Mathematical model of an innate immune response to cutaneous wound in the presence of local hypoxia

Abstract

We developed a 2D multi-agent stochastic model of interaction between cellular debris, bacteria and neutrophils in the surface cutaneous wound with local hypoxia. Bacteria, which grow logistically with a maximum carrying capacity, and debris are phagocytosed by neutrophils with probability determined by the partial pressure of oxygen in the tissue, pO2 = 4–400 mmHg, according to the Michaelis-Menten equation with Km = 40 mmHg. The influx of new neutrophils depends linearly (k = 0.05–0.2) on the amount of (a) platelets and (b) neutrophils, which are in contact with bacteria or debris. Each activated neutrophil can accomplish a certain amount of phagocytosis, nmax = 5–20, during its lifespan, T = 1–5 days. The universe of outcomes consists of (a) bacteria clearance (high k and nmax), (b) infection is not cleared by neutrophils (low k and nmax), and (c) intermittent (quasiperiodic) bursts of inflammation. In the absence of infection, phagocytosis stops within 48 h. We found that pO2 alone did not change the type of outcome, but affects the number of recruited neutrophils and inflammation duration (in the absence of infection by up to 10 and 5 %, respectively).