Thermo-electrical equivalents for simulating the electro-mechanical behavior of biological tissue

Equivalence is one of most popular techniques to simulate the behavior of systems governed by the same type of differential equation. In this case, a thermo-electrical equivalence is considered as a method for modelling the inter-dependence of electrical and mechanical phenomena in biological tissue. We seek to assess this approach for multi-scale models (from micro-structure to tissue scale) of biological media, such as nerve cells and cardiac tissue, in which the electrical charge distribution is modelled as a heat distribution in an equivalent thermal system. This procedure allows for the reduction in problem complexity and it facilitates the coupling of electrical and mechanical phenomena in an efficient and practical way. Although the findings of this analysis are mainly addressed towards the electro-mechanics of tissue within the biomedical domain, the same approach could be used in other studies in which a coupled finite element analysis is required.

[1]  C. Bédard,et al.  Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. , 2003, Biophysical journal.

[2]  Socrates Dokos,et al.  Modeling extracellular electrical stimulation: II. Computational validation and numerical results , 2012, Journal of neural engineering.

[3]  Angus M. Brown,et al.  Focal axonal swellings and associated ultrastructural changes attenuate conduction velocity in central nervous system axons: a computer modeling study , 2013, Physiological reports.

[4]  Andrew D. Jackson,et al.  Towards a thermodynamic theory of nerve pulse propagation , 2009, Progress in Neurobiology.

[5]  D R Hose,et al.  A Thermal Analogy for Modelling Drug Elution from Cardiovascular Stents , 2004, Computer methods in biomechanics and biomedical engineering.

[6]  Ellen Kuhl,et al.  The Living Heart Project: A robust and integrative simulator for human heart function. , 2014, European journal of mechanics. A, Solids.

[7]  Jonas Larsson,et al.  Electromagnetics from a quasistatic perspective , 2007 .

[8]  W. Rall.  Core Conductor Theory and Cable Properties of Neurons , 2011 .

[9]  Pascal Mailley,et al.  A New 3-D Finite-Element Model Based on Thin-Film Approximation for Microelectrode Array Recording of Extracellular Action Potential , 2008, IEEE Transactions on Biomedical Engineering.

[10]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[11]  Ursula van Rienen,et al.  A Comparison of the Hodgkin–Huxley Model and the Soliton Theory for the Action Potential in Nerves , 2012 .

[12]  Andrei Ludu,et al.  Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve. , 2010, Biophysical chemistry.

[13]  Bahman Tahayori,et al.  Modelling extracellular electrical stimulation: IV. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties , 2014, Journal of neural engineering.

[14]  Bahman Tahayori,et al.  Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations , 2012, Journal of neural engineering.

[15]  Patrizia Lamberti,et al.  A Finite Element Model for The Axon of Nervous Cells , 2009 .

[16]  C. Bédard,et al.  Macroscopic models of local field potentials and the apparent 1/f noise in brain activity. , 2008, Biophysical journal.