Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water selfdiffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, s and d) in agreement with theoretical bounds and experimental measurements presented here (syd ’ 0.844 6 0.0545 Szsymm3, r2 5 0.945). The extension to other biological transport phenomena is also discussed.

https://www.pnas.org/content/pnas/98/20/11697.full.pdf

Conductivity tensor mapping of the human brain using diffusion tensor MRI

A bidomain reaction-diffusion model of the human heart was developed, and potentials resulting from normal depolarization and repolarization were compared with results from a compatible monodomain model. Comparisons were made for an empty isolated heart and for a heart with fluid-filled ventricles. Both sinus rhythm and ectopic activation were simulated. The bidomain model took 2 days on 32 processors to simulate a complete cardiac cycle. Differences between monodomain and bidomain results were extremely small, even for the extracellular potentials, which in case of the monodomain model were computed with a high-resolution forward model. Propagation of activation was 2% faster in the bidomain model than in the monodomain model. Electrograms computed with monodomain and bidomain models were visually indistinguishable. We conclude that, in the absence of applied currents, propagating action potentials on the scale of a human heart can be studied with a monodomain model

/pdf/a-comparison-of-monodomain-and-bidomain-reaction-diffusion-5cat5b9n19.pdf

A Comparison of Monodomain and Bidomain Reaction-Diffusion Models for Action Potential Propagation in the Human Heart

We give an overview of "cardiac electrical imaging", which is a generalization of the ECG in which more information is acquired by using a larger array of electrodes to record a sequence of "electrical images". These image sequences can be measured noninvasively on the body surface or invasively on or in the heart muscle itself. Here we briefly discuss the motivation for cardiac electrical imaging, we describe some relevant background electrophysiology to indicate how cardiac electrical imaging can provide information about the heart' s health, and then we give an overview of the technical challenges that arise in displaying, representing, and analyzing these image sequences.

Electrical imaging of the heart

This contribution addresses the extraction of atrial activity (AA) from real electrocardiogram (ECG) recordings of atrial fibrillation (AF). We show the appropriateness of independent component analysis (ICA) to tackle this biomedical challenge when regarded as a blind source separation (BSS) problem. ICA is a statistical tool able to reconstruct the unobservable independent sources of bioelectric activity which generate, through instantaneous linear mixing, a measurable set of signals. The three key hypothesis that make ICA applicable in the present scenario are discussed and validated: 1) AA and ventricular activity (VA) are generated by sources of independent bioelectric activity; 2) AA and VA present non-Gaussian distributions; and 3) the generation of the surface ECG potentials from the cardioelectric sources can be regarded as a narrow-band linear propagation process. To empirically endorse these claims, an ICA algorithm is applied to recordings from seven patients with persistent AF. We demonstrate that the AA source can be identified using a kurtosis-based reordering of the separated signals followed by spectral analysis of the sub-Gaussian sources. In contrast to traditional methods, the proposed BSS-based approach is able to obtain a unified AA signal by exploiting the atrial information present in every ECG lead, which results in an increased robustness with respect to electrode selection and placement.

/pdf/atrial-activity-extraction-for-atrial-fibrillation-analysis-14tmrpfgn0.pdf

Atrial activity extraction for atrial fibrillation analysis using blind source separation

This article summarizes the theoretical underpinnings of both the forward and inverse problems of electrocardiography. Space limitations prohibit describing all of the research work done in these areas, and the author apologizes in advance for any omissions on this account or due to oversight. The article should enable one to gain a better qualitative and quantitative understanding of the heart's electrical activity.

The forward and inverse problems of electrocardiography

The aim of this study was to quantify the effects of selected inhomogeneities and anisotropies on computed electric potential fields associated with the electrocardiographic forward problem. The model construction was based on the Utah Torso model and included geometry for major anatomical structures such as subcutaneous fat, skeletal muscle, and lungs, as well as for epicardial fatpads, major arteries and veins, and the sternum, ribs, spine, and clavicles. Measured epicardial potentials served as the electrical source for solutions to the electrocardiographic forward problem computed using the finite element method (FEM). The geometry of the torso model for each simulation was constant, but different combinations of conductivities were assigned to individual organs or tissues. Comparisons of different conductivity combinations followed one of two basic schemes: 1) a homogeneous torso served as the reference against which we compared simulations with a single organ or tissue and assigned its nominal conductivity, or 2) a fully inhomogeneous torso served as the reference and we removed the effect of individual organs or tissues by assigning it the homogeneous conductivity value. When single inhomogeneities were added to an otherwise homogeneous isotropic model, anisotropic skeletal muscle (at a 15:1 anisotropy ratio) and the right and left lung had larger average effects (12.8, 12.7, and 12.1% relative error (RE), respectively) than the other inhomogeneities tested. Our results for removing single inhomogeneities show that the subcutaneous fat, the anisotropic skeletal muscle (with the degree of anisotropy equal to 7:1), and the lungs have larger average impacts on the body surface potential distributions than other elements of the model (with values of 14.9, 12.6, and 11.7% RE, respectively). The results also show that the size of the effect depended strongly on the distribution of epicardial potentials. The results of this study suggest that accurate representation of tissue inhomogeneity has a significant effect on the accuracy of the forward solution, with regions near the torso surface playing a larger role, in general, than those near the heart.

The effects of inhomogeneities and anisotropies on electrocardiographic fields: a 3-D finite-element study

We provide quantitative information on the effects of selected inhomogeneities and anisotropies on the finite element solution of the forward electrocardiographic field problem. The geometry of the model is based on the Utah Torso model and includes epicardial fatpads, cardiac chambers, major arteries and veins, sternum, ribs, spine and clavicles. Experimentally measured epicardial potentials were used for the electrical source and solutions were computed using the finite element (FE) method. Simulations were performed varying the conductivities assigned to the different structures in the model including anisotropic configurations of the skeletal muscle. Results showed the anisotropic skeletal muscle had a significant impact on the distribution of electrocardiographic fields with an average of 13% percent difference front the homogeneous isotropic case.

R.N. Klepfer

Papers

The effects of inhomogeneities and anisotropies on electrocardiographic fields: a 3-D finite-element study

The effects of inhomogeneities and anisotropies on electrocardiographic fields: a three-dimensional finite element study