Why a Single Number Cannot Capture the Body’s Capacity to Handle Stress

For decades, stress researchers have tried to compress the bewildering complexity of human physiology into a single score. Count the biomarkers that fall into high-risk ranges, sum the standardized deviations, and you get a number called allostatic load that modestly predicts who will develop disease. But a provocative new theoretical paper argues that this entire tradition rests on a hidden mathematical mistake: the assumption that the body’s regulatory capacity is a scalar at all. The work, published in Frontiers in Network Physiology, shows with simple arithmetic that two physiological systems with identical stability properties can reverse their apparent ranking the moment you change the perturbation you apply or the metric you use to score the damage.

The author, Lori Hogenkamp of the Center for Adaptive Stress in Cincinnati, frames the argument around a construct she calls Regulatory Bandwidth, which she previously introduced as the organism’s present coordinated capacity across interacting stress-responsive systems. Her central claim is stark: regulatory capacity is not an intrinsic property of an organism. It is a conditional relation among the architecture and current state of the regulatory system, the particular perturbations that reach it, the cost functional used to evaluate the response, the viability criterion, and the time horizon. Remove any one of those ingredients, and the question of which system has greater capacity has no answer.

The mathematical heart of the paper borrows from control theory, a field that engineers have used for decades to analyze feedback systems. Consider a biological system linearized around its operating state. The eigenvalues of the Jacobian matrix determine stability: if they all have negative real parts, perturbations eventually decay. But eigenvalues say nothing about what happens along the way. In non-normal systems, which are common in directed and hierarchical biological networks, non-orthogonal modes can combine to produce large transient excursions before recovery, so two systems with identical spectra can traverse wildly different paths and impose very different energetic or functional costs. Hogenkamp’s formal example drives this home with two three-dimensional models spanning autonomic, neuroendocrine, and inflammatory states. Both share the same eigenvalue spectrum, the same relaxation rate, and the same equilibrium, yet under one cost functional one system carries 14.7 times the other’s burden, while under a different metric the ranking flips entirely.

The tool that formalizes these reversals is the observability Gramian, a matrix that, in this setting, represents the accumulated weighted recovery burden of a trajectory starting from a given departure. For a declared quadratic cost, the Gramian solves a Lyapunov equation and quantifies exactly how much burden accrues given how perturbations propagate through the network’s coupling structure. Crucially, the paper separates three maps that routine biomarker composites silently conflate: the measurement map, which specifies what instruments can observe; the burden-evaluation map, which specifies which observed departures count as cost; and the latent state representation itself. A composite index inherits commitments from all three and then reports a single number as though it had recovered a property of the organism.

This is where the argument turns pointed. Standardization choices that researchers treat as neutral preprocessing are, in Hogenkamp’s framing, constitutive assumptions. Z-scoring cortisol and blood pressure together declares a one-standard-deviation departure in each to be commensurate, a geometric commitment with no biological justification. Changing the reference cohort can change a person’s standardized profile without any change in that person’s physiology. Cutoff methods, regression weights, and factor-analytic loadings each embed different commitments about what counts. And no amount of additional biomarkers or data-driven weighting solves the problem, because a model optimized to predict mortality estimates risk under a particular population and outcome definition; it does not thereby discover a context-free quantity called capacity. Prediction and construct identification, the paper insists, are different achievements.

The framework also draws sharp distinctions between concepts that stress science has long blurred. A resting snapshot indicates state, not dynamics: it cannot predict how the coupled system will respond to a challenge. Return rate is not recovery burden, because two systems may recover at similar asymptotic speeds while incurring very different transient costs. And recovery burden is not viability, which means remaining within declared physiological or functional constraints over a declared horizon. A trajectory can be costly yet remain viable, or it can cross a critical functional boundary despite a modest average-cost score. Most consequentially, viability is not adaptation. A response that preserves short-term function through costly compensation may produce delayed burden or narrow the range of perturbations manageable later; it may be adaptive for one function or horizon and maladaptively stabilized at another. Adaptation, in this account, is an indexed judgment tied to a specified level of organization, protected function, reference point, horizon, and cost criterion, not a synonym for stability or recovery.

What makes the framework scientifically serious rather than merely critical is that it generates falsifiable predictions. The primary comparison pits a flexible scalar-capacity model, which predicts one preserved ordering of systems across all declared perturbation classes, against a conditional-profile model, which permits reproducible system-by-perturbation rank reversals. Both models are fitted to the same data with the same covariates and evaluated by complexity-controlled held-out prediction on sessions, contexts, or perturbation classes they did not see. If the scalar model is non-inferior, the profile has no demonstrated value. If replicated crossing interactions survive adjustment for resting state, exposure history, and measurement error, capacity is better represented as conditional structure than as an intrinsic rank. The paper even specifies how measurement error in integrated burden outcomes grows with the observation horizon and must be estimated and removed before any rank comparison, because spurious crossings that replicate across sessions could otherwise masquerade as biology.

To show the framework is implementable, the paper walks through a prospective design specification using the orthostatic challenge, an established cardiovascular test in which a person transitions from lying down to standing or passive head-up tilt. Continuous beat-to-beat blood pressure and heart-rate recordings capture the multivariate response, while symptoms, task performance, and cerebral blood-flow velocity are recorded as functional outcomes. The reference trajectory, burden weights, viability endpoint, and time horizon are all declared before fitting. Notably, a retrospective tilt study cited in the paper found that cerebral blood-flow velocity and end-tidal carbon dioxide predicted lightheadedness while standard heart rate and blood pressure measures did not, illustrating exactly why the biological conclusion depends on which outputs are measured: preserved values in familiar cardiovascular channels do not establish preservation of cerebral perfusion or function.

The implications extend into contested territory. The framework offers a mathematical route to person-environment fit: two architectures can have similar average burden under one perturbation distribution and sharply different burden under another, so accommodations that change the input channel, timing, or predictability of demands can have large biological effects without changing a person’s underlying regulatory organization. Hogenkamp, an autistic scholar, is explicit that this framing is neurodiversity-affirming without insulating the theory from evidence. It does not deny impairment, energetic cost, or collapse; it changes the explanatory unit, locating costly outcomes in the interaction between a minority architecture and an environment concentrated along its fragility directions. At the same time, the paper is careful to note that rejecting the scalar model supports conditional structure but does not establish architectural heterogeneity, which requires a further comparison against a flexible shared-architecture model. Simple trajectory nonlinearity, the paper warns, is not evidence of architecture.

The author is candid about limits. The formal illustration is local, linear, and time invariant, while whole-organism physiology is nonlinear, stochastic, and nonstationary; the Gramian analysis does not characterize global regime transitions, which require separate nonlinear analyses. Identifying a biologically meaningful cost functional is an inverse problem, and viability boundaries are scale- and task-dependent. But the practical conclusion is direct and likely to unsettle a research field built on composite indices: perturb carefully, follow trajectories, justify the state and measurement maps, declare burden and viability criteria, model measurement error, and retain conditional response structure long enough to determine whether a scalar summary has earned the claims made for it. A number can still summarize, the paper concludes, but only after its conditions are fixed, and it can never convert a context-dependent relation into a universal rank.

Subject of Research: Measurement architecture for multisystem stress-regulatory capacity in network physiology

Article Title: Regulatory capacity is not a scalar: metrics, perturbations, and viability in network physiology

Article References: Hogenkamp, L. (2026). Regulatory capacity is not a scalar: metrics, perturbations, and viability in network physiology. Frontiers in Network Physiology, 6, Article 1961712. https://doi.org/10.3389/fnetp.2026.1961712

Image Credits: AI Generated

DOI: 10.3389/fnetp.2026.1961712

Keywords: network physiology, allostatic load, regulatory bandwidth, control theory, observability Gramian, stress physiology, viability theory, perturbation response, neurodiversity, allostasis, resilience, person-environment fit