State-space formulations to understand the nonlinear viscoelastic mechanical behavior of tricuspid valve chordae tendineae
Journal
Applied Mathematical Modelling
Journal Volume
149
Start Page
116262
ISSN
0307-904X
Date Issued
2026-01
Author(s)
Abstract
The state-space representation is an alternative description of a dynamical system to the input-output representation in 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 of TV tissue 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 non-negative sinusoidal cyclic force 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 unreachable. Thus, we developed a numerical scheme to solve the corresponding force response under the state-space representation framework. Based on the analytical solution, we further demonstrated that the conventional dynamic mechanical analysis (DMA), 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.
Subjects
Chordae tendineae
Dynamic mechanical test
The nonlinear generalized Kelvin model
The state-space representation
Viscoelastic model
Publisher
Elsevier BV
Type
journal article