Reduction of infarct size in vivo with ischemic preconditioning: Mathematical evidence for protection via non-ischemic tissue

Summary We constructed a mathematical model of ischemic preconditioning based on experimental data obtained from rat hearts. In this animal model of low collateral blood flow, we found that infarct size in preconditioned hearts, expressed as a percentage of area at risk, increased as the size of the area at risk increased (r=0.76, p=0.0007). In contrast, infarct size in control hearts appeared independent of changes in area at risk. Similarly, the lateral distance between the edge of the area at risk and the edge of the area of necrosis did not vary with risk region in control hearts, but in preconditioned hearts, lateral distance decreased as the size of the area at risk increased (r=–0.67, p=0.0046). We used these findings to develop a simple model which provided mathematical relationships between lateral distance and area at risk and between infarct size and area at risk for both control and preconditioned hearts that were consistent with the experimental data. These relationships led us to propose that in preconditioned hearts 1) a protective substance may be produced or activated throughout the heart, and 2) that the protective substance may be transported by diffusion. If we assumed uniform production of protective substance in an amount proportional to the size of the ischemic and non-ischemic areas, we were able to derive, using a simple diffusion model, relationships between the above variables that were consistent with our mathematical model and with the experimental data. Although our model does not identify the protective substance, its implications provide ideas for additional crucial experiments that may enhance our understanding of ischemic preconditioning.List of abbreviations used A_N area of necrosis - A_N/A_R area of necrosis expressed as a fraction of the area at risk - A_R area at risk - C concentration of protective substance; C₁ inside the area at risk, C₂ outside the area at risk - d diffusion distance - LV left ventricle - m amount of protective substance supplied to the area at risk - s lateral distance between the edge of the infarct and the edge of the area at risk - t thickness of the area at risk - w width of the area at risk