Linear algebraic transformations of the bidomain equations: Implications for numerical methods

• Published in: Mathematical biosciences Vol. 120; no. 2; pp. 127 - 145
• Main Authors: Hooke, N., Henriquez, C.S., Lanzkron, P., Rose, D.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.04.1994; Elsevier Science
• Subjects: Animals; Biological and medical sciences; Computerized, statistical medical data processing and models in biomedicine; Electrophysiology; Heart - physiology; Humans; Linear Models; Mathematics; Medical sciences; Models and simulation; Models, Cardiovascular; Tissue; Propagation; Linear transformation; Linear algebra; Myocardium; Numerical method; Membrane potential; Mathematical model
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/0025-5564(94)90049-3

A mathematical framework is presented for the treatment of the bidomain equations used to model propagation in cardiac tissue. This framework is independent of the model used to represent membrane ionic currents and incorporates boundary conditions and other constraints. By representing the bidomain equations in the operator notation Lφ = F ̃ , various algebraic transformations can be expressed as PLQ -1ψ = P F ̃ , where P and Q are linear operators. The authors show how previous work fits into this framework and discuss the implications of various transformation for numerical methods of solution. Although such transformations allow many choices of independent variable, these results emphasize the fundamental importance of the transmembrane potential.