Fast and efficient computer modeling of ferromagnetic seed arrays of arbitrary orientation for hyperthermia treatment planning

Purpose: Effective hyperthermia treatment planning requires an ability to predict temperatures quickly and accurately from an arbitrary distribution of power. Our purpose was to design such a fast executing computer code, MGARRAY, to compute steady-state temperatures from ferromagnetic seed heating, allowing seeds to have arbitrary orientations and to be curved to permit more realistic modeling of clinical situations. We further required flexibility for the tissue domain, allowing inhomogeneity with respect to thermal conductivity and blood perfusion, as well as an arbitrary shaped boundary. Methods and Materials: MGARRAY uses multigrid methods and a finite volume discretization to solve the Pennes bioheat transfer equation in three dimensions. We used MGARRAY to compare temperature distributions that result from an array of straight, parallel seeds and from an array of seeds that were curved and tilted randomly by 13°. Results: On a personal workstation the Central Processing Unit (CPU) time of MGARRAY was under 4 min. We found that the median temperature in a predetermined target volume was ∼0.8°C higher in the straight array than in the curved array. At specific locations within the target volume temperature differed by ∼0.5-0.9°C, but could differ by up to several degrees, depending on proximity to a seed and the level of blood perfusion. Conclusion: These differences can impact on retrospective analyses whereby temperatures at a few locations are used to infer the overall temperature field and blood perfusion levels. The flexibility and computational speed of MGARRAY could potentially lead to a substantial improvement in both retrospective and prospective hyperthermia treatment planning.