SIGEST

Abstract

It is hard to imagine a more captivating topic from human physiology than the heart. It is the engine of our human existence, and due to its centrality, something that we all know a moderate amount about, from the basic structural and operational principles we learn as school children, to the medical familiarity that we inevitably obtain through our life experiences. The heart also has a huge symbolic role in our society, for example, a coach telling a team that it needs to show more heart, and hearts with initials carved into trees. A simple web search on “have a heart” demonstrates the term being associated with everything from support for families of children with cancer, to guinea pig rescue. Correspondingly, it is hard to imagine a more comprehensive representative of the breadth and power of modern scientific computing than this issue's SIGEST paper from the SIAM Journal on Scientific Computing, “A Parallel Multilevel Technique for Solving the Bidomain Equation on a Human Heart with Purkinje Fibers and a Torso Model” by T. Washio, J. Okada, and T. Hisada. This paper contains all the elements of scientific computing research: a complex mathematical model utilizing partial and ordinary differential equations; mathematical analysis of the properties of the model; computational formulation of the model using sophisticated multigrid techniques; challenging implementation in a parallel computing environment; and meaningful, practical computational results. The property that is modeled in this paper is the electrical excitation propagation of the heart. Doing this accurately requires modeling both the heart and the torso that surrounds it. It also requires a complex three-dimensional set of equations that captures behavior within cells and across cell membranes. The multigrid approach that is applied to this set of equations utilizes finite element discretization with a fine mesh around the heart and a coarser mesh covering the torso. Two computational applications of the model that most readers are familiar with, and that require the full scope of complexity of the model, are a defibrillator (in particular an implantable cardioverter defibrillator) and an electrocardiogram. The modeling of the Purkinje fiber network that is referenced in the paper's title is indispensable to modeling these applications. This paper will be a wonderful reference for researchers interested in modeling of the heart, but much more generally, it will serve as an excellent example to students in applied mathematics and scientific computing of the current scope and value of these fields. And next time you walk by a defibrillator, you'll think not only about the heart, but also about partial differential equations, multigrid methods, and parallel computers.