Tissue–fluid interface analysis using biphasic finite element method

A Hybrid Biphasic Mixture Formulation for Modeling Dynamics in Porous Deformable Biological Tissues

The primary aim of this study is to establish the theoretical foundations for a solid-fluid biphasic mixture domain that can accommodate inertial effects and a viscous interstitial fluid, which can interface with a dynamic viscous fluid domain. Most mixture formulations consist of constituents that are either all intrinsically incompressible or compressible, thereby introducing inherent limitations. In particular, mixtures with intrinsically incompressible constituents can only model wave propagation in the porous solid matrix, whereas those with compressible constituents require internal variables, and related evolution equations, to distinguish the compressibility of the solid and fluid under hydrostatic pressure. In this study, we propose a hybrid framework for a biphasic mixture where the skeleton of the porous solid is intrinsically incompressible but the interstitial fluid is compressible. We define a state variable as a measure of the fluid volumetric strain. Within an isothermal framework, the Clausius-Duhem inequality shows that a function of state arises for the fluid pressure as a function of this strain measure. We derive jump conditions across hybrid biphasic interfaces, which are suitable for modeling hydrated biological tissues. We then illustrate this framework using confined compression and dilatational wave propagation analyses. The governing equations for this hybrid biphasic framework reduce to those of the classical biphasic theory whenever the bulk modulus of the fluid is set to infinity and inertia terms and viscous fluid effects are neglected. The availability of this novel framework facilitates the implementation of finite element solvers for fluid-structure interactions at interfaces between viscous fluids and porous-deformable biphasic domains, which can include fluid exchanges across those interfaces.

Finite Element Implementation of Biphasic-Fluid Structure Interactions in febio

In biomechanics, solid-fluid mixtures have commonly been used to model the response of hydrated biological tissues. In cartilage mechanics, this type of mixture, where the fluid and solid constituents are both assumed to be intrinsically incompressible, is often called a biphasic material. Various physiological processes involve the interaction of a viscous fluid with a porous-hydrated tissue, as encountered in synovial joint lubrication, cardiovascular mechanics, and respiratory mechanics. The objective of this study was to implement a finite element solver in the open-source software febio that models dynamic interactions between a viscous fluid and a biphasic domain, accommodating finite deformations of both domains as well as fluid exchanges between them. For compatibility with our recent implementation of solvers for computational fluid dynamics (CFD) and fluid-structure interactions (FSI), where the fluid is slightly compressible, this study employs a novel hybrid biphasic formulation where the porous skeleton is intrinsically incompressible but the fluid is also slightly compressible. The resulting biphasic-FSI (BFSI) implementation is verified against published analytical and numerical benchmark problems, as well as novel analytical solutions derived for the purposes of this study. An illustration of this BFSI solver is presented for two-dimensional (2D) airflow through a simulated face mask under five cycles of breathing, showing that masks significantly reduce air dispersion compared to the no-mask control analysis. In addition, we model three-dimensional (3D) blood flow in a bifurcated carotid artery assuming porous arterial walls and verify that mass is conserved across all fluid-permeable boundaries. The successful formulation and implementation of this BFSI solver offers enhanced multiphysics modeling capabilities that are accessible via an open-source software platform.

Characteristics of time-varying intracranial pressure on blood flow through cerebral artery: A fluid–structure interaction approach

Elevated intracranial pressure is a major contributor to morbidity and mortality in severe head injuries. Wall shear stresses in the artery can be affected by increased intracranial pressures and may lead to the formation of cerebral aneurysms. Earlier research on cerebral arteries and aneurysms involves using constant mean intracranial pressure values. Recent advancements in intracranial pressure monitoring techniques have led to measurement of the intracranial pressure waveform. By incorporating a time-varying intracranial pressure waveform in place of constant intracranial pressures in the analysis of cerebral arteries helps in understanding their effects on arterial deformation and wall shear stress. To date, such a robust computational study on the effect of increasing intracranial pressures on the cerebral arterial wall has not been attempted to the best of our knowledge. In this work, fully coupled fluid–structure interaction simulations are carried out to investigate the effect of the variation in intracranial pressure waveforms on the cerebral arterial wall. Three different time-varying intracranial pressure waveforms and three constant intracranial pressure profiles acting on the cerebral arterial wall are analyzed and compared with specified inlet velocity and outlet pressure conditions. It has been found that the arterial wall experiences deformation depending on the time-varying intracranial pressure waveforms, while the wall shear stress changes at peak systole for all the intracranial pressure profiles.

Modeling of adhesion, protrusion, and contraction coordination for cell migration simulations

Cell migration is a highly complex, dynamical biological phenomenon that involves precise spatio-temporal coordination of distinctive sub-processes including adhesion, protrusion, and contraction of the cell. Observations of individual tumor cell migration reveal that cells generally exhibit either mesenchymal-type or amoeboid-type migration modes in native like environments. However, it has also been observed that some migrating cells are capable of morphologically adapting to their environment by modifying their type of migration. Recent studies suggest in fact that changes in biophysical and biomechanical properties of tumor cells can reversibly control their transition from one type of migration to the other. These changes may be caused by internal cell biomechanical mechanisms as well as mechanical and topological properties of the extracellular matrix. In order to understand the complex transition between the two modes and the role played by internal cellular mechanics during migration, we have developed a novel axisymmetric hyperviscoelastic cell model to simulate the dynamical behavior of a migrating cell. Numerical results from our study quantitatively demonstrate that the biomechanical properties of the cell may play an important role in the amoeboid-mesenchymal transition during migration. Our study will therefore not only help in creating a new platform for simulating cellular processes but will also provide insights into the role of sub-cellular mechanics in regulating various modes of migration during tumor invasion and metastasis.