Whittaker P, Przyklenk K
Heart Institute, Hospital of the Good Samaritan, Los Angeles, California.
Basic Res Cardiol. 1994 Jan-Feb;89(1):6-15. doi: 10.1007/BF00788673.
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.
我们基于从大鼠心脏获得的实验数据构建了缺血预处理的数学模型。在这个低侧支血流的动物模型中，我们发现，预处理心脏中的梗死面积（以危险区域面积的百分比表示）随着危险区域面积的增加而增加（r = 0.76，p = 0.0007）。相比之下，对照心脏中的梗死面积似乎与危险区域的变化无关。同样，对照心脏中危险区域边缘与坏死区域边缘之间的横向距离并不随危险区域而变化，但在预处理心脏中，横向距离随着危险区域面积的增加而减小（r = -0.67，p = 0.0046）。我们利用这些发现开发了一个简单的模型，该模型提供了对照心脏和预处理心脏中横向距离与危险区域之间以及梗死面积与危险区域之间的数学关系，这些关系与实验数据一致。这些关系使我们提出，在预处理心脏中：1）可能在整个心脏产生或激活一种保护性物质；2）这种保护性物质可能通过扩散进行运输。如果我们假设保护性物质的产生量与缺血和非缺血区域的大小成比例且均匀，那么利用一个简单的扩散模型，我们能够推导出上述变量之间的关系，这些关系与我们的数学模型以及实验数据一致。尽管我们的模型未识别出保护性物质，但其所蕴含的意义为可能增进我们对缺血预处理理解的其他关键实验提供了思路。
