Heat loss and blood flow during hyperthermia in normal canine brain. II: Mathematical model.

A mathematical model for heating and cooling during hyperthermia has been developed from an appropriate solution of a bioheat transfer equation. Predicted cooling rates obtained from the model have been compared with cooling rates obtained from experiments performed on both perfused and non-perfused normal canine brain tissue. The agreement between the predicted and observed cooling rates in non-perfused tissue is satisfactory (within 6-11 per cent) and provides confidence that the conduction process is being accurately represented. The model is then used to estimate the relative contribution of conductive and convective (blood flow) heat loss during cooling for the in vivo experiments. Estimates of blood flow dynamics are made from cooling data taken early and late in a heating course using the model to correct for conductive heat loss. Simplified forms of the bioheat transfer equation are examined. An adequate model for the observed cooling data is one that treats heat loss (both conduction and blood flow) as a heat sink (i.e. an effective perfusion model) rather than an effective thermal conductivity model.