Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue

SIMPLE SUMMARY: The lymphatic system plays a crucial role in maintaining fluid and solute balance in biological tissue, which makes the subcutaneous injection a common approach for delivering therapeutic agents through the lymphatic pathway. The transport of drug solutes is regulated by the interstitial fluid pressure. In our study, a time-efficient poroelastic model is developed to mimic pressure relaxation and build-up in the soft skin tissue. This method can accurately and time-efficiently capture the evolution of pressure, which is validated against both the analytical solution and numerical solution of the previous poroelastic model. The increasing porosity and permeability due to deformation alleviate the high pressure caused by the injection. Furthermore, an improved solute transport model is developed to better address the microscopic properties of the lymphatic vessel membrane. The effects of a varying Stokes radius of drug solute and vessel network structures are investigated on lymphatic uptake. Our comprehensive computation model provides a time-efficient and reliable research tool for studying solute transport into the lymphatic system, which can be utilized to support decision-making regarding lymphatic disturbed diseases. ABSTRACT: Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. An improved Kedem–Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. At last, the effect of different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. In this paper, we provide a novel and time-efficient computational model for solute transport across the lymphatic vasculature connecting the microscopic properties of the lymphatic vessel membrane to the macroscopic drug absorption.