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 dist ribution of power. Our purpose was to design such a fast executing com puter code, MGARRAY, to compute steady-state temperatures from ferroma gnetic 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 inho mogeneity 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 str aight, parallel seeds and from an array of seeds that were curved and tilted randomly by 13 degrees. Results: On a personal workstation the Central Processing Unit (CPU) time of MGARRAY was under 4 min. We foun d that the median temperature in a predetermined target volume was sim ilar to 0.8 degrees C higher in the straight array than in the curved array. At specific locations within the target volume temperature diff ered by similar to 0.5-0.9 degrees C, but could differ by up to severa l degrees, depending on proximity to a seed and the level of blood per fusion. Conclusion: These differences can impact on retrospective anal yses whereby temperatures at a few locations are used to infer the ove rall temperature field and blood perfusion levels. The flexibility and computational speed of MGARRAY could potentially lead to a substantia l improvement in both retrospective and prospective hyperthermia treat ment planning.