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, pO ₂  = 4–400 mmHg, according to the Michaelis-Menten equation with K _m  = 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, n _max  = 5–20, during its lifespan, T = 1–5 days. The universe of outcomes consists of (a) bacteria clearance (high k and n _max ), (b) infection is not cleared by neutrophils (low k and n_max), and (c) intermittent (quasiperiodic) bursts of inflammation. In the absence of infection, phagocytosis stops within 48 h. We found that pO ₂ 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).