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 (∼0.3°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.