Perturbations in hyperthermia temperature distributions associated with counter-current flow: numerical simulations and empirical verification.

Two numerical techniques are used to calculate the effect of large vessel counter-current flow on hyperthermic temperature distributions. One is based on the Navier-Stokes equation for steady-state flow, and the second employs a convective-type boundary condition at the interface of the vessel walls. Steady-state temperature fields were calculated for two energy absorption rate distributions (ARD) in a cylindrical tissue model having two pairs of counter-current vessels (one pair with equal diameter vessels and another pair with unequal diameters). The first assumed a uniform ARD throughout cylinder; the second ARD was calculated for a tissue cylinder inside an existing four antenna Radiofrequency (RF) array. A tissue equivalent phantom was constructed to verify the numerical calculations. Temperatures induced with the RF array were measured using a noninvasive magnetic resonance imaging technique based on the chemical shift of water. Temperatures calculated using the two numerical techniques are in good agreement with the measured data. The results show: 1) the convective-type boundary condition technique reduces computation time by a factor of ten when compared to the fully conjugated method with little quantitative difference (approximately 0.3 degree C) in the numerical accuracy and 2) the use of noninvasive magnetic resonance imaging (thermal imaging) to quantitatively access the temperature perturbations near large vessels is feasible using the chemical shift technique.