A 2D Computational Model of Lymphedema and of its Management with Compression Device

Abstract

Abstract. The purpose of this study is to model a lymphedema following a mastectomy and its management (compression therapy). During surgery for breast cancer, an axillary node dissection can be done and cause damages to the lymphatic system leading to a secondary lymphedema located in upper limb. Limb lymphedema is an incurable disease associated with chronic and progressive limb swelling condition. The main clinical consequence of lymphedema is the limb edema, clinically resulting in pain, discomfort, strength reduction and musculoskeletal complications due to limb excessive heaviness. Some devices for lymphedema (e.g. bandaging and garments) could be more personalized, taking into account both characteristics of compressions and patients. Before the evaluation of these therapeutic strategies in humans, an "in silico" approach could be used to investigate the interest of gradual or intermittent compression testing in virtual patients. For that purpose, we developed a simplified model of the lymph flow through the lymphatic system in a whole upper limb including the corresponding interstitial fluid exchanges.

Mathematical Modelling of the Structure and Function of the Lymphatic System

“…Pathogenesis and treatment of lymphedema are one of the most important applications of models of lymph flow in lymphatic vessels. Direct models of lymph flow in lymphatic vessels are not the only way to address edema pathology: in [83], lymph filtration through the extremity was considered with diffusion equations instead of considering flow in separate vessels, and some clinical recommendations (for using of bandages) were proposed.…”

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

“…K) In silico model of the lymph flow through the lymphatic system in a whole upper limb including the corresponding interstitial fluid exchanges (e.g., the pressure of the fluid is shown with the gradient of color) and domain deformation. Reproduced with permission [ 260 ]. Copyright 2017, EDP Sciences.…”

“…developed a 2D computational model to simulate clinical characteristics of lymphedema and explore reports physical compression therapy may reduce limb swelling post-LN dissection ( Fig. 5 K) [ 260 ]. Despite omission of key factors, such as the biophysical properties of patient tissues, this model presents as a powerful tool to design personalized compressive devices for lymphedema management.…”

Simulation‐based reasoning of residual tissue deformations in a two‐chamber test of a lymphedematous leg

“…15 In order to incorporate independent motion of interstitial tissue fluid and solid matrix, important for explaining the reduction of volume of lymphedematous tissue by pneumatic compression, the subcutaneous tissue is modeled as an isotropic elastic permeable porous material filled with fluid. 5,6,12,13 The mass exchange between the interstitial fluid and the matrix fluid (in cells and the vascular system) is disregarded. The validity of the effective stress law and the model of neo-Hookean elastic strain energy for the matrix are assumed.…”

“…Modeling of edema tissue, its deformation and fluid displacement in the subcutaneous tissue (both processes should be included in the description of the chamber test) requires the use of a two-phase model. There are several examples of the application of linear poroelasticity to edema tissues in the literature (e.g., References [5,6,12,13]). These models assume small tissue deformations and linear constitutive relationships.…”