# The Preconditioning and Stress Relaxation of Skin Tissue

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3 separated by strain over a 12 second period to observe stress relaxation behaviour. The tests were repeated five times per strain amplitude, each time with a new sample. Testing details are shown in Table 1. Table 1: Sample groups for stress relaxation tests Cut Direction Sample Group No. Strain (%) Parallel Perpendicular Modelling The QLV constitutive model and the reduced relaxation function were employed for modelling in this study. The reduced relaxation function is defined as: σ ( t) G ( t) = (1) σ () where σ (t) is the stress at time t. σ () is the initial stress when the sample is firstly ramped up to designated strain. This reduced relaxation function is the viscoelastic constitutive function of the sample, which has the condition, G ( ) = 1 (2) The instantaneous stress follows the equation, σ e e σ ( t ) = G ( t ) σ ( ε ) (3) (ε ) where is the stress at instantaneous strain. The convolution integral that describes the stress history of the sample is then represented by e Bε σ ( ε ) = ( e 1) A (6) where A and B are constants determined by using experimental data, the reduced relaxation function can model the stress relaxation responses. Experimental data obtained from stress relaxation tests were used to determine coefficients A, B, a, b, c, d, g and h from (5) and (6). Optimisation was performed using MATLAB to generate model functions for each sample. 3 RESULTS 3.1 Preconditioning Figure 2 illustrates a typical change between the stressstrain loops during preconditioning. This stress-strain curve shows repeatability starting from the 4 th cycle of uniaxial tensile loading. Parallel samples required 4-6 cycles before reaching the preconditioned state, and the perpendicular samples required slightly more repeated loading cycles of The regularity of cycles required for the preconditioning of skin samples was higher in the parallel samples compared to the perpendicular samples. Details of the preconditioning cycles required for each group for both the parallel and perpendicular fibre directions at a low constant loading rate are shown in Table 2. The repeated cyclic loading indicated stressstrain loops moving towards the right, demonstrating preconditioning phenomenon of skin tissue. Table 2: Cycles required for preconditioning of samples Cut Direction Sample Group No. Cycles Required Parallel Perpendicular where and t σ e ( t G( t τ ) ε ) ε σ ( t) = (4) τ σ e (t) ε ε τ is the instantaneous elastic response, is the strain history of the sample. The reduced relaxation function is G t bt dt ht ( ) = ae + ce + ge (5) where a, b, c, d, g, h are constants, which could be determined empirically by experimental data. Together with the nonlinear elastic representation of the instantaneous stress response, Stress (MPa) Strain (%) Figure 2: Preconditioning result of a typical swine skin sample. 28 Biomedical & Pharmaceutical Engineering Cluster, Nanyang Technological University 24

4 3.2. Stress Relaxation Both parallel and perpendicular skin samples were raised to 5%, 1% or 15% strain individually before the stress relaxing. Figure 3(a) shows the normalised stress against time of parallel samples. The strains of 5% and 1% displayed a similar stress relaxation trend, whereas the strain of 15% displayed relatively rapid relaxation for the first 2 seconds, but the decaying rate was reduced after that and reached a similar level to the other two strains. Both 5% and 1% strains of the samples decayed to a normalised stress of approximately.6mpa, whereas the 15% strain of samples decayed to a normalised stress of approximately.4mpa. Figure 3(b) shows the stress relaxation behaviour of perpendicular samples under the same strain range. Decaying trends are similar to those of parallel samples, perpendicular samples of 5% and 1% strains relaxed to just above a normalised stress of.6mpa, and the 15% strain of sample relaxed to below.2mpa. Normalised Stress (MPa) Normalised Stress (MPa) (a) 5% 1% 15% (b) Figure 3: Stress relaxation trend of different strains in, (a) parallel samples with normalised stress versus time, (b) perpendicular samples of normalised stress versus time 5% 1% 15% 3.3 Modelling Calculation of the coefficients, A, B, a, b, c, d, g and h were carried out by using MATLAB. Results of values obtained for coefficients are shown in Table 3 and Table 4. Graphs of model and experimental data are shown in Figure 4, where instantaneous stress σ (t) is plotted against time for each graph. With Figure 3, the test data was normalised so that it is easier for comparison of different rates. However, for the groups of data individually in Figure 4, normalisation is not required. Figure 4 (a), (b) and (c) are the graphs of parallel samples, and Figures 4 (d), (e) and (f) are of perpendicular samples. The QLV model is suitable to describe the elastic component (A and B) and the viscous component (a,b, c, d, e, f, g and h) of the material. The skin tissue has viscoelastic behaviour with both parallel and perpendicular orientations which were well modelled by QVL. Comparing both fibre orientations under the same strain, the elastic components A of parallel orientation were greater than perpendicular orientation. Conversely, the components B were reversed. The results show the value of both A and B increasing slightly with the strain. Larger values of A and B would indicate higher peaks in stress and higher equilibriums in stress for the same level of extension. Table 3: Coefficient values of parallel samples Parallel Sample Groups Strain 5% 1% 15% A B a b c d g h Table 4: Coefficient values of perpendicular samples Perpendicular Sample Groups Strain 5% 1% 15% A B a b c d g h Biomedical & Pharmaceutical Engineering Cluster, Nanyang Technological University 25

5 (a) (d) (b) (e) (c) (f) Figure 4: Comparison of modelling with experimental data: (a) parallel with 5% strain, (b) parallel with 1% strain, (c) parallel with 15% strain, (d) perpendicular with 5% strain, (e) perpendicular with 1% strain, and (f) perpendicular with 15% strain. 28 Biomedical & Pharmaceutical Engineering Cluster, Nanyang Technological University 26

6 4 DISCUSSIONS The different directions of cutting on the samples were considered as an indication of the effect of fibre orientation on viscoelastic properties. During preconditioning, the parallel samples required fewer cycles to reach steady state consistently comparing with the perpendicular samples. This indicates that the viscoelastic properties are dependent upon fibre direction, and that the regular fibre realignment process only occurs when mechanical loading is exerted in a particular fibre direction. Fibre direction also seemed to affect the stress relaxation behaviour of the samples. The parallel samples to which were applied the 5% and 1% strains had a greater decaying rate in the first 2 seconds compared with the perpendicular samples. However, an application of 15% strain showed a greater relaxation rate in perpendicular sample than in the parallel sample, possibly indicating that the strainindependence of stress relaxation phenomenon only applies to certain strain levels. Further studies are encouraged for a clearer explanation of such behaviours. Experimental results from the stress relaxation tests showed relaxation rate approaching steady state after 2 seconds of strain displacement across all the samples, demonstrating the time dependent nature of the tissue. Due to the variation in each skin sample, it is acceptable the experimental output were slightly different within the same group. The number of cycles required for preconditioning only slightly differs from sample to sample in the same group. The results shown in Table 1 indicate the strain magnitude for both preconditioning and the afterward stress relaxation test for each group. It is clear that preconditioning cycles required for different group were caused by the strain magnitude. It is possible that some damages on the extracellular matrix proteins were caused by the high strain rate. However, the loading rate of 3N/mim for all the tests should be small enough to avoid such damages. In this study, the modelling of stress relaxation behaviour was performed using MATLAB based on the QLV theory with the reduced relaxation function. The success of this model is linked both to its ability to accurately capture experimental data as well as its ease in fitting material parameters because of the separation of the elastic response and time-dependent viscoelastic effects. Results of modelling show a close fit with fresh skin stress relaxation data. The benefit of using this reduced relaxation function is that it is less complicated compared to the most extensively used equation by Fung [5] and its modified version used by other researchers [14]. 5 CONCLUSION This study investigated preconditioning and stress relaxation effects of fresh swine skin. The results indicated that the fibre direction of skin samples affected the preconditioning cycles required, the consistency of viscoelastic response, and the stress relaxation rate at the beginning of the relaxation period. Skin tissue has similar stress relaxation behaviour characteristics of strain at 5% and 1%. However, it appeases different behaviours with much slower stress relaxation rate when the strain reaches 15%. This stress relaxation phenomenon implies the strain-independency only appeared in samples below 15% strain. All samples exhibited greater stress decaying rate in the first 2 seconds of the relaxation period, and began to approach steady decay after. The QLV theory and reduced relaxation function can be used to model the stress relaxation tests data of skin tissues. ACKNOWLEDGEMENT The authors would like acknowledge Dr Susan Hemsley of the Faculty of Veterinary Science and Mr Trevor Shearing of the Faculty of Engineering in the University of Sydney for their technical supports throughout this study. This research is financially supported by Australian Research Council Discovery Project, Rheological and Electrical Properties of Biological Soft Tissues. REFERENCES [1] Woo SLY, Gomez MA, Akeson WH. The time and history-dependent viscoelastic properties of the canine medial collateral ligament, J Biomech Eng, 1981; 13: [2] Johson GA, Liversay GA, Woo SLY, Rajagopal KR. A single integral finite strain viscoelastic model of ligaments and tendons, J Biomech Eng, 1996; 118: [3] Huyghe JM, Van Campen DH, Arts T, Heethaars RM. The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation, J Biomech, 1991; 24: [4] Chimich D, Shrive N, Frank C, Marchuk L, Bray R. Water content alters viscoelastic behaviour of the normal adolescent rabbit medial collateral ligament, J Biomech, 1992; 25: [5] Fung YC. Biomechanics: Mechanical properties of living tissues, Springer-Verlag, New York, 1993: [6] Hsu S, Jamieson AM, Blackwell AM. Viscoelastic studies of extracellular matrix interactions in a model native collagen gel system, Biorheology, 1994; 31: [7] Elsner P, Wilhelm KP, Maibach HI, Berardesca E. Bioengineering of the Skin: Skin Biomechanics, CRC Press, New York, 21. [8] Zeng YJ, Liu YH, Xu CQ, Xu XH, Xu H, Sun GC. Biomechanical properties of skin in vitro for different expansion methods, Clin Biomech., 24; 19: [9] Kwan MK, Lin THC, Woo SLY. On the viscoelastic properties of the anteromedial bundle of the anterior cruciate ligament, J Biomech, 1993; 26: Biomedical & Pharmaceutical Engineering Cluster, Nanyang Technological University 27

7 [1] Courtman DW, Pereira CA, Kashef V, McComb D, Lee JM, Wilson GJ. Development of a pericardial acellular matric biomaterial: biochemical and biomechanical effects of cell extraction, J Biomed Mat Res, 1984; 35: [11] Trowbridge EA, Black M, Daniel CL. The mechanical response of glutaraldehyde-fixed bovine pericardium to uniaxial load, J Mat Science, 1985; 2: [12] Kwan, M.K., Li, T.H.-D., Woo, S.L.-Y., On the viscoelastic properties of the anteromedial bundle of the anterior cruciate ligament. J Biomech, 1993; 26: [13] Abramowitch, S.D., Woo, S.L.-Y., Clineff, T.D., Debski, R.E., An evaluation of the quasi-linear viscoelastic properties of the healing medial collateral ligament in a goat model. Ann Biomed Eng, 24; 32: [14] Puso, M.A., Weiss, J.A., Finite element implementation of anisotropic quasi-linear viscoelasticity using a discrete spectrum approximation, J Biomech Eng, 1998; 12: [15] Sverdlik, A., Lanir, Y., Time-dependent mechanical behavior of sheep digital tendons, including the effects of preconditioning, J Biomech Eng, 22; 124: [16] Doehring, T.C., Carew, E.O., Vesely, I., The effect of strain rate on the viscoelastic response of aortic valve tissue: a direct-fit approach, Ann Biomed Eng, 24; 32: [17] Nagatomi, J., Gloeckner, D.C., Chancellor, M.B., DeGroat, W.C., Sacks, M.S., Changes in the biaxial viscoelastic response of the urinary bladder following spinal cord injury, Ann Biomed Eng, 24; 32: [18] Julie M. Giles, Amanda E. Black and Jeffrey E. Bischoff, Anomalous rate dependence of the preconditioned response of soft tissue during load controlled deformation. J Biomech, 27; 4(4): [19] Toms, SR, Dakin, GJ, Lemons, JE, and Eberhardt, AW. "Quasi-linear viscoelastic behavior of the human periodontal ligament", J. Biomech, 22; 35: [2] Middelkamp-Hup, M.A., et al., Detection of UV- Induced Pigmentary and Epidermal Changes Over Time Using In Vivo Reflectance Confocal Microscopy, J Invest Dermatol, 26; 126(2): 42. [21] U R Hengge et al., Expression of naked DNA in human, pig, and mouse skin. J Clin Invest. 1996, 97(12): [22] Oliver A. Shergold, Norman A. Fleck and Darren Radford, The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates Int J Impact Eng, 26, 32(9): Biomedical & Pharmaceutical Engineering Cluster, Nanyang Technological University 28

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