determining hyperelastic parameters of human skin

7/29/2019 Determining Hyperelastic Parameters of Human Skin

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Determining Hyperelastic Parameters of Human Skin

Using 2D Finite Element Modelling and Simulation

*,a

Nor Fazli Adull Manan, *Mohd Hanif Mohd Ramli, *Mohd Nor Azmi Ab. Patar, **Cathy Holt, ** Sam Evans,***Mahmoud Chizari and *

,bJamaluddin Mahmud

*: Faculty of Mechanical Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, MALAYSIA

**: Institute of Medical Engineering and Medical Physics, School of Engineering, Cardiff University, The Parade, Cardiff,

CF24 3AA, UNITED KINGDOM

***: School of Engineering and Design, Brunel University, Kingston Lane Uxbridge, Middlesex UB8 3PH, UNITED KINGDOM

Email: a [email protected], [email protected]

Abstract The behaviour of skin is still not well understood

and characterising skin properties is always challenging due to

its complex biological structure. Nevertheless, this paper

highlights the success of determining skin material parameters

using Ogdens model and finite element (FE) simulation. The

approach involved integrating experiment, FE modelling and

inverse-FE analysis. Data from in vivo experiments were used

to develop 2D hyperelastic finite element models based on

Ogdens constitutive equation and systematic case studies were

constructed. By iteratively varying several material

parameters and values, FE simulations were performed to

simulate the skin deformation according to the actual

experimental set up. The results were compared to the

experiments and the best match curve constitutes the material

parameters. The current results show that the Ogdens

coefficient and exponent for the subject was estimated to be =

10 Pa and = 40 respectively. Further analyses using other

models such as Mooney-Rivlin and Neo-Hookean could be

carried out for comparison. Nevertheless, this study has

contributed to the knowledge about skin behaviour.

Keywords: Skin in vivo, FEA, ANSYS, Ogden model.

I. INTRODUCTION

Skin is the largest organ of the human body with a

complicated multi-layered structure [1] that constitutes its

complex deformation behaviour. Until now skin behaviour

is still not well understood [2] and predicting its

deformation has always been very difficult [3].

Nevertheless, understanding skin mechanical behaviour is

important in many applications [4,5]. Recently, an

innovative experimental method utilising the motion capture

system has been developed, which has successfully been

used to measure the deformation of human skin in vivo [6].The experimental results were found to be reliable and

useful. The experimental data has been analysed extensively

to explore the viscoelastic, nonlinear and anisotropic

behaviour of skin deformation. However, it could not

directly determine the mechanical properties of human skin.

One approach that could lead to the establishment of skin

properties is by simulating skin deformation using finite

element model/software to replicate the experimental

procedure. At present there is no generally accepted modelreported that could be used directly for this study.

Therefore, this study attempts to develop a simple butrobust computational model employing the finite elementmethod that could simulate skin deformation with reasonableaccuracy. Its success could contribute to understanding betterthe skin behaviour. Moreover, it enriches the data currentlyavailable for skin parameters by comparing the experimentaloutput to results obtained by other earlier researches. Thus,this makes the current study significant and important in thearea of skin biomechanics.

II. LITERATURE REVIEW

The attempts to develop a computational model of skinstarted as early as in early 70s where skin was modelled asan elastic membrane [7] and a hyperelastic material [8]. Inthe early years, there was a lacking of practical computersoftware and powerful modelling tools Therefore,mathematical equations have been the main choice andapproach used to describe the deformation of human skin.Even so, the mathematical equation was limited incomputation size, and thus, usually were very basicequations with only small size of matrices. With theadvances in computer technology, engineering software hasbeen vigorously developed and commercially available.Using FE software, attempts to simulate and animate skinbehaviour has become possible. A few examples include the

work of Tsap et al [9] using ANSYS to analyse human tissuemotion analysis. Hendriks et al [10] using MSC.MARC tosimulate suction tests, Tham et al [11] using Abaqus tosimulate the cupping process, Retel et al [12] using SYSTUSto simulate wound closure, Molinari et al [13] using FEAP to

This research has been funded by Universiti Teknologi MARA,Malaysia via Excellent Fund Research Grant Scheme (FRGS), grant no.600-RMI/ST/DANA 5/3Dst(40/2010)

2012 IEEE Symposium on Humanities, Science and Engineering Research

978-1-4673-1310-0/12/$31.00 2012 IEEE 805


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simulate the biomechanical behaviour of the skin using datafrom a virtual surgery. However, all of this work simply usedthe available data from experiments and did not propose thematerial parameters for skin hyperelastic properties. Byadapting inverse finite element analysis (i-FEA) approachand replicating the experimental procedure, the hyperelasticparameters of human skin are estimated.

Therefore, this study is novel as it combines these twoapproaches (i-FEA and motion capture) to determine thehyperelastic material properties of skin, which up to date, hasstill not been reported by other researchers.

III. METHODOLOGY

Due to the extensive and multi-stages tasks that have been

carried out, this paper describes the methodology into two

(2) sections to segregate the difference in the nature of

work:

Information and data gathering (from experiments)

Development of the FE models

A.Information and Data from the ExperimentsAs mentioned in the first section, a novel experimental

technique has been developed [6] and the challenge is toreplicate and perform the simulations of that experiment. Inorder to simulate the experiment accurately and realistically,the information and data gained from the experiment weretranslated carefully and incorporated into the FE models. Theexperiments were conducted to measure the deformation ofskin utilising motion analysis technique. The in vivo testingconducted on the skin at the ventral forearm of a healthyvolunteer is shown in Fig. 1. Even though the actual testshave been conducted on 10 healthy volunteers, for thecurrent study, only the first subject is considered. Prior to

that, informed consent was obtained from all the volunteerswith ethical approval from the Cardiff School of EngineeringResearch Ethics Committee. Upon successful of the currentattempts, the current method could be applied to othersubjects. A set of reflective marker stickers was attached andthe deformation of the skin was induced by applying tensionby pulling a nylon filament attached at the centre of themarker set. The other end of the filament was attached to aload cell (5N, Interface Force Measurements, Crowthorne,UK) connected to an analog board of a computer system. Aset of 3 infrared cameras (Proflex-MCU1000, Qualisys ABSweden) was used to record the skin deformation. Finally,the system tracking-software (QTM 2008, v2.0, Qualisys AbSweden) was used to track the movement of the markers

corresponding to the load applied. The sample output of thesoftware is shown in Fig. 2. The markers parallel and align tothe direction of the load are labelled as L1 to L9, where L5refers to the point of load application. The information of theexperiments and the deformation data were then usedinnovatively to develop the FE models.

Figure 1. Inducing the skin deformation by pulling a nylon filament stuck atthe centre of the marker set.

Figure 2: Sample output from the tracking software showing the markerslabel and movement.

Figure 3: The 80 x 60 mm plate, meshed into 48 (8 x 6) quadratic elements.

The yellow arrows indicate the prescribed displacement.

B. The Development of 2D Skin ModelsA systematic parametric study was designed by

generating a series of FE models which has a variation ofmaterial parameters, elements types and mesh sizes.Nevertheless, it started with the simplest FE model. Then,the modelling procedures and results were evaluatediteratively and the models were improved accordingly tomatch the experiments. One of the aims was to investigate


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the effect of varying the material parameters. For everysimulation, the results were compared to the reference(experimental) data. The material parameters thatproducethe closest results (minimum error) to theexperiments constitute the estimated value of the mechanicalproperties of skin.

For this study, the 2D models of skin for Subject 1 (0.75N) were developed. Using ANSYS, skin was modelled as athin plate and meshed using the simplest 2D plane stressquad elements (hyperelastic, 4 noded-element, PLANE 182)as shown in Fig. 3.

Load and boundary conditions

The load and boundary conditions were appliedaccording to the experiment set up as shown in Fig. 3. A0.75N concentrated load was applied at the centre of themarker set (equivalent to the load point during tests) in thedirection parallel to the midline markers (crease-to-crease ofthe ventral forearm). The boundary conditions were appliedas prescribed displacements based on the data extracted

directly during experiments (from the measureddisplacements at the boundaries of the test area) [6]. Theactual measured displacements are input into thecorresponding nodes. This was to ensure that boundaries ofthe thin plate model to displace exactly according to theshape of the deformed human skin in vivo.

Choice of material

Although the results obtained from the experimentsrevealed that skin behaved viscoelastically, nonlinearlyhyperelastically and anisotropically, for this study only thenonlinear hyperelasticity was taken into consideration as toinclude all in one model would be very complicated. Thisassumption stems from the work of Tong and Fung [8]. AnOgden model was selected as it has been shown to give goodresults [3].

To investigate the effect of the Ogdens materialcoefficient, and exponent, , an initial study was conductedby varying from 10 to 110 for a constant =26 Pa. Theseinitial values were selected based on the findings of Evansand Holt [14] when they measured skin properties using theDIC technique and FE modelling (=10 Pa, =26). Thisprovided a better prediction of for the subsequent casestudy.

For the second case study, the deformation behaviour isinvestigated by varying from 10 to 60 Pa and retaining constant at = 10. The results were compared to theexperiments to determine the best match curve. The wholeiterative process is actually equivalent to inverse-FEA.

I. RESULTS

The general outputs from a FEA are displacement andstress information for a deformed body. In contrary, thedisplacement information of the deformed skin for thecurrent study is already known and obtained from theexperiments described earlier. Therefore, the current case

study used the outputs (displacements) to determine the skinproperties (inputs); by adapting a direct iterative approach torelate both experiments and simulations. The results of theexperiments were used to analyse the undeformed-deformedcontour for the skin of the subject at 0.75N load appliedparallel to the midline markers (L1 to L9). This serves as thereference data and all the case studies stemmed from it. It

required tremendous effort to compare the displacements forthe whole marker set, hence, in this study, the midlinemarkers parallel to the load direction (L1 to L9) wereobserved.

(a)

(b)

Figure 4. (a) The sample shape of element displacement (=26, = 20,subject 1, load 0.75 N), and

(b) its corresponding contour plot.Both are in good agreement compared to the experiments results.

Fig. 4 shows the shape of the deformed plate and its

corresponding displacement contour. The current approach

has successfully forced the plate to deform according to the

experiment results (Fig. 1). The individual elements,

especially their nodes at the midline have shown a similar


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trend of deformation and curve shape compared to the

results produced during experiments.

Figure 5 shows the graph of the displacement versus

midline-markers (L1 to L9) when was considered constant

at =26 and was varied from 80 to 110. Figure 6 shows

the graph of the displacement versus midline-markers (L1 to

L9) when was considered constant ( = 10) and varied( = 20 to 40). In general, it could be observed that the

midline markers (L1 to L9) displaced accordingly to the

skin deformation and thus, exhibiting a similar 2D profile of

deformation behaviour. From Fig. 5 and Fig. 6, it could be

observed that the curve closest (least error) to the

experiments result is when the Ogdens parameters are =

10 Pa and = 40.

II. DISCUSSION

Generally, the results of the simulations and findingsfrom all the case studies have drawn several issues that worthto discuss. In fact, producing a converged solution for each

analysis was already considered as an achievement as it hasalways been a great challenge to obtain a converged solutionwhen analysing a hyperelastic material which involves largedeformation in a non-linear system of equations. In this case,the current problem involves both material and geometrynon-linearity which produced excessive distortion ofelements. In the early attempts, the solution failed toconverge and therefore, the mathematical and modelingparameters were explored until results obtained. Severalreasons were found to contribute to the failure of solutionconvergence, for examples; the system matrix encounterednegative eigenvalues, too much step increment required, zeropivot and strains too large. Due to these, the programmeignored the hyperelasticiy calculation at several points and

thus contributed to computation error, which could be

cumulative. This is the main possible reason why the modeldid not behave as nonlinear as it should be and thus, becamea limiting factor for the mathematical and geometricalnonlinearity.

The current research has constructed several case studies(Subject 1, 0.75N) systematically where initially used

material parameters found by other researchers andprogressed up to developing a 2D skin model. The objectiveswere not only to model skin and determine its materialparameters, but more importantly, to investigate the effectsin the implementation; i.e. Ogdens material parameters,element type and element size; that contributed to enhancingthe knowledge about FE modelling and simulation of humanskin. From Fig. 5 and Fig. 6, it was found that the resultsobtained from the simulations produces almost similar valueand has a small difference when considering constant orconstant . The calculated percentage difference betweenFEA and experiment results are 44.3% for constant (=26)and 44.5% for constant (=10). Nevertheless, theimprovement of the FE models has produced better accuracy.

For the current study, it is found that for 2D simulations andanalyses using Ogden materials with one (1) term, the closestskin parameters compared to the experiments are when =10Pa and =40. The ultimate aim of the current study has beento determine skin properties; however, the main limitationlies in the tediousness in developing an accurate and reliableskin model. All the described case studies were conductedbased on the data referred to Subject 1 at 0.75N load appliedparallel to the crease-to-crease direction (Fig. 1 and Fig. 2).Although the number of subject is questionable, the sameapproach could be applied to other subjects (Subjects 2 to10). Applying the boundary conditions (prescribeddisplacements at every node) was the most tedious task andextremely difficult when applying to a 3D model.

Figure 5. Midline markers (L1 to L9) axial displacement (=26 and was varied from 80 to 110).

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III. CONCLUSION

The objective to determine the mechanical properties ofhuman skin using FE modelling and simulation has beenachieved successfully and based on the results, thehyperelastic properties for Subject 1 was estimated to be = 10 Pa, = 40. Although it was not close to the resultobtained by other researchers and the FE implementationwas found to be tedious, the thorough study conducted in thispaper has produced several useful findings that contribute toenhancing the knowledge about modelling skin using FEA

and ANSYS. Further case studies using different elementtypes, mesh sizes, load types and 3D models will bedeveloped; and the findings will reported in the near future.

IV. ACKNOWLEDGMENT

The authors would like to express their gratitude to

Universiti Teknologi MARA, Malaysia for sponsoring the

work related to computational approach via Excellent Fund

Research Grant Scheme (FRGS), grant no. 600-

RMI/ST/DANA 5/3Dst(40/2010). The experimental work

has been conducted at the Cardiff University Structural

Performance (CUSP) Laboratory, Cardiff University, UK.

REFERENCES[1] Payne PA. 1991. Measurement of properties and function of skin.

Clinical Physics & Physiological Measurement. 1991. vol. 12(2). pp105-129.

[2] Kuwazuru O, Miyamoto K, Yoshikawa N, Imayama S. 2012. Skinwrinkling morphology changes suddenly in the early 30s, SkinResearch and Technology, Article first published online: 11 Jan 2012,DOI: 10.1111/j.1600-0846.2011.00598.x

[3] Evans SL. 2009. On the implementation of a wrinkling hyperelasticmembrane model for skin and other materials. Computer Methods

on Biomechanics and Biomedical Engineering. vol. 12(3). pp 319-332.

[4] Mahmud J, Holt CA, Evans SL. An innovative tool to measurehuman skin strain distribution in vivo using motion capture anddelaunay mesh. Journal of Mechanics. 2012, vol. 28(2), pp 309-317.

[5] Flynn C, Taberner A, Nielsen P. 2011. Measurement of the forcedisplacement response of in vivo human skin under a rich set ofdeformations, Medical Engineering & Physic, vol. 33 (5), pp 610-619.

[6] Mahmud J, Holt CA, Evans SL. An innovative application of a smallscale motion analysis technique to quantify human skin deformationin vivo. Journal of Biomechanics. 2010, vol. 43, pp 1002-1006.

[7] Danielson DA. Human skin as an elastic membrane. Journal ofBiomechanics. 1973, vol. 6, pp 539-546.

[8] Tong P, Fung YC. The stress-strain relationship for the skin.Journal of Biomechanics. 1976, vol. 9(10), pp 649-657.

[9] Tsap, L. V., Goldgof, D. B., and Sarkar, S. Human Skin and HandMotion Analysis from Range Image Sequences Using NonlinearFEM. 1997. IEEE Nonrigid and Articulated Motion Workshop (inconjunction with IEEE Conference on Computer Vision and PatternRecognition CVPR'97), San Juan, Puerto Rico.

[10] Hendriks FM, Brokken D, Van Eemeren JTWM, Oomens CWJ,Baaijens FPT, Horsten JBAM. A numerical-experimental method tocharacterize the non-linear behaviour of human skin. Skin Researchand Technology. 2003, vol. 9(3), pp 274-283.

[11] Tham LM, Lee HP, Lu C. Cupping: from a biomechanicalperspective. Journal of Biomechanics. 2006, vol. 39, pp 2183-2193.

[12] Retel V, Vescovo P, Jacquet E, Trivaudey F, Varchon D, Burtheret A.Nonlinear model of skin mechanical behaviour analysis with finiteelement method. Skin Research and Technology. 2001, vol. 7(3), pp152-158.

[13] Molinari, E., Fato, M., Leo, G. D., Riccardo, D., and Beltrame, F.,Simulation of the biomechanical behavior of the skin in virtualsurgical applications by finite element method. IEEE Transactionson Biomedical Engineering. 2005, vol. 52, pp 1514-1521.

[14] Evans SL, Holt CA. 2009. Measuring the mechanical properties ofhuman skin in vivo using digital image correlation and finite elementmodelling. Journal of Strain Analysis for Engineering Design. 2009,vol. 44(5), pp 337-345.

Figure 6. Midline markers (L1 to L9) axial displacement (=10 and was varied from 20 to 40)

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determining hyperelastic parameters of human skin

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