Computational models for fluid exchange between microcirculation and tissue interstitium

Abstract

The aim of this work is to develop a computational model able to capture the interplay between microcirculation and interstitial flow. Such phenomena are at the basis of the exchange of nutrients, wastes and pharmacological agents between the cardiovascular system and the organs. They are particularly interesting for the study of effective therapies to treat vascularized tumors with drugs. We develop a model applicable at the microscopic scale, where the capillaries and the interstitial volume can be described as independent structures capable to propagate flow. We facilitate the analysis of complex capillary bed configurations, by representing the capillaries as a onedimensional network, ending up with a heterogeneous system characterized by channels embedded into a porous medium. We use the immersed boundary method to couple the one-dimensional with the three-dimensional flow through the network and the interstitial volume, respectively. The main idea consists in replacing the immersed network with an equivalent concentrated source term. After discussing the details for the implementation of a computational solver, we apply it to compare flow within healthy and tumor tissue samples.

The role of the microvascular network structure on diffusion and consumption of anticancer drugs

“…The existing homogenized model should also be significantly extended to capture the nanoparticles dynamics as a drug delivery vector and their adhesion to the tortuous capillary walls. Numerical results obtained from such a model could be then compared with those presented in the context of the immersed boundary method [42] (based on the fluid transport model [43]), where a simplified, 1D representation of the vascular network is taken into account. This comparison would clarify the impact of the hydraulic properties of the microvasculature on nanomolecules adhesion.…”

A computational model of drug delivery through microcirculation to compare different tumor treatments

“…For this reason, the function is such that the capillary bed is affected by the average of quantities in the interstitial tissue, calculated on a cylindrical surface that represents the actual size of capillaries (see Figure for a sketch). The average value of pressure, velocity or concentration fields, denoted by general function g , over the real surface of the capillary bed is denoted by For a more detailed derivation of this model from the problem formulation where also the capillaries are modeled as three‐dimensional channels, we refer the interested reader to .…”

“…We regulate the flow by enforcing the values of the blood pressure at the extrema of the capillaries. As a result, we prescribe the following conditions: where the total pressure drop Δ p is computed to ensure that the average blood velocity in the network fits with the measured values in healthy human microvasculature . In order to model the administration of the drug through the vascular system, we assume that a fixed drug concentration, denoted with c v , m a x , is injected in the blood stream for a period of time t ∈(0, T ).…”

A computational study of microscale flow and mass transport in vasculatized tumors

“…The non-dimensional groups corresponding to the equations (2) to (5) are the following (6) which denote the hydraulic conductivity of the tissue, the nondimensional lymphatic drainage, the hydraulic conductivity of the capillary walls, and the hydraulic conductivity of the capillary bed, respectively. Using Starling's law of filtration to model the leakage of the capillary walls, the following relation will be obtained with (7) where is an integral expression involving the computation of the mean value of the pressure in the interstitial tissue .…”

“…where the total pressure drop is calculated to ensure that the average velocity of the blood flow fits the measured values in healthy human microvasculature [6].…”