear, large displacement formulation was used. An Arruda- Boyce eight chain constitutive
model was used, following the work of Bischoff et al [7]. The formulation of Kalliske and Rothert [8 ] was used, assuming
plane stress and that the material was incompressible. The through- thickness stretch was found from the incompressibility
condition and used to calculate the through- thickness stress, which is then equal and opposite to the hydrostatic pressure.
The boundary conditions for the model were derived from the DIC data. Along the load line, symmetry conditions were
applied, while around the other edges prescribed displacements were used based on the DIC data. The nodes in the area
covered by the adhesive tape were constrained to move together and the load recorded during the test was applied to them
(divided by two due to symmetry). The displacements recorded by the DIC system were applied to the remaining nodes as an
initial estimate of the deformation, in order to speed up the solution and avoid difficulties due to the large initial displacements.
In practice it was necessary to apply these boundary conditions in a series of small increments to avoid numerical problems.
Results
A typical contour plot showing the strain distribution superimposed on an image of the skin is shown in Fig. 2. Fig. 3 shows the
predicted strains from the FE model and the measured strains in the longitudinal (along the arm, in the loading direction),
transverse and shear directions. It is evident that that the FE model did not provide a good representation of the actual strains.
The measured strain distribution was as ymmetrical, with the compressive strain mainly confined to a small area around the
loading region. On the tensile side, there was a broad wake of tensile strain spreading out at approximately 45° to either side
of the load line, and after an initial drop the strain remained almost constant to the edge of the measurement area. There are
two main reasons for this asymmetry, firstly the occurrence of wrinkling and secondly the effects of nonlinearity and prestress
in the skin. The first of these effects is not included at all in the finite element model and the second was not well represented.
Wrinkling is likely to occur wherever the minimum principal stress in the skin becomes negative, and will reduce its stiffness in
compression. This accounts for the limited region of compressive strain, since the strain is localised in a small area due to
wrinkling. In fact some compressive strain occurred away from the loading region, and this is due to the prestress in the skin,
which means that wrinkling only occurs at larger compressive strains. On the tensile side, the minimum principal stress is
positive within a region spreading at about 45° either side of the load line, which accounts for the clearly defined wake of
tensile strain on this side.
The simple model presented here did not incorporate prestressing, and this is a major limitation. Numerical difficulties can
arise at large strains when using the Arruda- Boyce model, since in this model the stress and stiffness rise asymptotically as
the stretch approaches the locking stretch. Since this locking stretch is typically about 1.1 [7], the strain in the skin cannot
exceed about 10%, which is clearly inaccurate. In fact, the prestrain in the skin should be of the order of 10-15%.
Convergence problems can arise in the vicinity of the locking stretch due to the rapid change in stiffness and the possibility of
the stretch exceeding the locking stretch, when the stress will no longer be defined. A more effective model needs to
incorporate wrinkling and prestressing and to deal more effectively with large strains. Shergold and Fleck obtained a good
correlation between experimental and numerical results in uniaxial tension using an Ogden model [9], and this approach is
promising since it is very straightforward to incorporate wrinkling when working in the principal stretch directions.
A further point of interest is that most of the published data on skin relate to uniaxial tension. It is clear from these results that
only a small proportion of the skin is under uniaxial tension in the wrinkled areas and that the vast majority is normally in biaxial
tension. Further work is needed to understand the behaviour of skin under biaxial tension and the DIC technique provides an
ideal tool for such investigations.
Conclusions
The digital image correlation technique is invaluable in testing skin and offers new insights into the behaviour of soft tissues. A
wealth of data can be generated for in vivo multiaxial loading, without the need to rigorously control the boundary conditions.
Using linked finite element models, a vareity of parameters can be identified giving new insights into the behaviour and
properties of the tissue. Preliminary results highlight some of the limitations of existing models and indicate areas where
further research is needed, including in particular the incorporation of wrinkling and biaxial tension behaviour.
Acknowledgments
The DIC system was purchased as part of the HEFCW funded SRIF3 Structural Performance Laboratories project, and their
support is gratefully acknowledged.
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Figure 1. A typical image, as seen by
one camera. The image is divided
into a series of overlapping 21x21
pixel regions, as shown, and each of
these
is
matched
with
the
corresponding region in the other
camera’s image and in subsequent
images. This allows the shape of
the surface and its subsequent
deformation to be measured in three
dimensions.
Figure 2. The strain distribution is
found by spline fitting to the
measured displacement at each
point in the image. Here a typical
strain contour plot is superimposed
on the original image.
(a).
(b).
(c).
(d).
Figure 3. Typical strain patterns as
predicted by the finite element model
and as measured using DIC.
Images (a) and (b) show the strain in
the longitudinal direction (left to right
in these images); (c) and (d) show
the transverse strain, and (e) and (f)
show the shear strain. In each case
the first image shows the FE
prediction and the second shows the
actual measured strain distribution.
(e).
(f).