Finite element analysis of biological soft tissue surrounded by a deformable membrane that controls transmembrane flow

Satoko Hirabayashi,Masami Iwamoto

doi:10.1186/s12976-018-0094-9

Abstract

BackgroundMany biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. Mechanical interactions between the solid and the fluid in hydrated porous tissues have been analyzed by finite element methods (FEMs) in which the mixture theory was introduced in various ways. Although most of the tissues are surrounded by deformable membranes that control transmembrane flows, the boundaries of the tissues have been treated as rigid and/or freely permeable in these studies. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows.ResultsFor this, we developed a new nonlinear finite element formulation of the mixture theory, where the nodal unknowns were the pore water pressure and solid displacement. This method allows the control of the fluid flow rate across the membrane using Neumann boundary condition. Using the method, we conducted a compression test of the hydrated porous hyperelastic tissue, which was surrounded by a flaccid impermeable membrane, and a part of the top surface of this tissue was pushed by a platen. The simulation results showed a stress relaxation phenomenon, resulting from the interaction between the elastic deformation of the tissue, pore water pressure gradient, and the movement of fluid. The results also showed that the fluid trapped by the impermeable membrane led to the swelling of the tissue around the platen.ConclusionsThese facts suggest that our new method can be effectively used for the analysis of a large deformation of hydrated porous hyperelastic material surrounded by a deformable membrane that controls transmembrane flow, and further investigations may allow more realistic analyses of the biological soft tissues, such as brain edema, brain trauma, the flow of blood and lymph in capillaries and pitting edema.

Highlights

Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids
The viscous behavior can protect the brain from the hit of skull in the subarachnoid space (SAS) when considering the trabecular network filled with cerebrospinal fluid (CSF) as the hydrated soft tissue
We could neither validate our proposed method using a simple problem with an analytical solution, such as one-dimensional compression, nor compare our results with the results obtained by previously presented numerical methods since there are no studies on numerical methods of the hydrated biological soft tissues surrounded by deformable membranes that control the transmembrane flows

Summary

Introduction

Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows. The subarachnoid space (SAS) between the skull and the brain is filled with a trabecular network and cerebrospinal fluid (CSF) [1,2,3,4,5] (Fig. 1). Most of these tissues are surrounded and partitioned by membranes, and transmembrane flows are controlled by various mechanisms such as valves, barriers, and channels. Consistent with the Monroe-Kellie doctrine, cerebral edemas lead to the development of severe conditions, such as cerebral ischemia, intracranial pressure (ICP) elevation, and intracranial compartmental shifts, resulting in the compression of vital brain structures (herniation) [6]

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