Analysis of Electrode Configurations for Measuring Cardiac Tissue Conductivities and Fibre Rotation

Which bidomain conductivity is the most important for modelling heart and torso surface potentials during ischaemia?

Mathematical simulations using the bidomain model, which represents cardiac tissue as consisting of an intracellular and an extracellular space, are a key approach that can be used to improve understanding of heart conditions such as ischaemia. However, key inputs to these models, such as the bidomain conductivity values, are not known with any certainty. Since efforts are underway to measure these values, it would be useful to be able to quantify the effect on model outputs of uncertainty in these inputs, and also to determine, if possible, which are the most important values to focus on in experimental studies. Our previous work has systematically studied the sensitivity of heart surface potentials to the bidomain conductivity values, and this was performed using a half-ellipsoidal model of the left ventricle. This study uses a bi-ventricular heart in a torso model and this time looks at the sensitivity of the torso surface potentials, as well as the heart surface potentials, to various conductivity values (blood, torso and the six bidomain conductivities). We found that both epicardial and torso potentials are the most sensitive to the intracellular longitudinal (along the cardiac fibres) conductivity (g_il) with more minor sensitivity to the torso conductivity, and that changes in g_il have a significant effect on the surface potential distributions on both the torso and the heart.

A modified approach to determine the six cardiac bidomain conductivities

Accurate values for the six cardiac bidomain conductivities are crucial for meaningful computational studies of conduction in cardiac tissue, and are yet to be determined by experimental means. Although previous studies have proposed an approach using a multi-electrode array to measure potentials, from which the conductivities can be determined, it has been found that the conductivities cannot be retrieved consistently when the noise in the potentials varies. This paper presents a protocol, which not only has been shown to retrieve the conductivities to a reasonable accuracy, but does so under the presence of a more appropriate additive Gaussian noise model, while using fewer computational resources. Through repetitions of the protocol, a comparison of two pre-fabricated 128 electrode arrays, one array with a square arrangement of electrodes and the other with a rectangular arrangement, was made against a 75-electrode array proposed in previous studies. Results indicated that the two pre-fabricated arrays were generally more capable of obtaining the cardiac conductivities to a higher degree of accuracy than the 75-electrode array. The 128-electrode rectangular array was orientated such that the length of the array first ran along the direction of the fibres, then was reorientated such that the length of the array ran perpendicular to the direction of the fibres. The 128-electrode rectangular array, when orientated in this manner, was more capable of retrieving the conductivities than the remainder of the arrays tested, and thus we suggest this arrangement be used during experimental trials.

Approaches for determining cardiac bidomain conductivity values: progress and challenges

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of four experimentally determined conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around 40 years ago, often produce different results in simulations and do not fully represent the three-dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques. Graphical abstract Epicardial potential distributions, arising from a subendocardial ischaemic region, modelled using conductivity data from the indicated studies.

Construction and validation of a plunge electrode array for three-dimensional determination of conductivity in the heart

The heart's response to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. Analysis of the microstructure of the heart predicts that three unique intracellular electrical conductances can be defined at any point in the ventricular wall; however, to date, there has been no experimental confirmation of this concept. We report the design, fabrication, and validation of a novel plunge electrode array capable of addressing this issue. A new technique involving nylon coating of 24G hypodermic needles is performed to achieve nonconductive electrodes that can be combined to give moderate-density multisite intramural measurement of extracellular potential in the heart. Each needle houses 13 silver wires within a total diameter of 0.7 mm, and the combined electrode array gives 137 sites of recording. The ability of the electrode array to accurately assess conductances is validated by mapping the potential field induced by a point current source within baths of saline of varying concentration. A bidomain model of current injection in the heart is then used to test an approximate relationship between the monodomain conductivities measured by the array, and the full set of bidomain conductivities that describe cardiac tissue.

Laminar Arrangement of Ventricular Myocytes Influences Electrical Behavior of the Heart

The response of the heart to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. A long-held view of cardiac electrical anisotropy is that electrical conductivity is greatest along the myocyte axis allowing most rapid propagation of electrical activation in this direction, and that conductivity is isotropic transverse to the myocyte axis supporting a slower uniform spread of activation in this plane. In this context, knowledge of conductivity in two directions, parallel and transverse to the myofiber axis, is sufficient to characterize the electrical action of the heart. Here we present new experimental data that challenge this view. We have used a novel combination of intramural electrical mapping, and experiment-specific computer modeling, to demonstrate that left ventricular myocardium has unique bulk conductivities associated with three microstructurally-defined axes. We show that voltage fields induced by intramural current injection are influenced by not only myofiber direction, but also the transmural arrangement of muscle layers or myolaminae. Computer models of these experiments, in which measured 3D tissue structure was reconstructed in-silico, best matched recorded voltages with conductivities in the myofiber direction, and parallel and normal to myolaminae, set in the ratio 4:2:1, respectively. These findings redefine cardiac tissue as an electrically orthotropic substrate and enhance our understanding of how external shocks may act to successfully reset the fibrillating heart into a uniform electrical state. More generally, the mechanisms governing the destabilization of coordinated electrical propagation into ventricular arrhythmia need to be evaluated in the light of this discovery.

The effect of lesion size and tissue remodeling on ST deviation in partial-thickness ischemia

BACKGROUND

Myocardial ischemia causes ST segment elevation or depression in electrocardiograms and epicardial leads. ST depression in epicardium overlying the ischemic zone indicates that the ischemia is nontransmural. However, nontransmural ischemia does not always cause ST depression. Especially in animal models, ST depression is hard to reproduce.

OBJECTIVE

The purpose of this study was to determine the circumstances in which ST depression could be expected.

METHODS

We studied ischemia in a large-scale computer model of the human heart. A realistic representation of the ischemia-induced changes in resting membrane potential was used, which was based on diffusion of extracellular potassium. Ischemia diameter, transmural extent, and tissue conductivity were varied.

RESULTS

Our simulations confirm earlier work showing that partial-thickness ischemia, like full-thickness ischemia, typically causes ST elevation in an anisotropic model of the ventricles. However, we identified three situations in which ST depression can occur in overlying leads. The first is a reduced anisotropy ratio of the intracellular conductivity, which may result from hypertrophy and gap-junctional remodeling, circumstances that are likely to accompany ischemia. Second, an increase of the extracellular anisotropy has the same effect. Third, ST depression was found, independent of the anisotropy ratios, in very large and thin ischemic regions, resembling those that may occur in left-main or multivessel disease.

CONCLUSION

Both tissue remodeling and geometric factors can explain ST depression in overlying epicardial leads. We note at the same time that ST elevation is found in most circumstances, while depression occurs as a reciprocal effect, even in partial-thickness ischemia.