State-space formulations to understand the nonlinear viscoelastic mechanical behavior of tricuspid valve chordae...

The state-space representation is an alternative description of a dynamical system to the input-output representation in the systems theory. In this paper, we used the state-space representation to study the mechanical behavior of the tricuspid valve (TV) chordae tendineae. The TV chordae behave viscoelastic features under the loading; hence, we cast the generalized Kelvin model with an additional nonlinear spring into the state-space description to develop the solution under different loading conditions. With the aid of the state-space representation, the closed-form solution of the displacement response can be analytically obtained, for the case of force control. Taking into account the in-resistance of compression of biological soft tissue, the exact response to a sinusoidal cyclic force with non-zero mean was for the first time derived. In contrast, under displacement input, the state-space representation resulted in a nonlinear dynamical system and made the analytical solution of the force response is unreachable. Thus, we developed a numerical scheme to solve the corresponding force response with the aid of the state-space representation. Based on the analytical solution, we further demonstrated that conventional dynamic mechanical analysis (DMA) testing, which has been widely used in modeling linear viscoelastic materials, is not suitable for the identification of the nonlinear, viscoelastic mechanical features of the TV chordae.