A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators

Cr, Katholi; Urthaler, Ferdinand; Macy, Jr J; James, T N

doi:10.1016/0010-4809(77)90011-8

Cited by 49 publications

(19 citation statements)

References 19 publications

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“…However, the extra peak in the histogram of spontaneous RR intervals in patient 4 and in the histogram of SR intervals in patient 8 (Fig. 3B) suggests that other mechanisms, such as dual AV nodal pathways or a subsidiary pacemaker, might have played a role in the generation of these ventricular events (Kirsh, et al, 1988).…”

Section: Limitations Of the Studymentioning

confidence: 99%

“…When these fibrillatory atrial potentials are randomly timed, the SD of the sum of N cycles does not increase with a factor N, but with the square root of N (Armitage and Berry, 1987). With a constant scaling factor, the finding of Kirsh et al (1988) would imply that the properties of the AV node as weIl as of the accessory AV connection contribute significantly to the irregularity of the ventricular rhythm. With a varying scaling factor, the irregularity of the RR intervals can reach any value, and conclusions about a relationship between the atrial and ventricular rhythm in individual patients cannot be drawn from correlations between both variation coefficients.…”

Section: Sealing Of the Atrial Rhythmmentioning

confidence: 99%

“…Several investigators have studied the behavior of the AV node with mathematical or electronic modeling (Grant, 1956;Katholi, et al, 1977;Cohen, et al, 1983;West, et al , 1985;van der Tweel, et al, 1986). The general outcome of these studies is that the electrophysiological properties ofthe AV node can indeed be explained on the basis of an entrained biological oscillator.…”

Section: The Atrioventricular Nodal Pacemaker Hypothesismentioning

confidence: 99%

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Atrioventricular Nodal Response to Retrograde Activation in Atrial Fibrillation

Wittkampf

Jongste²,

Meijler

1990

Cardiovasc electrophysiol

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. Atrioventricular Nodal Reset. Retrograde (ventriculoatrial) conduction that reaches the atrioventricular node simultaneous with, or just before an atrial impulse can facilitate subsequent anterograde conduction. However, a spontaneous or programmed ventricular extrasystole during atrial fibrillation is generally followed by a compensatory pause indicating subsequent delayed anterograde transmission. This characteristic response was used as a model to study the mechanism of atrioventricular no dal behavior during atrial fibrillation. In eight medically-treated patients with chronic atrial fibrillation and a relatively slow but random ventricular response, single premature right ventricular stimuli were delivered after every eighth spontaneous R wave during at least 1 hour~ A fixed coupling interval of the extrastimulus, considerably shorter than the shortest spontaneous RR interval, was used. The histograms of the postextrasystolic intervals were compared with those of the spontaneous noninterrupted RR intervals. The average postextrasystolic interval was 180 to 300 msec longer than the mean control RR interval, and in six of eight patients, the shape of the histogram of the postextrasystolic cycles was insignificantly different from that of the spontaneous RR intervals. This suggests that in those six patients, the retrogradeimpulse had reset the random timing cycle of atrioventricular nodal dis charge during atrial fibrillation. This observation is compatible with the hypothesis that electrotonically-mediated propagation across a weakly coupled junctional area within the atrioventricular node, rather than decremental conduction and extinction of anterograde atrial impulses at different levels within the node, may be the mechanism of atrioventricular transmission in atrial fibrillation.

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Section: Limitations Of the Studymentioning

confidence: 99%

Section: Sealing Of the Atrial Rhythmmentioning

confidence: 99%

Section: The Atrioventricular Nodal Pacemaker Hypothesismentioning

confidence: 99%

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Atrioventricular Nodal Response to Retrograde Activation in Atrial Fibrillation

Wittkampf

Jongste²,

Meijler

1990

Cardiovasc electrophysiol

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“…within last 50 years. We have tried both IPFM [16] and Vanderpol Oscillators [13][14][15] and simulated using Simulink. Finally, we have selected transfer function model [21] in current work.…”

Section: Heart Modelmentioning

confidence: 99%

Design and Presenting of a Novel Algorithm Using Anfis for New Generation of Cardiac Pacemakers

Aghdam

Dabanloo

Sattari

et al. 2017

Computing in Cardiology Conference (CinC)

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This paper presents a new intelligent control algorithm using Anfis (Adaptive neuro fuzzy inference system) for new generation of Cardiac Pacemakers. Anfis uses both merits of Fuzzy and Neural networks (Learning and speed). Based on various states of body (rest, walking and exercising) and preprogramed states of patient (Sex, age, blood pressure) heart rate and amplitude of exciting pulses will be changed. A feedback from output ECG signal fed back and compared in Anfis controller. Anfis compared with other fuzzy control algorithms provides better control scheme for estimation and generation of pacing pulse parameters including rate and amplitude. Accelerometer sensors and HRV and GSR are used for stabilization of ECG signal during the three body states [1]. Old designs of pacemakers cannot solve problems but Fuzzy can do the job very fast and accurately. Anfis method designed externally regarding patient conditions and normal ECG signals data captured from a known database (based on age and sex of patient) then calculated in MATLAB (Simulink) and programmed directly or wirelessly by ultrasound signals (a novel proposed method). Previous researches [4-19-20] are based on fuzzy PID and fuzzy logic controller in patients with cardiovascular diseases. Anfis controller offers good adaptation of the heart rate and other ECG parameters to the physiological needs of patient.

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“…Since the work of van der Pol and van der Mark, 5 other models using relaxation oscillators 6,[8][9][10] have been published. These models were mainly focused on the interaction between the AV and SA nodes.…”

mentioning

confidence: 99%

Nonlinear oscillator model reproducing various phenomena in the dynamics of the conduction system of the heart

Żebrowski

Grudziński

Buchner

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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On the authors' and employers' webpages: There are no format restrictions; files prepared and/or formatted by AIP or its vendors (e.g., the PDF, PostScript, or HTML article files published in the online journals and proceedings) may be used for this purpose. If a fee is charged for any use, AIP permission must be obtained. An appropriate copyright notice must be included along with the full citation for the published paper and a Web link to AIP's official online version of the abstract. A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained ͑models of the asystole͒. The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block ͑third degree͒. Human heart rate is not constant. In fact, heart rate variability is a major factor in the effective functioning of the cardiovascular system and an important factor in medical diagnosis. A large effort has gone into defining complexity measures using both chaos theory and statistical physics concepts in order to create tools for such diagnosis. In spite of this, the source of the variability is not completely understood and remains an open research subject. It is well known that the autonomous nervous system moderates heart rate in mammals. One way to understand how this occurs is to build models. A variety of models-including the so-called whole heart modelsexist today. However, usually such models are so complex that an investigation of the global dynamical properties of the heart is difficult. Consequently, very rarely do they address the problem of heart rate variability. In our approach, we return to the 20th Century attempts of van der Pol and van der Mark of using relaxation oscillators to study the conduction system of the heart and its interaction with the autonomous nervous system. Following the work of several groups in the field, we developed our own modified van der Pol oscillator. We show that it is able to reproduce certain phenomena that occur in clinically recorded human heart rate: irregular heart rate, asystole, sinus pause, vagal paradox, certai...

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A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators

Cited by 49 publications

References 19 publications

Atrioventricular Nodal Response to Retrograde Activation in Atrial Fibrillation

Atrioventricular Nodal Response to Retrograde Activation in Atrial Fibrillation

Design and Presenting of a Novel Algorithm Using Anfis for New Generation of Cardiac Pacemakers

Nonlinear oscillator model reproducing various phenomena in the dynamics of the conduction system of the heart

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