Spatio-temporal Models of Lymphangiogenesis in Wound Healing

TL;DR

This paper develops and compares two PDE models of lymphangiogenesis during wound healing, incorporating biological hypotheses, flow effects, and data-driven parameters, to better understand lymphatic network regeneration.

Contribution

It introduces two novel PDE models for lymphangiogenesis based on different biological hypotheses and includes flow effects, filling a gap in mathematical modeling of lymphatic regeneration.

Findings

Models align with biological literature

Flow effects influence lymphangiogenesis patterns

Parameter estimates are biologically plausible

Abstract

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.