Temperature-dependent versus constant-rate blood perfusion modelling in ferromagnetic thermoseed hyperthermia: results with a model of the human prostate.

Finite-element solutions to the Pennes bioheat equation are obtained with a model of a tumour-containing, human prostate and surrounding normal tissues. Simulations of ferromagnetic hyperthermia treatments are conducted on the tissue model in which the prostate is implanted with an irregularly spaced array of thermoseeds. Several combinations of thermoseed temperatures with different Curie points are investigated. Non-uniform, constant-rate blood perfusion models are studied and compared with temperature-dependent descriptions of blood perfusion. Blood perfusions in the temperature-dependent models initially increase with tissue temperature and then decrease at higher temperatures. Simulations with temperature-dependent versus constant-rate blood perfusion models reveal significant differences in temperature distributions in and surrounding the tumour-containing prostate. Results from the simulations include differences (between temperature-dependent and constant-rate models) in (1) the percentage of normal tissue volume and tumour volume at temperatures > 42 degrees C, and (2) temperature descriptors in the tumour (subscript t) and normal (subscript n) tissues including Tmax.t, Tmin.t and Tmax.n. Isotherms and grey-scale contours in the tumour and surrounding normal tissues are presented for four simulations that model a combination of high-temperature thermoseeds. Several simulations show that Tmin.t is between 1.7 and 2.6 degrees C higher and Tmax.n is between 2.1 and 3.3 degrees C higher with a temperature-dependent versus a comparable constant-rate blood perfusion model. The same simulations reveal that the percentages of tumour volume at temperatures > 42 degrees C are between 0 and 68% higher with the temperature-dependent versus the constant-rate perfusion model over all seed combinations studied. In summary, a numerical method is presented which makes it possible to investigate temperature-dependent, continuous functions of blood perfusion in simulations of hyperthermia treatments. Simulations with this numerical method reveal that the use of constant-rate instead of temperature-dependent blood perfusion models can be a conservative approach in treatment planning of ferromagnetic hyperthermia.