Mathematical Modeling of Ischemia–Reperfusion Injury and Postconditioning Therapy

Reperfusion (restoration of blood flow) after a period of ischemia (interruption of blood flow) can paradoxically place tissues at risk of further injury: so-called ischemia–reperfusion injury or IR injury. Recent studies have shown that postconditioning (intermittent periods of further ischemia applied during reperfusion) can reduce IR injury. We develop a mathematical model to describe the reperfusion and postconditioning process following an ischemic insult, treating the blood vessel as a two-dimensional channel, lined with a monolayer of endothelial cells that interact (respiration and mechanotransduction) with the blood flow. We investigate how postconditioning affects the total cell density within the endothelial layer, by varying the frequency of the pulsatile flow and the oxygen concentration at the inflow boundary. We find that, in the scenarios we consider, the pulsatile flow should be of high frequency to minimize cellular damage, while oxygen concentration at the inflow boundary should be held constant, or subject to only low-frequency variations, to maximize cell proliferation.