Hyperthermia Induced 3D Temperature Distribution in a Human Sarcoma With Tumor Perfusion Reconstructed Using Fractal Interpolation Functions

Essential to the success of optimized thermal treatment during hyperthermia is accurate modeling. Advection of energy due to blood perfusion significantly perturbs the temperature and without accurate estimates of the magnitude of the local tissue blood perfusion it is unlikely that accurate estimates of the temperature distribution can be made. It is shown here that the blood mass flow rate per unit volume of tissue in the Pennes’ bio-heat equation can be modeled using a relative perfusion index (RPI) determined with dynamic-enhanced magnetic resonance imaging (DE-MRI). The existing technology limits the DE-MRI perfusion data to be acquired in a limited number of slices. Consequently, the tumor perfusion data is interpolated using fractal interpolation functions (FIFs), as it has been shown that the RPI data is fractal, and that fractal interpolation is superior to linear interpolation when a 3D fractal-like scaling exists. For illustration, a patient treated with hyperthermia at Duke University Medical Center for a high-grade leg tissue sarcoma is modeled. For control, the resultant temperatures are compared to non-invasively measured temperatures using the MR thermometry technique. Strong correlation is found between the DE-MRI perfusion images, the MR chemical shift images during heating, and the numerical simulation of the temperature field, emphasizing the relation between the DE-MRI measured values and advective heat loss in tissue. The fractal interpolation of DE-MRI data to obtain the 3D perfusion gives a more accurate temperature distribution compared to linear interpolation. For even a better temperature reconstruction, further models need to include large vessels.