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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 ] ( ] ] ] ] ) ] ] ] – ] ] ]

1751-6161/$ - see frohttp://dx.doi.org/10.1

nCorresponding autE-mail addresses:

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Please cite this aMechanical Behav

Simulating the three-dimensional deformation ofin vivo facial skin

Cormac Flynna,n, Andrew J. Tabernerb,c, Poul M.F. Nielsenb,c, Sidney Felsa

aDepartment of Electrical and Computer Engineering, University of British Columbia, 2366 Main Mall, Vancouver BC, V6T 1Z4 CanadabAuckland Bioengineering Institute, The University of Auckland, 70 Symonds Street, Auckland, New ZealandcDepartment of Engineering Science, The University of Auckland, 70 Symonds Street, Auckland, New Zealand

a r t i c l e i n f o

Article history:

Received 29 October 2012

Received in revised form

1 March 2013

Accepted 5 March 2013

Keywords:

In vivo

Facial skinConstitutive modellingParameter identificationAnisotropy

nt matter & 2013 Elsevier016/j.jmbbm.2013.03.004

hor. Tel.: þ1 604 822 9081;cormacf@ece.ubc.ca (C. Flc.nz (P.M.F. Nielsen), ssfels

rticle as: Flynn, C., et aior of Biomedical Materi

a b s t r a c t

Characterising the mechanical properties of human facial skin is a challenging but importantendeavour with applications in biomedicine, surgery simulation, forensics, and animation. Manyexisting computer models of the face are not based on in vivo facial skin deformation data butrather on experiments using in vitro facial skin or other soft tissues. The facial skin of five

volunteers was subjected to a rich set of deformations using a micro-robotic device. The force–displacement response was recorded for each deformation. All volunteers' facial skin exhibited anon-linear, anisotropic, and viscoelastic force–displacement response. We propose a finiteelement model that simulated the experimental deformations with error-of-fits ranging from11% to 23%. The skin was represented by an Ogden strain energy function and a quasi-linearviscoelastic law. From non-linear optimisation procedures, we determined material parametersand in vivo pre-stresses for the central cheek area of five volunteers and five other facial points onone volunteer. Pre-stresses ranged from 15.9 kPa to 89.4 kPa.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

A good knowledge of the mechanical behaviour of facial skin isessential to many fields of study. It aids in the development ofaccurate face models, which are used in the prediction ofmaxillofacial surgical outcome (Levine et al., 2012; Marchettiet al., 2011). Improved surgical techniques gleaned from suchmodels could lead to reduced scarring and improved functionresulting in a better quality of life for the patient. For victims ofsevere burn injuries, accurate measurement of facial skinmechanical properties could be used to develop realistic pros-theses, which mimic the deformation of real skin (Gunay et al.,2008; Hatamleh and Watts, 2010).

There is a relative dearth of experimental data in the literatureto determine appropriate material parameters for facial skinconstitutive models. Existing models use experimental data from

Ltd. All rights reserved.

fax: þ1 604 822 5949.ynn), a.taberner@auckland.@ece.ubc.ca (S. Fels).

l., Simulating the three-als (2013), http://dx.doi.o

in vitro facial skin data (Barbarino et al., 2009), in vivo forearmskin data (Wang and Yang, 2009), tongue data (Nazari et al., 2010),or rabbit skin data (Beldie et al., 2010; Chabanas et al., 2003;Gladilin and Ivanov, 2009). It is well known that the mechanicalproperties of skin vary according to location on the body, species,and whether the skin is tested in vivo or in vitro (Fung, 1993;Wilkes et al., 1973). Therefore, there is a strong need to provide anin vivo facial skin experimental dataset for model parameterdetermination.

Many previous in vivo facial experiments use a protocol thatapplies suction to an area of skin and the resulting deformationis measured (Barbarino et al., 2011; Couturaud et al., 1995;Malm et al., 1995; Ohshima et al., 2011; Tsukahara et al., 2004).A variation on this approach blows air normal to the facialsurface of interest and measures the deformation (Fujimura et al.,2008). The drawback of these approaches is that an axisymmetrical

ac.nz (A.J. Taberner),

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

Fig. 1 – (a) Schematic of experimental apparatus;

(b) Boundary ring attached to the right central cheek

area of volunteer.

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loading is applied and so it is not possible to measure anyanisotropic characteristics. Ohshima et al. (2011) used a Revisc-ometer® (CourageþKhazaka electronic GmbH, Cologne, Germany)to measure anisotropic facial skin properties. However, thisapproach relates the wave speed in skin to its Young's modulus,thus ignoring the non-linear stress-strain characteristics of skinunder large deformations (Wilkes et al., 1973). Human skin is anon-linear, anisotropic, and viscoelastic material (Daly, 1982; Silveret al., 2001), so any experimental protocol to measure facial skinproperties should be able to characterise these phenomena. Flynnet al. (2011b) conducted in vivo experiments to characterise themechanical properties of skin on different points of volunteers'arms. The rich set of data from these experiments was used togenerate material parameters for computer models of skin (Flynnet al., 2011a).

Many recent facial models are based on the finite elementmethod (Barbarino et al., 2009; Beldie et al., 2010; Nazari et al.,2010). While, most of these models accurately represent anato-mical features such as the skull, jaw, and soft tissues, they alsomake several assumptions with respect to facial skin. Almost allfacial models in the literature assume the skin to be an isotropic,elastic material (Barbarino et al., 2009; Nazari et al., 2010) andsome assume skin to have a linear stress–strain curve (Beldieet al., 2010; Gladilin et al., 2004; Gladilin and Ivanov, 2009). Nofacial model considers the in vivo tension inherent in living skin, aparameter that is important in wrinkling phenomena (Cerda,2005; Flynn and McCormack, 2008). The in vivo tension field isalso an important factor in the determination of the shape andorientation of a surgical incision (Borges and Alexander, 1962;Cavicchi et al., 2009). In surgical simulators, computer facemodels, which include an initial stress field representing thein vivo tension, would be more effective as a training tool forsurgeons. Recent approaches using the finite element methodtreat the in vivo tension or strain as a model parameter in additionto the material parameters and determine it using non-linearoptimization techniques (Bischoff et al., 2000; Evans and Holt,2009; Flynn et al., 2011a). Flynn et al. (2011a) demonstrated thatapplying out-of-plane as well as in-plane deformations to the skinimproves the determinability of the material parameters andin vivo tension.

Skin is a complex non-linear, anisotropic, and viscoelasticmaterial and, so in order to make meaningful predictions, facialskin models must take these characteristics into account (Wilkeset al., 1973). The objective of this study is to determine materialparameters that best match the results of finite element analysesto the results of in vivo facial skin deformation tests. In addition tomaterial parameters, estimates of the in vivo skin tension will alsobe made. Specific parameters will be determined for the centralcheek area of five volunteers, and five other facial points of onevolunteer. The parameters determined in this study will be of useto anyone interested in computer face models.

2. Materials and methods

2.1. In vivo facial experiments

The experimental apparatus consists of a force-sensitive micro-robot, a support plate upon which the face of the volunteer isrested, and a boundary ring, which is attached to the volunteer's

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

face (Fig. 1). Details of the micro-robot can be found in Flynn et al.(2011b). To summarise, it consists of three parallel axes, eachdriven by a voice-coil actuator, which move a probe situated on aplatform. An arrangement of force transducers underneath theprobe allow the three-dimensional force vector applied to theprobe tip to be measured. A LabVIEW software interface (NationalInstruments, Austin, USA) controls the motion of the probe andrecords the position and force data.

The support plate was 10 mm thick with a central hole andkeyhole slot. The micro-robot probe was centred within the45 mm diameter hole by positioning a frame with cross-hairsconcentrically over the hole. The support plate was then posi-tioned such that the cross-hairs were located over the centre ofthe probe.

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

Table 1 – Prescribed deformations to the surface of theskin. The parameters are defined in Fig. 2.

Deformation θ (1) φ (1) d (mm)

In-plane 0–330 0 1.2–1.4

Out-of-plane 0, 45, 90 45 1.2–1.4

Normal 0 90 1.4

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The inside diameter of the boundary ring was 35 mm and itsoutside dimensions were such that it fit into the central hole onthe support plate. The key on the boundary ring and the keyholeslot on the support plate matched. This ensured that when thering was positioned into the hole on the support plate with thevolunteer's face attached, the orientation of the volunteer's facewith respect to the micro-robot probe was known.

Five volunteers were recruited for this study. Ethical approvalfor the study was granted by the University of Auckland HumanParticipants Ethics Committee (Reference Number 2010/093).All volunteers gave informed consent to participate. All volunteerswere male and their mean age was 26 years with a standarddeviation of 6 years. The youngest volunteer was 22 years and theoldest volunteer was 36 years.

In the first test, the boundary ring was attached to the centralcheek area of the right side of the face using double-sided tape(Fig. 1(b) and Fig. 2(a) labelled CC). The volunteer rested his headon the support plate with the boundary ring slotting into thecentral hole on the support plate. The 4 mm diameter cylindricalprobe of the micro-robot was attached to the skin with liquidcyanoacrylate adhesive. The probe was moved such that the skinwas subject to a rich set of three-dimensional deformation cycleswith a frequency of 0.1 Hz. Following Flynn et al. (2011b), threetriangular-wave cycles were performed to precondition the skin.The probe was first moved in the plane of the skin surface in adirection 01, which is defined in Fig. 2(a) and (b). The angle of thein-plane displacement was then increased in steps of 301 up to3301. Next, a series of out-of-plane deformations was applied. Theprobe was moved within planes oriented 01, 451, and 901, andnormal to the surface of the face (Fig. 2(a)). The final deformationmoved the probe in a direction normal to, and away from, thesurface of the skin. The prescribed probe displacements aredetailed in Table 1. The displacement, and reaction force on theprobe was measured and recorded for all tests. The time at whicheach data point was measured was also recorded.

The test was repeated for one volunteer on five more points onthe face to compare the behaviour of skin in different regions ofthe face (Fig. 2(b) and (c)). These locations were at the centre ofthe right-hand jaw (CJ), on the right-hand cheek near the lips

Fig. 2 – (a) Probe displacement parameters; d is the magnitude o

were tested and axes orientation; (c) Forehead test location and

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

(NL), the right-hand parotideomasseteric region (NE), and theright-hand zygomatic region (ZYG), and the centre of the forehead(FH). For one volunteer, all the tests were repeated several timesto assess the repeatability and variability of the results.

2.2. Finite element model

ANSYS Version 14.0 (Canonsburg, PA, USA) was used for the finiteelement analyses. The skin model consisted of a square domain ofside 50 mm with two circular partitions (Fig. 3). The largercircular partition represented the inner circumference of theboundary ring, which was attached to the volunteer's face duringthe experiment. Its diameter was 37.5 mm. The smaller circularpartition represented the area of contact between the skin andthe 4 mm diameter cylindrical probe used in the experiments. Theorientation of the global X–Z axes with respect to facial pointstested are defined in Fig. 2 and Fig. 3. A secondary coordinate axesX′ and Y′ was defined, which was rotated α degrees about theglobal Z axis from the global X and Y axes. The pre-stress(described later) was applied along the X′ and Y′ directions.α was 301 for all simulations of the central cheek area exceptVolunteer 4, where α was 601. α was 301 for all points of the faceexcept the forehead (FH) and near lip (NL) regions, where α was01. The domain was meshed using 2600 quadrilateral shellelements (SHELL181). This element has four nodes with threetranslational and three rotational degrees of freedom at each nodeand linear interpolation is used within the element. The use ofshell elements follows previous studies on skin (Evans, 2009;Flynn et al., 2011a). The implications of representing the facial

f the probe displacement; (b) Locations on the right face that

axes orientation.

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

Fig. 3 – Finite element model of the in vivo facial skin experiment.

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skin using a single flat layer of shell elements are detailed in theDiscussion. The thickness of the shell elements was 1.5 mm,which is within the range reported for skin thicknesses ofdifferent points on the face (Ha et al., 2005). The resolution ofthe mesh was such that doubling the mesh density did not have asignificant effect on the model results of interest, namely the totalreaction force of the nodes in the probe region.

The analysis consisted of two load-steps. In the first load-step, Edge 1 (specified in Fig. 3) was fixed in the Y′ direction andEdge 2 was fixed in the X′ direction. All four edges were fixed inthe global Z direction. A stress field representing the in vivotension in human skin was implemented by applying a stress sXalong Edge 4 and a stress sY along Edge 3. The stresses wereapplied during a period of 5 s. The load-step was solved as astatic analysis using the default convergence criteria. In this case,convergence was achieved when the l2-norms of the force andmoment imbalances were less than 0.5% of the l2-norms of theapplied restoring forces and moments. After the load-step wassolved, the stretch of the domain in the X′ and Y′ directions wascalculated. Using the stretch information, the geometry of thecircular partitions were scaled and the domain remeshed suchthat when the load-step was rerun, the diameter of theboundary-ring partition was 37.5 mm and the diameter of theprobe partition was 4 mm.

For the second load-step, all the nodes outside the boundary-ring partition were fixed in all degrees-of-freedom. This repre-sented the situation in the in vivo experiments where the skinsurface outside the boundary ring was prevented from movingusing double-sided adhesive tape. The nodes inside the proberegion were displaced and rotated in accordance to the displace-ment and rotation of the probe during the in vivo experiments.The total reaction force on the nodes in the probe region werecalculated and recorded for the full loading cycle.

2.3. Constitutive model

Following Flynn et al. (2011a) and Evans and Holt (2009), the skinwas represented using the isotropic Ogden strain energy function,which is given by

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

W ¼ ∑N

i ¼ 1

μiαiðλαi1 þ λαi2 þ λαi3 Þ þ

1diðJ−1Þ2 ð1Þ

where N, μi, αi, and di are material parameters; λ1, λ2, λ3 arethe principal stretches; and J is the volume ratio. In this study,the case where N¼2 was investigated and di was specified as0.0 kPa−1 to give incompressible behaviour.

The viscoelastic characteristics of skin were modelled usingthe quasi-linear viscoelastic (QLV) approach proposed by Fung(1993). Here, the stress at time t is

TðtÞ ¼ TeðtÞ þZ t

0Teðt−τÞ

∂gRðτÞ∂τ

dτ ð3Þ

where T is the total Cauchy stress tensor, Te is the elastic Cauchystress tensor, and gR(t) is the reduced relaxation function and isrepresented by a Prony series

gRðtÞ ¼ 1−gP1ð1−e−t=τG1 Þ ð4Þ

where gP1 and τG1 are material parameters.

2.4. Material parameter identification

We found the parameter values that best fit the model response tothe pre-conditioned experimental data using nonlinear optimisationtechniques. In addition to optimising μi, and αi, the initial stress in theX′ and Y′ directions sX and sY were also optimised. Following Flynnet al. (2011a), gP1 was fixed at 0.8 and τG1 was fixed at 0.4 s such thatthe hysteresis level in the model matched the hysteresis levelmeasured in the experiments. We used the lsqnonlin function inMATLAB Version 2012a (The MathWorks, Inc., Natick, MA, USA),which minimises the following objective function in a least-squaressense using a trust-region method

FðxÞ ¼ ∑M

i ¼ 1∑Ni

j ¼ 1

RmodelXj ðxÞ−Rexp

Xj

maxðRexpXj Þ

!2

þRmodelYj ðxÞ−Rexp

Yj

maxðRexpYj Þ

!224

þRmodelZj ðxÞ−Rexp

Zj

maxðRexpZj Þ

!235 ð5Þ

where M is the number of probe directions in the experiment(16 in the current study), Ni is the number of data points recorded

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

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for the ith probe direction, and x is a vector representing the modelparameters. Rmodel

Xj ðxÞ, RmodelYj ðxÞ, and Rmodel

Zj ðxÞ are the probe reactionforces in the global X–Z directions calculated from the model. Rexp

Xj ðxÞ,RexpYj ðxÞ, and Rexp

Zj ðxÞ are the measured experimental probe reactionforces in the X–Z directions at the jth datapoint.

A custom Matlab script assembles and executes the requiredANSYS input files. Upon completion of the analyses and post-processing, the Matlab script reads the results and the objectivefunction in Eq. (5) is calculated. The lsqnonlin function adjuststhe material parameters and pre-stresses. Updated ANSYS inputfiles with the adjusted model parameters are then assembledand executed. This iterative process continues until the objectivefunction of Eq. (5) achieves a local minimum.

We found optimised sets of model parameters that best fit themodel data to the sets of volunteer-specific in vivo data of the centralcheek area. The in-plane and out-of-plane deformation data setswere used in the objective function of Eq. (5). These deformationswere defined by the angles θ and φ, the probe displacementmagnitude d (Fig. 2(a) and Table 1). Model parameters were alsofound that provided the best-fit of the model data to the in vivo dataof other points of one volunteer's face (Fig. 2(b) and (c)). For eachoptimised parameter set, the error-of-fit was calculated as

A sensitivity analysis of the material parameters was alsoconducted. Starting with the simulated forehead skin deformation

Error-of -f it ¼∑M

i ¼ 1∑Ni

j ¼ 1

ðRmodelXj ðxÞ−Rexp

Xj =maxðRexpXj ÞÞ þ ðRmodel

Yj ðxÞ−RexpYj =maxðRexp

Yj ÞÞ þ ðRmodelZj ðxÞ−Rexp

Zj =maxðRexpZj ÞÞ

h i

∑M

i ¼ 1∑Ni

j ¼ 1

ðRexpXj =maxðRexp

Xj ÞÞ þ ðRexpYj =maxðRexp

Yj ÞÞ þ ðRexpZj =maxðRexp

Zj ÞÞh i ð6Þ

in the direction defined by θ¼301 and φ¼01, each optimisedparameter value was increased by 10%. The resulting reactionforce–displacement curve was plotted and the percentage changein the maximum probe reaction force calculated.

3. Results

The typical force–displacement response for in-plane and out-of-plane facial skin deformations was non-linear, anisotropic, and

Fig. 4 – Sample results from two different tests on the central che

response; (b) Probe reaction force for 1 mm probe displacement

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

viscoelastic. Repeated testing of the central cheek area of onevolunteer resulted in similar force–displacement responses forcorresponding deformations in each test (Fig. 4(a)). The force at1.0 mm in-plane probe displacement followed a similar trendfor both tests (Fig. 4(b)) with the stiffest response along the1501–3301 axis.

For all five volunteers, the force–displacement response for in-plane and out-of-plane deformations of the central cheek areawas non-linear and viscoelastic (Fig. 5). There was a largevariation in the stiffness of the response for the volunteers. Theforce–displacement response for all volunteers was also aniso-tropic. For each volunteer, the stiffest in-plane response was alongthe 1501–3301 or 1201–3001 axis (Fig. 6). The in-plane force–displacement response was least stiff along the 601–2401 axis orthe 301–2101 axis for all volunteers. The out-of-plane responsewas also anisotropic with the stiffest response for all but onevolunteer occurring when the probe was displaced in the {θ¼451;φ¼451} direction.

All six facial locations exhibited non-linear, viscoelastic, andanisotropic characteristics (Fig. 7). For the CC, CJ, NE and ZYG, thein-plane force–displacement response was stiffest approximatelyalong the 1501–3301 axis and least stiff approximately along the601–2401 axis (Fig. 8). At the NL and FH locations, the in-planeresponses were stiffest along the 01–1801 axis and least stiff along

the 901–2701 axis.The non-linear optimisation procedure determined the sets of

volunteer-specific material parameters and pre-stressesthat best fit the experimental data (Table 2). The correspondingpre-strain was also determined and ranged from 0.10 to 0.33. Thefinite element model simulated the non-linear force–displace-ment response observed in the experiments, as well as theanisotropic and viscoelastic characteristics (Fig. 5). The mechan-ical response of the central cheek area of five volunteers wassimulated with error-of-fits ranging from 12% to 23% (Table 2).

ek area of one volunteer: (a) Out-of-plane force displacement

in different in-plane directions.

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

Fig. 5 – Comparison of experimental and model force–displacement response of central cheek area of five volunteers subject

to rich set of deformations. Volunteer #1 (a) and (b); Volunteer #2 (c) and (d); Volunteer #3 (e) and (f); Volunteer #4 (g) and (h);

Volunteer #5 (i) and (j);

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Material parameters and in vivo pre-stresses were also deter-mined for the six different areas of the face of one volunteer(Table 3). The finite element model simulated the force responseto the rich set of deformations applied to the different points ofthe face with error-of-fits ranging from 16% to 23% (Fig. 7).

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

There was a broad range in the sensitivity of the force–dis-placement response of the model to the model parameters (Fig. 9).For the direction defined by θ¼301 and φ¼01, increasing α2 by10% resulted in an increase in the maximum probe reaction forceby 132%. The force–displacement response was least sensitive to

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

Fig. 6 – In-plane force reaction at 1.1 mm displacement for

all volunteers.

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μ2 with only a 4% increase in the maximum force (Rmax) afterincreasing that parameter by 10%.

4. Discussion

Quantifying the mechanical response of human facial skin is animportant undertaking with many uses. Computer face modelapplications are becoming so complex and sophisticated that theyrequire material parameters to simulate the anisotropic andinelastic characteristics of facial skin in addition to its nonlinearstress–strain behaviour (Tepole et al., 2012; Zoellner et al., 2012).State of the art tissue engineering techniques can generatereplacement skin to repair major burns, chronic ulcers, and giantnevi (Wood, 2012). These techniques also require mechanicalcharacterisation data from in vivo experiments and computermodels so that the engineered skin has the appropriate mechan-ical properties for the area that it is replacing.

This study presented experimental data of the in vivo force–displacement response of the facial skin of five volunteers subjectto a rich set of deformations. The results demonstrated goodrepeatability of the method. All volunteers' facial skin exhibited anon-linear, anisotropic, and viscoelastic response. The resultsrepresent a significant improvement over previous facial skindata where either the anisotropic characteristics of facial skinwere not measured or the non-linear stress–strain response wasignored (Barbarino et al., 2011; Ohshima et al., 2011).

The finite element model simulated the force-response ofdifferent volunteers with error-of-fits ranging from 12% to 23%.The corresponding material parameters determined using the non-linear optimisation procedure varied considerably with, for example,m1 ranging from 35.97 kPa to 60 kPa. The model had a similaraccuracy (16% to 23%) and similar wide range of material parametervalues (m1 from 41.29 kPa to 65.00 kPa) when simulating thedeformation of different regions of one volunteers face. No otherstudy in the literature used the Ogden model to simulate humanfacial skin. Barbarino et al. (2011) used the Rubin-Bodner model anda second order reduced polynomial equation. Nazari et al. (2010)used a Mooney–Rivlin model, while Gladilin and Ivanov (2009) use a

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

linear elastic model with an assigned Young's modulus. The materialparameters presented here are different from the material para-meters that best-fit the in vivo arm skin deformation data of Flynnet al. (2011a). In that study, m1 values were lower and ranged from14 kPa to 34 kPa, α1 and m2 were within the range presented in thecurrent study, and α2 values were higher ranging from 38 to 54.(Note that the m values in Flynn et al. (2011a) need to be convertedbecause a different form of the Ogden model was used.) The interand intra-volunteer material parameter variation demonstrates theneed to measure the mechanical response of different points of theface of many volunteers, especially when developing volunteer-specific models.

To the best of the authors' knowledge, there are no reportedmeasurements of in vivo tension on facial skin in the literature.The calculated in vivo tensions in this study ranged from 15.9 kPato 89.4 kPa, which are similar to the range reported in Flynn et al.(2011a) for arm skin. The corresponding pre-strains ranged from0.06 to 0.33. Flynn et al. (2011a) reported pre-strains ranging from0.05 to 0.45 in arm skin, while Evans and Holt (2009) reported apre-strain of 0.2 in forearm skin.

While the stiffness of each volunteer's facial skin in the centralcheek area was different, the anisotropic characteristics were verysimilar. The direction of stiffest response in-plane for all volun-teers was approximately along the 1501–3301 axis (Fig. 6). Thedirection of least stiffness was orthogonal to this axis. Thedirection of stiffest response would approximately correspondwith the direction of the relaxed skin tension lines (RSTLs) in thecentral cheek region according to Borges (1984). The RSTLs are thedirections of the greatest tension when the skin is at rest. It is also inagreement with the anisotropic measurements of Ohshima et al.(2011) in the central cheek region. The directions of stiffest responsein the jaw, near the ear, and zygomatic regions are also along the1501–3301 axis and correspond to the direction of the RSTLs in theseregions. Similarly, near the lips the direction of stiffest response isalong the 01–1801 axis and approximately corresponds with thereported direction of RSTLs in this region. For the forehead region,the direction of stiffest response is approximately along the 01–1801direction, which is orthogonal to the RSTLs in this region butcorresponds to the direction of the Langer lines (Langer, 1978).Langer lines represent the orientations of the long axes ofelliptically-shaped wounds, which are a result of puncturing theskin of cadavers with an awl or spike. Langer lines are similar toRSTLs in most regions on the body but they differ on the face.

The boundary ring used in the experiment isolated the facialskin of interest somewhat from the surrounding skin andprovided a well-defined boundary condition for the finite elementmodel. It is possible that underlying soft tissue layers andconnections had an effect on the force–displacement response.It is assumed that the relatively small displacement of the probeminimised these effects. However, there was some asymmetryobserved in the force–displacement response (Fig. 6 and Fig. 8),which could be attributed to underlying tissue connections. Thisis particularly evident in the force–displacement response in thezygomatic region, where the skin is attached to the maxilla via thezygomatic ligament (Furnas, 1989). Also, the simulated out-of-plane force–displacement response was not stiff enough in somecases (Fig. 5 and Fig. 7). Accurate knowledge of the structure andthe nature of the underlying connections acquired using appro-priate imaging modalities would be needed to quantify theseeffects. It is a problem common to all in vivo testing of human

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

Fig. 7 – Comparison of experimental and model force–displacement response of different facial areas of one volunteer:

In-plane response of (a) central jaw location (CJ); (b) forehead location (FH); (c) location near ear (NE); (d) location near lips (NL);

(e) zygomatic location (ZYG); Out-of-plane response of (f) CJ; (g) FH; (h) NE; (i) NL; (j) ZYG.

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soft tissues. The probe was displaced using a 0.1 Hz triangularwaveform. Investigating any frequency dependent properties offacial skin was beyond the scope of this study.

There are, of course, several simplifying assumptions withrespect to the model. The skin is assumed to be materially isotropicand the experimentally observed anisotropy is assumed to beentirely due to the in vivo tension field. The material anisotropy

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

present in skin (Groves et al., 2013; Annaidh et al., 2012) has beenignored. Incorporation of an anisotropic constitutive equation, suchas one used in Flynn et al. (2011a) or Jor et al. (2011), may improvethe fit between the experimental data and model results. However,the use of a more complex anisotropic constitutive model presentsadditional challenges in relation to identifying unique materialparameters and the in vivo tension field.

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

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Identifying unique parameters sets through non-linear opti-misation is a challenging task. Ogden et al. (2004) fitted a modelto simple tension and equibiaxial tension data with similaraccuracy using several model parameter sets. A richer set ofexperimental data was used in the current study. For each facialskin location, the model was simultaneously fitted to sixteen setsof deformation data. Using a similar protocol, Flynn et al. (2011a)demonstrated that the identifiability of the material para-meters increased when more experimental data was includedin the objective function. In that study, the model was fittedsimultaneously to only seven deformation data sets. Using an

Fig. 8 – In-plane force reaction at 0.7 mm displacement for

different locations on one volunteer’s face.

Table 3 – Optimised material parameters to fit different the re

and τG1 ¼ 0:4 s. See Fig. 2 for specification of regions.

Region μ1 (kPa) μ2 (Pa) α1 α2 rX (kPa)

CC 58.27 0.14 2.334 33.081 89.4

NE 57.40 0.27 3.000 44.060 84.0

NL 41.29 0.16 1.658 54.964 24.2

FH 53.95 0.30 1.868 68.998 34.1

CJ 57.73 0.42 2.265 34.689 81.3

ZYG 65.00 0.44 2.161 44.966 64.4

Table 2 – Optimised material parameters to fit specific volunte

and τG1 ¼ 0:4s.

Volunteer no μ1 (kPa) μ2 (Pa) α1 α2 rX (kPa)

1 57.80 0.10 2.322 33.693 89.5

2 53.58 0.35 2.080 38.207 62.0

3 44.59 0.27 1.945 33.770 50.9

4 35.97 0.37 1.829 35.956 34.9

5 60.00 0.50 2.347 34.619 78.3

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

appropriately rich set of deformations increases the likelihoodof determining a unique parameter set (Flynn et al., 2011a;Gamage et al., 2011). As the current study uses a richer data set

sponse of different regions of one volunteer’s face. gp1 ¼ 0:8

rY (kPa) Equivalent Pre-strain Residual (N2) Error (%)

εX εY

71.8 0.33 0.24 51.0 23.3

77.7 0.20 0.17 41.5 18.0

15.9 0.13 0.04 44.4 20.6

26.7 0.11 0.06 34.9 19.6

75.4 0.30 0.27 31.7 16.1

58.3 0.20 0.17 47.7 22.9

er deformation data from the central right cheek. gp1 ¼ 0:8

rY (kPa) Equivalent Pre-strain Residual (N2) Error (%)

εX εY

70.4 0.33 0.24 42.2 23.3

42.8 0.24 0.11 17.5 11.8

42.9 0.26 0.19 35.7 18.4

27.2 0.22 0.13 13.8 12.4

73.8 0.11 0.10 42.0 21.9

Fig. 9 – Parameter sensitivity analysis. Curve labelled

‘Original’ is the simulated probe reaction force–

displacement response in the direction θ¼301 and φ¼01

using the optimised forehead skin parameters. Each curve

labelled with a parameter is the corresponding force–

displacement response with that parameter increased by

10%. The percentage change in the maximum probe

reaction force is indicated in each label.

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than Flynn et al. (2011a), the identifiability of the parameters hasprobably been improved.

In each case, the model was fitted to pre-conditioned facialskin data. The QLV model using a one-term Prony series is toosimple to simulate the pre-conditioning phenomenon. A one-term Prony series was used to simulate the hysteresis levelobserved in the experiments. Using additional terms in the serieswould possibly improve the fit between the model and experi-ment. Soft tissues exhibit nonlinear viscoelasticity, in general, andthe assumptions of the QLV model do not hold in all cases (Einatand Lanir, 2009). In order to simulate the skin pre-conditioning,alternative approaches such as those taken in Rubin and Bodner(2002) and Lokshin and Lanir (2009) could be taken. However,these approaches come with the expense of additional materialparameters, which increase the difficulty of finding uniquematerial parameter sets.

The representation of facial skin by a flat single homo-geneous layer of shell elements is a simplification. While someof the facial regions tested are relatively flat (e.g. central cheekand forehead areas), other areas are less so. The assumptionof flatness is probably weakest for the zygomatic region andcontributes to the larger discrepancies between the model resultsand experimental data calculated in this region. Future develop-ments would include using the geometries of the volunteers' facesin the model.

Human skin is a multi-layer material with each layer con-tributing to the overall mechanical response of the composite(Flynn and McCormack, 2008). A multi-layer representation iscertainly needed to simulate needle penetration (Groves et al.,2012) and interactions between finger-tips and objects (Wanget al., 2012). However, three-dimensional multi-layer finite ele-ment models of large areas of skin require large numbers ofelements. It can take many CPU hours to solve just one analysis(Flynn and McCormack, 2009). The time cost becomes prohibi-tively expensive when these models are used within materialparameter optimisation routines. So, while single-layer shellelement representations of skin are less realistic, they are usefulwithin a parameter optimisation framework (Evans, 2009; Flynnet al., 2011a).

The representation of facial skin as a single layer also ignoresthe connection of the skin to the underlying soft-tissue and bonystructures. The main effect of this is probably to increase theestimated stiffness and in vivo tension of the facial skin. We haveassumed that softer sub-dermal layers have a relatively smalleffect on the mechanical response for probe displacements up to1.5 mm. However, as discussed earlier, the attachment of the skinto the maxilla via the zygomatic ligament possibly has a sig-nificant effect on the deformations.

Future developments of this combined numerical–experimen-tal technique will address the limitations outlined above. Thecalculated material parameters and in vivo tensions will be ofgreat use to anyone interested in the mechanical properties offacial skin and to those developing finite element models ofthe face.

Acknowledgments

CF was supported by a fellowship from the Michael SmithFoundation for Health Research. We would like to acknowledge

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

Matthew Parker, Mihailo Azhar, and Gabriel Loh for assistancewith the experiments and also the volunteers who took part inthis study.

r e f e r e n c e s

Annaidh, A.N., Bruyere, K., Destrade, M., Gilchrist, M.D., Maurini, C.,Ottenio, M., Saccomandi, G., 2012. Automated estimation ofcollagen fibre dispersion in the dermis and its contribution to theanisotropic behaviour of skin. Annals of Biomedical Engineering 40(8), 1666–1678.

Barbarino, G.G., Jabareen, M., Trzewik, J., Nkengne, A., Stamatas, G.,Mazza, E., 2009. Development and validation of a three-dimensional finite element model of the face. Journal ofBiomechanical Engineering 131 (4), 041006–041011.

Barbarino, G.G., Jabareen, M., Mazza, E., 2011. Experimental andnumerical study on the mechanical behavior of the superficiallayers of the face. Skin Research and Technology 17 (4), 434–444.

Beldie, L., Walker, B., Lu, Y., Richmond, S., Middleton, J., 2010. Finiteelement modelling of maxillofacial surgery and facial expressions—a preliminary study. International Journal of Medical Roboticsand Computer Assisted Surgery 6 (4), 422–430.

Bischoff, J.E., Arruda, E.M., Grosh, K., 2000. Finite element modeling ofhuman skin using an isotropic, nonlinear elastic constitutivemodel. Journal of Biomechanics 33 (6), 645–652.

Borges, A., 1984. Relaxed skin tension lines (Rstl) versus other skinlines. Plastic and Reconstructive Surgery 73 (1), 144–150.

Borges, A.F., Alexander, J.E., 1962. Relaxed skin tension lines, z-plastieson scars, and fusiform excision of lesions. British Journal of PlasticSurgery 15, 242–254.

Cavicchi, A., Gambarotta, L., Massabò, R., 2009. Computationalmodeling of reconstructive surgery: the effects of the naturaltension on skin wrinkling. Finite Elements in Analysis and Design45 (8–9), 519–529.

Cerda, E., 2005. Mechanics of scars. Journal of Biomechanics 38 (8),1598–1603.

Chabanas, M., Luboz, V., Payan, Y., 2003. Patient specific finite elementmodel of the face soft tissues for computer-assisted maxillofacialsurgery. Medical Image Analysis 7 (2), 131–151.

Couturaud, V., Coutable, J., Khaiat, A., 1995. Skin biomechanicalproperties: in vivo evaluation of influence of age and body site by anon-invasive method. Skin Research and Technology 1 (2), 68–73.

Daly, C.H., 1982. Biomechanical properties of dermis. The Journal ofInvestigative Dermatology 79, 17s–20s 17s.

Einat, R., Lanir, Y., 2009. Recruitment viscoelasticity of the tendon.Journal of Biomechanical Engineering-Transactions of the Asme131 (11), 111008.

Evans, S.L., 2009. On the implementation of a wrinkling, hyperelasticmembrane model for skin and other materials. Computer Methodsin Biomechanics and Biomedical Engineering 12 (3), 319–332.

Evans, S.L., Holt, C.A., 2009. Measuring the mechanical properties ofhuman skin in vivo using digital image correlation and finiteelement modelling. Journal of Strain Analysis for EngineeringDesign 44 (5), 337–345.

Flynn, C., Taberner, A., Nielsen, P., 2011a. Modeling the nechanicalresponse of in vivo human skin under a rich set of deformations.Annals of Biomedical Engineering 39 (7), 1935–1946.

Flynn, C., Taberner, A., Nielsen, P., 2011b. Measurement of the force–displacement response of in vivo human skin under a rich set ofdeformations. Medical Engineering & Physics 33 (5), 610–619.

Flynn, C., McCormack, B.A.O., 2009. Simulating the wrinkling andaging of skin with a multi-layer finite element model. Journal ofBiomechanics 43 (3), 442–448.

Flynn, C., McCormack, B.A.O., 2008. Finite element modelling offorearm skin wrinkling. Skin Research and Technology 14 (3),261–269.

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004

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 ] ( ] ] ] ] ) ] ] ] – ] ] ] 11

Fujimura, T., Osanai, O., Moriwaki, S., Akazaki, S., Takema, Y., 2008.Development of a novel method to measure the elastic propertiesof skin including subcutaneous tissue: new age-related parametersand scope of application. Skin Research and Technology 14 (4),504–511.

Fung, Y.C., 1993. Biomechanics:Mechanical Properties of LivingTissues. Springer-Verlag, New York.

Furnas, D., 1989. The retaining ligaments of the cheek. Plastic andReconstructive Surgery 83 (1), 11–16.

Gamage, T.P.B., Rajagopal, V., Ehrgott, M., Nash, M.P., Nielsen, P.M.F.,2011. Identification of mechanical properties of heterogeneous softbodies using gravity loading. International Journal for NumericalMethods in Biomedical Engineering 27 (3), 391–407.

Gladilin, E., Zachow, S., Deuflhard, P., Hege, H.C., 2004. Anatomy- andphysics-based facial animation for craniofacial surgerysimulations. Medical & Biological Engineering & Computing 42 (2),167–170.

Gladilin, E., Ivanov, A., 2009. Computational modelling andoptimisation of soft tissue outcome in cranio-maxillofacial surgeryplanning. Computer Methods in Biomechanics and BiomedicalEngineering 12 (3), 305–318.

Groves, R.B., Coulman, S.A., Birchall, J.C., Evans, S.L., 2012. Quantifyingthe mechanical properties of human skin to optimise futuremicroneedle device design. Computer Methods in Biomechanicsand Biomedical Engineering 15 (1), 73–82.

Groves, R.B., Coulman, S.A., Birchall, J.C., Evans, S.L., 2013. Ananisotropic, hyperelastic model for skin: experimentalmeasurements, finite element modelling and identification ofparameters for human and murine skin. Journal of the MechanicalBehavior of Biomedical Materials 18 (0), 167–180.

Gunay, Y., Kurtoglu, C., Atay, A., Karayazgan, B., Gurbuz, C.C., 2008.Effect of tulle on the mechanical properties of a maxillofacialsilicone elastomer. Dental Materials Journal 27 (6), 775–779.

Ha, R., Nojima, K., Adams, W., Brown, S., 2005. Analysis of facial skinthickness: defining the relative thickness index. Plastic andReconstructive Surgery 115 (6), 1769–1773.

Hatamleh, M.M., Watts, D.C., 2010. Mechanical properties and bondingof maxillofacial silicone elastomers. Dental Materials 26 (2),185–191.

Jor, J., Nash, M., Nielsen, P., Hunter, P., 2011. Estimating materialparameters of a structurally based constitutive relation for skinmechanics. Biomechanics and Modeling in Mechanobiology 10 (5),767–778.

Langer, K., 1978. On the anatomy and physiology of the skin: II. Skintension (With 1 Figure). British Journal of Plastic Surgery 31 2, 93–106.

Levine, J.P., Patel, A., Saadeh, P.B., Hirsch, D.L., 2012. Computer-aideddesign and manufacturing in craniomaxillofacial surgery: the newstate of the art. Journal of Craniofacial Surgery 23 (1), 288–293.

Please cite this article as: Flynn, C., et al., Simulating the three-Mechanical Behavior of Biomedical Materials (2013), http://dx.doi.o

Lokshin, O., Lanir, Y., 2009. Micro and macro rheology of planartissues. Biomaterials 30 (17), 3118–3127.

Malm, M., Samman, M., Serup, J., 1995. In vivo skin elasticity of 22anatomical sites. Skin Research and Technology 1 (2), 61–67.

Marchetti, C., Bianchi, A., Muyldermans, L., Di Martino, M., Lancellotti,L., Sarti, A., 2011. Validation of new soft tissue software inorthognathic surgery planning. International Journal of Oral andMaxillofacial Surgery 40 (1), 26–32.

Nazari, M.A., Perrier, P., Chabanas, M., Payan, Y., 2010. Simulation ofdynamic orofacial movements using a constitutive law varyingwith muscle activation. Computer Methods in Biomechanics andBiomedical Engineering 13 (4), 469–482.

Ogden, R.W., Saccomandi, G., Sgura, I., 2004. Fitting hyperelasticmodels to experimental data. Computational Mechanics 34 (6),484–502.

Ohshima, H., Tada, A., Kanamaru, A., Akamatsu, H., Sakai, Y., Itoh, M.,Kanto, H., 2011. Relevance of the directionality of skin elasticity toaging and sagging of the face. Skin Research and Technology 17 (1),101–107.

Rubin, M., Bodner, S., 2002. A three-dimensional nonlinear model fordissipative response of soft tissue. International Journal of Solidsand Structures 39 (19), 5081–5099.

Silver, F.H., Freeman, J.W., DeVore, D., 2001. Viscoelastic properties ofhuman skin and processed dermis. Skin Research and Technology7 (1), 18–23.

Tepole, A.B., Gosain, A.K., Kuhl, E., 2012. Stretching skin: thephysiological limit and beyond. International Journal of Non-LinearMechanics 47 (8), 938–949.

Tsukahara, K., Moriwaki, S., Hotta, M., Fujimura, T., Kitahara, T., 2004.A study of diurnal variation in wrinkles on the human face.Archives of Dermatological Research 296, 169–174, http://dx.doi.org/10.1007/s00403-004-0500-5.

Wang, Z., Wang, L., Van Anh, Ho, Morikawa, S., Hirai, S., 2012. A 3-Dnonhomogeneous FE model of human fingertip based on MRImeasurements. IEEE Transactions on Instrumentation andMeasurement 61 (12), 3147–3157.

Wang, S., Yang, J., 2009. An improved finite element model forcraniofacial surgery simulation. International Journal of ComputerAssisted Radiology and Surgery 4 (6), 579–587.

Wilkes, G.L., Brown, I.A., Wildnauer, R.H., 1973. The biomechanicalproperties of skin. CRC Critical Reviews in Bioengineering 1 (4),453–495.

Wood, F., 2012. Tissue engineering of skin. Clinics in Plastic Surgery39 (1), 21–32.

Zoellner, A.M., Tepole, A.B., Kuhl, E., 2012. On the biomechanics andmechanobiology of growing skin. Journal of Theoretical Biology297, 166–175.

dimensional deformation of in vivo facial skin. Journal of therg/10.1016/j.jmbbm.2013.03.004