Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue

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.

Computational fluid dynamic modeling of the lymphatic system: a review of existing models and future directions

“…Lymphatic drainage is susceptible to pressure and volume changes in the interstitium, and many studies have included the interstitium in their models (Table 1 ). Some studies modeled fluid drainage through the interstitium using Darcy’s law (Ashworth et al 2023 ; Gortberg and Romano (2023); Han et al 2023a , b ; Heppell et al 2013 , 2015 ; Ikhimwin et al 2020 ; Possenti et al 2019 ), which neglects viscous and inertial effects. However, viscous effects can be present in the interstitium under normal conditions (Moore and Bertram 2018 ).…”

“…They also found that the injection depth does not affect lymphatic uptake, which contrasts with the findings of Jayathungage Don et al ( 2021 ). Following this, Han et al ( 2023b ) later improved their transport model to investigate the effects of the drug radius. Additionally, they enhanced the model’s time-efficiency, reducing the computational expense that was a limitation in the prior model, so it could be used in a clinical setting.…”