The role of structural viscoelasticity in deformable porous media with incompressible constituents: applications in biomechanics

TL;DR

This paper uses mathematical analysis to show how structural viscoelasticity influences fluid velocity in deformable porous media, with implications for biological tissues and preventing tissue damage during sudden load changes.

Contribution

First explicit solutions for a 1D poro-visco-elastic model under step and trapezoidal loads are derived, highlighting the importance of viscoelasticity in tissue response.

Findings

Fluid velocity can become unbounded with insufficient viscoelasticity.

Dimensionless parameters help design tissue properties to prevent damage.

Application to biological tissues like cartilage and brain tissues.

Abstract

The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.