A stabilized linear finite element method for anisotropic poroelastodynamics with application to cardiac perfusion

Area of Science:

• Computational mechanics
• Biomedical engineering
• Solid mechanics

Background:

• Nonlinear poroelasticity is essential for modeling biological tissues like the heart.
• Anisotropic properties of the solid skeleton significantly influence poroelastic behavior.
• Accurate numerical methods are needed for implicit time integration of complex poroelastic formulations.

Purpose of the Study:

• To develop and verify a stabilized finite element method for nonlinear poroelasticity.
• To investigate the influence of anisotropic myocardial properties on left ventricle (LV) pore pressure dynamics.
• To correlate pore pressure variations with LV dynamics and added mass.

Main Methods:

• A variational multiscale method was employed for stabilization of a linear finite element method.
• A monolithic formulation integrating structural dynamics and Darcy flow was implemented.
• The method was verified using hyperelastic and poroelastic benchmark cases and validated on a human LV model.

Main Results:

• The numerical method demonstrated second-order accuracy in grid convergence studies.
• Simulations showed that myocardial anisotropicity substantially affects pore pressure.
• Pore pressure variations were correlated with LV dynamics, peaking at systole.

Conclusions:

• The proposed method accurately simulates nonlinear poroelasticity, particularly for anisotropic biological tissues.
• Myocardial anisotropicity plays a critical role in cardiac pore pressure regulation.
• The findings provide valuable insights into the biomechanics of the left ventricle.