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R C Barr

Publications and source records attributed to R C Barr.

At least 19 recordsLinked to original sources
PubMed1992

Propagation model using the DiFrancesco-Noble equations. Comparison to reported experimental results.

Propagation, re-entry and the effects of stimuli within the conduction system can be studied effectively with computer models when the pertinent membrane properties can be represented accurately in mathematical form. To date, no membrane models have been shown to be accurate representations during repolarisation and recovery of excitability, although for the Purkinje membrane the DiFrancesco-Noble (DN) model has become a possibility. The paper examines the DN model, restates its equations and compares simulated waveforms in a number of propagation contexts to experimental measurements reported in the literature. The objective is to determine whether or not the DN model reproduced phenomena such as supernormality, shortening in action potential duration during pacing rate increases, alternation of duration with changes in rhythm, graded responses and 'all-or-none' repolarisation in a quantitatively realistic way, as each of these come from time and space dependencies not directly a part of the ionic current measurements on which the DN model is based. The results show that the DN equations correctly simulate these situations and support the goal of having a model that is broadly applicable to Purkinje tissue, including refractory period properties and response to electrical stimulation.

Action Potentials↗
PubMed1992

Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers.

The influence of interstitial or extracellular potentials on propagation usually has been ignored, often through assuming these potentials to be insignificantly different from zero, presumably because both measurements and calculations become much more complex when interstitial interactions are included. This study arose primarily from an interest in cardiac muscle, where it has been well established that substantial interstitial potentials occur in tightly packed structures, e.g., tens of millivolts within the ventricular wall. We analyzed the electrophysiological interaction between two adjacent unmyelinated fibers within a restricted extracellular space. Numerical evaluations made use of two linked core-conductor models and Hodgkin-Huxley membrane properties. Changes in transmembrane potentials induced in the second fiber ranged from nonexistent with large intervening volumes to large enough to initiate excitation when fibers were coupled by interstitial currents through a small interstitial space. With equal interstitial and intracellular longitudinal conductivities and close coupling, the interaction was large enough (induced Vm approximately 20 mV peak-to-peak) that action potentials from one fiber initiated excitation in the other, for the 40-microns radius evaluated. With close coupling but no change in structure, propagation velocity in the first fiber varied from 1.66 mm/ms (when both fibers were simultaneously stimulated) to 2.84 mm/ms (when the second fiber remained passive). Although normal propagation through interstitial interaction is unlikely, the magnitudes of the electrotonic interactions were large and may have a substantial modulating effect on function.

Animals↗
PubMed1992

Reflection after delayed excitation in a computer model of a single fiber.

Reflection (reflected reentry) is a case of reentry in a one-dimensional structure, divided into proximal and distal segments, in which tissue excited by a wave front propagating in a forward direction is reexcited by electrical activity coming backward from the original direction of propagation. Cases of reflection have been demonstrated in Purkinje fibers and in ventricular muscle preparations containing multiple fibers. Several mechanisms possibly responsible for reflected reentry have been proposed. However, the difficulty in the interpretation of the experimental results, as well as the limited number of different conditions in which reflection was obtained, has kept open the question about conditions and mechanisms for reflection. We have developed a computer model in which reflection occurs. The model involves a single fiber and uses the DiFrancesco-Noble equations for the Purkinje fiber to model the ionic currents. The results show that reflection is possible in a single fiber and that diastolic depolarization (automaticity) is not a requirement for reflection. Active membrane responses to a just-above-threshold stimulus were important for achieving the necessary time delay. Systematic simulations showed further that reflection occurred only when the right coupling conditions linked a short or long proximal fiber to a short distal segment.

Action Potentials↗
PubMed1991

One-dimensional model of cardiac defibrillation.

The response of a single strand of cardiac cells to a uniform defibrillatory shock assuming steady-state linear conditions is examined. It is argued that the effect of this current is quantitatively described by the induced transmembrane potential even under passive conditions. The characteristics of the single strand are those that would exist if the heart was a system of equivalent parallel pathways from apex to base. It is shown that essentially every cell is both hyperpolarized and depolarised from the shock by an amount proportional to the stimulus intensity and the intercellular junctional resistance. For physiological values of model parameters the evaluated depolarisations are consistent with levels necessary to affect electrophysiological behaviour.

Electric Countershock↗
PubMed1991

Computer simulations of activation in an anatomically based model of the human ventricular conduction system.

Simulations of the electrical activity during excitation were performed in an anatomically based model of the human ventricular conduction system. Each of the 33,000 elements of this model represented a unit bundle of Purkinje or atrioventricular nodal tissue. The Ebihara-Johnson model for sodium defined the active membrane characteristics. Using a combination of new and existing modeling techniques, simulations of excitation were completed in approximately 5 min CPU time on an IBM 3090 at the Cornell National Supercomputer Facility. Activation times at sites in the model were compared to experimental measurements for the excitation of the ventricular myocardium on the endocardial surface. These "literature-based" times were estimated from a number of reported human heart mapping studies. Initially, the times fit poorly. The major factor for the discrepancy was the conduction velocities of the elements, which were a result of the physical and electrical parameters derived from a review of histologic and electrical properties studies. In addition, there was a latency between activation of the system in the left ventricle of the model and that in the right ventricle when compared to the experimental work. When the times were scaled to adjust for the conduction velocity and ventricular latency effects, the match between the simulation and literature-based times was much improved. Quantitative comparison between normalized times resulted in correlation coefficients CCF = 0.76 for the right ventricle and CCF = 0.64 for the left ventricle.

Atrial Function↗
PubMed1990

The construction of an anatomically based model of the human ventricular conduction system.

The ventricular conduction system is a complicated network of specialized muscle cells responsible for the transmission of electrical activity between the atria and the ventricles of the human heart. It has been the focus of numerous electrical and anatomical studies at both the microscopic and macroscopic levels. An understanding of its behavior at both levels is considered important, because it is primarily responsible for the spread of excitation in the ventricles. Previous computer models have been very simple ones that have been primarily adjuncts to models of the ventricles. This paper describes a strategy for the construction of conduction system models which is based on real microscopic and macroscopic features, although the model still is much simpler than reality. The model contains almost 35,000 individual cylindrical elements, each of whose physical dimensions approximate unit bundles of Purkinje and atrioventricular nodal cells. The model, whose physical appearance closely resembles that of the conduction system, was generated from limited anatomical data in less than 2 min CPU time on an IBM 3090 at the Cornell National Supercomputer Facility.

Atrioventricular Node↗
PubMed1988

Adaptive sampling of cardiac waveforms.

In recent years cardiac electrocardiograms and electrograms often have been measured using automated sampling systems that record samples periodically, with a fixed sample-to-sample interval. In contrast, adaptive sampling systems envision variable sample-to-sample intervals, and new information about such systems has emerged in the last few years. The author summarizes these reports. On the whole, they show that the fan algorithm is an effective basis for adaptive sampling of cardiac waveforms, that it works well on electrocardiograms, electrograms, and action potentials, and that prototype sampling systems based on the fan can be constructed to run in real time.

Algorithms↗
PubMed1979

Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic canine cardiac muscle.

This paper considers a quantitative description of intracellular and transmembrane currents in anisotropic muscle, with emphasis on the factors that determine the extracellular potentials. Although Vmax of the intracellular action potential had no relation to changes in conduction velocity in anisotropic tissue with constant membrane properties, the extracellular waveforms were quite sensitive to velocity changes. Large amplitude biphasic deflection occurred in the fast areas, and in the slow areas the waveforms were of lower amplitude and triphasic in shape; i.e., negative potentials preceded the biphasic positive-negative deflection. The extracellular potentials were simulated on the bases of a model of intracellular currents, and the theoretical and measured results showed good agreement. In tissue with anisotropic conductivity, the relationship between the spatial intracellualr potential gradient and the magnitude of the extracellular potential of the excitation wave was opposite to the classical relationship in isotropic tissue. Due to the influence of the effective intracellular conductivity on the spread of intracellular currents and on conduction velocity, in anisotropic tissue the extracellular potential decreased as the intracellular potential gradient increased. The peak values of the positive and negative potentials and the spatial distribution of the potential gradients varied considerably along the activation front. These findings were accounted for by differences in the distribution and spatial extent of the transmembrane currents, which were determined by the intracellular currents. The theoretical analysis showed that intracellular and transmembrane currents were proportional to the local conduction velocities of the wavefront. Thereby, it was not possible to have a "uniform layer" of current when there were differences in conduction velocity along the length of the excitation wave. The implications of the analysis are considerable, since the gratifying agreement between the theoretical and measured results indicates that the details of the extracellular waveforms can be explained on the basis of the distribution of intracellular currents; i.e., extracellular potentials provide a sensitive index of intracellular current flow.

Action Potentials↗
PubMed1977

Sampling rates required for digital recording of intracellular and extracellular cardiac potentials.

Electrocardiograms and cardiac electrograms now frequently are measured for both clinical and experimental purposes by direct digital sampling, with no recording of the signal in analog form. This study examined the question of what sampling rates were required to measure accurately the continuous waveforms from the digital samples. Body surface waveforms and intracellular and extracellular waveforms measured directly from cardiac tissues were evaluated. Cardiac measurements included waveforms from the atrium, ventricle, atrioventricular transmission system and individual Purkinje strands. Sampling rates as high as 15,000 samples/sec were required to record accurately extracellular waveforms of the ventricular conduction system. Decreasing sampling rates were required as the recording site shifted through the ventricle to the body surface, where sampling rates as high as 1500 samples/sec were necessary.

Action Potentials↗