isotropic or anisotropic with fiber orientation along the loading direction. These observations suggest that modeling the heterogeneous structure of the leaflet is important. Thus, qualitatively the response of mitral valve to uniaxial stretch is similar to that of the aortic valve leaflet. However, quantitatively their responses are different. Though all the tested mitral valve leaflets show qualitatively similar response as the sample 6, whose response is presented here, quantitatively they are different. Figure 11 plots the variation of the invariants when the mitral valve is stretched biaxially holding the stretch along one direction fixed and cyclically stretching along a direction perpendicular to the direction along which the stretch ratio is held fixed. Figure 12 plots the variation of the stretch ratios along three principal directions of C and figure 13 plots the variation of the principal directions for this experiment. We do these for various selections of markers whose configuration is given in figure 15b. It can be seen from these graphs that the deformation is not homogeneous, since different marker selections lead to different values for the invariants. This may be because the leaflets are inhomogeneous. Further it is evident from figure 11c that the mitral valve leaflet is compressible, since det(C) is not equal to 1, even approximately. Also, from figures 12 we infer that none of the principle stretch ratios is constant. Moreover, even though we stretched the leaflet only up to a stretch ratio of 1.2, locally the tissue seems to have been stretched even up to a stretch ratio of 2. This may be because of the heterogeneous nature of the tested specimen. Further, from figure 13 we find that the principal directions do not change significantly with applied load, implying the material under observation is isotropic or anisotropic with fiber orientation along the loading direction. In this work, we presented the results in terms of the load rather than the stress because the stress distribution is non-uniform. The thickness of the specimen varies, thus making the stress distribution non-uniform. Hence, we are exploring on ways to characterize the non-uniform stress distribution. These results suggest that contrary to what is assumed in the literature [9], these valve leaflets are compressible. Further, it seems that it is important to consider the heterogeneous nature of these tissues. These have implications with respect to the development of the constitutive relation for these leaflets. Acknowledgement We thank Department of Biotechnology, Government of India for funding this work. References [1.] Stella, J.A., Sacks, M.S., On the biaxial mechanical properties of the layers of the aortic valve leaflet, Journal of Biomechanical Engineering, 129(5), 757–766, 2007. [2.] Sacks, M.S., Merryman, D.W., Schmidt, D.E., On the biomechanics of heart valve function, Journal of Biomechanics, 42 (12), 1804–1824, 2009. [3.] Adamczyk, M.M., Vesely, I., Characteristics of compressive strains in porcine aortic valves cusps, Journal of Heart Valve Disease 11 (1), 75–83, 2002. [4.] Billiar, K.L., Sacks, M.S., Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp. Part I: experimental results, Journal of Biomechanical Engineering, 122 (1), 23–30, 2000. [5.] Billiar, K.L., Sacks, M.S., Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: part II-A structural constitutive model, Journal of Biomechanical Engineering, 122 (4), 327–335, 2000. [6.] Christie, G.W., Barratt-Boyes, B.G., Age-dependent changes in the radial stretch of human aortic valve leaflets determined by biaxial stretching, Annals of Thoracic Surgery, 60, S156–S159, 1995. [7.] May-Newman, K., Yin, F.C.P., Biaxial mechanical behavior of excised porcine mitral valve leaflets, American Journal of physics, 269, H1319-H1327, 1995. [8.] Gorman 3rd, J.H., Gupta, K.B., Streicher, J.T., Gorman, R.C., Jackson, B.M., Ratcliffe, M.B., Bogen, D.K., Edmunds Jr., L.H., Dynamic three-dimensional imaging of the mitral valve and left ventricle by rapid sonomicrometry array localization, Journal of Thoracic and Cardiovascular Surgery, 112 (3), 712–726, 1996. [9.] May-Newman, K., Yin, F.C.P., A constitutive law for mitral valve tissue, Journal of Biomechanical Engineering, 120, 38-47, 1998. [10.] Gorman 3rd, J.H., Jackson, B.M., Enomoto, Y., Gorman, R.C., The effect of regional ischemia on mitral valve annular saddle shape, Annals of Thoracic Surgery, 77 (2), 544–548, 2004. [11.] Sacks, M.S., He, Z., Baijens, L., Wanant, S., Shah, P., Sugimoto, H., Yoganathan, A.P., Surface strains in the anterior leaflet of the functioning mitral valve, Annals of Biomedical Engineering 30 (10), 1281–1290, 2002. 72
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