Fadil Santosa, Principal Investigator

Mathematical Model of Human Atrial Fibrillation; Two-Dimensional Guillotine and Non-Guillotine Cutting Stock Problems

This research involved the study of electrophysiology in the heart. Specifically, it centered in the spatial propagation of waves of electrical activity occurring in normal and diseased hearts with a view toward exploring various therapeutic strategies such as tissue ablation, electrical defibrillation, and pharmacological treatments.

An object-oriented approach was adopted in order to attempt simulation of electrical activity in the entire human atria using detailed biophysical models of atrial cell electrophysiology. A sound numerical time-integration scheme with backward-differentiation time-stepping, a modified Newton nonlinear solver, and an iterative linear solver were all used along with an explicit integrator. Parallel versions of these codes were implemented on the Origin 2000. A parallel version was tested on the IBM SP using a beta-version c++ compiler.

These models were supplemented by finite element models of radio-frequency ablation of atrial tissue as well as boundary element models of sensing of electrical activation using leads currently under research at Medtronic.

The use of mathematical models in the design of therapies holds considerable promise. With detailed information on the effects of genetic mutations on protein function, the ability to incorporate such data into cellular models, and better models of the action of drugs on cellular processes, the researchers found themselves in a position to reconstruct the function and disease of human organs and to explore therapeutic strategies.

This research group continued to investigate ways to find stock-cutting patterns so that order demands are not exceeded and waste is minimized. The group developed and coded several algorithms for solving various twodimensional cutting stock problems. The methods include simulated annealing technique and an integer programming approach. The large size of realistic problems required the use of the Supercomputing Institute’s resources.

Research Group

Anton Leykin, Graduate Student Researcher