While figures 4 through 7 depict the response of sample 2, figure 9 shows the response of sample 1. Comparing these figures we observe that sample 1 has been stretched more for the same pressure since the value of I1 C and I 3 C realized are greater for this sample. Also, the variation in the invariants with spatial location is more pronounced in sample 1. These markedly different responses is at the least surprising given the work of Donovan et al. [4] because the factors that are known to affect the mechanical property of these saphenous veins is different between these two samples. Following the work of Saravanan [8] and the observation here that the residual stresses could vary even along the circumferential and axial directions we did not measure the opening angles of these veins. This is because if the residual stresses vary even along the circumferential and axial direction a radial cut will not relieve the residual stresses and hence making opening angle measurement is of little use. On the other hand if the residual stresses vary only along the radial direction, Saravanan [8] showed that inflation test itself can be used to infer the residual stresses. Further we observe that if the vein is anisotropic, then reporting the three invariants as done here alone would not suffice to characterize the vein. Ways to address this lacuna is being explored. Conclusion Our studies seem to suggest that the saphenous vein is compressible. Further, we observe that the deformation gradient evaluated at the surface of the vein varies circumferentially and axially, suggesting that the material response functions and/or residual stresses can depend on circumferential direction or axial direction or both. These have implications with respect to the development of the constitutive relation for these veins. Thus, at Indian Institute of Technology Madras, a systematic study of soft tissues has just begun with the necessary infrastructure being created. It is hoped that on testing more samples and development of constitutive relations for these tissues, the factors that influence the mechanical response of the soft tissues like age, sex, food habits, etc. can be quantified and correlated. Acknowledgement We thank Department of Biotechnology, Government of India for funding this work. References [1.] Dobrin, P.B., Littooy, F.N., Endean, E.D., Mechanical factors predisposing to intimal hyperplasia and medial thickening in autogenous vein grafts, Surgery, 105, 393–400, 1989. [2.] Fung, Y.C., Biomechanics: Mechanical Properties of Living Tissue, Springer, New York, 1993. [3.] Zhaoa,_J., Andreasenb, J.J., Yanga, J., Rasmussenc, B.S., Liaoa, D., Gregersena, H., Manual pressure distension of the human saphenous vein changes its biomechanical properties—implication for coronary artery bypass grafting, Journal of Biomechanics, 40, 2268–2276, 2007. [4.] Donovan, D.L., Schmidt, S.P., Townshend, S.P., Njus, G.O., Sharp, W.V., Material and structural characterization of human saphenous vein, Journal of Vascular Surgery, 12, 531-537, 1990. [5.] Stooker, W., Gok, M., Sipkema, P., Niessen, H.W.M., Baidoshvili, A., Westerhof, N., Jansen, E.K., Wildervuur, C.R.H., Eijsman, L., Pressure-diameter relationship in the human greater saphenous vein, Annals of Thoracic Surgery, 76, 1533-1538, 2003. [6.] Molnar, G.F., Nemes, A., Kekesi, V., Monos, E., Nadasy, G.L., Maintained geometry, elasticity and contractility of human saphenous vein segments stored in a complex tissue culture medium, European Journal of Vascular and Endovascular Surgery, 40, 88-93, 2010. [7.] Psaila, J.V., Melhuish, J., Viscoelastic properties and collagen content of the long saphenous vein in normal and varicose veins, British Journal of Surgery, 76, 37-40, 1988. [8.] Saravanan, U., On large elastic deformation of prestressed right circular annular cylinders, International Journal of Non-Linear Mechanics, 46(1), 96-113, 2011. 85
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