A multi-electrode array and inversion technique for retrieving six conductivities from heart potential measurements

A method for accurately finding cardiac bidomain conductivity parameters is a crucial part of efforts to study and understand the electrical functioning of the heart. The bidomain model considers current flowing along (longitudinal) and across (transverse) sheets of cardiac fibres, as well as between these sheets (normal), in both the extracellular and intracellular domains, which leads to six conductivity values. To match experimental studies, such a method must be able to determine these six conductivity values, not just the four where it is assumed that the transverse and normal conductivities are equal. This study presents a mathematical model, solution technique, multi-electrode array and two-pass inversion method, which can be used to retrieve all six conductivities from measurements of electrical potential made on the array. Simulated measurements of potential, to which noise is added, are used to demonstrate the ability of the method to retrieve the conductivity values. It is found that not only is it possible to accurately retrieve all six conductivity values, as well as a value for fibre rotation angle, but that the accuracy of such retrievals is comparable to the accuracy found in a previous study when only four conductivities (and fibre rotation) were retrieved.

[1]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[2]  David Kilpatrick,et al.  Estimation of the Bidomain Conductivity Parameters of Cardiac Tissue From Extracellular Potential Distributions Initiated by Point Stimulation , 2010, Annals of Biomedical Engineering.

[3]  Bruce H Smaill,et al.  Three Distinct Directions of Intramural Activation Reveal Nonuniform Side-to-Side Electrical Coupling of Ventricular Myocytes , 2009, Circulation. Arrhythmia and electrophysiology.

[4]  Bruce H Smaill,et al.  Laminar Arrangement of Ventricular Myocytes Influences Electrical Behavior of the Heart , 2007, Circulation research.

[5]  Mark L. Trew,et al.  Construction and Validation of a Plunge Electrode Array for Three-Dimensional Determination of Conductivity in the Heart , 2008, IEEE Transactions on Biomedical Engineering.

[6]  A. M. Scher,et al.  Influence of Cardiac Fiber Orientation on Wavefront Voltage, Conduction Velocity, and Tissue Resistivity in the Dog , 1979, Circulation research.

[7]  Transmyocardial ST potential distributions in ischaemic heart disease , 2005 .

[8]  L. Clerc.  Directional differences of impulse spread in trabecular muscle from mammalian heart. , 1976, The Journal of physiology.

[9]  P. Steendijk,et al.  The four-electrode resistivity technique in anisotropic media: theoretical analysis and application on myocardial tissue in vivo , 1993, IEEE Transactions on Biomedical Engineering.

[10]  Otto H. Schmitt,et al.  Biological Information Processing Using the Concept of Interpenetrating Domains , 1969 .

[11]  Darren A Hooks,et al.  Myocardial segment-specific model generation for simulating the electrical action of the heart , 2007, Biomedical engineering online.

[12]  Peter R. Johnston,et al.  The effect of conductivity values on ST segment shift in subendocardial ischaemia , 2003, IEEE Transactions on Biomedical Engineering.

[13]  K. Foster,et al.  Dielectric properties of tissues and biological materials: a critical review. , 1989, Critical reviews in biomedical engineering.

[14]  B. Roth.  Electrical conductivity values used with the bidomain model of cardiac tissue , 1997, IEEE Transactions on Biomedical Engineering.

[15]  B. Taccardi,et al.  Spread of Excitation in a Myocardial Volume: , 1993, Journal of cardiovascular electrophysiology.

[16]  Joakim Sundnes,et al.  Simulation of ST segment changes during subendocardial ischemia using a realistic 3-D cardiac geometry , 2005, IEEE Transactions on Biomedical Engineering.

[17]  P. Hunter,et al.  Laminar structure of the heart: a mathematical model. , 1997, The American journal of physiology.

[18]  Robert Plonsey,et al.  The Four-Electrode Resistivity Technique as Applied to Cardiac Muscle , 1982, IEEE Transactions on Biomedical Engineering.

[19]  Elad Gilboa,et al.  Estimating Electrical Conductivity Tensors of Biological Tissues Using Microelectrode Arrays , 2012, Annals of Biomedical Engineering.

[20]  Peter R. Johnston,et al.  The importance of anisotropy in modeling ST segment shift in subendocardial ischaemia , 2001, IEEE Transactions on Biomedical Engineering.

[21]  R. Coronel,et al.  The effect of lesion size and tissue remodeling on ST deviation in partial-thickness ischemia. , 2007, Heart rhythm.

[22]  Barbara M. Johnston,et al.  A new approach to the determination of cardiac potential distributions: application to the analysis of electrode configurations. , 2006, Mathematical biosciences.

[23]  Peter R. Johnston,et al.  Cardiac conductivity values — A challenge for experimentalists? , 2011, 2011 8th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the 2011 8th International Conference on Bioelectromagnetism.

[24]  Barbara M. Johnston,et al.  Possible Four-Electrode Configurations for Measuring Cardiac Tissue Fiber Rotation , 2007, IEEE Transactions on Biomedical Engineering.

[25]  Roger C Barr,et al.  A biophysical model for cardiac microimpedance measurements. , 2010, American journal of physiology. Heart and circulatory physiology.

[26]  Karl A. Tomlinson,et al.  Cardiac Microstructure: Implications for Electrical Propagation and Defibrillation in the Heart , 2002, Circulation research.

[27]  William H. Press,et al.  Numerical recipes , 1990 .

[28]  H Zhang,et al.  Models of cardiac tissue electrophysiology: progress, challenges and open questions. , 2011, Progress in biophysics and molecular biology.

[29]  Robert Michael Kirby,et al.  Application of Stochastic Finite Element Methods to Study the Sensitivity of ECG Forward Modeling to Organ Conductivity , 2008, IEEE Transactions on Biomedical Engineering.

[30]  A. M. Scher,et al.  Effect of Tissue Anisotropy on Extracellular Potential Fields in Canine Myocardium in Situ , 1982, Circulation research.

[31]  William M. Smith,et al.  Linear Electrode Arrays for Stimulation and Recording Within Cardiac Tissue Space Constants , 2008, IEEE Transactions on Biomedical Engineering.

[32]  Barbara M. Johnston,et al.  Analysis of Electrode Configurations for Measuring Cardiac Tissue Conductivities and Fibre Rotation , 2006, Annals of Biomedical Engineering.

[33]  Y. Kim,et al.  Geometric effects on resistivity measurements with four-electrode probes in isotropic and anisotropic tissues , 1998, IEEE Transactions on Biomedical Engineering.