Sensitivity analysis and material identification for activated smooth muscle

Eduard Rohan; Robert Cimrman

Eduard Rohan University of West Bohemia
Robert Cimrman University of West Bohemia

Abstract

The paper deals with the problem of material identification for smooth muscle tissue in activated, or passive states. In [17] a composite type mathematical model has been proposed describing the complexity of the tissue reduced to the networks of muscle and collagen fibres. The computational model is based on the total Lagrangian formulation with incompressibility of the bulk material. The problem of inflating vessels is considered in order to allow simulation of real experimental conditions and, thus, to determine constitutive parameters of muscle in active state. These parameters are identified also from hysteresis, or relaxation curves. The direct differentiation, or the adjoint systems techniques are applied to the sensitivity analysis. Results of numerical tests are given.

Keywords

References

[1] H. Abé, K. Hayashi, M. Sato. Data Book on Mechanical Properties of Living Cells, Tissues, and Organs. Springer-Verlag, Tokyo, 1996.
[2] J.M. Ball. Constitutive inequalities and existence theorems in nonlinear elastostatics. Nonlin. Anal. Mech., 1: 187- 241. Heriot-Watt Symp., Edinburgh 1976, 1977.
[3] R. Cimrman, E. Rohan. FE simulation of muscle behaviour in dynamic problems, Proceedings of the conference ECCM 2001, full paper on CD-ROM, Kraków, 2001.
[4] M.A. Crisfield. Non-linear Finite Element Analysis of Solids and Structures, Vol. 2, J. Wiley & Sons, Chichester, 1997.
[5] Y.C. Fung. Biomechanics. Mechanical Properties of Living Tissues. (Second edition), Springer-Verlag, New York, 1993.