The Mathematical Modelling of Cooling and Rewarming Patients during Cardiac Surgery

The process of cooling bodies, by the use of a heart lung machine (HLM), is utilised in a number of surgical procedures primarily to reduce the metabolic rate of the organs and hence their consumption of oxygen. On completion of surgery the blood is rewarmed by the HLM. A major consequence at the end of this process is afterdrop: a rapid decrease in the core organ temperature as a result of spatial temperature differences between the core organs and remainder of the body, which can lead to post-operative complications. This report details two mathematical models developed to understand heat transfer processes between the core organs, rectal region and peripheral body parts (primarily skin, muscle and fat). A one compartment spatially independent model, describing the temperature distribution of a single tissue type through which blood perfuses, shows that temperature dependent perfusion reproduces the observed differences in blood and tissue temperatures, whilst temperature independent perfusion does not. The model is extended to account for heat transfer between the blood pool (core), rectal regions and periphery. This three compartmental model is able to qualitatively reproduce the observed temperature differences in the three regions. Analysis of the model shows that a period of constant warming at the end of the rewarming period has a positive effect in reducing afterdrop.