Multifield Modeling and Simulation of Nutrient Transport in Mechanically Stressed Meniscus Tissue

Abstract

Insights into the transport mechanisms of nutrients are essential for understanding the pathophysiology of menisci. In the present work, we focus on the modeling and numerical simulation of the transport of glucose molecules in mechanically stressed meniscus tissue. Therefore, a multifield model based on the theory of porous media is created. Due to a biphasic approach, the major phases of the solid and the fluid are represented. The description of the transport processes of the uncharged nutrient molecules, such as convection and diffusion, is given by three coupled partial differential equations valid for large deformations. Numerical simulations are performed for everyday types of stress such as (I) lying, (II) two-legged stance, (III) one-legged stance, (IV) level walking, and (V) stair descending using the finite element method. The results show that diffusion is the dominant process. However, in parts of the meniscus, the delivery of glucose can be improved by convection due to mechanical loading. Based on these basic insights, the model can now be adapted to individual patient's meniscus geometries. The model can thus give insights into the suitability of loading scenarios for rehabilitation after meniscus damage.