Identification of relaxation modulus of biological soft tissues using low-pass filter and low-order model

Abstract

To predict traumatic injuries using a computational model, accurate mechanical properties of biological materials are required. Especially, soft tissue is a viscoelastic and rate sensitive material that exhibits the decaying stress response when a constant displacement is applied. Thus, it is important to precisely formulate the phenomenon of a stress relaxation, which is readily applicable to computational models. In the current work, we newly developed an identification method of time constants and Young’s moduli for the stress relaxation response of biological soft tissues by assuming that soft tissues can be described by a generalized Maxwell model. Firstly, the decaying stress response was decomposed into a set of slow-to-fast stress components using a low-pass filter. Subsequently, we identified the time constants and Young’s moduli for slow and fast variations independently by solving the optimal problem, in which the correlation coefficient was maximized between each stress component and a corresponding normalized stress component. This method is computationally cost efficient and can semi-automatically determine the number of springs of Maxwell model. By applying the newly proposed method to the experimental data obtained for neural fiber bundles and skeletal muscle fiber bundles subjected to uniaxial stretching, we successfully demonstrated that the stress relaxation response can be well predicted for the mechanical change even in the short time range (0.1–1 s) in addition to the long time range (10–100 s).

Keywords

• relaxation modulus
• biological soft tissues
• low-pass filter
• low-order model
• maximization problem
• curve fitting