Experimental validation for the interconversion between generalized Kelvin–Voigt and Maxwell models using human skin tissues

Abstract

Mechanical properties of biological systems provide essential insights into their component, physiological function, and disease mechanism under various conditions, such as age, health, and other environmental factors. Viscoelasticity is one of the most important and investigated properties to study biomaterials, cells, and tissues, as they exhibit the characteristics of both fluid-like behavior, viscosity, and solid-like behavior, elasticity. Various mathematical models, such as the Kelvin–Voigt and Maxwell models, have been developed and practiced to estimate and extract viscoelastic properties. However, one of the inherent challenges with the use of these models is the poor transferability of mathematically estimated viscoelastic properties across different models, largely due to variations in constituent elements and their arrangements within each model. This issue impedes the interconversion of parameters of one model to another and complicates comparison across models. In this study, we demonstrate the equivalence between the generalized Maxwell and generalized Kelvin-Voigt models through two distinct approaches: indirect, Maxwell model-based Kelvin-Voigt model estimation and direct, curve fitting-based Kelvin-Voigt model estimation. We utilized human melanoma skin tissues to estimate viscoelastic properties using the Prony series. The estimated parameters and resulting viscoelastic properties revealed no significant difference between the two approaches and between the two patients. This study is the first experimental validation of the mathematical interconversion of the two models, signifying that this approach will enable an accurate and objective analysis and comparison of mechanical properties across various viscoelastic models.