A new computer method to quickly and accurately compute steady-state temperatures from ferromagnetic seed heating.

A new, very fast, yet accurate program, MGSEED, has been developed that computes steady-state temperatures from the three-dimensional bioheat transfer equation due to heating by a ferromagnetic seed. Seeds have a self-regulating power absorption characteristic such that their temperatures remain within a few degrees of their Curie transition point. The code is also very flexible, being able to model a seed of any orientation embedded in a tissue domain that can be inhomogeneous with respect to blood perfusion or thermal conductivity. MGSEED uses multigrid (or multilevel) programming techniques as well as a finite volume discretization that exploits knowledge of the approximate shape of the temperature solution very near to a seed. These techniques allow the code to sample the seed very coarsely, requiring only one or two nodes to cross the seed. With these coarse samplings MGSEED calculated very accurate temperatures in under 3 min of CPU time on a Sun Sparcstation 2. The accuracy of MGSEED is demonstrated at different levels of perfusion by comparing its solution in a perpendicular plane that bisects the seed with the known analytical solution. The speed of MGSEED is compared to other methods of solution and it is found that MGSEED performs 14 times faster than successive over relaxation and conjugate gradient methods, and 2.5 times faster than a preconditioned (modified block incomplete Cholesky) conjugate gradient method. It is concluded that the techniques for discretization and solution incorporated into MGSEED can greatly improve the flexibility and speed of hyperthermia treatment planning, which could ultimately lead to an increased level of control over treatment outcome.