Bioheat Transfer - Bioheat Models

Bioheat Models

Here we present a simplified model of the bioheat equation for steady-state, one-dimensional heat transfer. From a one-dimensional energy balance in the x-direction:

Where is the metabolic heat source term and is the perfusion heat source term, both per unit volume. The thermal conductivity, is a constant.

Pennes proposed an expression for the perfusion term by assuming that the temperatures of blood entering and exiting capillaries are both constant for any small volume of tissue. We can say that the temperatures of the blood at each state are the same as that of the surroundings, namely the arterial temperature and the local tissue temperature. Now we must define the perfusion rate, . This is the ratio of the volumetric flow rate of blood per volume of tissue. Thus we have for the perfusion term:

Where and are the density and specific heat capacity of the blood, respectively.

Combining these two equations results in:

Which is the Pennes Bioheat Equation for one-dimensional, steady-state, heat transfer.