A study of synchronization of the sinus unit upon stimulation from auricles

The excitation of the sinoatrial unit from heart auricles of the frog has been studied. Potentials were recorded by means of microelectrodes inserted to pacemaker of the sinoatrial unit. It has been established that auricles can impart the rhythm to the sinoatrial unit due to electric and electromechanical influence, and electromechanical influence is of greater significance. Specific transitions accompanying the establishment of the stationary rhythm have been studied. A mathematical model of transitions of the establishment of the rhythm of the sinoatrial unit, which is based on diophant methods is offered. The catculations performed by means of the mathematical model coincide well with results of experimental studies. The stabilizing role of auricles in the formation of the rhythm of the sinoatrial unit has been established.     

Rhythmogenesis in the heart sinoatrial node

The most significant experimental data on the formation of the common rhythm of the heart sinoatrial node are presented for both the intact heart sinoatrial node and cardiomyocytes in cell structures. The basic mathematical models for studying the synchronization processes in the sinoatrial node, including the Noble equation, Bonhoffer-van der Pol model, and modified axiomatic models, are described. The basic results obtained with the mathematical models are presented. The most important causes affecting the formation of the common rhythm—the pacemaker potential shape in the slow diastolic depolarization phase, its porosity, the coupling force between pacemakers, and the electrical power of pacemakers—are revealed. Rhythmogenesis is studied using the modified axiomatic model. The method allows the calculation of the common rhythm of the sinoatrial node, with allowance for the mutual effect of the pacemaker cells, including the coupling force, electric power of cells, and possibility of the cells clustering. It has been shown that the common rhythm of the sinoatrial node is generally formed at the intermediate level of the rhythms of all pacemaker cells.     

Rhythmogenesis in the sinoatrial unit of the heart

The most significant experimental data about the formation of a uniform rhythm of the sinoatrial unit of the heart for both the intact sinoatrial unit of the heart and cardiomyocytes in cellular structures are presented. The basic mathematical models for studying the processes of synchronization in the sinoatrial unit of the heart are described, including equations of Noble, Bonhoffer, and van der Pol and modified axiomatic models. The basic results obtained using the mathematical models are presented. The major reasons influencing the formation of a uniform rhythm were revealed: the form of a potential pacemaker in the phase of slow diastolic depolarization, its porosity, the force of connection between pacemaker and electric capacity of pacemakers. A study of rhythmogenisis on the basis of the modified axiomatic model was carrud out. The method allows one to calculate the uniform rhythm of the sinoatrial unit of the heart in view of the mutual influence of pacemaker cells, including the force of connection, electric capacity of cells, their possible clusterization. It was shown that generally the uniform rhythm of the sinoatrial unit of the heart is formed on an intermediate level of all pacemaker cells.     

The mechanism of setting the common rhythm of the pacemaker pair in the sinoatrial node

Principal physiological hypotheses concerning the setting of united rhythm in the heart sinoatrial node (SAN) are considered. A mathematical model of SAN is proposed which takes into account properties of individual elementary pacemakers and their interaction. Assuming paired interaction of the pacemakers there are revealed the main P.D. parameters, affecting the setting of the united rhythm. Quantitative expressions are obtained for the united rhythm period, delay and propagation velocity of the excitation. The calculated data are compared with the experimental ones. The hypothesis concerning the setting of the united rhythm as a result of the interaction of SAN pacemakers is confirmed.     

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria - the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.     

Mathematical model of heart rate variability

The study presents a mathematical model of non-linear dynamics of the heart rate variability (HRV). The model is based on quantitative characteristics of pulse conduction in the heart conducting system: the delays of sinoatrial (SA) and atrioventricular (AV) pulse conduction and refractors periods of the SA and AV nodes. The model predicts heart rate disturbances in fast electric activity of the atria, increase in the delay of the AV conduction, the critical value of atrial period where transition to non-linear dynamics of the heart rate variability starts. The correlation between indexes of HRV and period of stimulation of atria for 1-contour cardiac control model has been demonstrated.     

Minor contribution of cytosolic Ca2+ transients to the pacemaker rhythm in guinea pig sinoatrial node cells

The question of the extent to which cytosolic Ca(2+) affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the "Ca(2+) clock" (C) and "membrane clock" (M) hypotheses, together with patch-clamp experiments in isolated guinea pig sinoatrial node cells. By applying lead potential analysis to the models, the C mechanism, which is dependent on potentiation of Na(+)/Ca(2+) exchange current via spontaneous Ca(2+) release from the sarcoplasmic reticulum (SR) during diastole, was found to overlap M mechanisms in the C model. Rapid suppression of pacemaker rhythm was observed in the C model by chelating intracellular Ca(2+), whereas the M model was unaffected. Experimental rupturing of the perforated-patch membrane to allow rapid equilibration of the cytosol with 10 mM BAPTA pipette solution, however, failed to decrease the rate of spontaneous action potential within ～30 s, whereas contraction ceased within ～3 s. The spontaneous rhythm also remained intact within a few minutes when SR Ca(2+) dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca(2+) dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca(2+)-mediated inactivation of the L-type Ca(2+) currents induced by BAPTA, were well explained by assuming Ca(2+) chelation, even in the proximity of the channel pore in addition to the bulk cytosol in the M model. Taken together, the experimental and model findings strongly suggest that the C mechanism explicitly described by the C model can hardly be applied to guinea pig sinoatrial node cells. The possible involvement of L-type Ca(2+) current rundown induced secondarily through inhibition of Ca(2+)/calmodulin kinase II and/or Ca(2+)-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca(2+) concentration reduction for >5 min.     

Analysis of changes in heart rate variability during fast extracardial impulsation in the sinoatrial node

It is known that fast extracardial impulsation in the sinoatrial node modifies the degree of heart rare variability. The present study presents theoretical and experimental investigation of this effect. Theoretical investigation is based on the mathematical modelling of impulse conduction in the cardiac conduction system. Experimental investigation on dogs revealed quantitative correlations between the frequency of extracardial impulsation in the sinoatrial node and changes of heart rate variability. Computer simulation shows that the mathematical model can account for most principal properties of the heart rate disturbances during fast extracardial impulsation in the sinoatrial node: transitions between different regimens of heart rate dynamics; increase in the delay of atrio-ventricular conduction; Wenkebach's periodicity.     

Analysis of the nonlinear heart rate dynamics by two-contour mathematical model

Using a two-contour mathematical model, changes in the degree of heart rate variability induced by an increased extracardial impulsation in the sinoatrial node have been studied. The model is based on quantitative characteristics of impulse conduction in the cardiac conduction system. A mathematical and computer modeling revealed the following three regimes of heart rate variability: linear dynamics, the 1st-degree chaos, and the 2nd-degree chaos. Transitions between these regimes have been studied. A comparative analysis of the one- and two-contour models of heart rate regulation has been performed.     

Bifurcation analysis and effects of changing ionic conductances on pacemaker rhythm in a sinoatrial node cell model

The electrical excitation (action potential generation) of sinoatrial node (cardiac pacemaker) cells is directly related to various ion channels (pore-forming proteins) in cell membranes. In order to analyze the relation between action potential generation and ion channels, we use the Yanagihara-Noma-Irisawa (YNI) model of sinoatrial node cells, which is described by the Hodgkin-Huxley-type equations with seven variables. In this paper, we analyze the global bifurcation structure of the YNI model by varying various conductances of ion channels, and examine the effects of these conductance changes on pacemaker rhythm (frequency of action potential generation). The coupling effect on pacemaker rhythm is also examined approximately by applying external current to the YNI model.     

Dynamics of cardiac rhythm in the transitional period during controlled physical exercises in persons of various ages

The transitional cardiac rhythm processes of work-in and recovery under standard dynamic loads of 25 and 50 W were studied in 90 healthy people aged 20-89 and in 15 elderly people being trained for endurance. The rhythmographic method was used for that purpose. Duration of the transitional processes (work-in and recovery) was revealed to considerably increase with age, while the cardiac rhythm increment--to decrease within the first 10 seconds of the work-in period. The data obtained suggest a worsened quality of the cardiac rhythm regulation in the transitional periods during aging, that is a result of an impairment of the vegetative influences on the sinoatrial node.     

Effects of Regulatory Peptides on Electrophysiological Properties of the Human Heart

During transesophageal electrical stimulation of the left atria in patients with heart diseases, an intravenous administration of Sandostatin prolonged the cardiac cycle and the effective refractory period of the atrioventricular junction, slowed down the sinoatrial conduction and the sinus node recovery time, and shifted the Wenckebach's point downwards. Neurotensin produced effects opposite to those of Sandostatin. During the Valsalva maneuver, Sandostatin strengthened bradycardia and broadened the range of heart rate changes associated with the vagal tone variations. The latter effect was also observed after the administration of neurotensin. Met-enkephalin and dalargin shortened the cardiac cycle, increased the corrected time of sinus node recovery time, but did not affect the cardiac rhythm dynamics during the Valsalva maneuver. These findings suggest that the regulatory peptides can be involved in control mechanisms determining the electrophysiological parameters of the human heart.     

Pacemaker activity of the rabbit sinoatrial node. A comparison of mathematical models.

In the past decade, three mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed: the Bristow-Clark model, the Irisawa-Noma model, and the Noble-Noble model. In a comparative study it is demonstrated that these models, as well as subsequent modifications, all have several drawbacks. A more accurate model, describing the pacemaker activity of a single pacemaker cell isolated from the rabbit sinoatrial node, was constructed. Model equations, including equations for the T-type calcium current, are based on experimental data from voltage clamp experiments on single cells that were published during the last few years. In contrast to the other models, only a small amount of background current contributes to the overall electrical charge flow. The action potential parameters of the model cell, its responses to voltage clamp steps and its current-voltage relationships have been computed. The model is used to discuss the relative contribution of membrane current components to the slow diastolic depolarization phase of the action potential.     

Morphological study of the innervation pattern of the rabbit sinoatrial node

The pattern of nerves, ganglia, and fine nerve processes in the adult rabbit sinoatrial node, identified by microelectrode recording, was defined by staining histochemically for cholinesterase followed by silver impregnation. A generalized repeatable pattern of innervation was recognized, including 1) a large ganglionic complex inferior to the sinoatrial node; 2) two or three moderately large nerves traversing the sinoatrial node parallel to the crista terminalis; 3) nerves entering the region from the atrial septum, the superior vena cava, and the inferior vena cava; and 4) a fine network of nerve processes, particularly extensive in the morphologically dense small-cell part of the sinoatrial node. When the site of initial depolarization in the node was located and marked by a broken-off electrode tip, it was found, after cholinesterase staining, to be characterized by a cluster of cells enclosed in a nest or basket of fine nerves. Similar nested cell clusters were observed elsewhere in the sinoatrial node in this same preparation and in other hearts. A complex interweaving of atrial muscle fibers was observed medial and inferomedial to the sinoatrial node, which may form the anatomical basis for the lack of conduction through this region. The morphological pattern of nerves, ganglia, and myocardial cells described in this study emphasizes the complexity of innervation of the sinoatrial node, including its intrinsic neural elements. Cholinesterase/silver staining can be useful in the definition and comparison of electrophysiologically identified sites within the sinoatrial node.     

Postnatal development of chronotropic responses to chemical and electrical stimulation of adrenergic nerve endings in the sinoatrial node of the heart of the albino rat

The positive chronotropic response to stimulation of adrenergic nerve endings in the sinoatrial node was studied in isolated atria from the hearts of rats of different ages. Dimethylphenylpiperazinium (DMPP) was used for chemical stimulation and transmural stimulation of the sinoatrial node region as electrical stimulation; in both cases noradrenaline is released from the nerve endings. With both stimulation methods, postnatal development was recorded in two phases. In the first phase, positive chronotropic responses are markedly increased and attained the maximum at the age of 14 days on using DMPP and of 24 days on using electrical stimulation. In the second phase, positive chronotropic responses diminish and at the age of about 45 days, with both stimulation methods, they become reduced to adult level. The first developmental phase can be attributed to an increase in the noradrenaline content of the nerve endings and the release of a larger amount of the transmitter during stimulation, together with an increase in the noradrenaline sensitivity of the cells of the sinoatrial node. It is not clear why positive chronotropic responses decrease in the second phase, when the noradrenaline content of the myocardial tissue continues to rise and pacemaker sensitivity to noradrenaline is not reduced.     

The effects of intracellular calcium dynamics on the electrical activity of the cells of the sinoatrial node

We studied the effects of intracellular calcium dynamics on the spontaneous activity of the pacemaker cells using mathematical modeling. We compared the responses to the suppression of L-type calcium currents in several models of the electrical activity of cells of the sinoatrial node. All models showed a decrease in the maximum depolarization rate, the amplitude of action potentials, and the duration of the action potential. The model of the calcium clock showed an increase in the oscillation period by 12%. Models with the spontaneous activity, which is determined by the current activated by hyperpolarization, showed a decrease of the oscillation period by 15%. The comparison of the theoretic results with the experimental data showed that intracellular mechanisms had a different input in the spontaneous activity of pacemakers in the center and periphery of the sinoatrial node.