Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

A Three-Dimensional Engineered Cardiac In Vitro Model: Controlled Alignment of Cardiomyocytes in 3D Microphysiological Systems

Cardiomyocyte alignment in myocardium tissue plays a significant role in the physiological, electrical, and mechanical functions of the myocardium. It remains, however, difficult to align cardiac cells in a 3D in vitro heart model. This paper proposes a simple method to align cells using microfabricated Polydimethylsiloxane (PDMS) grooves with large dimensions (of up to 350 µm in width), similar to the dimensions of trabeculae carneae, the smallest functional unit of the myocardium. Two cell groups were used in this work; first, H9c2 cells in combination with Nor10 cells for proof of concept, and second, neonatal cardiac cells to investigate the functionality of the 3D model. This model compared the patterned and nonpatterned 3D constructs, as well as the 2D cell cultures, with and without patterns. In addition to alignment, we assessed the functionality of our proposed 3D model by comparing beating rates between aligned and non-aligned structures. In order to assess the practicality of the model, the 3D aligned structures should be demonstrated to be detachable and alignable. This evaluation is crucial to the use of this 3D functional model in future studies related to drug screening, building blocks for tissue engineering, and as a heart-on-chip by integrating microfluidics.

The virtual sinoatrial node: What did computational models tell us about cardiac pacemaking?

Since its discovery, the sinoatrial node (SAN) has represented a fascinating and complex matter of research. Despite over a century of discoveries, a full comprehension of pacemaking has still to be achieved. Experiments often produced conflicting evidence that was used either in support or against alternative theories, originating intense debates. In this context, mathematical descriptions of the phenomena underlying the heartbeat have grown in importance in the last decades since they helped in gaining insights where experimental evaluation could not reach. This review presents the most updated SAN computational models and discusses their contribution to our understanding of cardiac pacemaking. Electrophysiological, structural and pathological aspects - as well as the autonomic control over the SAN - are taken into consideration to reach a holistic view of SAN activity.

Hyperglycaemia-induced impairment of the autorhythmicity and gap junction activity of mouse embryonic stem cell-derived cardiomyocyte-like cells

Diabetes mellitus with hyperglycaemia is a major risk factor for malignant cardiac dysrhythmias. However, the underlying mechanisms remain unclear, especially during the embryonic developmental phase of the heart. This study investigated the effect of hyperglycaemia on the pulsatile activity of stem cell-derived cardiomyocytes. Mouse embryonic stem cells (mESCs) were differentiated into cardiac-like cells through embryoid body (EB) formation, in either baseline glucose or high glucose conditions. Action potentials (APs) were recorded using a voltage-sensitive fluorescent dye and gap junction activity was evaluated using scrape-loading lucifer yellow dye transfer assay. Molecular components were detected using immunocytochemistry and immunoblot analyses. High glucose decreased the spontaneous beating rate of EBs and shortened the duration of onset of quinidine-induced asystole. Furthermore, it altered AP amplitude, but not AP duration, and had no impact on neither the expression of the hyperpolarisation-activated cyclic nucleotide-gated isoform 4 (HCN4) channel nor on the EB beating rate response to ivabradine nor isoprenaline. High glucose also decreased both the intercellular spread of lucifer yellow within an EB and the expression of the cardiac gap junction protein connexin 43 as well as upregulated the expression of transforming growth factor beta 1 (TGF-β1) and phosphorylated Smad3. High glucose suppressed the autorhythmicity and gap junction conduction of mESC-derived cardiomyocytes, via mechanisms probably involving TGF-β1/Smad3 signalling. The results allude to glucotoxicity related proarrhythmic effects, with potential clinical implications in foetal diabetic cardiac disease.

Active force generation contributes to the complexity of spontaneous activity and to the response to stretch of murine cardiomyocyte cultures

Abstract

Cardiomyocyte cultures exhibit spontaneous electrical and contractile activity, as in a natural cardiac pacemaker. In such preparations, beat rate variability exhibits features similar to those of heart rate variability in vivo. Mechanical deformations and forces feed back on the electrical properties of cardiomyocytes, but it is not fully elucidated how this mechano‐electrical interplay affects beating variability in such preparations. Using stretchable microelectrode arrays, we assessed the effects of the myosin inhibitor blebbistatin and the non‐selective stretch‐activated channel blocker streptomycin on beating variability and on the response of neonatal or fetal murine ventricular cell cultures against deformation. Spontaneous electrical activity was recorded without stretch and upon predefined deformation protocols (5% uniaxial and 2% equibiaxial strain, applied repeatedly for 1 min every 3 min). Without stretch, spontaneous activity originated from the edge of the preparations, and its site of origin switched frequently in a complex manner across the cultures. Blebbistatin did not change mean beat rate, but it decreased the spatial complexity of spontaneous activity. In contrast, streptomycin did not exert any manifest effects. During the deformation protocols, beat rate increased transiently upon stretch but, paradoxically, also upon release. Blebbistatin attenuated the response to stretch, whereas this response was not affected by streptomycin. Therefore, our data support the notion that in a spontaneously firing network of cardiomyocytes, active force generation, rather than stretch‐activated channels, is involved mechanistically in the complexity of the spatiotemporal patterns of spontaneous activity and in the stretch‐induced acceleration of beating.

Key points

Monolayer cultures of cardiac cells exhibit spontaneous electrical and contractile activity, as in a natural cardiac pacemaker. Beating variability in these preparations recapitulates the power‐law behaviour of heart rate variability in vivo. However, the effects of mechano‐electrical feedback on beating variability are not yet fully understood.

Using stretchable microelectrode arrays, we examined the effects of the contraction uncoupler blebbistatin and the non‐specific stretch‐activated channel blocker streptomycin on beating variability and on stretch‐induced changes of beat rate.

Without stretch, blebbistatin decreased the spatial complexity of beating variability, whereas streptomycin had no effects.

Both stretch and release increased beat rate transiently; blebbistatin attenuated the increase of beat rate upon stretch, whereas streptomycin had no effects.

Active force generation contributes to the complexity of spatiotemporal patterns of beating variability and to the increase of beat rate upon mechanical deformation. Our study contributes to the understanding of how mechano‐electrical feedback influences heart rate variability.

Engineering and Assessing Cardiac Tissue Complexity

Cardiac tissue engineering is very much in a current focus of regenerative medicine research as it represents a promising strategy for cardiac disease modelling, cardiotoxicity testing and cardiovascular repair. Advances in this field over the last two decades have enabled the generation of human engineered cardiac tissue constructs with progressively increased functional capabilities. However, reproducing tissue-like properties is still a pending issue, as constructs generated to date remain immature relative to native adult heart. Moreover, there is a high degree of heterogeneity in the methodologies used to assess the functionality and cardiac maturation state of engineered cardiac tissue constructs, which further complicates the comparison of constructs generated in different ways. Here, we present an overview of the general approaches developed to generate functional cardiac tissues, discussing the different cell sources, biomaterials, and types of engineering strategies utilized to date. Moreover, we discuss the main functional assays used to evaluate the cardiac maturation state of the constructs, both at the cellular and the tissue levels. We trust that researchers interested in developing engineered cardiac tissue constructs will find the information reviewed here useful. Furthermore, we believe that providing a unified framework for comparison will further the development of human engineered cardiac tissue constructs displaying the specific properties best suited for each particular application.

Cyclophosphamide arrhythmogenicitytesting using human-induced pluripotent stem cell-derived cardiomyocytes

Cyclophosphamide (CP) is an anticancer drug, an alkylating agent. Cardiotoxicity of CP is associated with one of its metabolites, acrolein, and clinical cardiotoxicity manifestations are described for cases of taking CP in high doses. Nevertheless, modern arrhythmogenicity prediction assays in vitro include evaluation of beat rhythm and rate as well as suppression of cardiac late markers after acute exposure to CP, but not its metabolites. The mechanism of CP side effects when taken at low doses (i.e., < 100 mg/kg), especially at the cellular level, remains unclear. In this study conduction properties and cytoskeleton structure of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) obtained from a healthy donor under CP were evaluated. Arrhythmogenicity testing including characterization of 3 values: conduction velocity, maximum capture rate (MCR) measurements and number of occasions of re-entry on a standard linear obstacle was conducted and revealed MCR decrease of 25% ± 7% under CP. Also, conductivity area reduced by 34 ± 15%. No effect of CP on voltage-gated ion channels was found. Conduction changes (MCR and conductivity area decrease) are caused by exposure time-dependent alpha-actinin disruption detected both in hiPSC-CMs and neonatal ventricular cardiomyocytes in vitro. Deviation from the external stimulus frequency and appearance of non-conductive areas in cardiac tissue under CP is potentially arrhythmogenic and could develop arrhythmic effects in vivo.

Heart rate fragmentation gives novel insights into non-autonomic mechanisms governing beat-to-beat control of the heart's rhythm

To demonstrate how heart rate fragmentation gives novel insights into non-autonomic mechanisms of beat-to-beat variability in cycle length, and predicts survival of cardiology clinic patients, over and above traditional clinical risk factors and measures of heart rate variability.

Approach: We studied 2893 patients seen by cardiologists with clinical data including 24-hour Holter monitoring. Novel measures of heart rate fragmentation alongside canonical time and frequency domain measures of heart rate variability, as well as an existing local dynamics score were calculated. A proportional hazards model was utilized to relate the results to survival.

Main results: The novel heart rate fragmentation measures were validated and characterized with respect to the effects of age, ectopy and atrial fibrillation. Correlations between parameters were determined. Critically, heart rate fragmentation results could not be accounted for by undersampling respiratory sinus arrhythmia. Increased heart rate fragmentation was associated with poorer survival (p ≪ 0.01 in the univariate model). In multivariable analyses, increased heart rate fragmentation and more abnormal local dynamics (p 0.045), along with increased clinical risk factors (age (p ≪ 0.01), tobacco use (p ≪ 0.01) and history of heart failure (p 0.019)) and lower low- to high-frequency ratio (p 0.022) were all independent predictors of 2-year mortality.

Significance: Analysis of continuous ECG data with heart rate fragmentation indices yields information regarding non-autonomic control of beat-to-beat variability in cycle length that is independent of and additive to established parameters for investigating heart rate variability, and predicts mortality in concert with measures of local dynamics, frequency content of heart rate, and clinical risk factors.

Dynamic Properties of Heart Fragments from Different Regions and Their Synchronization

The dynamic properties of the heart differ based on the regions that effectively circulate blood throughout the body with each heartbeat. These properties, including the inter-beat interval (IBI) of autonomous beat activity, are retained even in in vitro tissue fragments. However, details of beat dynamics have not been well analyzed, particularly at the sub-mm scale, although such dynamics of size are important for regenerative medicine and computational studies of the heart. We analyzed the beat dynamics in sub-mm tissue fragments from atria and ventricles of hearts obtained from chick embryos over a period of 40 h. The IBI and contraction speed differed by region and atrial fragments retained their values for a longer time. The major finding of this study is synchronization of these fragment pairs physically attached to each other. The probability of achieving this and the time required differ for regional pairs: atrium-atrium, ventricle-ventricle, or atrium-ventricle. Furthermore, the time required to achieve 1:1 synchronization does not depend on the proximity of initial IBI of paired fragments. Various interesting phenomena, such as 1:n synchronization and a reentrant-like beat sequence, are revealed during synchronization. Finally, our observation of fragment dynamics indicates that mechanical motion itself contributes to the synchronization of atria.

Multifractal Spectrum Curvature of RR Tachograms of Healthy People and Patients with Congestive Heart Failure, a New Tool to Assess Health Conditions

We calculate the multifractal spectra of heartbeat RR-interval time series (tachograms) of healthy subjects and patients with congestive heart failure (CHF). From these time series, we obtained new subseries of 6 h durations when healthy persons and patients were asleep and awake respectively. For each time series and subseries, we worked out the multifractal spectra with the Chhabra and Jensen method and found that their graphs have different shapes for CHF patients and healthy persons. We suggest to measure two parameters: the curvature around the maximum and the symmetry for all these multifractal spectra graphs, because these parameters were different for healthy and CHF subjects. Multifractal spectra of healthy subjects tend to be right skewed especially when the subjects are asleep and the curvature around the maximum is small compared with the curvature around the maximum of the CHF multifractal spectra; that is, the spectra of patients tend to be more pointed around the maximum. In CHF patients, we also have encountered differences in the curvature of the multifractal spectra depending on their respective New York Heart Association (NYHA) index.

Differentiation of Heart Failure Patients by the Ratio of the Scaling Exponents of Cardiac Interbeat Intervals

Heart failure (HF) is one of the most frequent heart diseases. It is usually characterized with structural and functional cardiac abnormalities followed by dysfunction of autonomic cardiac control. Current methods of heartbeat interval analysis are not capable to differentiate HF patients and some new differentiation of HF patients could be useful in the determination of the direction of their treatment. In this study, we examined potential of the ratio of the short-term and long-term scaling exponents (α 1 and α 2) to separate HF patients with similar level of reduced cardiac autonomic nervous system control and with no significant difference in age, left ventricular ejection fraction (LVEF) and NYHA class. Thirty-five healthy control subjects and 46 HF patients underwent 20 min of continuous supine resting ECG recording. The interbeat interval time series were analyzed using standardized power spectrum analysis, detrended fluctuation analysis method and standard Poincaré plot (PP) analysis with measures of asymmetry of the PP. Compared with healthy control group, in HF patients linear measures of autonomic cardiac control were statistically significantly reduced (p < 0.05), heart rate asymmetry was preserved (C up > C down, p < 0.01), and long-term scaling exponent α 2 was significantly higher. Cluster analysis of the ratio of short- and long-term scaling exponents showed capability of this parameter to separate four clusters of HF patients. Clusters were determined by interplay of presence of short-term and long-term correlations in interbeat intervals. Complementary measure, commonly accepted ratio of the PP descriptors, SD2/SD1, showed tendency toward statistical significance to separate HF patients in obtained clusters. Also, heart rate asymmetry was preserved only in two clusters. Finally, a multiple regression analysis showed that the ratio α 1/α 2 could be used as an integrated measure of cardiac dynamic with complex physiological background which, besides spectral components as measures of autonomic cardiac control, also involves breathing frequency and mechanical cardiac parameter, left ventricular ejection fraction.

Modifications of short-term intrinsic pacemaker variability in diet-induced metabolic syndrome: a study on isolated rabbit heart

Metabolic syndrome (MetS) describes a condition associated with multiple diseases concomitantly such as diabetes, hypertension, obesity, and dyslipidemia. It has been linked with higher prevalence of cardiovascular disease, atrial fibrillation, and sudden cardiac death. One of the underlying mechanisms could be altered automaticity, which would reflect modifications of sinus node activity. These phenomena can be evaluated analyzing the components of heart rate variability (HRV). Our aim was to examine the modifications of sinus node variability in an isolated heart model of diet-induced obesity and MetS. Male NZW rabbits were randomly assigned to high-fat (HF, n = 8), control (HF-C, n = 7), high-fat, high-sucrose (HFHS, n = 9), and control (HFHS-C, n = 9) groups, fed with their respective diets during 18/28 weeks. After euthanasia, their hearts were isolated in a Langendorff system. We recorded 10-15 min of spontaneous activity. Short RR time series were analyzed, and standard HRV parameters were determined. One-way ANOVA, Kruskal-Wallis test, and bivariate correlation were used for statistical analysis (p < 0.05). We did find an increase in the complexity and irregularity of intrinsic pacemaker activity as shown by modifications of approximate entropy, sample entropy, minimum multiscale entropy, and complexity index in HFHS animals. Even though no differences were found in standard time and frequency-domain analyses, spectral heterogeneity increased in HFHS group. Animal weight and glucose intolerance were highly correlated with the modifications of intrinsic pacemaker variability. Finally, modifications of intrinsic HRV seemed to be reliant on the number of components of MetS present, given that only HFHS group showed significant changes towards an increased complexity and irregularity of intrinsic pacemaker variability.

Patterns of cardiovascular variability after long-term sino-aortic denervation in unanesthetized adult rats

Baroreflex dysfunction is a diffuse chronic condition that is expected to be followed by a profound loss of organization of BP and HR variability. Nevertheless, long-term effects of baroreflex withdrawal are still debated. Aim of our work was to study BP and HR changes long term after sino-aortic denervation (SAD). Inter-beat-interval (IBI) and intra-arterial BP were recorded beat-by-beat in 43 Wistar-Kyoto rats (Controls, n = 33; SAD rats, n = 10). Power spectra were calculated in controls and in SAD rats within three days and at seven months from denervation. Compared to controls, chronic SAD rats showed 1) similar mean BP (control vs SAD: 95 ± 16 vs 87 ± 22 mmHg) and IBI (171 ± 22 vs 181 ± 15 ms) values, 2) dramatically higher values of BP variance (12 ± 2 vs 64 ± 2 mmHg2, p < 0.01) and of ultra- (ULF) and very-low-frequency (VLF) BP oscillations, 3) dramatically higher values of IBI variability (24 ± 2 vs 71 ± 4 ms2, p < 0.01) and of ULF-IBI oscillations that were synchronized with BP oscillations. Chronic SAD rats reveal a marked change in the pattern of cardiovascular variability characterized by the appearance of synchronized slower oscillations of BP and HR. The cardiovascular system, therefore, retains a high level of organization despite the absence of a reflex control mechanism.

Inconsistent relation of nonlinear heart rate variability indices to increasing vagal tone in healthy humans

BACKGROUND

Prior work has found that linear heart rate variability (HRV) indices do not accurately reflect cardiac vagal control, and nonlinear indices of HRV have been proposed as alternative tools that may better capture cardiac vagal effects. We used progressive low dose atropine to induce changes in cardiac vagal tone to test the hypotheses that nonlinear HRV indices accurately reflect cardiac vagal control, and that their changes in response to low dose atropine correlate with those in RR interval.

METHODS

Changes in RR interval and HRV indices during intravenous injections of saline (control) and 6 cumulative doses of atropine (from 1.4 to 7.2 μg/kg) during controlled breathing at 15 breaths per minute were assessed in 14 young healthy individuals.

RESULTS

As expected, low dose atropine increased average RR interval (vagotonic effect). There was no strong association between vagotonic changes in RR interval and the majority of nonlinear HRV indices, either within or among subjects.

CONCLUSIONS

These data suggest an inconsistent relationship between responses of nonlinear HRV indices and RR interval to changes in cardiac vagal tone. Therefore, nonlinear HRV indices may not be reliable indices of cardiac vagal control in healthy humans.

Sinoatrial Beat to Beat Variability Assessed by Contraction Strength in Addition to the Interbeat Interval

Beat to beat variability of cardiac tissue or isolated cells is frequently investigated by determining time intervals from electrode measurements in order to compute scale dependent or scale independent parameters. In this study, we utilize high-speed video camera recordings to investigate the variability of intervals as well as mechanical contraction strengths and relative contraction strengths with nonlinear analyses. Additionally, the video setup allowed us simultaneous electrode registrations of extracellular potentials. Sinoatrial node tissue under control and acetylcholine treated conditions was used to perform variability analyses by computing sample entropies and Higuchi dimensions. Beat to beat interval variabilities measured by the two recording techniques correlated very well, and therefore, validated the video analyses for this purpose. Acetylcholine treatment induced a reduction of beating rate and contraction strength, but the impact on interval variability was negligible. Nevertheless, the variability analyses of contraction strengths revealed significant differences in sample entropies and Higuchi dimensions between control and acetylcholine treated tissue. Therefore, the proposed high-speed video camera technique might represent a non-invasive tool that allows long-lasting recordings for detecting variations in beating behavior over a large range of scales.

In silico study of multicellular automaticity of heterogeneous cardiac cell monolayers: Effects of automaticity strength and structural linear anisotropy

The biological pacemaker approach is an alternative to cardiac electronic pacemakers. Its main objective is to create pacemaking activity from added or modified distribution of spontaneous cells in the myocardium. This paper aims to assess how automaticity strength of pacemaker cells (i.e. their ability to maintain robust spontaneous activity with fast rate and to drive neighboring quiescent cells) and structural linear anisotropy, combined with density and spatial distribution of pacemaker cells, may affect the macroscopic behavior of the biological pacemaker. A stochastic algorithm was used to randomly distribute pacemaker cells, with various densities and spatial distributions, in a semi-continuous mathematical model. Simulations of the model showed that stronger automaticity allows onset of spontaneous activity for lower densities and more homogeneous spatial distributions, displayed more central foci, less variability in cycle lengths and synchronization of electrical activation for similar spatial patterns, but more variability in those same variables for dissimilar spatial patterns. Compared to their isotropic counterparts, in silico anisotropic monolayers had less central foci and displayed more variability in cycle lengths and synchronization of electrical activation for both similar and dissimilar spatial patterns. The present study established a link between microscopic structure and macroscopic behavior of the biological pacemaker, and may provide crucial information for optimized biological pacemaker therapies.

Implantation of electronic pacemakers is a standard treatment to pathologically slow heart rhythm. Despite improving quality of life, those devices display many shortcomings. Bioengineered tissue pacemakers may be a therapeutic alternative, but associated design methods usually lack control of the way cells with spontaneous activity are scattered throughout the tissue. Our study is the first to use a mathematical model to rigorously define and thoroughly characterize how pacemaker cells scattering at the microscopic level may affect macroscopic behaviors of the bioengineered tissue pacemaker. Automaticity strength (ability of pacemaker cell to drive its non-pacemaker neighbors) and anisotropy (preferential orientation of cell shape) are also implemented and give unparalleled insights on how effects of uncontrollable scattered pacemaker cells may be modulated by available experimental techniques. Our model is a powerful tool to aid in optimized bioengineered pacemaker therapies.

Regularity of beating of small clusters of embryonic chick ventricular heart-cells: experiment vs. stochastic single-channel population model

The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of ∼20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincaré plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (I_Ks), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noise-current into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of time-scales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channel-noise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.

Noise-induced effects on multicellular biopacemaker spontaneous activity: Differences between weak and strong pacemaker cells

Self-organization of spontaneous activity of a network of active elements is important to the general theory of reaction-diffusion systems as well as for pacemaking activity to initiate beating of the heart. Monolayer cultures of neonatal rat ventricular myocytes, consisting of resting and pacemaker cells, exhibit spontaneous activation of their electrical activity. Similarly, one proposed approach to the development of biopacemakers as an alternative to electronic pacemakers for cardiac therapy is based on heterogeneous cardiac cells with resting and spontaneously beating phenotypes. However, the combined effect of pacemaker characteristics, density, and spatial distribution of the pacemaker cells on spontaneous activity is unknown. Using a simple stochastic pattern formation algorithm, we previously showed a clear nonlinear dependency of spontaneous activity (occurrence and amplitude of spontaneous period) on the spatial patterns of pacemaker cells. In this study, we show that this behavior is dependent on the pacemaker cell characteristics, with weaker pacemaker cells requiring higher density and larger clusters to sustain multicellular activity. These multicellular structures also demonstrated an increased sensitivity to voltage noise that favored spontaneous activity at lower density while increasing temporal variation in the period of activity. This information will help researchers overcome the current limitations of biopacemakers.

Modulation of cardiac pacemaker inter beat intervals by sinoatrial fibroblasts -a numerical study

The potential effect of sinoatrial fibroblasts on beat rate and variability of the cardiac pacemakers is not yet fully understood. Heterocellular coupling formation and fibroblast proliferation during diseased conditions may further signify the impact of those cells on sinoatrial node function. In this study we numerically modeled the impact of varying numbers of fibroblasts that are electrically coupled to a single pacemaker cell on several electrophysiological parameters. We employed cellular kinetics of the rabbit sinoatrial myocyte, and employed a range of potential gap junctional coupling between fibroblasts and myocytes. We show that increasing numbers of attached and coupled fibroblasts result in depolarization of the resting membrane potential of the pacemaker cell, as well as in attenuation in its action potential magnitude. We also demonstrate that the mean pacemaker inter-beat interval (IBI) was modulated in a non-linear, bi-phasic way by increasing numbers of attached fibroblasts, whereby an initial phase of decreasing IBIs was followed by a significant phase of exponentially increasing IBIs. These observations were more substantial for increased gap junctional coupling between the two cell types. We finally show that IBI variability exponentially increased with increasing numbers of attached and electrically coupled fibroblasts. Again, this effect was stronger with higher values of gap junctional coupling. We postulate that the last observation is related to the role of fibroblasts in amplifying membrane voltage fluctuations of attached myocytes.

Variations of high frequency parameter of heart rate variability following osteopathic manipulative treatment in healthy subjects compared to control group and sham therapy: randomized controlled trial

Context: Heart Rate Variability (HRV) indicates how heart rate changes in response to inner and external stimuli. HRV is linked to health status and it is an indirect marker of the autonomic nervous system (ANS) function.

Objective: To investigate the influence of osteopathic manipulative treatment (OMT) on cardiac autonomic modulation in healthy subjects, compared with sham therapy and control group.

Methods: Sixty-six healthy subjects, both male and female, were included in the present 3-armed randomized placebo controlled within subject cross-over single blinded study. Participants were asymptomatic adults (26.7 ± 8.4 y, 51% male, BMI 18.5 ± 4.8), both smokers and non-smokers and not on medications. At enrollment subjects were randomized in three groups: A, B, C. Standardized structural evaluation followed by a patient need-based osteopathic treatment was performed in the first session of group A and in the second session of group B. Standardized evaluation followed by a protocoled sham treatment was provided in the second session of group A and in the first session of group B. No intervention was performed in the two sessions of group C, acting as a time-control. The trial was registered on clinicaltrials.gov identifier: NCT01908920.

Main Outcomes Measures: HRV was calculated from electrocardiography before, during and after the intervention, for a total amount time of 25 min and considering frequency domain as well as linear and non-linear methods as outcome measures.

Results: OMT engendered a statistically significant increase of parasympathetic activity, as shown by High Frequency power (p < 0.001), expressed in normalized and absolute unit, and possibly decrease of sympathetic activity, as revealed by Low Frequency power (p < 0.01); results also showed a reduction of Low Frequency/High Frequency ratio (p < 0.001) and Detrended fluctuation scaling exponent (p < 0.05).

Conclusions: Findings suggested that OMT can influence ANS activity increasing parasympathetic function and decreasing sympathetic activity, compared to sham therapy and control group.

Spatiotemporal stability of neonatal rat cardiomyocyte monolayers spontaneous activity is dependent on the culture substrate

In native conditions, cardiac cells must continuously comply with diverse stimuli necessitating a perpetual adaptation. Polydimethylsiloxane (PDMS) is commonly used in cell culture to study cellular response to changes in the mechanical environment. The aim of this study was to evaluate the impact of using PDMS substrates on the properties of spontaneous activity of cardiomyocyte monolayer cultures. We compared PDMS to the gold standard normally used in culture: a glass substrate. Although mean frequency of spontaneous activity remained unaltered, incidence of reentrant activity was significantly higher in samples cultured on glass compared to PDMS substrates. Higher spatial and temporal instability of the spontaneous rate activation was found when cardiomyocytes were cultured on PDMS, and correlated with decreased connexin-43 and increased CaV3.1 and HCN2 mRNA levels. Compared to cultures on glass, cultures on PDMS were associated with the strongest response to isoproterenol and acetylcholine. These results reveal the importance of carefully selecting the culture substrate for studies involving mechanical stimulation, especially for tissue engineering or pharmacological high-throughput screening of cardiac tissue analog.

Using local scale exponent to characterize heart rate variability in response to postural changes in people with spinal cord injury

Heart rate variability (HRV) is a promising marker for evaluating the remaining autonomic function in people with spinal cord injury (SCI). HRV is commonly assessed by spectral analysis and detrended fluctuation analysis (DFA). This study aimed to investigate whether local scale exponent α(t) can reveal new features of HRV that cannot be reflected by spectral measures and DFA coefficients. We studied 12 participants with SCI and 15 healthy able-bodied controls. ECG signals were continually recorded during 10 min sitting and 10 min prone postures. α(t) was calculated for scales between 4 and 60 s. Because α(t) could be overestimated at small scales, we developed an approach for correcting α(t) based on previous studies. The simulation results on simulated monofractal time series with α between 0.5 and 1.3 showed that the proposed method can yield improved estimation of α(t). We applied the proposed method to raw RR interval series. The results showed that α(t) in healthy controls monotonically decreased with scale at scales between 4 and 12 s (0.083–0.25 Hz) in both the sitting and prone postures, whereas in participants with SCI, α(t) slowly decreased at almost all scales. The sharp decreasing trend in α(t) in controls suggests a more complex dynamics of HRV in controls. α(t) at scales between 4 (0.25 Hz) and around 7 s (0.143 Hz) was lower in subjects with SCI than in controls in the sitting posture; α(t) at a narrow range of scales around 12 s (0.083 Hz) was higher in participants with SCI than in controls in the prone posture. However, none of normalized low frequency (0.04–0.15 Hz) power, the ratio of low frequency power to high frequency (0.15–0.4 Hz) power and long-term (>11 beats) DFA coefficient showed significant difference between healthy controls and subjects with SCI in the prone posture. Our results suggest that α(t) can reveal more detailed information in comparison to spectral measures and the standard DFA parameters.

Interbeat interval modulation in the sinoatrial node as a result of membrane current stochasticity-a theoretical and numerical study

A single isolated sinoatrial pacemaker cell presents intrinsic interbeat interval (IBI) variability that is believed to result from the stochastic characteristics of the opening and closing processes of membrane ion channels. To our knowledge, a novel mathematical framework was developed in this work to address the effect of current fluctuations on the IBIs of sinoatrial pacemaker cells. Using statistical modeling and employing the Fokker-Planck formalism, our mathematical analysis suggests that increased stochastic current fluctuation variance linearly increases the slope of phase-4 depolarization, hence the rate of activations. Single-cell and two-dimensional computerized numerical modeling of the sinoatrial node was conducted to validate the theoretical predictions using established ionic kinetics of the rabbit pacemaker and atrial cells. Our models also provide, to our knowledge, a novel complementary or alternative explanation to recent experimental observations showing a strong reduction in the mean IBI of Cx30 deficient mice in comparison to wild-types, not fully explicable by the effects of intercellular decoupling.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Neural innervation of white adipose tissue and the control of lipolysis

White adipose tissue (WAT) is innervated by the sympathetic nervous system (SNS) and its activation is necessary for lipolysis. WAT parasympathetic innervation is not supported. Fully-executed SNS-norepinephrine (NE)-mediated WAT lipolysis is dependent on β-adrenoceptor stimulation ultimately hinging on hormone sensitive lipase and perilipin A phosphorylation. WAT sympathetic drive is appropriately measured electrophysiologically and neurochemically (NE turnover) in non-human animals and this drive is fat pad-specific preventing generalizations among WAT depots and non-WAT organs. Leptin-triggered SNS-mediated lipolysis is weakly supported, whereas insulin or adenosine inhibition of SNS/NE-mediated lipolysis is strongly supported. In addition to lipolysis control, increases or decreases in WAT SNS drive/NE inhibit and stimulate white adipocyte proliferation, respectively. WAT sensory nerves are of spinal-origin and sensitive to local leptin and increases in sympathetic drive, the latter implicating lipolysis. Transsynaptic viral tract tracers revealed WAT central sympathetic and sensory circuits including SNS-sensory feedback loops that may control lipolysis.

Morning surge of ventricular arrhythmias in a new arrhythmogenic canine model of chronic heart failure is associated with attenuation of time-of-day dependence of heart rate and autonomic adaptation, and reduced cardiac chaos

Patients with chronic heart failure (CHF) exhibit a morning surge in ventricular arrhythmias, but the underlying cause remains unknown. The aim of this study was to determine if heart rate dynamics, autonomic input (assessed by heart rate variability (HRV)) and nonlinear dynamics as well as their abnormal time-of-day-dependent oscillations in a newly developed arrhythmogenic canine heart failure model are associated with a morning surge in ventricular arrhythmias. CHF was induced in dogs by aortic insufficiency & aortic constriction, and assessed by echocardiography. Holter monitoring was performed to study time-of-day-dependent variation in ventricular arrhythmias (PVCs, VT), traditional HRV measures, and nonlinear dynamics (including detrended fluctuations analysis α1 and α2 (DFAα1 & DFAα2), correlation dimension (CD), and Shannon entropy (SE)) at baseline, as well as 240 days (240 d) and 720 days (720 d) following CHF induction. LV fractional shortening was decreased at both 240 d and 720 d. Both PVCs and VT increased with CHF duration and showed a morning rise (2.5-fold & 1.8-fold increase at 6 AM-noon vs midnight-6 AM) during CHF. The morning rise in HR at baseline was significantly attenuated by 52% with development of CHF (at both 240 d & 720 d). Morning rise in the ratio of low frequency to high frequency (LF/HF) HRV at baseline was markedly attenuated with CHF. DFAα1, DFAα2, CD and SE all decreased with CHF by 31, 17, 34 and 7%, respectively. Time-of-day-dependent variations in LF/HF, CD, DFA α1 and SE, observed at baseline, were lost during CHF. Thus in this new arrhythmogenic canine CHF model, attenuated morning HR rise, blunted autonomic oscillation, decreased cardiac chaos and complexity of heart rate, as well as aberrant time-of-day-dependent variations in many of these parameters were associated with a morning surge of ventricular arrhythmias.

Population of computational rabbit-specific ventricular action potential models for investigating sources of variability in cellular repolarisation

Variability is observed at all levels of cardiac electrophysiology. Yet, the underlying causes and importance of this variability are generally unknown, and difficult to investigate with current experimental techniques. The aim of the present study was to generate populations of computational ventricular action potential models that reproduce experimentally observed intercellular variability of repolarisation (represented by action potential duration) and to identify its potential causes. A systematic exploration of the effects of simultaneously varying the magnitude of six transmembrane current conductances (transient outward, rapid and slow delayed rectifier K⁺, inward rectifying K⁺, L-type Ca²⁺, and Na⁺/K⁺ pump currents) in two rabbit-specific ventricular action potential models (Shannon et al. and Mahajan et al.) at multiple cycle lengths (400, 600, 1,000 ms) was performed. This was accomplished with distributed computing software specialised for multi-dimensional parameter sweeps and grid execution. An initial population of 15,625 parameter sets was generated for both models at each cycle length. Action potential durations of these populations were compared to experimentally derived ranges for rabbit ventricular myocytes. 1,352 parameter sets for the Shannon model and 779 parameter sets for the Mahajan model yielded action potential duration within the experimental range, demonstrating that a wide array of ionic conductance values can be used to simulate a physiological rabbit ventricular action potential. Furthermore, by using clutter-based dimension reordering, a technique that allows visualisation of multi-dimensional spaces in two dimensions, the interaction of current conductances and their relative importance to the ventricular action potential at different cycle lengths were revealed. Overall, this work represents an important step towards a better understanding of the role that variability in current conductances may play in experimentally observed intercellular variability of rabbit ventricular action potential repolarisation.

The effect of endotoxin on the controllability of cardiac rhythm in rats

Decreased heart rate variability (HRV) has both diagnostic and prognostic value in patients with sepsis. However, it is not known whether reduced HRV in sepsis reflects an altered input from the autonomic nervous system or a remodeling of the cardiac pacemaker cells by inflammatory mediators. The present study aimed to investigate the effect of endotoxin on the heart rate dynamics of a denervated isolated heart in rats. Saline or endotoxin was injected into rats and their hearts were isolated and perfused. Atrial electrical activity was recorded and memory length in the time-series was assessed using inverse statistical analysis. Memory was defined as a statistical feature that lasts for a period of time and distinguishes the time-series from a random process. Endotoxaemic hearts exhibited a prolonged memory compared to the controls with respect to observing rare events. This indicates that a sudden decelerating event could potentially affect the cardiac rhythm of an endotoxaemic heart for a longer time than the controls. The prolongation of memory is indirectly linked to a reduced controllability in a complex system; therefore our data may provide evidence for a reduced controllability in cardiac rhythm following endotoxaemia.

The role of α7 nicotinic acetylcholine receptor in modulation of heart rate dynamics in endotoxemic rats

Previous reports have indicated that artificial stimulation of the vagus nerve reduces systemic inflammation in experimental models of sepsis. This phenomenon is a part of a broader cholinergic anti-inflammatory pathway which activates the vagus nerve to modulate inflammation through activation of alpha7 nicotinic acetylcholine receptors (α7nACHR). Heart rate variability represents the complex interplay between autonomic nervous system and cardiac pacemaker cells. Reduced heart rate variability and increased cardiac cycle regularity is a hallmark of clinical conditions that are associated with systemic inflammation (e.g. endotoxemia and sepsis). The present study was aimed to assess the role of α7nACHR in modulation of heart rate dynamics during systemic inflammation. Systemic inflammation was induced by injection of endotoxin (lipopolysaccharide) in rats. Electrocardiogram and body temperature were recorded in conscious animals using a telemetric system. Linear and non-linear indices of heart rate variability (e.g. sample entropy and fractal-like temporal structure) were assessed. RT-PCR and immunohistochemistry studies showed that α7nACHR is expressed in rat atrium and is mainly localized at the endothelial layer. Systemic administration of an α7nACHR antagonist (methyllycaconitine) did not show a significant effect on body temperature or heart rate dynamics in naïve rats. However, α7nACHR blockade could further reduce heart rate variability and elicit a febrile response in endotoxemic rats. Pre-treatment of endotoxemic animals with an α7nACHR agonist (PHA-543613) was unable to modulate heart rate dynamics in endotoxemic rats but could prevent the effect of endotoxin on body temperature within 24 h experiment. Neither methyllycaconitine nor PHA-543613 could affect cardiac beating variability of isolated perfused hearts taken from control or endotoxemic rats. Based on our observations we suggest a tonic role for nicotinic acetylcholine receptors in modulation of heart rate dynamics during systemic inflammation.

The emergence of subcellular pacemaker sites for calcium waves and oscillations

Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self-organization of Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca(2+), however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well-approximated by a Gaussian distribution. This same Ca(2+) oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca(2+) oscillations.

Intracardiac origin of heart rate variability, pacemaker funny current and their possible association with critical illness

Heart rate variability (HRV) is an indirect estimator of autonomic modulation of heart rate and is considered a risk marker in critical illness, particularly in heart failure and severe sepsis. A reduced HRV has been found in critically ill patients and has been associated with neuro-autonomic uncoupling or decreased baroreflex sensitivity. However, results from human and animal experimental studies indicate that intracardiac mechanisms might also be responsible for interbeat fluctuations. These studies have demonstrated that different membrane channel proteins and especially the so-called 'funny' current (If), an hyperpolarization-activated, inward current that drives diastolic depolarization resulting in spontaneous activity in cardiac pacemaker cells, are altered during critical illness. Furthermore, membrane channels kinetics seem to have significant impact upon HRV, whose early decrease might reflect a cellular metabolic stress. In this review article we present research findings regarding intracardiac origin of HRV, at the cellular level and in both isolated sinoatrial node and whole ex vivo heart preparations. In addition, we will review results from various experimental studies that support the interrelation between If and HRV during endotoxemia. We suggest that reduced HRV during sepsis could also be associated with altered pacemaker cell membrane properties, due to ionic current remodeling.

Functional cardiac tissue engineering

Heart attack remains the leading cause of death in both men and women worldwide. Stem cell-based therapies, including the use of engineered cardiac tissues, have the potential to treat the massive cell loss and pathological remodeling resulting from heart attack. Specifically, embryonic and induced pluripotent stem cells are a promising source for generation of therapeutically relevant numbers of functional cardiomyocytes and engineering of cardiac tissues in vitro. This review will describe methodologies for successful differentiation of pluripotent stem cells towards the cardiovascular cell lineages as they pertain to the field of cardiac tissue engineering. The emphasis will be placed on comparing the functional maturation in engineered cardiac tissues and developing heart and on methods to quantify cardiac electrical and mechanical function at different spatial scales.

Criticality in intracellular calcium signaling in cardiac myocytes

Calcium (Ca) is a ubiquitous second messenger that regulates many biological functions. The elementary events of local Ca signaling are Ca sparks, which occur randomly in time and space, and integrate to produce global signaling events such as intra- and intercellular Ca waves and whole-cell Ca oscillations. Despite extensive experimental characterization in many systems, the transition from local random to global synchronous events is still poorly understood. Here we show that criticality, a ubiquitous dynamical phenomenon in nature, is responsible for the transition from local to global Ca signaling. We demonstrate this first in a computational model of Ca signaling in a cardiac myocyte and then experimentally in mouse ventricular myocytes, complemented by a theoretical agent-based model to delineate the underlying dynamics. We show that the interaction between the Ca release units via Ca-induced Ca release causes self-organization of Ca spark clusters. When the coupling between Ca release units is weak, the cluster-size distribution is exponential. As the interactions become strong, the cluster-size distribution changes to a power-law distribution, which is characteristic of criticality in thermodynamic and complex nonlinear systems, and facilitates the formation and propagation of Ca waves and whole-cell Ca oscillations. Our findings illustrate how criticality is harnessed by a biological cell to regulate Ca signaling via self-organization of random subcellular events into cellular-scale oscillations, and provide a general theoretical framework for the transition from local Ca signaling to global Ca signaling in biological cells.

Human embryonic and induced pluripotent stem cell-derived cardiomyocytes exhibit beat rate variability and power-law behavior

BACKGROUND

The sinoatrial node is the main impulse-generating tissue in the heart. Atrioventricular conduction block and arrhythmias caused by sinoatrial node dysfunction are clinically important and generally treated with electronic pacemakers. Although an excellent solution, electronic pacemakers incorporate limitations that have stimulated research on biological pacing. To assess the suitability of potential biological pacemakers, we tested the hypothesis that the spontaneous electric activity of human embryonic stem cell-derived cardiomyocytes (hESC-CMs) and induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) exhibit beat rate variability and power-law behavior comparable to those of human sinoatrial node.

METHODS AND RESULTS

We recorded extracellular electrograms from hESC-CMs and iPSC-CMs under stable conditions for up to 15 days. The beat rate time series of the spontaneous activity were examined in terms of their power spectral density and additional methods derived from nonlinear dynamics. The major findings were that the mean beat rate of hESC-CMs and iPSC-CMs was stable throughout the 15-day follow-up period and was similar in both cell types, that hESC-CMs and iPSC-CMs exhibited intrinsic beat rate variability and fractal behavior, and that isoproterenol increased and carbamylcholine decreased the beating rate in both hESC-CMs and iPSC-CMs.

CONCLUSIONS

This is the first study demonstrating that hESC-CMs and iPSC-CMs exhibit beat rate variability and power-law behavior as in humans, thus supporting the potential capability of these cell sources to serve as biological pacemakers. Our ability to generate sinoatrial-compatible spontaneous cardiomyocytes from the patient's own hair (via keratinocyte-derived iPSCs), thus eliminating the critical need for immunosuppression, renders these myocytes an attractive cell source as biological pacemakers.

A multiscale investigation of repolarization variability and its role in cardiac arrhythmogenesis

Enhanced temporal and spatial variability in cardiac repolarization has been related to increased arrhythmic risk both clinically and experimentally. Causes and modulators of variability in repolarization and their implications in arrhythmogenesis are however not well understood. At the ionic level, the slow component of the delayed rectifier potassium current (I(Ks)) is an important determinant of ventricular repolarization. In this study, a combination of experimental and computational multiscale studies is used to investigate the role of intrinsic and extrinsic noise in I(Ks) in modulating temporal and spatial variability in ventricular repolarization in human and guinea pig. Results show that under physiological conditions: i), stochastic fluctuations in I(Ks) gating properties (i.e., intrinsic noise) cause significant beat-to-beat variability in action potential duration (APD) in isolated cells, whereas cell-to-cell differences in channel numbers (i.e., extrinsic noise) also contribute to cell-to-cell APD differences; ii), in tissue, electrotonic interactions mask the effect of I(Ks) noise, resulting in a significant decrease in APD temporal and spatial variability compared to isolated cells. Pathological conditions resulting in gap junctional uncoupling or a decrease in repolarization reserve uncover the manifestation of I(Ks) noise at cellular and tissue level, resulting in enhanced ventricular variability and abnormalities in repolarization such as afterdepolarizations and alternans.

Competing oscillators in cardiac pacemaking: historical background

Interaction between a membrane oscillator generated by voltage-dependent ion channels and an intracellular calcium signal oscillator was present in the earliest models (1984 to 1985) using representations of the sarcoplasmic reticulum. Oscillatory release of calcium is inherent in the calcium-induced calcium release process. Those historical results fully support the synthesis proposed in the articles in this review series. The oscillator mechanisms do not primarily compete with each; they entrain each other. However, there is some asymmetry: the membrane oscillator can continue indefinitely in the absence of the calcium oscillator. The reverse seems to be true only in pathological conditions. Studies from tissue-level work and on the development of the heart also provide valuable insights into the integrative action of the cardiac pacemaker.

Epilepsy as a dynamic disease: a tutorial of the past with an eye to the future

How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating, and shaping the direction of the efforts of each other.

The transfer functions of cardiac tissue during stochastic pacing

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K(+)]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.

Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated Guinea Pig ventricular myocytes

Experimental action potential (AP) recordings in isolated ventricular myoctes display significant temporal beat-to-beat variability in morphology and duration. Furthermore, significant cell-to-cell differences in AP also exist even for isolated cells originating from the same region of the same heart. However, current mathematical models of ventricular AP fail to replicate the temporal and cell-to-cell variability in AP observed experimentally. In this study, we propose a novel mathematical framework for the development of phenomenological AP models capable of capturing cell-to-cell and temporal variabilty in cardiac APs. A novel stochastic phenomenological model of the AP is developed, based on the deterministic Bueno-Orovio/Fentonmodel. Experimental recordings of AP are fit to the model to produce AP models of individual cells from the apex and the base of the guinea-pig ventricles. Our results show that the phenomenological model is able to capture the considerable differences in AP recorded from isolated cells originating from the location. We demonstrate the closeness of fit to the available experimental data which may be achieved using a phenomenological model, and also demonstrate the ability of the stochastic form of the model to capture the observed beat-to-beat variablity in action potential duration.

Fractal properties of human heart period variability: physiological and methodological implications

Fractal frequency scaling of heart period variability is used as a concise index of overall cardiac control. However, no prior study has assessed within-individual reproducibility of fractal indices of heart period, or reported how the estimated indices respond to autonomic blockade. Therefore, we examined fractal properties of the heart period from ten young, healthy individuals during three separate experimental sessions under control (saline) conditions and twice under combined autonomic blockade (atenolol and atropine sulfate) conditions. Under each condition, R-R intervals were recorded with the subject in the supine and the 40 deg upright tilt positions during 20 min of controlled breathing in each position. We calculated the fractal scaling exponent using detrended fluctuation analysis and estimated confidence intervals of the scaling exponents for each R-R interval time series within each individual. In the control condition, upright tilt significantly increased the scaling exponents (from 0.73 +/- 0.11 (+/-S.D., session 1), 0.72 +/- 0.10 (session 2) and 0.75 +/- 0.13 (session 3) to 0.82 +/- 0.12, 0.82 +/- 0.11 and 0.84 +/- 0.10; Student's paired t-test, t = 2.79, P = 0.02; t = 2.80, P = 0.02; and t = 2.07, P = 0.07). However, neither the absolute scaling exponents nor their change in response to upright tilt were reproducible (Lin's concordance coefficient less than 0.9, P > 0.1 for all comparisons). Following autonomic blockade, the scaling exponents were significantly increased (supine: 1.08 +/- 0.13 and 1.08 +/- 0.14; tilt: 1.07 +/- 0.21 and 1.08 +/- 0.14) for both experimental sessions (two-way repeated-measures ANOVA; F(17,1) = 40.89, P < 0.001 and F(17,1) = 42.72, P < 0.001) regardless of position. However, within individuals, the scaling exponents failed to distinguish between control and blockade for half of the subjects in at least one experimental session. Thus, fractal scaling exponents are not reproducible within individuals and do not reliably reflect the autonomic mechanisms responsible for heart period variability. In fact, data from combined blockade suggest that physiological effects of autonomic outflow may mask intrinsic fractal behaviour of the sinoatrial node.

Generality of a power-law long-term correlation in beat timings of single cardiac cells

Statistical properties of spontaneous contractions of atrial muscle cells were examined and compared to those of ventricular muscle cells. The cells derived from atria of neonatal rats exhibit spindle morphology, and they were found to express alpha-smooth muscle actin and hyperpolarization-activated cation channel 4, both of which are known marker of neonatal atrial muscle cells. The short-term properties of spontaneous contractions of atrial cells, characterized by considerably large beat rate and absence of bursts, are distinct from those of ventricular muscle cells. Despite of these differences, the long-term properties of the beat-rate fluctuations exhibit a remarkable similarity to those of ventricular cells. In particular, the presence of power-law correlation characterized as 1/f(beta) noise (beta approximately 1) was also confirmed for atrial cells for the first time. The observed similarity of the long-term characteristics of beat-rate fluctuation suggests the presence of a general regulatory mechanism of the cellular function.

Intrinsic dynamics of heart regulatory systems on short time-scales: from experiment to modelling

We discuss open problems related to the stochastic modeling of cardiac function. The work is based on an experimental investigation of the dynamics of heart rate variability (HRV) in the absence of respiratory perturbations. We consider first the cardiac control system on short time scales via an analysis of HRV within the framework of a random walk approach. Our experiments show that HRV on timescales of less than a minute takes the form of free diffusion, close to Brownian motion, which can be described as a non-stationary process with stationary increments. Secondly, we consider the inverse problem of modeling the state of the control system so as to reproduce the experimentally observed HRV statistics of. We discuss some simple toy models and identify open problems for the modelling of heart dynamics.

The relevance of non-excitable cells for cardiac pacemaker function

Age-dependent changes in the architecture of the sinus node comprise an increasing ratio between fibroblasts and cardiomyocytes. This change is discussed as a potential mechanism for sinus node disease. The goal of this study was to determine the mechanism through which non-excitable cells influence the spontaneous activity of multicellular cardiomyocyte preparations. Cardiomyocyte monolayers (HL-1 cells) or embryonic stem cell-derived cardiomyocytes were used as two- and three-dimensional cardiac pacemaker models. Spontaneous activity and conduction velocity (theta) were monitored by field potential measurements with microelectrode arrays (MEAs). The influence of fibroblasts (WT-fibs) was determined in heterocellular cultures of different cardiomyocyte and fibroblast ratios. The relevance of heterocellular gap junctional coupling was evaluated by the use of fibroblasts deficient for the expression of Cx43 (Cx43(-/-)-fibs). The beating frequency and of heterocellular cultures depended negatively on the fibroblast concentration. Interspersion of fibroblasts in cardiomyocyte monolayers increased the coefficient of the interbeat interval variability. Whereas Cx43(-/-)-fibs decreased theta significantly less than WT-fibs, their effect on the beating frequency and the beat-to-beat variability seemed largely independent of their ability to establish intercellular coupling. These results suggest that electrically integrated, non-excitable cells modulate the excitability of cardiac pacemaker preparations by two distinct mechanisms, one dependent and the other independent of the heterocellular coupling established. Whereas heterocellular coupling enables the fibroblast to depolarize the cardiomyocytes or to act as a current sink, the mere physical separation of the cardiomyocytes by fibroblasts induces bradycardia through a reduction in frequency entrainment.