Stabilized isogeometric formulation of the multi-network poroelasticity and transport model (MPET[formula omitted]) for subcutaneous injection of monoclonal antibodies

Abstract

The MPET2 model couples the multi-network poroelastic theory (MPET) with solute transport equations and provides predictions of the material deformation, fluid dynamics, and solute transport in different compartments of a deformable multiple-porosity medium. MPET2 offers a comprehensive framework for understanding complex porous media across multiple disciplines. Examples of its applications include studying rock formations, soil mechanics and subsurface reservoirs, investigating biological tissues, modeling groundwater flow and contaminant transport, and optimizing the design of porous materials. Despite the wide range of applications of the model, its numerical discretization has received little attention. Here we propose a stabilized formulation of the MPET2 model. To address the unique challenges posed by the discretization of the MPET2 model, we use multiple techniques including the Fluid Pressure Laplacian stabilization, Streamline Upwind Petrov–Galerkin stabilization, and discontinuity capturing. Our spatial discretization is based on Isogeometric Analysis with higher-order continuity basis functions. The fully discretized governing equations are solved simultaneously with a monolithic algorithm. We perform a convergence study of the proposed formulation. Then, we conduct a series of simulations of subcutaneous injection of monoclonal antibodies under different injection conditions. Our simulations show that the stabilized MPET2 formulation can provide oscillation-free solutions for tissue deformation, fluid flow in the interstitial tissue, blood vessels, and lymphatic vessels, drug absorption in blood vessels and lymphatic vessels, as well as drug transport in each compartment. We also study the effects of different injection conditions on drug absorption, showing the potential of the proposed model and algorithm in the future optimization of injection strategy.