On the Passive Cardiac Conductivity

Stinstra, J.G.; Hopenfeld, Bruce; MacLeod, Rob S.

doi:10.1007/s10439-005-7257-7

Cited by 89 publications

(105 citation statements)

References 32 publications

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“…On the other hand, detailed spatial models have shown that geometry plays an important role in the conduction velocity but are too expensive to implement for a full 3D tissue (11,12,(15)(16)(17)(18)(19).…”

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confidence: 99%

Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling

Lin

Keener

2010

Proc. Natl. Acad. Sci. U.S.A.

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Existing models of electrical activity in myocardial tissue are unable to easily capture the effects of ephaptic coupling. Homogenized models do not account for cellular geometry, while detailed spatial models are too complicated to simulate in three dimensions. Here we propose a unique model that accurately captures the geometric effects while being computationally efficient. We use this model to provide an initial study of the effects of changes in extracellular geometry, gap junctional coupling, and sodium ion channel distribution on propagation velocity in a single 1D strand of cells. In agreement with previous studies, we find that ephaptic coupling increases propagation velocity at low gap junctional conductivity while it decreases propagation at higher conductivities. We also find that conduction velocity is relatively insensitive to gap junctional coupling when sodium ion channels are located entirely on the cell ends and cleft space is small. The numerical efficiency of this model, verified by comparison with more detailed simulations, allows a thorough study in parameter variation and shows that cellular structure and geometry has a nontrivial impact on propagation velocity. This model can be relatively easily extended to higher dimensions while maintaining numerical efficiency and incorporating ephaptic effects through modeling of complex, irregular cellular geometry.cardiac electrophysiology | extracellular conductivity | microdomain effects W hile gap junctional coupling is usually considered to be the primary mechanism for action potential propagation, there is evidence that other mechanisms are important. In particular, only a moderate reduction of cardiac propagation velocity was found in murine hearts with inactivated Connexin43 (Cx43) gene (1). In mice with heterozygous Cx43AE down-regulation, either a 23-44% decrease in propagation velocity (2-4) or no discernible decrease in propagation velocity (5-8) was found. In Cx43 − ∕− mice with no expression of the protein, propagation was still found, although discontinuous and at much slower speeds (7). These experimental findings are in conflict with the classical understanding of how gap junctions determine propagation velocity.One possible explanation for these intriguing observations is that ephaptic (i.e., field effect) coupling may be significant (1, 9-12). However, the study of ephaptic effects is made difficult by the fact that these effects are most important in microdomains such as junctional clefts.Existing homogenized models, while computationally accessible, are not able to deal with the effects of microdomains and hence do not capture the effects of ephaptic coupling (13,14). On the other hand, detailed spatial models have shown that geometry plays an important role in the conduction velocity but are too expensive to implement for a full 3D tissue (11,12,(15)(16)(17)(18)(19).Here we present a model that captures the effects of the intricate cellular geometry with simplifications that will allow the model to be extended more readily to t...

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confidence: 99%

Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling

Lin

Keener

2010

Proc. Natl. Acad. Sci. U.S.A.

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“…In previous work, simulations aimed at computing the bulk conductivity of tissue using the same underlying tissue model showed that reducing the extracellular space raised the impedance both along as well as across the fiber [6]. Hence, the examples presented in this paper show that one cannot directly translate the changes in macroscopic tissue conductivity into the bidomain model, as the bidomain model predicts assumes a similar relation between resistance and propagation velocity for both directions.…”

Section: Discussionmentioning

confidence: 82%

“…The geometrical model that underlies the simulation was based on previous work that focused on computing passive electrical characteristics of myocardial tissue such as the conductivity tensor for a bidomain [2,6]. We created a computer algorithm for filling up a space with realistically shaped myocytes that fit together like pieces of a jigsaw puzzle of which the average length and cross section could be altered to fit histological data.…”

Section: Methodsmentioning

confidence: 99%

A model for estimating the anisotropy of the conduction velocity in cardiac tissue based on the tissue morphology

Stinstra

Poelzing

MacLeod

et al. 2007

2007 Computers in Cardiology

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IntroductionIn the quest to better understand the mechanisms underlying cardiac arrhythmias, the use of computer simulations is a common tool. Computer simulations have the advantage of being able to resolve potentials and currents with a finer level of detail than is possible with measurements. However, in order to be useful, simulations need to reproduce observations, in this case from electrophysiology, and hence they must produce results against which to compare with experimental findings.The most common approach to the simulation of the propagation of depolarization fronts inside the myocardium is the use of the "bidomain model" [1]. The bidomain model is based on the notion that the myocardium can be separated into intracellular and extracellular spaces, which are joined to each other by a membrane that acts both as a current source and a pathway allowing current to flow between both spaces. More specifically, the bidomain model assumes that the intracellular space, the extracellular space and the membrane all coexist at each point in space. Hence at each location the myocardium can be characterized by a conductivity tensor for the intracellular space, a conductivity tensor for the extracellular space, and an ionic model that describes the current flowing through the membrane.The two conductivity tensors describing the electrical properties of the tissue represent the homogenized conductivity of either the intracellular or the extracellular space. The most common way of estimating these parameters is to choose them so that simulated cardiac propagation speeds fit experimentally observed values. Although this is a valid way of setting these parameters, it fails to relate them to the underlying tissue structure and composition.In this paper, we describe a model that simulates cardiac propagation based on a more detailed description of the microscopic tissue morphology than that provided by the standard bidomain. One of the reasons for including more details into the model is to be able to simulate pathologies like ischemia based on their physiological origins rather than by assigning parameters to fit experiments. For instance, during an episode of]ischemia the amount of extracellular space changes with time [2] altering the way a depolarization front propagates along the fiber [3].In order to create such a model, we built on the models of Spach et al. [4], who created a 2D model of cardiac tissue that consisted of several hundred realistically shaped myocytes that were coupled by gap junctions. Their model was limited by the fact that it did not include an extracellular space. Two-dimensional models are intrinsically limited because the intracellular and extracellular current paths cannot cross each other, thereby limiting the amount of available extracellular and intracellular pathways.To avoid these limitations of a 2D model, we created a full 3D model of cardiac tissue that included realistically shaped myocytes coupled by gap junctions and embedded in an extracellular matrix. We present here pr...

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“…Intracellular resistivity is higher in transverse than in longitudinal direction. Thus, anisotropy in the intracellular space ranges from ∼5 to 10 (Clerc, 1976;Roberts and Scher, 1982;Stinstra et al, 2005) and mainly results from cardiomyocyte shape and cellular distribution of connexins. In many cardiac diseases the expression of connexins (Cx43, Cx40, Cx45) is altered.…”

Section: Anisotropy and Non-uniformity (Inhomogeneity)mentioning

confidence: 99%

“…The concept of electrical anisotropy also applies to resistivity of the extracellular space and, besides influencing impulse propagation, has a strong effect on the distribution of epicardial potentials (Roberts and Scher, 1982;Johnston et al, 2001;Stinstra et al, 2005;Schwab et al, 2013). Experimental and computational studies reported anisotropies in the extracellular space ranging from 1.5 to 3.5 (Clerc, 1976;Roberts et al, 1979;Stinstra et al, 2005;Hand et al, 2009).…”

Section: Anisotropy and Non-uniformity (Inhomogeneity)mentioning

confidence: 99%

Remodeling of cardiac passive electrical properties and susceptibility to ventricular and atrial arrhythmias

2015

Frontiers Research Topics

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On the Passive Cardiac Conductivity

Cited by 89 publications

References 32 publications

Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling

Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling

A model for estimating the anisotropy of the conduction velocity in cardiac tissue based on the tissue morphology

Remodeling of cardiac passive electrical properties and susceptibility to ventricular and atrial arrhythmias

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