| Heating rates for hyperthermic treatment of cancer are simulated in three dimensions with finite element methods. The 3D finite element formulations of the Maxwell's equations with various types of boundary conditions including radiation boundary conditions are formulated, implemented and tested on analytically known problems. Sparse storage structure is thoroughly studied. Several iterative methods of the conjugate gradient type together with techniques for improving convergence, such as preconditioning and matrix reordering, are implemented and compared. Graphical post-processing capabilities are also explored. The simulation results are shown to compare favorably with measurement data on a phantom treatment model. A real patient model is developed directly from patient CT informations. The interior of the patient is well preserved by generating a finite element mesh from the CT-scan images of the patient. Finite element meshes with element size as small as 0.5cm in the critical regions are generated with more than 80,000 nodes. Resulting matrix equations with over 240,000 unknowns are successfully solved within a couple of hours on an IBM RS6000-320H with 128Mbytes of physical memory and 12Mflops of LINPACK rating (15). Simulation studies from various points of view on the patient model are vividly revealed with color graphics, from which several important conclusions are drawn. This work culminates with a treatment planning procedure for the purpose of making computer simulations a real tool in the clinics. |
