Mixture Theory-Based Finite Element Approach for Analyzing the Edematous Condition of Biological Soft Tissues

In hydrated soft biological tissues experiencing edema, which is typically associated with various disorders, excessive fluid accumulates and is encapsulated by impermeable membranes. In certain cases of edema, an indentation induced by pressure persists even after the load is removed. The depth and duration of this indentation are used to assess the treatment response. This study presents a mixture theory-based approach to analyzing the edematous condition. The finite element analysis formulation was grounded in mixture theory, with the solid displacement, pore water pressure, and fluid relative velocity as the unknown variables. To ensure tangential fluid flow at the surface of tissues with complex shapes, we transformed the coordinates of the fluid velocity vector at each time step and node, allowing for the incorporation of the transmembrane component of fluid flow as a Dirichlet boundary condition. Using this proposed method, we successfully replicated the distinct behavior of pitting edema, which is characterized by a prolonged recovery time from indentation. Consequently, the proposed method offers valuable insights into the finite element analysis of the edematous condition in biological tissues.