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

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.

Weak Solutions in Nonlinear Poroelasticity with Incompressible Constituents

“…First, [13] works explicitly with c 0 > 0 and fully homogeneous Dirichlet boundary conditions; [7] considers mixed boundary conditions in all variables (a Lipschitz domain) and boundary sources, obtaining weak solutions for c 0 = 0, as well as accommodating the case of viscoelasticity in the porous matrix. Further work incorporating and analyzing viscoelasticity in Biot can be found in [5,43]. Both nonlinear works [7,13] utilize Rothe's method for the construction of weak solutions.…”

“…In the case of nonlinear poro-visco-elasticity, viable energy estimates on constructed weak solutions are obtained in[7], from which uniqueness can be deduced. See also[5,43].…”

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

“…We remark that the virtual study illustrated in this section is by no means exhaustive, as it only serves the purpose of providing a general idea of the potential use of mechanism-driven models in the study of the eye-brain connections. Importantly, the multiscale/multiphysics platform provided by OMVS could be further extended to quantitatively explore additional hypotheses on pathogenic mechanisms, such as the role of elastic and viscoelastic properties of the ocular tissues (Bociu et al, 2016(Bociu et al, , 2019Verri et al, 2018) and the effect of microgravity (Salerni et al, 2019). Furthermore, the circuit-based model of the fluid-dynamical connections between the eye and the brain proposed in Salerni et al (2019) could be used to couple the three-dimensional model of the eye shown in Figure 2 with three-dimensional models of the brain such as those shown in Figure 4.…”

Slightly deformable Darcy drop in linear flows

“…Mathematical analyses on the behavior and properties of a fully hydrated poro-elastic or poro-viscous-elastic network focus on either the Biot system where the inertia of the poroelastic or poro-visco-elastic skeleton is important 7,8 , or a similar Darcy poroelastic fluid but without the friction between the fluid phase and the solid phase [9][10][11] . In this work we focus on regimes where the skeleton inertia is negligible and yet the skeleton undergoes elastic displacement, such as connective tissues or intracellular cytosols in many biological appli-cations.…”