Heartbeat States in Astrophysics & Cardiology

• Heartbeat States are distinct oscillatory regimes observed as quasi-periodic flare cycles in astrophysics and as discrete waveform patterns in cardiac monitoring.
• In astrophysics, heartbeat states reveal disk–corona coupling through metrics like 20–200 s recurrence times and 20–30% RMS amplitude variations, illuminating radiation pressure instabilities.
• In cardiac physiology, heartbeat states are classified using machine learning and statistical analyses of features such as equality rates and time irreversibility, enabling robust arrhythmia detection.

Heartbeat states refer to recurring, distinct temporal or spectral regimes in oscillatory time series that originate either from astrophysical accretion flows or from biological cardiac dynamics. In modern research, the term has specific meaning in both high-energy astrophysics—the quasi-periodic flare cycles seen in black hole X-ray binaries—and in physiological cardiac monitoring, where it denotes discrete classes or regimes of heartbeat waveform, rhythm, or interval sequence. This article systematically reviews the concept and manifestations of heartbeat states across astrophysical and biomedical domains, the methodologies used for their analysis and classification, and their mechanistic interpretations.

1. Heartbeat States in Black Hole X-ray Binaries

The archetypal "heartbeat" state in X-ray binaries, particularly observed in GRS 1915+105 and 4U 1630–47, consists of quasi-periodic, large-amplitude X-ray oscillations characterized by slow-rise, fast-decay flare cycles. Individual cycles exhibit a recurrence time spanning $\sim$20–200 s (GRS 1915+105), typically displaying sharply peaked periodicities with RMS amplitudes 20–30% (Weng et al., 2018, Patel et al., 23 Oct 2025, Fan et al., 10 Dec 2024). The light curves show a robust morphology: each cycle begins near a minimum count rate $C_{\min}$, rises gradually to a narrow maximum $C_{\max}$, and collapses nearly exponentially.

Statistical analyses of hundreds of RXTE and NICER observations reveal multimodal distributions for recurrence times (e.g., bimodal peaks at $b_1$ ≈ 46 s, $b_2$ ≈ 73 s for GRS 1915+105) (Weng et al., 2018), and $T_{\rm hb} ≈ 40$ s for 4U 1630–47 (Patel et al., 23 Oct 2025). Spectral-timing properties, such as hard lags at the heartbeat frequency (τ ≈ +1 s at $f\sim0.05$ Hz), high coherence ($\gamma^2 \gtrsim 0.8$), and a phase-resolved correlation between disk parameters and flux, have been robustly documented (Fan et al., 10 Dec 2024). These signatures are interpreted as direct evidence of radiation pressure–driven limit cycles in inner accretion disks.

The power density spectrum transitions, especially the disappearance of type-C quasi-periodic oscillations (QPOs) during the onset of heartbeat states, support a physical model where the accretion disk moves from a precessing hot inner flow to a thermally and viscously unstable, radiation-dominated regime (Patel et al., 23 Oct 2025). The heartbeat state thus acts as a probe of disk–corona coupling, accretion–ejection processes, and provides empirical constraints on viscous timescales, inner radius stability, and coronal geometry (Rawat et al., 2022, Janiuk et al., 2014).

2. Biomarker and Signal-Theoretic Heartbeat States in Human Cardiac Data

Differentiated heartbeat states are central to cardiac physiology and diagnostics. These are defined either in terms of discrete classes in the cardiac cycle (e.g., S1, systole, S2, diastole), or states of interval dynamics (healthy young, elderly, congestive heart failure), or as waveform and rhythm classes (normal, supraventricular, ventricular, fusion, paced/other) (Akan et al., 6 Jan 2024, Herry et al., 2015, Wen-po et al., 2019).

Permutation-based order pattern analysis identifies equality-involved "heartbeat states" within RR-interval time series, quantifying the prevalence and distribution of equal intervals (equality rate, $eR$) and time irreversibility (asymmetry index $Y_s$). Distinct states are empirically separated:

• CHF: $eR = 20.31\% \pm 7.34\%$
• Elderly: $eR = 6.48\% \pm 2.19\%$
• Healthy young: $eR = 2.61\% \pm 1.92\%$

High $eR$ values indicate pathologic or aging-related reduction in nonlinear complexity, while $Y_s$ stratifies the directionality and nonlinearity of heartbeat dynamics; neglecting equality leads to wholly erroneous ranking of nonlinearity across states (Wen-po et al., 2019).

Phase-space and statistical learning approaches—such as the extraction of instantaneous phase by synchrosqueezing transform, RR features, and subsequent SVM/transformer-based classification—segment heartbeats into discrete waveform/rhythm states, achieving high detection sensitivities (>98% for normal beats, lower for less prevalent arrhythmias) (Herry et al., 2015, Akan et al., 6 Jan 2024).

3. Physiological, Astrophysical, and Algorithmic State Definitions

In cardiac auscultation, states are defined by physiological events within each heartbeat: S1 (mitral/tricuspid closure), systole, S2 (aortic/pulmonary closure), and diastole. Markov-switching autoregressive models cast the heart sound signal as a stochastic process switching between four regimes, each with distinct autocorrelation structure (Noman et al., 2018). Accurate state segmentation directly informs downstream multilabel classification of pathological vs. normal heartbeats; the best MSAR+Viterbi scheme yields per-beat segmentation accuracy ≈84.2% (Noman et al., 2018).

In X-ray binaries, astrophysical heartbeat states map to regime-switching of the inner accretion flow. Theoretical modeling (Shakura-Sunyaev $\alpha$-disk, with radiation–pressure instability) produces a limit cycle: the disk alternates between cold (gas-pressure dominated) and hot (radiation-pressure dominated) branches, with the period set by the viscous timescale at the instability radius (Fan et al., 10 Dec 2024, Patel et al., 23 Oct 2025). The amplitude and existence of these flares are further regulated by wind outflows: strong disk winds quench the heartbeat cycle (effectively eliminating this state for sufficiently high wind mass-loss rates) (Janiuk et al., 2014).

4. Methodologies for Heartbeat State Detection and Analysis

Heartbeat state detection leverages both statistical signal modeling and machine learning. In astrophysics, time-resolved spectroscopy with phase-folded light curves, power spectral analysis, and empirical timing–spectral correlations (such as $T_{\rm rec} \propto L_X^{1.10}$, $C_{\min} \propto T_{\rm rec}^{0.49}$) are standard (Weng et al., 2018, Rawat et al., 2022). Disc parameters (apparent inner radius $R_{\rm in}$, mass accretion rate, coronal fraction) are extracted by spectral fits employing models such as tbabs*highecut*(diskbb+powerlaw), diskpn+comptt, or tbfeo × thcomp⊗diskbb (Fan et al., 10 Dec 2024, Rawat et al., 2022).

In cardiac physiology, state-of-the-art transformer and support vector machine classifiers operate on temporally windowed ECG traces, either as fixed-length embedded sequences or as handcrafted feature sets (phase, interval, amplitude). Segmentation of heart sounds applies Markov-switching state-space models, which substantially improve boundary detection when explicitly incorporating dwell-time distributions (Noman et al., 2018). Neural state machines, using spiking AdEx neuron populations, instantiate discrete HR bands as one-hot latent codes, enabling low-power monotonic change detection in neuromorphic hardware (Carpegna et al., 4 Sep 2024).

Empirically validated datasets (e.g., MIT-BIH Arrhythmia, HEART-Watch) supply ground-truth states under diverse physical and physiological conditions, enabling robust cross-modal benchmarking (Kaetheeswaran et al., 3 Dec 2025).

5. Physical Mechanisms and State Transitions

In accreting black hole systems, heartbeat states are underpinned by radiation pressure instability. When the inner disk reaches near-Eddington accretion rates, local instabilities drive cyclic evacuation and refilling of the inner flow, manifesting as quasi-periodic X-ray variability. The limit-cycle period naturally corresponds to the viscous time at several gravitational radii, while state transitions (e.g., from type-C QPO to heartbeat) correspond to changes in accretion rate and disk truncation (Patel et al., 23 Oct 2025, Weng et al., 2018). Disk winds act as a control parameter: increased wind mass-loss directly suppresses or quenches the heartbeat state (Janiuk et al., 2014).

In human cardiac time series, transitions among RR-interval states or sound regimes reflect physiological or pathophysiological processes—autonomic modulation, conduction system transitions, or emergent disorder in heart failure/arrhythmia. Equality rate and time irreversibility serve as real-time markers for such transitions, while neuromorphic circuits provide durable state tracking during slow HR ramps in ambulatory settings (Wen-po et al., 2019, Carpegna et al., 4 Sep 2024).

6. Practical Applications and Implications

Heartbeat states in astrophysics yield insight into the coupling of disk, corona, jet, and wind across accretion-powered systems, providing constraints on energy transport, jet launching, and accretion–ejection feedback (Weng et al., 2018, Fan et al., 10 Dec 2024, Janiuk et al., 2014). Observationally, the detection (or absence) of the heartbeat state constrains both local and global accretion parameters, including the role of disk winds in system stabilization.

In clinical and real-world health monitoring, robust classification and segmentation of heartbeat states underpin arrhythmia detection, risk stratification, and stress/agitation monitoring in vulnerable populations. Equality rate and irreversibility emerge as computationally simple, discriminatory biomarkers for cardiac health grading (Wen-po et al., 2019). Integrated multimodal devices now simultaneously record and synchronize accelerometry, PPG, and ECG, enabling algorithmic state recognition across physical states with sampling synchronization and signal quality controls (Kaetheeswaran et al., 3 Dec 2025). Neuromorphic NSM architectures enable ultra-low-power, always-on detection of monotonic HR state transitions, directly supporting wearable and ambient health applications (Carpegna et al., 4 Sep 2024).

7. Empirical Laws, Challenges, and Future Prospects

In black hole X-ray binaries, empirical relationships such as $T_{\rm rec} \propto L_X^{1.10}$, $T_{\rm rec} \propto L_{\rm PL}^{1.66}$, and $C_{\min} \propto T_{\rm rec}^{0.49}$ summarize robust timing–spectral scaling in the heartbeat state (Weng et al., 2018). Variability in apparent $R_{\rm in}$ and color-correction factor $f_{\rm col}$ are interpreted as evidence for variable coronal geometry even when the true disk edge remains at the ISCO (Rawat et al., 2022). In the presence of strong winds ($A \gg 1$), the heartbeat state is fully quenched, supporting the mechanistic role of wind-driven disk stabilization (Janiuk et al., 2014).

Cardiological state analyses face the challenge of robustly extracting and classifying heartbeat states in the presence of noise, movement, and signal artifact. Equality-aware time irreversibility and phase-dispersion indices demonstrate superior discriminatory power over classic methods, especially for short-duration or ambulatory data (Wen-po et al., 2019, Herry et al., 2015). Neuromorphic implementation of state tracking offers promising scalability for persistent, energy-constrained health monitoring (Carpegna et al., 4 Sep 2024).

A comprehensive understanding of heartbeat states—across both astrophysical and physiological systems—hinges upon precise statistical analysis, matched modeling, and physically motivated mechanistic insight. These states not only illuminate the underlying physics and biology of complex oscillatory systems but also advance practical diagnostics and monitoring across domains.