On modeling two-dimensional time-dependent low-density lipoprotein (LDL) transport to the arterial intima: Effect of anisotropic permeability and diffusivity

A two-dimensional time-dependent single-layer model is presented to describe the low-density lipoprotein (LDL) transport inside the intima region of the arterial wall. The intima is treated as a homogeneous anisotropic porous medium with anisotropic permeability and diffusivity. The Darcy–Brinkman and mass transport equations are employed to model hydrodynamic and LDL transport phenomena within the intima, while the endothelial cell layer and internal elastic lamina are treated as a permeable wall with relevant boundary conditions. The governing equations for the hydrodynamic problem are solved analytically. In contrast, mass transport equations are tackled by using the Finite Difference Method (FDM), employing the method of lines for discretization. Understanding the impact of anisotropic permeability and anisotropic diffusivity on LDL concentration in the intima with time is one of the novel aspects of this work. The analysis reveals that when horizontal diffusivity prevails over vertical diffusivity, a lower LDL concentration contributes to a reduction in LDL buildup within the intima. Furthermore, the influence of anisotropic diffusivity is more significant compared to the effect of anisotropic permeability inside the intima. The present study demonstrates that the LDL distribution remains uniform throughout the intima and approaches a steady-state condition over time. This model comprehends our understanding of how LDL accumulates within the intima. These findings offer valuable insights into preventing the initiation of plaque formation and the early phases of atherosclerosis.