Cardiac conduction system: the graph theoretic approach

Abstract

Cardiac conduction system (CCS) describes the mode of transmission of ionic current through the cardiac myocytes. An unperturbed conduction system is required for the integrity of blood flow and for the prevention of cardiac events. In keeping with the CCS as an electrical system, this paper treated the ionic current as an electrical circuit flow with nodal and conducting structures. This is not novel. What may be unique and appealing is the graph theoretic method by which the work is couched. As electric current is a directed flow, directed graph (digraph) theory was used in the conduction system schematics, which in turn aided the resulting matrix analysis. Make no mistake, this work does not model the electrical behaviour of the components of the CCS. In a bid to have an insight into the patho-physiology inherent in the system, the concept of efficiency (of the CCS) was discussed using the nodal and conducting structures. Reasonable clues suggest that undue resistance to flow may be culpable in cardiac events. Keywords: circuit; source and sink; matrix; efficiency; patho-physiology.