A Neurodynamic Manifold of Autonomic Function: Integrating Magnitude and Dynamical Regimes in Heart Rate Variability

A Neurodynamic Manifold of Autonomic Function: Integrating Magnitude and Dynamical Regimes in Heart Rate Variability | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 3 January 2026 V1 Latest version Share on A Neurodynamic Manifold of Autonomic Function: Integrating Magnitude and Dynamical Regimes in Heart Rate Variability Author : Caio Amaral Gabriel 0000-0003-0870-3686 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176743454.46178243/v1 389 views 91 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The vagal paradox—where elevated vagal activity indexes both safety and shutdown—persists because conventional autonomic metrics quantify fluctuation magnitude while remaining insensitive to the structural organization of underlying dynamics. To address this conceptual gap, I introduce the Neurodynamic Manifold, a topological framework that recontextualizes fluctuation magnitude. By jointly integrating fractal scaling (DFA α 1 ), entropy (Sample Entropy), and Poincaré geometry (SD2/SD1) within a unified dynamical space, the framework maps autonomic activity onto distinct regulatory regimes. It theoretically delineates a quasicritical zone of adaptive complexity, flanked by subcritical and supercritical attractors associated with rigidity and instability. Importantly, it reveals that identical magnitudes may arise from fundamentally opposing dynamical organizations, resolving the vagal paradox and clarifying the interpretative limits of amplitude-based metrics such as RMSSD. By synthesizing clinical physiology, statistical physics, complexity science, and dynamical systems theory, the Neurodynamic Manifold reconceptualizes autonomic health and regulation as the metastable capacity to sustain and navigate the quasicritical regime, providing a unified foundation for translational research and psychophysiological assessment across health, dysfunction, and performance. Title: A Neurodynamic Manifold of Autonomic Function: Integrating Magnitude and Dynamical Regimes in Heart Rate Variability Author: Caio Amaral Gabriel, Independent Scholar, Brazil, [email protected] Running Head: A Neurodynamic Manifold of Autonomic Function Abstract: The vagal paradox—where elevated vagal activity indexes both safety and shutdown—persists because conventional autonomic metrics quantify fluctuation magnitude while remaining insensitive to the structural organization of underlying dynamics. To address this conceptual gap, I introduce the Neurodynamic Manifold, a topological framework that recontextualizes fluctuation magnitude. By jointly integrating fractal scaling (DFA α₁), entropy (Sample Entropy), and Poincaré geometry (SD2/SD1) within a unified dynamical space, the framework maps autonomic activity onto distinct regulatory regimes. It theoretically delineates a quasicritical zone of adaptive complexity, flanked by subcritical and supercritical attractors associated with rigidity and instability. Importantly, it reveals that identical magnitudes may arise from fundamentally opposing dynamical organizations, resolving the vagal paradox and clarifying the interpretative limits of amplitude-based metrics such as RMSSD. By synthesizing clinical physiology, statistical physics, complexity science, and dynamical systems theory, the Neurodynamic Manifold reconceptualizes autonomic health and regulation as the metastable capacity to sustain and navigate the quasicritical regime, providing a unified foundation for translational research and psychophysiological assessment across health, dysfunction, and performance. Keywords: Autonomic nervous system, autonomic regulation, heart rate variability, neurodynamic manifold, nonlinear dynamics, vagal paradox 1. THE VAGAL PARADOX AND THE LIMITS OF MAGNITUDE-BASED METRICS For decades, autonomic research has noted a striking phenomenon: vagal activity indexes two fundamentally opposing physiological states. The vagus nerve supports social engagement and metabolic recovery, yet it can also mediate bradycardia and cardiorespiratory collapse (Porges, 1995). This duality, termed the vagal paradox (Porges, 2023), presents a central challenge: high vagal activity may indicate safety or pathological inhibition, and misinterpreting one for the other carries significant clinical risk. Efforts to resolve this paradox have often focused on anatomical distinctions between ventral and dorsal vagal branches (Porges, 2023; Grossman, 2023). While these distinctions provide the structural substrate, anatomy alone cannot determine when a specific vagal output reflects adaptive regulation or maladaptive collapse. A reliable functional biomarker remains elusive because the challenge arises not from the paradox itself, but from the structural insensitivity of conventional metrics. Widely used heart rate variability (HRV) metrics continue to prioritize fluctuation magnitude, implicitly equating higher variability with physiological benefit. Linear measures like RMSSD cannot differentiate healthy complexity from dysfunctional rigidity, as both can appear as high magnitude (Billman, 2013; Hayano & Yuda, 2019). Even geometric refinements such as the SD1 descriptor remain mathematically tied to amplitude (Brennan et al., 2001). By collapsing a multidimensional system into a single scalar, these approaches obscure the qualitative distinction between safety and shutdown. This ambiguity highlights a conceptual problem: if vagal activity can be adaptive or maladaptive, quantifying only “how much” misses “what kind” of physiological organization is present. Resolving the paradox requires a framework that captures the topological structure of fluctuations, not merely their size. Here, I introduce the Neurodynamic Manifold. Rather than replacing traditional metrics, it complements them, recontextualizing magnitude by integrating it with the temporal organization of vagal dynamics. This approach offers a path toward a functional physiology that directly addresses the vagal paradox while preserving the clinical insights that first revealed it. As a theoretical review, this article is organized around conceptual, methodological, and translational sections rather than a conventional Methods–Results structure, with the aim of clarifying the dynamical principles that underlie autonomic regulation. 2. CONCEPTUAL METHODS: HEALTH AS A QUASICRITICAL REGIME The limitations of magnitude-based metrics become evident when health is reconceived not as a static setpoint, but as the capacity to sustain a quasicritical regime—an extended dynamical region along the boundary between order and chaos, rather than a finely tuned critical point (Williams-García et al., 2014; Beggs, 2022; Fosque et al, 2022; 2021; Hengen & Shew, 2025). In heterogeneous biological networks, this region corresponds to a Griffiths phase, in which rare-region effects broaden and stabilize critical-like dynamics across a range of parameters (Muñoz, 2018). This regime is inherently metastable, balancing functional segregation and integration to enable fluid adaptation (Tognoli & Kelso, 2014). Within this zone, biological systems exhibit heightened sensitivity, efficient signal propagation, and long-range correlations (Beggs, 2022), while avoiding instability through active allostatic regulation (McEwen, 1998). Rather than maintaining a fixed setpoint, allostasis dynamically shifts control parameters in response to internal and external demands, stabilizing the system within an extended quasicritical region (Shew et al., 2015; Rusch et al., 2025). In this regime, physiological variability is not noise, but a functional resource that supports recursive adaptation, multiscale integration, and resilience. Quasicritical dynamics exhibit a distinct signature: fractal, 1/f temporal structure (Goldberger et al, 2002). Healthy cardiac (Goldberger et al, 2002) and neural signals (Müller et al., 2025) show multiscale organization, reflecting extended critical regimes where cross-scale coordination peaks. Deviations toward the subcritical phase produce excessive integration and rigid patterns, whereas shifts toward the supercritical phase produce disorganized stochastic behavior. Functionally, these deviations correspond to decomplexification, reflecting reduced integrative capacity rather than instability per se (Pincus & Goldberger, 1994). This multiscale fractal architecture emerges from recursive neurovisceral integration (Smith et al., 2017; He, 2014; Buzsáki & Mizuseki, 2014). The central autonomic network (CAN) orchestrates this integration, coupling cardiac rhythms with cortical activity (Benarroch, 1993; Beissner et al., 2013). Ascending cardiac signals modulate cortical excitability (Sargent et al., 2024), while descending vagal outputs fine-tune emotional regulation through oscillatory feedback (Mather & Thayer, 2018). Interventions like vagus nerve stimulation demonstrate that peripheral signals can reorganize central network connectivity, confirming the bidirectional nature of this system (Liu et al., 2016). Thus, the vagal paradox reflects a transition between dynamical regimes. Healthy function corresponds to quasicriticality, maintained by intact feedback loops. Whether vagal activity indicates adaptation or dysfunction depends not on magnitude, but on its dynamical signature: the system’s capacity to sustain an open, flexible regime versus collapsing into a restricted, low-capacity attractor. 3. CONCEPTUAL MAPPING OF AUTONOMIC REGULATION This framework builds upon the foundational Doctrine of Autonomic Space (Berntson et al., 1991), which established that autonomic states require a multidimensional representation. Extending this principle from static levels to dynamic organization, the Neurodynamic Manifold maps the temporal and geometric structure of autonomic fluctuations, defining physiological state by its organization rather than by magnitude alone. Autonomic regulation is thus reframed as a trajectory within a structured dynamical landscape, rather than a position along a linear spectrum. 3.1. The Dynamical Functional Triad of Autonomic Regulation The Neurodynamic Manifold is defined by a minimal set of complementary dimensions, each capturing a distinct organizational property of autonomic dynamics. Rather than indexing variance alone, these dimensions characterize how physiological fluctuations are structured across time, information, and geometry. Together, they form a Dynamical Functional Triad that operationalizes quasicritical regulation. The triad consists of three metrics: 1. Detrended Fluctuation Analysis alpha 1 (DFA α₁), indexing fractal temporal scaling (Peng et al., 1995); 2. Sample Entropy (SampEn), measuring informational irregularity (Richman & Moorman, 2000); 3. and the Poincaré ratio (SD2/SD1), describing the geometric correlation structure of heart rate fluctuations (Brennan et al, 2001). Temporal structure (DFA α₁) serves as the biophysical anchor of the manifold. Fractal scaling reflects scale-invariant organization, a hallmark of quasicritical neural and physiological dynamics (He, 2011; Grosu et al., 2022). Such correlations index cross-timescale integration, enabling coordination between fast reactivity and slow regulatory processes. The breakdown of fractal structure marks a collapse of this integration under strain, signaling loss of adaptive capacity rather than mere reduction in variability (Linkenkaer-Hansen et al., 2001; Churchill et al., 2016). Informational irregularity (SampEn) captures the integrity of neurovisceral feedback by reflecting the density and richness of information embedded in physiological signals, extending beyond the limits of linear correlations. Recent evidence suggests that brain complexity, as quantified by SampEn, reflects the allocation of neural resources required to incorporate sensory nuances into internal models, thereby indexing uncertainty about the environment (Beni et al., 2025). Notably, SampEn shows a significantly stronger association with the entropy of posterior distributions than traditional measures of surprise, indicating that fluctuations in complexity mirror the brain’s effort to reduce cognitive ambiguity through information integration (Beni et al., 2025). Within the autonomic domain, this informational signature reliably predicts large-scale functional connectivity in the central autonomic network (CAN), indexing the system’s capacity for recursive regulation and providing a computational marker of habituation processes essential for adaptive health (Valenza et al., 2017; Riganello et al., 2018). Geometric correlation (SD2/SD1) quantifies longitudinal anisotropy in autonomic control. This ratio captures the balance between rapid beat-to-beat reactivity (SD1) and slower integrative modulation (SD2) (Balocchi et al., 2006). Unlike conventional spectral metrics, SD2/SD1 is structurally robust to nonstationarity and trends inherent in physiological time series. It characterizes a trait-like dimension of regulation, emphasizing sustained adaptability rather than transient responsiveness (Borghesi et al., 2024). The clinical relevance of this geometric balance is underscored by machine-learning models of critical illness. In intensive care cohorts, an SD2/SD1 threshold near 1.59 emerges as a strong predictor of survival (Bodenes et al., 2022). This empirically derived value closely approximates the golden ratio (φ ≈ 1.618), a proportion independently associated with optimal multiscale coordination. Deviations away from this region—toward excessive anisotropy (SD2/SD1 ≫ φ) or toward isotropic collapse (SD2/SD1 → 1)—signal loss of geometric coordination and heightened vulnerability to subcritical rigidity or supercritical stochasticity, respectively. Building on these convergent findings, I propose the Golden Ratio Hypothesis of Autonomic Coordination. Importantly, φ is not proposed as a fixed optimum or universal constant of autonomic regulation, but as an empirically recurrent attractor emerging from constraints on multiscale coordination across biological systems. This hypothesis posits that SD2/SD1 converges toward φ because this proportion optimizes coordination across nested temporal scales. Here, φ is not invoked as an aesthetic ideal but as a functional solution. Mathematically, φ corresponds to a maximally irrational ratio, which minimizes phase locking and reduces the likelihood of destructive interference between coupled oscillatory processes (Klimesch, 2018; Pletzer et al., 2010). Evidence for this principle appears in resting-state EEG, where canonical frequency bands are organized as a geometric series with a ratio of approximately 1.618 (Pletzer et al., 2010). In neural systems, such spacing supports uncoupled yet readily recruitable dynamics, maintaining a flexible resting state poised for selective engagement (Roopun, 2008). This convergence suggests that, within the autonomic domain, proximity to φ may similarly stabilize regulation within the quasicritical regime—the “virtuous middle” ( in medio stat virtus )—where information processing capacity is maximized without tipping into rigidity or chaos (Borghesi et al., 2024; Klimesch, 2018). The triad is selected not only for conceptual coherence but for functional orthogonality. DFA α₁ captures scaling independent of amplitude, SampEn quantifies informational structure beyond linear variance, and SD2/SD1 reflects geometric relations between temporal scales. Together, they define a minimally redundant coordinate system that exposes architectural features of autonomic regulation inaccessible to variance-based measures such as RMSSD. This framework distinguishes genuinely adaptive modulation from dysfunctional rigidity, in which variability may remain high in magnitude while the underlying control dynamics lose flexibility. No physiological metric is artifact-proof, but the orthogonality of the triad provides a form of internal validation. Noise can perturb any single metric, yet it rarely produces a coherent triadic configuration that mimics a genuine dynamical regime. Discordance among dimensions flags artifact or unstable transitional dynamics; concordance indicates a reproducible organizational signature. For reliable application, standard preprocessing—including ectopic beat correction and appropriate band-pass filtering (0.04–0.4 Hz)—remains essential. The Neurodynamic Manifold thus characterizes dynamic organization, complementing rather than replacing careful signal inspection and clinical judgment. Consequently, these metrics are not independent indicators but interlocking components of a unified structure. Only as an integrated triad do they form a coherent proxy for quasicritical regulation (Gabriel, 2025), revealing neurodynamic states that amplitude-based metrics inevitably conflate. 3.2. Magnitude as Resource: A Functional Taxonomy Before mapping autonomic states within the Neurodynamic Manifold, traditional HRV metrics must be situated within a dynamical framework. This section reframes linear measures as functional descriptors of vagal resources, rather than indicators of autonomic health per se. These metrics do not define the organizational regime; instead, they index surface-level attributes of vagal output—such as mode and volume—without describing the generative architecture that produces them. Within the manifold, magnitude-based metrics are recontextualized as measures of resource availability: 1. RMSSD—Vagal Capacitance (“How much?”): RMSSD reflects the amplitude of efferent vagal fluctuations, indexing the size of the available parasympathetic resource pool. While informative about the magnitude of vagal influence, it remains structurally insensitive to the temporal organization through which these resources are deployed (Shaffer & Ginsberg, 2017; Laborde et al., 2017). 2. pNN50 — Vagal Intermittency (“How abruptly?”): pNN50 functions as a threshold-based detector of abrupt, short-latency vagal reflex shifts, particularly those mediated by rapid brainstem and baroreflex circuits. It captures the system’s capacity for sudden behavioral reorientation and threat disengagement—an essential feature of the vagal brake—without resolving the broader dynamical regime in which these responses occur (Ewing et al., 1984; Mietus, 2002). 3. HF Power — Oscillatory Mode (“In what rhythm?”): HF power indexes the respiratory-locked oscillatory mode of vagal output. Importantly, high HF power in the absence of corresponding fractal complexity indicates preserved oscillation but impaired multiscale integration. Conversely, its attenuation—even when overall vagal amplitude remains elevated—signals a decoupling of respiratory–vagal phase synchronization. These interpretations hold when respiratory influences are appropriately controlled or modeled (Berntson et al., 1997; Grossman & Taylor, 2006). When normalized (e.g., Z-scored) to incorporate individual baselines, linear metrics often diverge from the regime classifications identified by the dynamical triad. This divergence reflects a categorical distinction: magnitude-based measures quantify signal intensity relative to a reference state, whereas the triad identifies the dynamical regime that generates the signal. Longitudinal tracking remains essential—not for normalization alone, but for detecting regime drift and identifying early-warning indicators of impending critical transitions. Magnitude may fluctuate substantially without any change in the underlying regime. The dynamical triad resolves neurodynamic distinctions that amplitude-based metrics inherently collapse, distinguishing adaptive modulation from superficially variable but functionally rigid states. 3.3. The Landscape of Safety and Shutdown Plotting the triad’s coordinates yields a three-dimensional manifold in which magnitude provides elevation, while topology defines the governing landscape. Three principal dynamical regimes emerge, each defined by a characteristic geometric and temporal signature (Figure 1). 1. The Quasicritical Zone: This regime is characterized by fractal temporal organization (DFA α₁ ≈ 1.0), elevated informational irregularity (high SampEn), and geometric coordination near the golden ratio (SD2/SD1 ≈ φ). The resulting “comet-shaped” attractor reflects maximal integrative capacity, supporting information-rich, non-interfering coordination across temporal scales. 2. The Subcritical Bank: As dynamics shift toward excessive persistence (DFA α₁ ≈ 1.5), informational degrees of freedom collapse (low SampEn), and longitudinal modulation dominates, with SD2/SD1 diverging upward from φ. This “needle-shaped” geometry captures the vagal paradox: high vagal magnitude (e.g., elevated RMSSD) masking a decomplexified, rigid, low-capacity regulatory state. 3. The Supercritical Bank: Here, dynamics dissolve toward randomness (DFA α₁ ≈ 0.5), irregularity increases in a stochastic rather than informational manner (inflated but non-structured SampEn), and geometric structure collapses toward isotropy (SD2/SD1 → 1). This “circular” configuration reflects loss of longitudinal adaptability and breakdown of coordinated regulation. Empirically, sustained deviations of DFA α₁ away from unity signal exit from the quasicritical regime. Notably, sustained divergence of SD2/SD1 away from the ~1.59 threshold—either toward excessive anisotropy or toward isotropy—marks the loss of geometric coordination that normally buffers the quasicritical regime, identifying zones of sharply elevated clinical risk and systemic decomplexification. These α-values represent idealized attractors situated relative to the system’s Widom line—the locus of maximal susceptibility where small perturbations produce disproportionate systemic effects (Williams-García et al., 2014). In practice, physiological states occupy probabilistic basins within this manifold rather than fixed coordinates. The quasicritical zone corresponds to a broad, shallow basin near the Widom line, permitting flexible exploration, whereas subcritical and supercritical regimes occupy deeper, more restrictive basins farther from criticality. This formulation replaces rigid thresholds with a continuous, probability-weighted mapping of dynamical organization. Figure 1 | The Neurodynamic Manifold: A Topological Representation of Autonomic Regimes. The surface illustrates a conceptual manifold in which autonomic regulation is organized by dynamical structure rather than magnitude alone. The horizontal axes represent fractal temporal scaling (DFA α₁) and informational irregularity (Sample Entropy), while surface curvature reflects Fisher Information, interpreted here as a measure of dynamical sensitivity—indexing susceptibility to small perturbations rather than information content per se. Geometric organization along the manifold is constrained by longitudinal anisotropy (SD2/SD1), with coordination near the golden ratio (φ ≈ 1.618) stabilizing the quasicritical regime. Data points (spheres) represent vagal magnitude (scalar HRV amplitude), depicted as elevation orthogonal to the governing topology. Importantly, identical magnitudes populate distinct regions of the manifold, illustrating the vagal paradox: equivalent signal strength can emerge from fundamentally different dynamical regimes. The Quasicritical Zone (Adaptive Complexity) occupies the region near DFA α₁ ≈ 1.0 and SD2/SD1 ≈ φ, forming a broad, shallow basin of high susceptibility and flexible regulation. In contrast, the Subcritical Regime (Systemic Redundancy) lies in a region of excessive temporal persistence (DFA α₁ ≈ 1.5), increased geometric rigidity, and reduced dynamical sensitivity, reflecting pathological shutdown despite preserved magnitude. The surface is a conceptual illustration intended to convey topological relations and regime structure rather than an empirically fitted manifold. These regimes extend beyond cardiac physiology. Cardiac rhythms modulate cortical excitability (Sargent et al., 2024), and a heart constrained to a highly persistent, Brownian-like attractor narrows the brain’s dynamical repertoire, reinforcing defensive modes of processing. Topological collapse is therefore not merely a marker of shutdown; it may actively participate in the maintenance of reduced-capacity states by constraining ascending precision signals—that is, the reliability weighting of interoceptive inputs within hierarchical predictive circuits. 3.4. Use of AI-Generated Content (AIGC) and Tools The author declares the use of AI-assisted tools during manuscript preparation. Gemini (Google, December 2025) was used exclusively to assist in the translation of the original manuscript from Portuguese into academic English and for subsequent stylistic and terminological refinement. The AI tool was not used to generate scientific content, develop original concepts, select or interpret empirical findings, simulate or analyze data, or produce figures or tables. All conceptual frameworks, theoretical arguments, and interpretations were developed by the author. All AI-generated suggestions were critically reviewed, edited, and verified for accuracy, coherence, and conceptual integrity. The author assumes full responsibility for the content of the manuscript, including the accuracy of citations and the absence of bias. 4. THEORETICAL RESULTS: IDENTICAL MAGNITUDE, OPPOSITE DYNAMICAL REGIMES To demonstrate its discriminatory power, the Neurodynamic Manifold is applied to two high-magnitude states that are phenomenologically similar in amplitude yet fundamentally opposed in their dynamical organization (Table 1). 4.1. Case A: Quasicritical Zone (A regime commonly—but not exclusively—associated with metabolic recovery and efficient resource allocation) • DFA α₁ ≈ 1.0: Fractal (1/f) dynamics indicate scale-invariant temporal organization, balancing rapid responsiveness with long-range stability and enabling cross-timescale coordination. • Sample Entropy (High): Elevated irregularity reflects high informational richness rather than stochastic noise, indexing intact neurovisceral feedback and flexible inferential updating. • Poincaré Ratio (SD2/SD1 ≈ 1.618): A coherent “comet-shaped” geometry reflects optimal coordination between beat-to-beat flexibility (SD1) and slower integrative modulation (SD2), preserving longitudinal adaptability across scales. • Magnitude profile: High RMSSD (vagal capacitance) and elevated pNN50 (intermittency) indicate substantial vagal outflow coupled with precise micro-adjustments. Coherent HF power confirms intact respiratory–vagal coupling. The system remains open, multiscale, and adaptively poised. Here, magnitude aligns with organization—but does not define it. Only the dynamical triad reveals the underlying regime. Crucially, both regimes can present with comparably elevated vagal magnitude, rendering amplitude-based interpretation insufficient. 4.2. Case B: Subcritical Low-Complexity Attractor (A regime consistent with clinical presentations of shutdown) • DFA α₁ ≈ 1.5: Persistent, Brownian-like dynamics reflect excessive temporal correlation and history dependence, signaling collapse of multiscale integration into a rigid, low-capacity state. • Sample Entropy (Low): Informational degrees of freedom contract, rendering the signal increasingly predictable despite preserved amplitude. • Poincaré Ratio (SD2/SD1 ≫ 1.618). Longitudinal modulation dominates, producing exaggerated anisotropy. Slow, history-bound dynamics (SD2) overwhelm beat-to-beat flexibility (SD1), reflecting constrained temporal organization rather than adaptive integration. • Magnitude profile. High RMSSD frequently co-occurs with reduced pNN50, indicating preserved vagal capacitance but impaired reflexive intermittency. HF power is often decoupled from fractal organization. The system is trapped in a rigid attractor—high in magnitude yet minimal in adaptability. Linear amplitude metrics inherently collapse these states into a single category. The Neurodynamic Manifold disentangles them, assigning quasicritical complexity and low-complexity rigidity to distinct topological regimes. In doing so, it resolves a longstanding methodological error: mistaking shutdown for safety simply because both express elevated vagal magnitude. Table 1 | Comparative Dynamics of High-Magnitude Vagal States — Comparison of linear and nonlinear metrics across two physiological states characterized by similarly high vagal magnitude (RMSSD). While linear amplitude metrics conflate these states, the Neurodynamic Manifold differentiates them based on temporal scaling (DFA α₁), informational irregularity (SampEn), and geometric coordination (SD2/SD1). DFA α₁ (Scaling) ≈ 1.0 (pink-noise dynamics) Scale-invariant, multiscale coordination ≈ 1.5 (Brownian-like dynamics) Excessive persistence, history-bound rigidity SampEn (Irregularity) High Rich structural variability and intact recursive integration Low Predictable patterns reflecting loss of degrees of freedom SD2/SD1 (Geometric coordination) ≈ φ (≈ 1.618) Balanced longitudinal anisotropy supporting adaptability ≫ φ Excessive dominance of slow modulation, rigid temporal geometry RMSSD (Magnitude) High Reflects available vagal resources High Preserved magnitude despite collapsed organization pNN50 (Intermittency) High Frequent short-latency adjustments Low Reduced reflexive intermittency despite high variance HF Power (RSA) Coherently phase-coupled to respiration Suppressed, decoupled, or irregularly coupled System Functionality Open, multiscalar, metastable Decomplexified, constrained to a low-capacity attractor Manifold Topology Quasicritical Zone Subcritical basin (Systemic Redundancy) Clinical Implication Adaptive regulation / functional health Pathological shutdown / false positive for recovery 5. DISCUSSION: A NEURODYNAMIC ONTOLOGY FOR AUTONOMIC SCIENCE 5.1. Beyond Magnitude: Integrating Levels and Dynamical Regimes Physiological autonomy should not be conceptualized as a static equilibrium of opposing forces, but rather as a metastable trajectory within a nonequilibrium potential and flux landscape (Stikvoort et al., 2025). Within this ontology, variability magnitude becomes an incomplete descriptor unless interpreted in relation to the dynamical regime from which it emerges (Lucente et al., 2025). Conventional HRV metrics quantify how much variability is present—an indispensable but incomplete description of autonomic function (Billman, 2013; Hayano & Yuda, 2019). The Neurodynamic Manifold introduces a second, previously under-specified dimension: regime, the dynamical organization from which magnitude emerges. This distinction resolves long-standing paradoxes. Similar levels of variability can arise from fundamentally different dynamical organizations—adaptive quasicriticality, marked by multiscale coherence and expanded information capacity, or maladaptive decomplexification, characterized by rigidity, dimensional collapse, and reduced responsiveness. The manifold provides an operational framework for discriminating these organizations by jointly indexing fractal scaling (α), multiscale entropy, and geometric anisotropy (SD2/SD1). Magnitude is therefore not abandoned but recontextualized. Physiological states do not lie on a one-dimensional continuum of “vagal tone,” but instead occupy regions within a structured topological landscape defined by dynamical regimes. In this perspective, magnitude reflects resource availability, whereas regime captures how those resources are organized, deployed, and constrained. This dual framing extends Goldstein’s principle of primitive specificity—originally formulated to describe patterned sympathetic efference (Goldstein, 2013)—into a unified dynamic ontology that also subsumes the autonomic space described by Berntson et al., (1991). Rather than treating sympathetic and parasympathetic activity as independent axes or simple combinations, the Neurodynamic Manifold positions autonomic states as topologically distinct configurations within a regime-defined landscape. Hybrid physiological states—such as sympathetic–ventral vagal coactivation during playful mobilization, or ventral–dorsal vagal coupling during safe immobility—are thus not merely mixed outputs, but occupy specific regions of the manifold characterized by their underlying dynamical organization. In this framework, autonomic outputs emerge as task-dependent, multiscale configurations shaped by regime topology, rather than as fixed reflexes or linear balances between branches. Situating the manifold within statistical physics, complexity science and dynamical systems theory clarifies why healthy regulation reliably expresses quasicritical structure—the regime that maximizes adaptability, information throughput, and cross-scale coordination. Departures from quasicriticality map onto two complementary failure modes: subcritical rigidity and supercritical randomness, both largely opaque when assessed solely through magnitude-based approaches. Within this formulation, autonomic health reflects the capacity to inhabit—and fluidly traverse—the quasicritical regime. Adaptive regulation does not correspond to a homeostatic setpoint but to orchestrated metastability: the ability to explore neighboring topological basins while remaining anchored in a high-coherence, high-capacity zone defined by fractal organization, elevated entropy, and geometric stability. Resilience thus emerges from the synthesis of two components: adequate physiological resources (magnitude), which are necessary but not sufficient, structured through an adaptive dynamical regime. This framework unifies neurovisceral integration with dynamical systems theory, transforming autonomic function from a balance of opposing branches into an ongoing process of topologically constrained self-organization. 5.2. Methodological Implications: Disentangling Structure from Magnitude The Neurodynamic Manifold also introduces a methodological refinement that resolves longstanding analytical limitations in autonomic science. First, it reframes HRV from a scalar biomarker into a multifeature dynamical signal, where physiological meaning emerges from organization across features rather than amplitude alone (Billman, 2013; Hayano & Yuda, 2019). By integrating fractal scaling (DFA α₁), multiscale entropy, and geometric anisotropy (SD2/SD1), the manifold recovers the signal’s latent organizational structure, providing a principled alternative to the widespread assumption that “high HRV” uniformly reflects healthy regulation. Second, it reduces the field’s reliance on stationarity assumptions and fixed-window summaries. Autonomic regulation is nonlinear, history-dependent, and prone to regime shifts, yet most analyses are derived from time-averaged segments that obscure organizational transitions (Shaffer & Ginsberg, 2017). The manifold captures dynamical geometry rather than windowed aggregates, enabling the tracking of transitions among quasicritical, subcritical, and supercritical regimes—an approach consistent with emerging time-resolved analyses (Gronwald et al., 2020; Rogers et al., 2021). Third, its core metrics are intrinsically robust to amplitude inflation and common physiological confounders. RMSSD can be artifactually elevated by noise, ectopy, or abrupt modulation; in contrast, DFA, Sample Entropy, and SD2/SD1 quantify structure rather than magnitude. DFA isolates scale-invariant temporal correlations, reducing sensitivity to respiratory frequency and transient bursts of variance. Sample Entropy estimates the conditional probability of pattern recurrence independently of absolute signal scale. Geometric anisotropy captures the asymmetric coordination between short-latency reactivity and longer-timescale integration that characterizes adaptive autonomic control. Crucially, stochastic noise and arrhythmic bursts cannot reproduce the coherent triad of quasicriticality—DFA α₁ ≈ 1, elevated entropy, and SD2/SD1 ≈ 1.618. This structural specificity allows the manifold to distinguish adaptive complexity from pathological rigidity, directly correcting the clinical misinterpretation of shutdown as recovery. Finally, the manifold provides a standardized coordinate system for neurovisceral integration. By mapping cardiac variability into a shared dynamical phase space, it enables direct comparison with neural markers of quasicriticality (Fosque et al., 2022; 2021) and facilitates cross-modal integration with fMRI, EEG, and behavioral measures. This establishes a unified framework for multimodal dynamical biomarkers that transcend organ-specific silos (Sargent et al., 2024; Valenza et al., 2017). 5.3. Neurodynamic Integration: Vagal Physiology as a Peripheral Readout of Brain Organization The Neurodynamic Manifold reframes vagal physiology as a peripheral expression of the brain’s intrinsic dynamical organization. The identified quasicritical regime—marked by fractal structure, elevated entropy, and geometric anisotropy—mirrors the statistical architecture of large-scale neural dynamics, including scale-free fluctuations, metastability, and spontaneous network reconfiguration. Adaptive autonomic regulation thus reflects the same organizing principles that support efficient, flexible neural computation (Hengen & Shew, 2025; Tognoli & Kelso, 2014; Müller et al., 2025). Within this framework, the manifold positions vagal regulation as an accessible physiological index of the brain’s proximity to quasicriticality. Transitions toward subcritical (shutdown) or supercritical (hyperreactive) attractors correspond to well-characterized dynamical signatures of network dysfunction—respectively, excessive temporal persistence and erosion of long-range correlations. These shifts reflect changes in global system organization rather than isolated alterations in peripheral output (Pincus & Goldberger, 1994). Finally, the manifold clarifies the construct of vagal tone. Rather than denoting inhibitory efference alone, vagal tone reflects the degree of coordinated coupling between central autonomic networks and peripheral effectors (Sargent et al., 2024). This coupling can degrade even when vagal magnitude remains high (Valenza et al., 2017), explaining how substantial parasympathetic output may coexist with impaired neural integration—the essence of the vagal paradox, now resolved within a neurodynamic framework. 5.4. Clinical Implications: Reframing Diagnostic Inference The Neurodynamic Manifold clarifies a long-standing diagnostic limitation in autonomic science: magnitude-based HRV metrics often fail to distinguish adaptive vagal engagement from pathological shutdown. By recontextualizing variability within its generative regime, the framework reinterprets states historically labeled as “parasympathetic dominance”—including shutdown and dissociative profiles—not as benign rest states but as low-complexity, subcritical organizations. This reduces the risk that elevated RMSSD is misclassified as recovery when underlying regulatory capacity remains compromised. Clinically, this reframing shifts the therapeutic objective from merely increasing HRV toward restoring the dynamical signature of health: scale-free fractal organization, elevated informational entropy, and coherent geometric structure. By mapping dysfunction onto distinct topological regimes—subcritical rigidity (shutdown), supercritical disorganization (hyperreactive states), and degraded metastability—the manifold supports a precision-oriented approach that targets the governing regime rather than isolated symptoms or amplitudes. Finally, the manifold provides a unifying translational lens across heterogeneous clinical conditions. Disorders such as depression, PTSD, and long COVID—despite distinct etiologies—exhibit convergent signatures of network decomplexification and reduced adaptive capacity (Pincus & Goldberger, 1994). Within this framework, such conditions can be understood as occupying maladaptive regions of a shared neurodynamic landscape, motivating transdiagnostic biomarkers and interventions aimed at restoring neurovisceral quasicriticality rather than normalizing magnitude alone. 5.5. Implications for High-Performance and Adaptation The Neurodynamic Manifold clarifies a persistent inconsistency in athletic HRV monitoring. Although practical limitations of RMSSD for readiness assessment are well recognized—including sensitivity to confounders, breathing patterns, and interindividual baselines (Buchheit, 2014; Bellenger et al., 2016)—a deeper conceptual gap remains: linear magnitude metrics cannot reliably distinguish the high variability associated with adaptive recovery from the equally high variability arising from maladaptive, low-capacity states. The manifold resolves this ambiguity by revealing that identical RMSSD values can emerge from distinct dynamical regimes. One reflects a quasicritical organization marked by fractal flexibility, elevated informational richness, and preserved geometric coordination—conditions that support performance adaptation. The other reflects a subcritical, low-entropy regime in which anisotropy becomes rigid and regulatory degrees of freedom collapse, despite preserved amplitude. This distinction helps explain why HRV often underperforms in predicting fatigue, injury risk, or overreaching, even under well-controlled monitoring protocols. Accordingly, the manifold shifts the operational focus from maximizing “high HRV” toward identifying and maintaining healthy complexity—a regime-defined signature characterized by α₁ ≈ 1, elevated entropy, and coherent geometric organization. By embedding readiness assessment within a topological framework, it enables individualized interpretation of training and recovery states, aligning performance science with a physiology of quasicritical adaptability rather than amplitude optimization alone. 6. FUTURE DIRECTIONS: CHARTING THE UNMAPPED TERRITORY The Neurodynamic Manifold offers a unifying framework, yet several frontiers invite systematic investigation to consolidate its empirical, methodological, and translational foundations. • Methodological Ground Truth: Although the triad’s structure-based metrics are structurally less vulnerable to amplitude inflation and common HRV confounders, their empirical operating boundaries remain incompletely characterized. Future work should benchmark the manifold under controlled perturbations—respiratory modulation, ectopic activity, arrhythmias, and motion artifacts—to quantify sensitivity, specificity, and conditions under which regime inference remains stable. Standardized preprocessing pipelines and cross-laboratory comparisons will be essential for assessing reproducibility relative to traditional HRV metrics. • Temporal Resolution and Multiscale Dynamics: Current implementations rely predominantly on short-term HRV segments, capturing fast-timescale regulation while overlooking slower oscillatory and circadian processes. Integrating ambulatory recordings, sleep dynamics, and joint cardiorespiratory measures will enable detection of multiscale transitions inaccessible to brief recordings. • Mapping Individual Topologies: The manifold’s geometry is likely idiographic rather than population-averaged. Progress will require characterizing the range of healthy topological configurations and examining how age, sex, training state, and context shape an individual’s neurovisceral landscape. Moving from group norms to personalized dynamical maps represents a necessary conceptual shift. An associated question is whether geometric signatures such as convergence toward SD2/SD1 ≈ φ track successful transitions into quasicritical organization, or merely index one of several possible recovery trajectories. • Neural Validation of the Topology: Strengthening the proposed brain–heart correspondence will require multimodal datasets—ideally simultaneous EEG–fMRI–HRV—to relate manifold topology to neural markers of metastability, integration–segregation balance, and quasicriticality. Establishing these links is essential for grounding the framework in measurable neural dynamics. • Predictive Power: The manifold’s translational value ultimately depends on whether topological signatures provide incremental predictive insight into clinical trajectories, performance fluctuations, or responsiveness to interventions. Prospective longitudinal studies are required to test this claim. • Mechanisms of Transition: The processes governing movement across dynamical regimes—particularly recovery from rigid or collapsed states—remain poorly understood. Determining whether targeted interventions can restore quasicritical dynamics, and whether regime mobility itself constitutes a marker of resilience, represents a key next step. In sum, the Neurodynamic Manifold is not presented as a finished instrument but as a testable hypothesis and a new coordinate system for autonomic science. Its value will be determined not by theoretical elegance alone, but by its capacity to generate predictive, mechanistic, and clinically meaningful insights across the neurovisceral continuum. Realizing this potential will require integrative, multimodal, and longitudinal research capable of charting its geometry across individuals, timescales, and the shifting landscapes of health, dysfunction, and performance. 7. CONCLUSION: TOWARD A PHYSICS OF LIVING SYSTEMS The Neurodynamic Manifold reframes autonomic physiology not as a continuum of vagal magnitude, but as a landscape of dynamic regimes shaped by fractal complexity, entropy, and multiscale correlation. In doing so, it provides a principled resolution to the decades-old vagal paradox, offering an operational framework that distinguishes adaptive quasicriticality from maladaptive shutdown. This resolution links the clinical intuition underlying the paradox with the formal language of statistical physics and complexity science, transforming a long-standing ambiguity into a measurable dynamical transition. This shift restructures inquiry across health and performance. By mapping the brain–heart axis within a functional topology, the manifold reveals that resilience is not the preservation of a fixed setpoint but the metastable capacity to traverse a space of possible states. It reframes the goals of intervention: not simply increasing vagal magnitude, but identifying and restoring the quasicritical regime in which flexibility, robustness, and informational richness co-emerge. Ultimately, the Neurodynamic Manifold establishes conceptual foundations for an integrated science of neurovisceral health. By bridging physiology, computation, and dynamical systems theory, it enables more precise assessment and principled modulation of neurovisceral function. Its contribution lies not only in resolving a central paradox, but in proposing a reconception of health itself as a property of dynamical organization—a physics of living systems in which vitality is indexed not by amplitude alone, but by the coherence and adaptability of dynamical structure. 8. DATA AND CODE AVAILABILITY STATEMENT No new human or animal data were collected for this article. The illustrative implementation of the Neurodynamic Manifold, including the generation of the geometric state-space representation, was developed in Python and executed using Google Colab. The code supporting the figures and computational procedures described in this article is publicly available in a GitHub repository https://github.com/caio-outliers/neurodynamic-manifold, ensuring transparency and reproducibility of the proposed framework. REFERENCES Balocchi, R., Cantini, F., Varanini, M., Raimondi, G., Legramante, J. M., & Macerata, A. (2006). Revisiting the potential of time-domain indexes in short-term HRV analysis. Biomedizinische Technik/Biomedical Engineering , 51 (4), 190–193. https://doi.org/10.1515/bmt.2006.034 Beggs, J. M. (2022). The cortex and the critical point. In The MIT Press eBooks . https://doi.org/10.7551/mitpress/13588.001.0001 Beissner, F., Meissner, K., Bar, K., & Napadow, V. (2013). The Autonomic Brain: an Activation Likelihood Estimation Meta-Analysis for central processing of autonomic function. Journal of Neuroscience , 33 (25), 10503–10511. https://doi.org/10.1523/jneurosci.1103-13.2013 Bellenger, C. R., Fuller, J. T., Thomson, R. L., Davison, K., Robertson, E. Y., & Buckley, J. D. (2016). Monitoring Athletic Training Status Through Autonomic Heart Rate Regulation: A Systematic Review and Meta-Analysis. Sports Medicine , 46 (10), 1461–1486. https://doi.org/10.1007/s40279-016-0484-2 Benarroch, E. E. (1993). The central autonomic network: functional organization, dysfunction, and perspective. Mayo Clinic Proceedings , 68 (10), 988–1001. https://doi.org/10.1016/s0025-6196(12)62272-1 Beni, M. H. H., Hosseinpour, K., Seyednejad, M. R., & Aghajan, H. (2025). Brain complexity represents uncertainty in sequence learning and corroborates habituation deficit in Parkinson disease patients. Scientific Reports , 15 (1), 22320. https://doi.org/10.1038/s41598-025-00826-5 Berntson, G. G., Bigger, J. T., Eckberg, D. L., Grossman, P., Kaufmann, P. G., Malik, M., Nagaraja, H. N., Porges, S. W., Saul, J. P., Stone, P. H., & Van Der Molen, M. W. (1997). Heart rate variability: Origins, methods, and interpretive caveats. Psychophysiology , 34 (6), 623–648. https://doi.org/10.1111/j.1469-8986.1997.tb02140.x Berntson, G. G., Cacioppo, J. T., & Quigley, K. S. (1991). Autonomic determinism: The modes of autonomic control, the doctrine of autonomic space, and the laws of autonomic constraint. Psychological Review , 98 (4), 459–487. https://doi.org/10.1037/0033-295x.98.4.459 Billman, G. E. (2013). The LF/HF ratio does not accurately measure cardiac sympatho-vagal balance. Frontiers in Physiology , 4 , 26. https://doi.org/10.3389/fphys.2013.00026 Bodenes, L., N’Guyen, Q., Mao, R. L., Ferrière, N., Pateau, V., Lellouche, F., & L’Her, E. (2022). Early heart rate variability evaluation enables to predict ICU patients’ outcome. Scientific Reports , 12 (1), 2498. https://doi.org/10.1038/s41598-022-06301-9 Borghesi, F., Simoncini, G., Chirico, A., & Cipresso, P. (2024). In medio stat virtus: Moderate Cognitive flexibility as a key to Affective Flexibility Responses in Long-Term HRV. Sensors , 24 (24), 8047. https://doi.org/10.3390/s24248047 Brennan, M., Palaniswami, M., & Kamen, P. (2001). Do existing measures of Poincare plot geometry reflect nonlinear features of heart rate variability? IEEE Transactions on Biomedical Engineering , 48 (11), 1342–1347. https://doi.org/10.1109/10.959330 Buchheit, M. (2014). Monitoring training status with HR measures: do all roads lead to Rome? Frontiers in Physiology , 5 , 73. https://doi.org/10.3389/fphys.2014.00073 Buzsáki, G., & Mizuseki, K. (2014). The log-dynamic brain: how skewed distributions affect network operations. Nature Reviews. Neuroscience , 15 (4), 264–278. https://doi.org/10.1038/nrn3687 Churchill, N. W., Spring, R., Grady, C., Cimprich, B., Askren, M. K., Reuter-Lorenz, P. A., Jung, M. S., Peltier, S., Strother, S. C., & Berman, M. G. (2016). The suppression of scale-free fMRI brain dynamics across three different sources of effort: aging, task novelty and task difficulty. Scientific Reports , 6 (1), 30895. https://doi.org/10.1038/srep30895 Ewing, D. J., Neilson, J. M., & Travis, P. (1984). New method for assessing cardiac parasympathetic activity using 24 hour electrocardiograms. Heart , 52 (4), 396–402. https://doi.org/10.1136/hrt.52.4.396 Fosque, L. J., Alipour, A., Zare, M., Williams-García, R. V., Beggs, J. M., & Ortiz, G. (2022). Quasicriticality explains variability of human neural dynamics across life span. Frontiers in Computational Neuroscience , 16 , 1037550. https://doi.org/10.3389/fncom.2022.1037550 Fosque, L. J., Williams-García, R. V., Beggs, J. M., & Ortiz, G. (2021). Evidence for quasicritical brain dynamics. Physical Review Letters , 126 (9), 098101. https://doi.org/10.1103/physrevlett.126.098101 Gabriel, C. A. (2025). Martial arts induce quasicritical brain states: a unified, multiscale, and mechanistic theory of brain health optimization. Frontiers in Psychology , 16 , 1661566. https://doi.org/10.3389/fpsyg.2025.1661566 Goldberger, A. L., Amaral, L. a. N., Hausdorff, J. M., Ivanov, P. C., Peng, C., & Stanley, H. E. (2002). Fractal dynamics in physiology: Alterations with disease and aging. Proceedings of the National Academy of Sciences , 99 (suppl_1), 2466–2472. https://doi.org/10.1073/pnas.012579499 Goldstein, D. S. (2013). Concepts of scientific integrative medicine applied to the physiology and pathophysiology of catecholamine systems. Comprehensive Physiology , 3 (4), 1569–1610. https://doi.org/10.1002/j.2040-4603.2013.tb00532.x Gronwald, T., Rogers, B., & Hoos, O. (2020). Fractal correlation Properties of heart rate variability: a new biomarker for intensity distribution in endurance exercise and training Prescription? Frontiers in Physiology , 11 , 550572. https://doi.org/10.3389/fphys.2020.550572 Grossman, P. (2023). Fundamental challenges and likely refutations of the five basic premises of the polyvagal theory. Biological Psychology , 180 , 108589. https://doi.org/10.1016/j.biopsycho.2023.108589 Grossman, P., & Taylor, E. W. (2006). Toward understanding respiratory sinus arrhythmia: Relations to cardiac vagal tone, evolution and biobehavioral functions. Biological Psychology , 74 (2), 263–285. https://doi.org/10.1016/j.biopsycho.2005.11.014 Grosu, G. F., Hopp, A. V., Moca, V. V., Bârzan, H., Ciuparu, A., Ercsey-Ravasz, M., Winkel, M., Linde, H., & Mureșan, R. C. (2022). The fractal brain: scale-invariance in structure and dynamics. Cerebral Cortex , 33 (8), 4574–4605. https://doi.org/10.1093/cercor/bhac363 Hayano, J., & Yuda, E. (2019). Pitfalls of assessment of autonomic function by heart rate variability. Journal of PHYSIOLOGICAL ANTHROPOLOGY , 38 (1), 3. https://doi.org/10.1186/s40101-019-0193-2 He, B. J. (2011). Scale-Free Properties of the Functional Magnetic Resonance Imaging Signal during Rest and Task. Journal of Neuroscience , 31 (39), 13786–13795. https://doi.org/10.1523/jneurosci.2111-11.2011 He, B. J. (2014). Scale-free brain activity: past, present, and future. Trends in Cognitive Sciences , 18 (9), 480–487. https://doi.org/10.1016/j.tics.2014.04.003 Hengen, K. B., & Shew, W. L. (2025). Is criticality a unified setpoint of brain function? Neuron , 113 (16), 2582-2598.e2. https://doi.org/10.1016/j.neuron.2025.05.020 Klimesch, W. (2018). The frequency architecture of brain and brain body oscillations: an analysis. European Journal of Neuroscience , 48 (7), 2431–2453. https://doi.org/10.1111/ejn.14192 Laborde, S., Mosley, E., & Thayer, J. F. (2017). Heart rate variability and cardiac vagal tone in psychophysiological research – recommendations for experiment planning, data analysis, and data reporting. Frontiers in Psychology , 08 , 213. https://doi.org/10.3389/fpsyg.2017.00213 Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J. (2001). Long-Range temporal correlations and scaling behavior in human brain oscillations. Journal of Neuroscience , 21 (4), 1370–1377. https://doi.org/10.1523/jneurosci.21-04-01370.2001 Liu, J., Fang, J., Wang, Z., Rong, P., Hong, Y., Fan, Y., Wang, X., Park, J., Jin, Y., Liu, C., Zhu, B., & Kong, J. (2016). Transcutaneous vagus nerve stimulation modulates amygdala functional connectivity in patients with depression. Journal of Affective Disorders , 205 , 319–326. https://doi.org/10.1016/j.jad.2016.08.003 Lucente, D., Gradenigo, G., & Salasnich, L. (2025). Entropy production and irreversibility in the linearized stochastic Amari neural model. Entropy , 27 (11), 1104. https://doi.org/10.3390/e27111104 Mather, M., & Thayer, J. F. (2018). How heart rate variability affects emotion regulation brain networks. Current Opinion in Behavioral Sciences , 19 , 98–104. https://doi.org/10.1016/j.cobeha.2017.12.017 McEwen, B. S. (1998). Stress, adaptation, and disease: allostasis and allostatic load. Annals of the New York Academy of Sciences , 840 (1), 33–44. https://doi.org/10.1111/j.1749-6632.1998.tb09546.x Mietus, J. E. (2002). The pNNx files: re-examining a widely used heart rate variability measure. Heart , 88 (4), 378–380. https://doi.org/10.1136/heart.88.4.378 Müller, E. J., Munn, B. R., & Shine, J. M. (2025). The brain that controls itself. Current Opinion in Behavioral Sciences , 63 , 101499. https://doi.org/10.1016/j.cobeha.2025.101499 Muñoz, M. A. (2018). Colloquium: Criticality and dynamical scaling in living systems. Reviews of Modern Physics , 90 (3). https://doi.org/10.1103/revmodphys.90.031001 Peng, C., Havlin, S., Stanley, H. E., & Goldberger, A. L. (1995). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos an Interdisciplinary Journal of Nonlinear Science , 5 (1), 82–87. https://doi.org/10.1063/1.166141 Pincus, S. M., & Goldberger, A. L. (1994). Physiological time-series analysis: what does regularity quantify? American Journal of Physiology-Heart and Circulatory Physiology , 266 (4), H1643–H1656. https://doi.org/10.1152/ajpheart.1994.266.4.h1643 Pletzer, B., Kerschbaum, H., & Klimesch, W. (2010). When frequencies never synchronize: The golden mean and the resting EEG. Brain Research , 1335 , 91–102. https://doi.org/10.1016/j.brainres.2010.03.074 Porges, S. W. (1995). Orienting in a defensive world: Mammalian modifications of our evolutionary heritage. A Polyvagal Theory. Psychophysiology , 32 (4), 301–318. https://doi.org/10.1111/j.1469-8986.1995.tb01213.x Porges, S. W. (2023). The vagal paradox: A polyvagal solution. Comprehensive Psychoneuroendocrinology , 16 , 100200. https://doi.org/10.1016/j.cpnec.2023.100200 Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology , 278 (6), H2039–H2049. https://doi.org/10.1152/ajpheart.2000.278.6.h2039 Riganello, F., Larroque, S. K., Bahri, M. A., Heine, L., Martial, C., Carrière, M., Charland-Verville, V., Aubinet, C., Vanhaudenhuyse, A., Chatelle, C., Laureys, S., & Di Perri, C. (2018). A heartbeat away from consciousness: Heart rate variability entropy can discriminate disorders of consciousness and is correlated with Resting-State FMRI brain connectivity of the central autonomic network. Frontiers in Neurology , 9 , 769. https://doi.org/10.3389/fneur.2018.00769 Rogers, B., Giles, D., Draper, N., Hoos, O., & Gronwald, T. (2021). A new detection method defining the aerobic threshold for endurance exercise and training prescription based on fractal correlation properties of heart rate variability. Frontiers in Physiology , 11 , 596567. https://doi.org/10.3389/fphys.2020.596567 Roopun, A. K. (2008). Temporal interactions between cortical rhythms. Frontiers in Neuroscience , 2 (2), 145–154. https://doi.org/10.3389/neuro.01.034.2008 Rusch, F. R., Kinouchi, O., & Roque, A. C. (2025). Influence of topology on the critical behavior of hierarchical modular neuronal networks. Communications Physics , 8 (1). https://doi.org/10.1038/s42005-025-02074-5 Sargent, K. S., Martinez, E. L., Reed, A. C., Guha, A., Bartholomew, M. E., Diehl, C. K., Chang, C. S., Salama, S., Popov, T., Thayer, J. F., Miller, G. A., & Yee, C. M. (2024). Oscillatory coupling between neural and cardiac rhythms. Psychological Science , 35 (5), 517–528. https://doi.org/10.1177/09567976241235932 Shaffer, F., & Ginsberg, J. P. (2017). An overview of heart rate variability metrics and norms. Frontiers in Public Health , 5 , 258. https://doi.org/10.3389/fpubh.2017.00258 Shew, W. L., Clawson, W. P., Pobst, J., Karimipanah, Y., Wright, N. C., & Wessel, R. (2015). Adaptation to sensory input tunes visual cortex to criticality. Nature Physics , 11 (8), 659–663. https://doi.org/10.1038/nphys3370 Smith, R., Thayer, J. F., Khalsa, S. S., & Lane, R. D. (2017). The hierarchical basis of neurovisceral integration. Neuroscience & Biobehavioral Reviews , 75 , 274–296. https://doi.org/10.1016/j.neubiorev.2017.02.003 Stikvoort, W., Pérez-Ordoyo, E., Mindlin, I., Escrichs, A., Sitt, J. D., Kringelbach, M. L., Deco, G., & Perl, Y. S. (2025). Nonequilibrium brain dynamics elicited as the origin of perturbative complexity. PLoS Computational Biology , 21 (6), e1013150. https://doi.org/10.1371/journal.pcbi.1013150 Tognoli, E., & Kelso, J. a. S. (2014). The metastable brain. Neuron , 81 (1), 35–48. https://doi.org/10.1016/j.neuron.2013.12.022 Valenza, G., Duggento, A., Passamonti, L., Diciotti, S., Tessa, C., Toschi, N., & Barbieri, R. (2017). Resting-state brain correlates of cardiovascular complexity. Annu Int Conf IEEE Eng Med Biol Soc , 31 , 3317–3320. https://doi.org/10.1109/embc.2017.8037566 Williams-García, R. V., Moore, M., Beggs, J. M., & Ortiz, G. (2014). Quasicritical brain dynamics on a nonequilibrium Widom line. Physical Review E , 90 (6), 062714. https://doi.org/10.1103/physreve.90.062714 Author Notes 1. Funding Statement: The author received no financial support for the research, authorship, and/or publication of this article. 2. Conflict of Interest Statement: The author declares that there are no competing interests. 3. Use of Artificial Intelligence (IA) Tools: The author used Gemini (Google, December 2025) to assist in the translation of the original manuscript from Portuguese into academic English and in subsequent stylistic and terminological refinement. This process involved an iterative dialogue in which the author provided original conceptual frameworks and draft materials to ensure accurate rendering of technical terminology and adherence to academic conventions. All AI-assisted suggestions were critically reviewed, edited, and verified by the author, who retains full responsibility for the accuracy, originality, and conceptual integrity of the final manuscript. Table 1 | Comparative Dynamics of High-Magnitude Vagal States — Comparison of linear and nonlinear metrics across two physiological states characterized by similarly high vagal magnitude (RMSSD). While linear amplitude metrics conflate these states, the Neurodynamic Manifold differentiates them based on temporal scaling (DFA α₁), informational irregularity (SampEn), and geometric coordination (SD2/SD1). DFA α₁ (Scaling) ≈ 1.0 (pink-noise dynamics) Scale-invariant, multiscale coordination ≈ 1.5 (Brownian-like dynamics) Excessive persistence, history-bound rigidity SampEn (Irregularity) High Rich structural variability and intact recursive integration Low Predictable patterns reflecting loss of degrees of freedom SD2/SD1 (Geometric coordination) ≈ φ (≈ 1.618) Balanced longitudinal anisotropy supporting adaptability ≫ φ Excessive dominance of slow modulation, rigid temporal geometry RMSSD (Magnitude) High Reflects available vagal resources High Preserved magnitude despite collapsed organization pNN50 (Intermittency) High Frequent short-latency adjustments Low Reduced reflexive intermittency despite high variance HF Power (RSA) Coherently phase-coupled to respiration Suppressed, decoupled, or irregularly coupled System Functionality Open, multiscalar, metastable Decomplexified, constrained to a low-capacity attractor Manifold Topology Quasicritical Zone Subcritical basin (Systemic Redundancy) Clinical Implication Adaptive regulation / functional health Pathological shutdown / false positive for recovery Figure 1 | The Neurodynamic Manifold: A Topological Representation of Autonomic Regimes. The surface illustrates a conceptual manifold in which autonomic regulation is organized by dynamical structure rather than magnitude alone. The horizontal axes represent fractal temporal scaling (DFA α₁) and informational irregularity (Sample Entropy), while surface curvature reflects Fisher Information, interpreted here as a measure of dynamical sensitivity—indexing susceptibility to small perturbations rather than information content per se. Geometric organization along the manifold is constrained by longitudinal anisotropy (SD2/SD1), with coordination near the golden ratio (φ ≈ 1.618) stabilizing the quasicritical regime. Data points (spheres) represent vagal magnitude (scalar HRV amplitude), depicted as elevation orthogonal to the governing topology. Importantly, identical magnitudes populate distinct regions of the manifold, illustrating the vagal paradox: equivalent signal strength can emerge from fundamentally different dynamical regimes. The Quasicritical Zone (Adaptive Complexity) occupies the region near DFA α₁ ≈ 1.0 and SD2/SD1 ≈ φ, forming a broad, shallow basin of high susceptibility and flexible regulation. In contrast, the Subcritical Regime (Systemic Redundancy) lies in a region of excessive temporal persistence (DFA α₁ ≈ 1.5), increased geometric rigidity, and reduced dynamical sensitivity, reflecting pathological shutdown despite preserved magnitude. The surface is a conceptual illustration intended to convey topological relations and regime structure rather than an empirically fitted manifold. Information & Authors Information Version history V1 Version 1 03 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Authors Affiliations Caio Amaral Gabriel 0000-0003-0870-3686 [email protected] Independent Scholar View all articles by this author Metrics & Citations Metrics Article Usage 389 views 91 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Caio Amaral Gabriel. A Neurodynamic Manifold of Autonomic Function: Integrating Magnitude and Dynamical Regimes in Heart Rate Variability. Authorea . 03 January 2026. DOI: https://doi.org/10.22541/au.176743454.46178243/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.176743454.46178243/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fe2758a7e05300f',t:'MTc3OTE4Njk3MQ=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();