A software framework for solving problems of bioelectricity applying high-order finite elements

Electrical activity in biological media can be described in a mathematical way, which is applicable to computer-based simulation. Biophysically mathematical descriptions provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Examples of these descriptions are Maxwell´s and Poisson´s equations for electromagnetic and electric fields. Commonly, numerical techniques are applied to calculate electrical fields, e.g. the finite element method. Finite elements can be classified on the order of the underlying Interpolation. High-order finite elements provide enhanced geometric flexibility and can increase the accuracy of a solution. The aim of this work is the design of a framework for describing and solving high-order finite elements in the SCIRun/BioPSE software system, which allows geometric modeling, simulation, and visualization for solving bioelectric field problems. Currently, only low-order elements are supported. Our design for high-order elements concerns interpolation of geometry and physical fields. The design is illustrated by an implementation of one-dimensional elements with cubic interpolation of geometry and field variables.