Biomedical subjects

C S Henriquez

Publications and source records attributed to C S Henriquez.

At least 19 recordsLinked to original sources

PubMed2001

Influence of dynamic gap junction resistance on impulse propagation in ventricular myocardium: a computer simulation study.

The gap junction connecting cardiac myocytes is voltage and time dependent. This simulation study investigated the effects of dynamic gap junctions on both the shape and conduction velocity of a propagating action potential. The dynamic gap junction model is based on that described by Vogel and Weingart (J. Physiol. (Lond.). 1998, 510:177-189) for the voltage- and time-dependent conductance changes measured in cell pairs. The model assumes that the conductive gap junction channels have four conformational states. The gap junction model was used to couple 300 cells in a linear strand with membrane dynamics of the cells defined by the Luo-Rudy I model. The results show that, when the cells are tightly coupled (6700 channels), little change occurs in the gap junction resistance during propagation. Thus, for tight coupling, there are negligible differences in the waveshape and propagation velocity when comparing the dynamic and static gap junction representations. For poor coupling (85 channels), the gap junction resistance increases 33 MOmega during propagation. This transient change in resistance resulted in increased transjunctional conduction delays, changes in action potential upstroke, and block of conduction at a lower junction resting resistance relative to a static gap junction model. The results suggest that the dynamics of the gap junction enhance cellular decoupling as a possible protective mechanism of isolating injured cells from their neighbors.

Action Potentials↗

PubMed2001

Myocardial fiber orientation mapping using reduced encoding diffusion tensor imaging.

A precise knowledge of the myocardial fiber architecture is essential to accurately understand and interpret cardiac electrical and mechanical functions. Diffusion tensor imaging has been used to noninvasively and quantitatively characterize myocardial fiber orientations. However, because the approach necessitates diffusion to be measured in multiple encoding directions and frequently at multiple weighting levels, the required data set size may present a limitation on its acquisition time efficiency. Applying the principles of reduced encoding imaging (REI), four basic reconstruction schemes, keyhole using direct substitution, keyhole with baseline correction, symmetrically encoded REI with generalized-series reconstruction (RIGR), and asymmetrically encoded RIGR, are evaluated in terms of their accuracy in diffusion tensorfiber orientation mapping of excised myocardial samples. Results show that the performances of all REI schemes, at approximately 50% reduced encoding, are at least comparable with that of a control experiment consisting of proportionally reduced number of full k-space images. Moreover, although performances of the symmetrically and asymmetrically encoded RIGR schemes are similar, both methods provide significant improvements over the control experiment and the direct-substitution keyhole technique. These findings demonstrate the potential of the general REI methodology for diffusion tensor imaging and pave the way for modified schemes involving rapid imaging sequences or alternative k-space sampling strategies to achieve even better data acquisition time efficiency and performance.

Analysis of Variance↗

PubMed2001

Simulation and prediction of functional block in the presence of structural and ionic heterogeneity.

Inhomogeneities in myocardial structure and action potential duration (APD) lead to dispersion of APD throughout the heart. APD gradients in the range of 20-125 ms/cm have been reported to produce functional block. In this study, a multicellular fiber model was used to examine the effect of structural and ionic inhomogeneities on the likelihood of premature stimuli to produce functional block. With the use of both the Fenton-Karma and Luo-Rudy phase II membrane models, functional block is found to occur in tissue with a maximum gradient <45 ms/cm and depends on the spatial extent. In general, the narrower the extent the larger the magnitude needed for block. A simple relationship for predicting block is presented that only requires information about the conduction velocity (CV) restitution properties of the tissue and the APD gradients. Analysis reveals that the effects of a steep CV restitution slope may be beneficial in overcoming intrinsic cellular heterogeneity for a single premature beat.

Action Potentials↗

PubMed2000

A space-time adaptive method for simulating complex cardiac dynamics.

For plane-wave and many-spiral states of the experimentally based Luo-Rudy 1 model of heart tissue in large (8 cm square) domains, we show that a space-time-adaptive time-integration algorithm can achieve a factor of 5 reduction in computational effort and memory-but without a reduction in accuracy-when compared to an algorithm using a uniform space-time mesh at the finest resolution. Our results indicate that such an algorithm can be extended straightforwardly to simulate quantitatively three-dimensional electrical dynamics over the whole human heart.

Algorithms↗

PubMed2000

A flexible method for simulating cardiac conduction in three-dimensional complex geometries.

In this article we present a method for creating a membrane-based computer model capable of representing a three-dimensional irregular domain. The spatial discretization of our model is based on the Finite Volume Method. In combination with a robust meshmaking tool, our method may be used to simulate conduction in an arbitrarily shaped, complex region. In this way, conduction in specific subregions of cardiac anatomy may be examined. The capabilities of this methodology are demonstrated through 3 examples. The first shows the influence of abrupt changes in tissue geometry on conduction parameters. The second highlights the ability of the model to incorporate interior boundaries and altered membrane properties. The final example shows the inclusion of a full description of the fiber architecture in a portion of the canine left ventricle. Future applications will make use of the model's capabilities to conduct investigations in complex regions including the atria.

Animals↗

PubMed1998

Validation of three-dimensional conduction models using experimental mapping: are we getting closer?

The anisotropic material properties, irregular geometry, and specialized conduction system of the heart all affect the three-dimensional (3D) spread of electrical activation. A limited number of research groups have tried accounting for these features in 3D conduction models to investigate more thoroughly their observations of cardiac electrical activity in 3D experimental preparations. The full potential of these large scale conduction models, however, has not been realized because of a lack of quantitative validation with experiment. Such validation is critical in order to use the models to predict the electrical response of the myocardium to drugs or electrical stimulation. In this paper, a quantitative, experimental validation of paced activation in a 3D conduction model of a 3 cm x 3 cm x 1 cm section of the ventricular wall is presented. Epicardial and intramural pacing stimuli were applied in the center of a 528 channel electrode plaque sutured to the left ventricle in dogs. Unipolar electrograms were recorded at 2 kHz during and after pacing. Fiber directions within the tissue below the electrodes were estimated histologically and from pace-mapping. Simulated epicardial electrograms were computed for surface paced beats using our 3D bidomain model of the mapped tissue volume incorporating the measured fiber directions. Extracellular potentials and isochronal maps resulting from paced activations in both model and experiment were directly compared. Preliminary results demonstrate that our 3D model reproduces qualitatively such key features of the experimental data as electrogram morphologies and epicardial conduction velocities. Though quantitative agreement between model and experiment was only moderate, the validation approach described herein is an essential first step in assessing the predictive capability of present day conduction models.

Animals↗

PubMed1998

Bipolar stimulation of a three-dimensional bidomain incorporating rotational anisotropy.

A bidomain model of cardiac tissue was used to examine the effect of transmural fiber rotation during bipolar stimulation in three-dimensional (3-D) myocardium. A 3-D tissue block with unequal anisotropy and two types of fiber rotation (none and moderate) was stimulated along and across fibers via bipolar electrodes on the epicardial surface, and the resulting steady-state interstitial (phi e) and transmembrane (Vm) potentials were computed. Results demonstrate that the presence of rotated fibers does not change the amount of tissue polarized by the point surface stimuli, but does cause changes in the orientation of phi e and Vm in the depth of the tissue, away from the epicardium. Further analysis revealed a relationship between the Laplacian of phi e, regions of virtual electrodes, and fiber orientation that was dependent upon adequacy of spatial sampling and the interstitial anisotropy. These findings help to understand the role of fiber architecture during extracellular stimulation of cardiac muscle.

Anisotropy↗

PubMed1998

Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation.

Functional properties of the myocardium are mediated by the tissue structure. Consequently, proper physiological studies and modeling necessitate a precise knowledge of the fiber orientation. Magnetic resonance (MR) diffusion tensor imaging techniques have been used as a nondestructive means to characterize tissue fiber structure; however, the descriptions so far have been mostly qualitative. This study presents a direct, quantitative comparison of high-resolution MR fiber mapping and histology measurements in a block of excised canine myocardium. Results show an excellent correspondence of the measured fiber angles not only on a point-by-point basis (average difference of -2.30 +/- 0.98 degrees, n = 239) but also in the transmural rotation of the helix angles (average correlation coefficient of 0.942 +/- 0.008 with average false-positive probability of 0.004 +/- 0.001, n = 24). These data strongly support the hypothesis that the eigenvector of the largest MR diffusion tensor eigenvalue coincides with the orientation of the local myocardial fibers and underscore the potential of MR imaging as a noninvasive, three-dimensional modality to characterize tissue fiber architecture.

Animals↗

PubMed1997

Paced activation mapping reveals organization of myocardial fibers: a simulation study.

INTRODUCTION: A three-dimensional bidomain model of a block section of both the right and left ventricular walls that included rotational anisotropy and fiber curvature was used to investigate potential distributions generated during paced activation mapping. Unlike previous large-scale tissue models, the extracellular stimulus was included. METHODS AND RESULTS: The model was used to test the hypothesis that information about the underlying tissue structure (surface fiber angle gradients, amount of fiber rotation per unit depth, and anisotropy) can be extracted from surface potential distributions during stimulation. Results from distributions during stimulation were compared to those obtained using the distributions during activation. To better correlate results to possible experimental measurements, the analysis was performed using a 21 X 21 grid of "electrode" sites, each separated by 1 mm. Fiber orientation was estimated from the surface data by: (1) curve-fitting the elliptical shape of the epicardial potential distribution during stimulation; (2) identifying the location of the potential maxima leading the wavefront during early activation; and (3) for epicardial stimuli, curve-fitting the elliptical shape of the activation isochrones. Results show that surface potential distributions from the stimulus can be used to estimate fiber orientation; however, the accuracy of the reconstruction is highly dependent on the amount of fiber rotation per unit depth. CONCLUSIONS: Extracellular potential data during and after stimulation is shown to reflect the organization of myocardial fibers and, as such, could be used to characterize the three-dimensional anisotropic electrical properties in situ.

Electric Stimulation↗

PubMed1996

Anisotropy, fiber curvature, and bath loading effects on activation in thin and thick cardiac tissue preparations: simulations in a three-dimensional bidomain model.

INTRODUCTION: A modeling study is presented to explore the effects of tissue conductivity, fiber orientation, and presence of an adjoining extracellular volume conductor on electrical conduction in cardiac muscle. Simulated results are compared with those of classical in vitro experiments on superfused thin layer preparations and on whole hearts. METHODS AND RESULTS: The tissue is modeled as a three-dimensional bidomain block adjoining an isotropic bath. In the thin layer model, the fibers are assumed parallel. In the thick block model, fiber rotation, curvature, and tipping are incorporated. Results from the thin layer model explain experimental observations that the rate of rise of the entire action potential upstroke is faster and the magnitude of the extracellular potential is smaller across fibers than along fibers in a uniformly propagating front. The simulation identified that this behavior only arises in tissue with unequal anisotropy in the two spaces and adjoining an extracellular bath. Simulated conduction and potential distributions in the thick block model are shown to well approximate experimental maps. The potentials are sensitive to changes in the fiber orientations. A slight 5 degrees tipping of intramural fibers out of the planes parallel to the epicardium and endocardium will lead to an asymmetry of the magnitudes of the positive regions. In addition, the introduction of fiber curvature leads to more realistic isochrone and extracellular potential distributions. The orientation of the central negative region of the extracellular potential is shown to be determined by the average of the fiber direction at the plane of pacing and the plane of recording. CONCLUSIONS: The simulations demonstrate the sensitivity of spread of activation and potential time courses and distributions to the underlying electrical properties in both thick and thin slabs. The bidomain model is shown to be a useful representation of cardiac tissue for interpreting experimental data of activation.

Action Potentials↗

PubMed1994

Linear algebraic transformations of the bidomain equations: implications for numerical methods.

A mathematical framework is presented for the treatment of the bidomain equations used to model propagation in cardiac tissue. This framework is independent of the model used to represent membrane ionic currents and incorporates boundary conditions and other constraints. By representing the bidomain equations in the operator notation L phi = F, various algebraic transformations can be expressed as PLQ-1 psi = PF, where P and Q are linear operators. The authors show how previous work fits into this framework and discuss the implications of various transformation for numerical methods of solution. Although such transformations allow many choices of independent variable, these results emphasize the fundamental importance of the transmembrane potential.

Animals↗

PubMed1993

Simulating the electrical behavior of cardiac tissue using the bidomain model.

The complex microstructure of cardiac muscle comprised of coupled cells, enveloped by an interstitium made up of blood vessels, connective tissue, and fluid, presents some obvious problems to those interested in understanding the tissue as an electrical medium. One approach that has gained considerable favor in recent years views the tissue not as a discrete structure, but rather as two coupled, continuous domains: one for the intracellular space and the other for the interstitial space. For convenience, the averaged potentials and currents in both domains are defined at every point in space. The structure is partially preserved by assigning a conductivity tensor at each point. One advantage of using this space-averaged model is that the governing equations for the electric fields can be described by partial differential equations that on occasion lead to analytical solutions. This formal treatment of cardiac tissue as two coupled continua is referred to as the bidomain model. This article presents a mathematical description of the bidomain model and reviews the use of the model for simulating the electrical behavior of cardiac tissue.

Action Potentials↗

PubMed1992

Cardiac propagation simulation.

We have completed a range of membrane-based simulations of action potential propagation in two- and three-dimensional models of ventricular myocardium. The two-dimensional simulations included a bidomain representation of the myocardium which explicitly characterized the component volume conductors in the intracellular, interstitial, and extracellular spaces. With these simulations, we studied the contribution of the extracellular volume conductor to transmural myocardial propagation during depolarization. We also used two-dimensional bidomain simulations to study the effect of the interstitial volume conductor in the setting of planar myocardial depolarization with nominal and extreme tissue conductivities. Our three-dimensional simulations included a monodomain representation of the myocardium which characterized the three component volume conductors as a single lumped conductor. With these simulations, we examined the effects of the intramural rotation of the fiber axes on the timing and pattern of activation. To achieve practical solution times, we extended numerical techniques from previous reports and developed a range of new techniques applicable to this class of problems. Simulations of the depolarization wavefront used the nonlinear Ebihara and Johnson membrane equations for the fast sodium current as the membrane model. Simulations of the full action potential cycle combined the Ebihara and Johnson fast sodium current with the Beeler and Reuter membrane equations. Our results demonstrated that the individual volume conductors and the rotation of fiber axes have unique and identifiable consequences on the electrical activation in models of ventricular myocardium.

Action Potentials↗

PubMed1991

Examination of the choice of models for computing the extracellular potential of a single fibre in a restricted volume conductor.

The paper compares the rigorous and the conventional approximate line source solution of Laplace's equation used to evaluate the potential of a single cylindrical fibre. Particular attention is given to the solutions for a radially restricted circular cylindrical volume conductor. The effect of the extent of the volume conductor b on the difference between the potentials evaluated according to the different models is examined. For values of b larger than 10 times the fibre radius, the relative difference is less than 1 per cent and the values of b around 2 times the fibre radii, the error reaches as much as 17 per cent.

Action Potentials↗

PubMed1991

Modification of a cylindrical bidomain model for cardiac tissue.

Previous models based on a cylindrical bidomain assumed either that the ratio of intracellular and interstitial conductivities in the principal directions were the same or that there was no radial variation in potential (i.e., a planar front, delta Vm/delta rho = 0). This paper presents a formulation and the expressions for the intracellular, interstitial, extracellular, and transmembrane potentials arising from nonplanar propagation along a cylindrical bundle of cardiac tissue represented as a bidomain with arbitrary anisotropy. For unequal anisotropy, the transmembrane current depends not only on the local change of the transmembrane potential but also on the nature of the transmembrane potential throughout the volume.

Animals↗

PubMed1990

A planar slab bidomain model for cardiac tissue.

A fully three-dimensional model of the ventricular or atrial free wall will involve a planar geometry of finite thickness. The governing equations for the interstitial and extracellular potential of a planar slab of cardiac tissue comprised of parallel fibers undergoing uniform plane-wave activation are presented. A comparison with a bidomain of cylindrical geometry with the same half-thickness shows that the potentials in the planar bidomain (as a function of depth) approach core-conductor behavior more quickly.

Animals↗

PubMed1990

Extracellular potentials and currents of a single active fiber in a restricted volume conductor.

Based on mathematical expressions governing the electric field, the extracellular potentials generated by a single active fiber in a restricted circular cylindrical volume conductor are evaluated. This paper examines the effect of the extent of the volume conductor, with radius b, on the extracellular potentials at different field points. For values of b less than 1.5 times the fiber radius, the extracellular potentials in the volume conductor are always the core conductor potentials, independent of the shape and amplitude of the transmembrane potential. For b greater than a critical radius (a value that depends on the transmembrane potential waveform), the extracellular potentials at and near the membrane are the same as if the volume conductor were unbounded. Near the boundary with the insulator, the amplitude of the extracellular potentials is equal to the core conductor amplitude, although the potentials are much broader than the core conductor potential.

Action Potentials↗

PubMed1990

Limitations of approximate solutions for computing the extracellular potential of single fibers and bundle equivalents.

The mathematical description of the extracellular field generated by activity in an excitable fiber in an unbounded volume conductor will depend on assumptions made about the sources and the source-field relationship. This paper examines and compares the rigorous and conventional approximate solutions of Laplace's equation used to evaluate the extracellular potential of a single, cylindrical fiber. The single fiber is considered as both a prototypical element (such as a nerve or muscle fiber) and an elementary model of an entire multicellular preparation (e.g., nerve bundle or Purkinje strand). The effects of the fiber radius, the intracellular and extracellular conductivities, and the shape and extent of the source function (either the transmembrane potential or the intracellular potential) on the solutions are discussed. The results show that, in general, the approximate solutions are unsatisfactory for computing the surface extracellular potential when the single fiber is used to represent a large bundle (greater than 300 microns).

Fourier Analysis↗