The fractal-like complexity of heart rate variability beyond neurotransmitters and autonomic receptors: signaling intrinsic to sinoatrial node pacemaker cells

Emergence of heartbeat frailty in advanced age I: perspectives from life-long EKG recordings in adult mice

The combined influences of sinoatrial nodal (SAN) pacemaker cell automaticity and its response to autonomic input determine the heart's beating interval variability and mean beating rate. To determine the intrinsic SAN and autonomic signatures buried within EKG RR interval time series change in advanced age, we measured RR interval variability before and during double autonomic blockade at 3-month intervals from 6 months of age until the end of life in long-lived (those that achieved the total cohort median life span of 24 months and beyond) C57/BL6 mice. Prior to 21 months of age, time-dependent changes in intrinsic RR interval variability and mean RR interval were relatively minor. Between 21 and 30 months of age, however, marked changes emerged in intrinsic SAN RR interval variability signatures, pointing to a reduction in the kinetics of pacemaker clock mechanisms, leading to reduced synchronization of molecular functions within and among SAN cells. This loss of high-frequency signal processing within intrinsic SAN signatures resulted in a marked increase in the mean intrinsic RR interval. The impact of autonomic signatures on RR interval variability were net sympathetic and partially compensated for the reduced kinetics of the intrinsic SAN RR interval variability signatures, and partially, but not completely, shifted the EKG RR time series intervals to a more youthful pattern. Cross-sectional analyses of other subsets of C57/BL6 ages indicated that at or beyond the median life span of our longitudinal cohort, noncardiac, constitutional, whole-body frailty was increased, energetic efficiency was reduced, and the respiratory exchange ratio increased. We interpret the progressive reduction in kinetics in intrinsic SAN RR interval variability signatures in this context of whole-body frailty beyond 21 months of age to be a manifestation of "heartbeat frailty."

Evaluation of non-linear heart rate variability using multi-scale multi-fractal detrended fluctuation analysis in mice: Roles of the autonomic nervous system and sinoatrial node

Nonlinear analyses of heart rate variability (HRV) can be used to quantify the unpredictability, fractal properties and complexity of heart rate. Fractality and its analysis provides valuable information about cardiovascular health. Multi-Scale Multi-Fractal Detrended Fluctuation Analysis (MSMFDFA) is a complexity-based algorithm that can be used to quantify the multi-fractal dynamics of the HRV time series through investigating characteristic exponents at different time scales. This method is applicable to short time series and it is robust to noise and nonstationarity. We have used MSMFDFA, which enables assessment of HRV in the frequency ranges encompassing the very-low frequency and ultra-low frequency bands, to jointly assess multi-scale and multi-fractal dynamics of HRV signals obtained from telemetric ECG recordings in wildtype mice at baseline and after autonomic nervous system (ANS) blockade, from electrograms recorded from isolated atrial preparations and from spontaneous action potential recordings in isolated sinoatrial node myocytes. Data demonstrate that the fractal profile of the intrinsic heart rate is significantly different from the baseline heart rate in vivo, and it is also altered after ANS blockade at specific scales and fractal order domains. For beating rate in isolated atrial preparations and intrinsic heart rate in vivo, the average fractal structure of the HRV increased and multi-fractality strength decreased. These data demonstrate that fractal properties of the HRV depend on both ANS activity and intrinsic sinoatrial node function and that assessing multi-fractality at different time scales is an effective approach for HRV assessment.

Ca2+ and Membrane Potential Transitions During Action Potentials Are Self-Similar to Each Other and to Variability of AP Firing Intervals Across the Broad Physiologic Range of AP Intervals During Autonomic Receptor Stimulation

Ca2+ and V m transitions occurring throughout action potential (AP) cycles in sinoatrial nodal (SAN) cells are cues that (1) not only regulate activation states of molecules operating within criticality (Ca2+ domain) and limit-cycle (V m domain) mechanisms of a coupled-clock system that underlies SAN cell automaticity, (2) but are also regulated by the activation states of the clock molecules they regulate. In other terms, these cues are both causes and effects of clock molecular activation (recursion). Recently, we demonstrated that Ca2+ and V m transitions during AP cycles in single SAN cells isolated from mice, guinea pigs, rabbits, and humans are self-similar (obey a power law) and are also self-similar to trans-species AP firing intervals (APFIs) of these cells in vitro, to heart rate in vivo, and to body mass. Neurotransmitter stimulation of β-adrenergic receptor or cholinergic receptor-initiated signaling in SAN cells modulates their AP firing rate and rhythm by impacting on the degree to which SAN clocks couple to each other, creating the broad physiologic range of SAN cell mean APFIs and firing interval variabilities. Here we show that Ca2+ and V m domain kinetic transitions (time to AP ignition in diastole and 90% AP recovery) occurring within given AP, the mean APFIs, and APFI variabilities within the time series of APs in 230 individual SAN cells are self-similar (obey power laws). In other terms, these long-range correlations inform on self-similar distributions of order among SAN cells across the entire broad physiologic range of SAN APFIs, regardless of whether autonomic receptors of these cells are stimulated or not and regardless of the type (adrenergic or cholinergic) of autonomic receptor stimulation. These long-range correlations among distributions of Ca2+ and V m kinetic functions that regulate SAN cell clock coupling during each AP cycle in different individual, isolated SAN cells not in contact with each other. Our numerical model simulations further extended our perspectives to the molecular scale and demonstrated that many ion currents also behave self-similar across autonomic states. Thus, to ensure rapid flexibility of AP firing rates in response to different types and degrees of autonomic input, nature "did not reinvent molecular wheels within the coupled-clock system of pacemaker cells," but differentially engaged or scaled the kinetics of gears that regulate the rate and rhythm at which the "wheels spin" in a given autonomic input context.

Impacts of frailty on heart rate variability in aging mice: Roles of the autonomic nervous system and sinoatrial node

BACKGROUND

Heart rate variability (HRV) is determined by intrinsic sinoatrial node (SAN) activity and the autonomic nervous system (ANS). HRV is reduced in aging; however, aging is heterogeneous. Frailty, which can be measured using a frailty index (FI), can quantify health status in aging separately from chronological age.

OBJECTIVE

The purpose of this study was to investigate the impacts of age and frailty on HRV in mice.

METHODS

Frailty was measured in aging mice between 10 and 130 weeks of age. HRV was assessed using time domain, frequency domain, and Poincaré plot analyses in anesthetized mice at baseline and after ANS blockade, as well as in isolated atrial preparations.

RESULTS

HRV was reduced in aged mice (90-130 weeks and 50-80 weeks old) compared to younger mice (10-30 weeks old); however, there was substantial variability within age groups. In contrast, HRV was strongly correlated with FI score regardless of chronological age. ANS blockade resulted in reductions in heart rate that were largest in 90- to 130-week-old mice and were correlated with FI score. HRV after ANS blockade or in isolated atrial preparations was increased in aged mice but again showed high variability among age groups. HRV was correlated with FI score after ANS blockade and in isolated atrial preparations.

CONCLUSION

HRV is reduced in aging mice in association with a shift in sympathovagal balance and increased intrinsic SAN beating variability; however, HRV is highly variable within age groups. HRV was strongly correlated with frailty, which was able to detect differences in HRV separately from chronological age.

Natriuretic peptide receptor B maintains heart rate and sinoatrial node function via cyclic GMP-mediated signaling

AIMS

Heart rate (HR) is a critical indicator of cardiac performance that is determined by sinoatrial node (SAN) function and regulation. Natriuretic peptides, including C-type NP (CNP) have been shown to modulate ion channel function in the SAN when applied exogenously. CNP is the only NP that acts as a ligand for natriuretic peptide receptor-B (NPR-B). Despite these properties, the ability of CNP and NPR-B to regulate HR and intrinsic SAN automaticity in vivo, and the mechanisms by which it does so, are incompletely understood. Thus, the objective of this study was to determine the role of NPR-B signaling in regulating HR and SAN function.

METHODS AND RESULTS

We have used NPR-B deficient mice (NPR-B+/-) to study HR regulation and SAN function using telemetry in conscious mice, intracardiac electrophysiology in anesthetized mice, high resolution optical mapping in isolated SAN preparations, patch-clamping in isolated SAN myocytes, and molecular biology in isolated SAN tissue. These studies demonstrate that NPR-B+/- mice exhibit slow HR, increased corrected SAN recovery time, and slowed SAN conduction. Spontaneous AP firing frequency in isolated SAN myocytes was impaired in NPR-B+/- mice due to reductions in the hyperpolarization activated current (If) and L-type Ca2+ current (ICa,L). If and ICa,L were reduced due to lower cGMP levels and increased hydrolysis of cAMP by phosphodiesterase 3 (PDE3) in the SAN. Inhibiting PDE3 or restoring cGMP signaling via application of 8-Br-cGMP abolished the reductions in cAMP, AP firing, If, and ICa,L, and normalized SAN conduction, in the SAN in NPR-B+/- mice. NPR-B+/- mice did not exhibit changes in SAN fibrosis and showed no evidence of cardiac hypertrophy or changes in ventricular function.

CONCLUSIONS

NPR-B plays an essential physiological role in maintaining normal HR and SAN function by modulating ion channel function in SAN myocytes via a cGMP/PDE3/cAMP signaling mechanism.

Fetal Cardiovascular Decompensation During Labor Predicted From the Individual Heart Rate Tracing: A Machine Learning Approach in Near-Term Fetal Sheep Model

Background: When exposed to repetitive umbilical cord occlusions (UCO) with worsening acidemia, fetuses eventually develop cardiovascular decompensation manifesting as pathological hypotensive arterial blood pressure (ABP) responses to fetal heart rate (FHR) decelerations. Failure to maintain cardiac output during labor is a key event leading up to brain injury. We reported that the timing of the event when a fetus begins to exhibit this cardiovascular phenotype is highly individual and was impossible to predict. Objective: We hypothesized that this phenotype would be reflected in the individual behavior of heart rate variability (HRV) as measured by root mean square of successive differences of R-R intervals (RMSSD), a measure of vagal modulation of HRV, which is known to increase with worsening acidemia. This is clinically relevant because HRV can be computed in real-time intrapartum. Consequently, we aimed to predict the individual timing of the event when a hypotensive ABP pattern would emerge in a fetus from a series of continuous RMSSD data. Study Design: Fourteen near-term fetal sheep were chronically instrumented with vascular catheters to record fetal arterial blood pressure, umbilical cord occluder to mimic uterine contractions occurring during human labor and ECG electrodes to compute the ECG-derived HRV measure RMSSD. All animals were studied over a ~6 h period. After a 1-2 h baseline control period, the animals underwent mild, moderate, and severe series of repetitive UCO. We applied the recently developed machine learning algorithm to detect physiologically meaningful changes in RMSSD dynamics with worsening acidemia and hypotensive responses to FHR decelerations. To mimic clinical scenarios using an ultrasound-based 4 Hz FHR sampling rate, we recomputed RMSSD from FHR sampled at 4 Hz and compared the performance of our algorithm under both conditions (1,000 Hz vs. 4 Hz). Results: The RMSSD values were highly non-stationary, with four different regimes and three regime changes, corresponding to a baseline period followed by mild, moderate, and severe UCO series. Each time series was characterized by seemingly randomly occurring (in terms of timing of the individual onset) increase in RMSSD values at different time points during the moderate UCO series and at the start of the severe UCO series. This event manifested as an increasing trend in RMSSD values, which counter-intuitively emerged as a period of relative stationarity for the time series. Our algorithm identified these change points as the individual time points of cardiovascular decompensation with 92% sensitivity, 86% accuracy and 92% precision which corresponded to 14 ± 21 min before the visual identification. In the 4 Hz RMSSD time series, the algorithm detected the event with 3 times earlier detection times than at 1,000 Hz, i.e., producing false positive alarms with 50% sensitivity, 21% accuracy, and 27% precision. We identified the overestimation of baseline FHR variability by RMSSD at a 4 Hz sampling rate to be the cause of this phenomenon. Conclusions: The key finding is demonstration of FHR monitoring to detect fetal cardiovascular decompensation during labor. This validates the hypothesis that our HRV-based algorithm identifies individual time points of ABP responses to UCO with worsening acidemia by extracting change point information from the physiologically related fluctuations in the RMSSD signal. This performance depends on the acquisition accuracy of beat to beat fluctuations achieved in trans-abdominal ECG devices and fails at the sampling rate used clinically in ultrasound-based systems. This has implications for implementing such an approach in clinical practice.

SDNN24 Estimation from Semi-Continuous HR Measures

The standard deviation of the interval between QRS complexes recorded over 24 h (SDNN24) is an important metric of cardiovascular health. Wrist-worn fitness wearable devices record heart beats 24/7 having a complete overview of users' heart status. Due to motion artefacts affecting QRS complexes recording, and the different nature of the heart rate sensor used on wearable devices compared to ECG, traditionally used to compute SDNN24, the estimation of this important Heart Rate Variability (HRV) metric has never been performed from wearable data. We propose an innovative approach to estimate SDNN24 only exploiting the Heart Rate (HR) that is normally available on wearable fitness trackers and less affected by data noise. The standard deviation of inter-beats intervals (SDNN24) and the standard deviation of the Average inter-beats intervals (ANN) derived from the HR (obtained in a time window with defined duration, i.e., 1, 5, 10, 30 and 60 min), i.e., ANN=60HR (SDANNHR24), were calculated over 24 h. Power spectrum analysis using the Lomb-Scargle Peridogram was performed to assess frequency domain HRV parameters (Ultra Low Frequency, Very Low Frequency, Low Frequency, and High Frequency). Due to the fact that SDNN24 reflects the total power of the power of the HRV spectrum, the values estimated from HR measures (SDANNHR24) underestimate the real values because of the high frequencies that are missing. Subjects with low and high cardiovascular risk show different power spectra. In particular, differences are detected in Ultra Low and Very Low frequencies, while similar results are shown in Low and High frequencies. For this reason, we found that HR measures contain enough information to discriminate cardiovascular risk. Semi-continuous measures of HR throughout 24 h, as measured by most wrist-worn fitness wearable devices, should be sufficient to estimate SDNN24 and cardiovascular risk.

Impact of Chronic Fetal Hypoxia and Inflammation on Cardiac Pacemaker Cell Development

Chronic fetal hypoxia and infection are examples of adverse conditions during complicated pregnancy, which impact cardiac myogenesis and increase the lifetime risk of heart disease. However, the effects that chronic hypoxic or inflammatory environments exert on cardiac pacemaker cells are poorly understood. Here, we review the current evidence and novel avenues of bench-to-bed research in this field of perinatal cardiogenesis as well as its translational significance for early detection of future risk for cardiovascular disease.

Hypothetical Control of Heart Rate Variability

In the last three decades, the analysis of heart rate variability by nonlinear methods demonstrated the complexity of cardiovascular regulation. Additionally to the observations of periodic heart rate regulation by the autonomic nervous system, the long-term statistics of the heart rate has been determined to reminisce a tempered Lévy process. A number of heuristic arguments have previously been made to support a tempering conjecture, using exponentially truncated waiting times for the time intervals between heart beats. Herein we use the fractional probability calculus to frame our arguments and to parameterize the control process that tempers the Lévy process through a collective-induced potential. We also determine that the hypothesis of a self-induced nonlinear potential control resulting in such a tempered Lévy process is consistent with the hypothesis of disease being the loss of physiologic complexity made over 25 years ago.

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.

PhysioZoo: A Novel Open Access Platform for Heart Rate Variability Analysis of Mammalian Electrocardiographic Data

Background: The time variation between consecutive heartbeats is commonly referred to as heart rate variability (HRV). Loss of complexity in HRV has been documented in several cardiovascular diseases and has been associated with an increase in morbidity and mortality. However, the mechanisms that control HRV are not well understood. Animal experiments are the key to investigating this question. However, to date, there are no standard open source tools for HRV analysis of mammalian electrocardiogram (ECG) data and no centralized public databases for researchers to access. Methods: We created an open source software solution specifically designed for HRV analysis from ECG data of multiple mammals, including humans. We also created a set of public databases of mammalian ECG signals (dog, rabbit and mouse) with manually corrected R-peaks (>170,000 annotations) and signal quality annotations. The platform (software and databases) is called PhysioZoo. Results: PhysioZoo makes it possible to load ECG data and perform very accurate R-peak detection (F 1 > 98%). It also allows the user to manually correct the R-peak locations and annotate low signal quality of the underlying ECG. PhysioZoo implements state of the art HRV measures adapted for different mammals (dogs, rabbits, and mice) and allows easy export of all computed measures together with standard data representation figures. PhysioZoo provides databases and standard ranges for all HRV measures computed on healthy, conscious humans, dogs, rabbits, and mice at rest. Study of these measures across different mammals can provide new insights into the complexity of heart rate dynamics across species. Conclusion: PhysioZoo enables the standardization and reproducibility of HRV analysis in mammalian models through its open source code, freely available software, and open access databases. PhysioZoo will support and enable new investigations in mammalian HRV research. The source code and software are available on www.physiozoo.com.

Assessing mood symptoms through heartbeat dynamics: An HRV study on cardiosurgical patients

BACKGROUND

Heart Rate Variability (HRV) is reduced both in depression and in coronary heart disease (CHD) suggesting common pathophysiological mechanisms for the two disorders. Within CHD, cardiac surgery patients (CSP) with postoperative depression are at greater risk of adverse cardiac events. Therefore, CSP would especially benefit from depression early diagnosis. Here we tested whether HRV-multi-feature analysis discriminates CSP with or without depression and provides an effective estimation of symptoms severity.

METHODS

Thirty-one patients admitted to cardiac rehabilitation after first-time cardiac surgery were recruited. Depressive symptoms were assessed with the Center for Epidemiologic Studies Depression Scale (CES-D). HRV features in time, frequency, and nonlinear domains were extracted from 5-min-ECG recordings at rest and used as predictors of "least absolute shrinkage and selection" (LASSO) operator regression model to estimate patients' CES-D score and to predict depressive state.

RESULTS

The model significantly predicted the CES-D score in all subjects (the total explained variance of CES-D score was 89.93%). Also it discriminated depressed and non-depressed CSP with 86.75% accuracy. Seven of the ten most informative metrics belonged to non-linear-domain.

LIMITATIONS

A higher number of patients evaluated also with a structured clinical interview would help to generalize the present findings.

DISCUSSION

To our knowledge this is the first study using a multi-feature approach to evaluate depression in CSP. The high informative power of HRV-nonlinear metrics suggests their possible pathophysiological role both in depression and in CHD. The high-accuracy of the algorithm at single-subject level opens to its translational use as screening tool in clinical practice.

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.

Systolic blood pressure but not electrocardiogram QRS duration is associated with heart rate variability (HRV): a cross-sectional study in rural Australian non-diabetics

BACKGROUND

A positive correlation between ECG derived QRS duration and heart rate variability (HRV) parameters had previously been reported in young healthy adults. We note this study used a narrow QRS duration range, and did not adjust for systolic blood pressure. Our aims are to investigate associations between systolic blood pressure (SBP), QRS duration and HRV in a rural aging population.

METHODS

A retrospective cross sectional population was obtained from the CSU Diabetes Screening Research Initiative data base where 200 participants had no diabetes or pre-diabetes. SBP data were matched with ECG derived QRS duration and HRV parameters. HRV parameters were calculated from R-R intervals. Resting 12-lead electrocardiograms were obtained from each subject using a Welch Allyn PC-Based ECG system.

RESULTS

Pearson correlation analysis revealed no statistically significant associations between HRV parameters and QRS duration. No significant mean differences in HRV parameter subgroups across defined QRS cut-offs were found. SBP > 146 mmHg was associated with increasing QRS durations, however this association disappeared once models were adjusted for age and gender. SBP was also significantly associated with a number of HRV parameters using Pearson correlation analysis, including high frequency (HF) (p < 0.05), HFln (p < 0.02), RMSDD (p < 0.02) and non-linear parameters; ApEN (p < 0.001) were negatively correlated with increasing SBP while the low frequency to high frequency ratio (LF/HF) increased with increasing SBP (p < 0.03).

CONCLUSIONS

Our results do not support associations between ECG derived R-R derived HRV parameters and QRS duration in aging populations. We suggest that ventricular conduction as determined by QRS duration is independent of variations in SA-node heart rate variability.

The end effector of circadian heart rate variation: the sinoatrial node pacemaker cell

Cardiovascular function is regulated by the rhythmicity of circadian, infradian and ultradian clocks. Specific time scales of different cell types drive their functions: circadian gene regulation at hours scale, activation-inactivation cycles of ion channels at millisecond scales, the heart's beating rate at hundreds of millisecond scales, and low frequency autonomic signaling at cycles of tens of seconds. Heart rate and rhythm are modulated by a hierarchical clock system: autonomic signaling from the brain releases neurotransmitters from the vagus and sympathetic nerves to the heart’s pacemaker cells and activate receptors on the cell. These receptors activating ultradian clock functions embedded within pacemaker cells include sarcoplasmic reticulum rhythmic spontaneous Ca²⁺ cycling, rhythmic ion channel current activation and inactivation, and rhythmic oscillatory mitochondria ATP production. Here we summarize the evidence that intrinsic pacemaker cell mechanisms are the end effector of the hierarchical brain-heart circadian clock system. [BMB Reports 2015; 48(12): 677-684]

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Deterioration of autonomic neuronal receptor signaling and mechanisms intrinsic to heart pacemaker cells contribute to age-associated alterations in heart rate variability in vivo

We aimed to determine how age‐associated changes in mechanisms extrinsic and intrinsic to pacemaker cells relate to basal beating interval variability (BIV) reduction in vivo. Beating intervals (BIs) were measured in aged (23–25 months) and adult (3–4 months) C57BL/6 male mice (i) via ECG in vivo during light anesthesia in the basal state, or in the presence of 0.5 mg mL⁻¹ atropine + 1 mg mL⁻¹ propranolol (in vivo intrinsic conditions), and (ii) via a surface electrogram, in intact isolated pacemaker tissue. BIV was quantified in both time and frequency domains using linear and nonlinear indices. Although the average basal BI did not significantly change with age under intrinsic conditions in vivo and in the intact isolated pacemaker tissue, the average BI was prolonged in advanced age. In vivo basal BIV indices were found to be reduced with age, but this reduction diminished in the intrinsic state. However, in pacemaker tissue BIV indices increased in advanced age vs. adults. In the isolated pacemaker tissue, the sensitivity of the average BI and BIV in response to autonomic receptor stimulation or activation of mechanisms intrinsic to pacemaker cells by broad‐spectrum phosphodiesterase inhibition declined in advanced age. Thus, changes in mechanisms intrinsic to pacemaker cells increase the average BIs and BIV in the mice of advanced age. Autonomic neural input to pacemaker tissue compensates for failure of molecular intrinsic mechanisms to preserve average BI. But this compensation reduces the BIV due to both the imbalance of autonomic neural input to the pacemaker cells and altered pacemaker cell responses to neural input.

Potential effects of intrinsic heart pacemaker cell mechanisms on dysrhythmic cardiac action potential firing

The heart's regular electrical activity is initiated by specialized cardiac pacemaker cells residing in the sinoatrial node. The rate and rhythm of spontaneous action potential firing of sinoatrial node cells are regulated by stochastic mechanisms that determine the level of coupling of chemical to electrical clocks within cardiac pacemaker cells. This coupled-clock system is modulated by autonomic signaling from the brain via neurotransmitter release from the vagus and sympathetic nerves. Abnormalities in brain-heart clock connections or in any molecular clock activity within pacemaker cells lead to abnormalities in the beating rate and rhythm of the pacemaker tissue that initiates the cardiac impulse. Dysfunction of pacemaker tissue can lead to tachy-brady heart rate alternation or exit block that leads to long atrial pauses and increases susceptibility to other cardiac arrhythmia. Here we review evidence for the idea that disturbances in the intrinsic components of pacemaker cells may be implemented in arrhythmia induction in the heart.

Stochasticity intrinsic to coupled-clock mechanisms underlies beat-to-beat variability of spontaneous action potential firing in sinoatrial node pacemaker cells

Recent evidence indicates that the spontaneous action potential (AP) of isolated sinoatrial node cells (SANCs) is regulated by a system of stochastic mechanisms embodied within two clocks: ryanodine receptors of the "Ca(2+) clock" within the sarcoplasmic reticulum, spontaneously activate during diastole and discharge local Ca(2+) releases (LCRs) beneath the cell surface membrane; clock crosstalk occurs as LCRs activate an inward Na(+)/Ca(2+) exchanger current (INCX), which together with If and decay of K(+) channels prompts the "M clock," the ensemble of sarcolemmal-electrogenic molecules, to generate APs. Prolongation of the average LCR period accompanies prolongation of the average AP beating interval (BI). Moreover, the prolongation of the average AP BI accompanies increased AP BI variability. We hypothesized that both the average AP BI and AP BI variability are dependent upon stochasticity of clock mechanisms reported by the variability of LCR period. We perturbed the coupled-clock system by directly inhibiting the M clock by ivabradine (IVA) or the Ca(2+) clock by cyclopiazonic acid (CPA). When either clock is perturbed by IVA (3, 10 and 30 μM), which has no direct effect on Ca(2+) cycling, or CPA (0.5 and 5 μM), which has no direct effect on the M clock ion channels, the clock system failed to achieve the basal AP BI and both AP BI and AP BI variability increased. The changes in average LCR period and its variability in response to perturbations of the coupled-clock system were correlated with changes in AP beating interval and AP beating interval variability. We conclude that the stochasticity within the coupled-clock system affects and is affected by the AP BI firing rate and rhythm via modulation of the effectiveness of clock coupling.

Synchronization of sinoatrial node pacemaker cell clocks and its autonomic modulation impart complexity to heart beating intervals

BACKGROUND

A reduction of complexity of heart beating interval variability that is associated with an increased morbidity and mortality in cardiovascular disease states is thought to derive from the balance of sympathetic and parasympathetic neural impulses to the heart. However, rhythmic clocklike behavior intrinsic to pacemaker cells in the sinoatrial node (SAN) drives their beating, even in the absence of autonomic neural input.

OBJECTIVE

To test how this rhythmic clocklike behavior intrinsic to pacemaker cells interacts with autonomic impulses to the heart beating interval variability in vivo.

METHODS

We analyzed beating interval variability in time and frequency domains and by fractal and entropy analyses: (1) in vivo, when the brain input to the SAN is intact; (2) during autonomic denervation in vivo; (3) in isolated SAN tissue (ie, in which the autonomic neural input is completely absent); (4) in single pacemaker cells isolated from the SAN; and (5) after autonomic receptor stimulation of these cells.

RESULTS

Spontaneous beating intervals of pacemaker cells residing in the isolated SAN tissue exhibit fractal-like behavior and have lower approximate entropy compared with those in the intact heart. Isolation of pacemaker cells from SAN tissue, however, leads to a loss in the beating interval order and fractal-like behavior. β-Adrenergic receptor stimulation of isolated pacemaker cells increases intrinsic clock synchronization, decreases their action potential period, and increases system complexity.

CONCLUSIONS

Both the average beating interval in vivo and beating interval complexity are conferred by the combined effects of clock periodicity intrinsic to pacemaker cells and their response to autonomic neural input.

Age-associated abnormalities of intrinsic automaticity of sinoatrial nodal cells are linked to deficient cAMP-PKA-Ca(2+) signaling

A reduced sinoatrial node (SAN) functional reserve underlies the age-associated decline in heart rate acceleration in response to stress. SAN cell function involves an oscillatory coupled-clock system: the sarcoplasmic reticulum (SR), a Ca(2+) clock, and the electrogenic-sarcolemmal membrane clock. Ca(2+)-activated-calmodulin-adenylyl cyclase/CaMKII-cAMP/PKA-Ca(2+) signaling regulated by phosphodiesterase activity drives SAN cells automaticity. SR-generated local calcium releases (LCRs) activate Na(+)/Ca(2+) exchanger in the membrane clock, which initiates the action potential (AP). We hypothesize that SAN cell dysfunctions accumulate with age. We found a reduction in single SAN cell AP firing in aged (20-24 mo) vs. adult (3-4 mo) mice. The sensitivity of the SAN beating rate responses to both muscarinic and adrenergic receptor activation becomes decreased in advanced age. Additionally, age-associated coincident dysfunctions occur stemming from compromised clock functions, including a reduced SR Ca(2+) load and a reduced size, number, and duration of spontaneous LCRs. Moreover, the sensitivity of SAN beating rate to a cAMP stress induced by phosphodiesterase inhibitor is reduced, as are the LCR size, amplitude, and number in SAN cells from aged vs. adult mice. These functional changes coincide with decreased expression of crucial SR Ca(2+)-cycling proteins, including SR Ca(2+)-ATPase pump, ryanodine receptors, and Na(+)/Ca(2+) exchanger. Thus a deterioration in intrinsic Ca(2+) clock kinetics in aged SAN cells, due to deficits in intrinsic SR Ca(2+) cycling and its response to a cAMP-dependent pathway activation, is involved in the age-associated reduction in intrinsic resting AP firing rate, and in the reduction in the acceleration of heart rate during exercise.

Impaired signaling intrinsic to sinoatrial node pacemaker cells affects heart rate variability during cardiac disease

The normal heart beat intervals are neither strictly stationary nor completely random, and continuously shift from one period to another. Decoding the ECG identifies this "hidden" information that imparts inherent complexity to the heart-beating interval time series. Loss of this complexity in cardiovascular disease is manifested as a reduction in heart rate variability (HRV) and this reduction correlates with an increase in both morbidity and mortality. Because HRV measurements are noninvasive and easy to perform, they have emerged as an important tool in cardiology. However, the identities of specific mechanisms that underline the changes in HRV that occur in cardiovascular diseases remain largely unknown. Changes in HRV have mainly been interpreted on a neural basis, ie due to changes in autonomic impulses to the heart: sympathetic activity decreases both the average heart beat interval and HRV, and parasympathetic activity increases both. It has now become clear, however, that the heart rate and HRV are also determined by intrinsic properties of the pacemaker cells that comprise the sinoatrial node, and the responses of these properties to autonomic receptor stimulation. Here we review how changes in the properties of coupled-clock mechanisms intrinsic to pacemaker cells that comprise the sinoatrial node and their impaired response to autonomic receptor stimulation are implicated in the changes of HRV observed in heart diseases.