Robust information transfer calculation reveals dynamic networks during sleep arousal

Every night, the sleeping brain and heart stage a brief but revealing drama. When a sleeper is momentarily aroused — a spontaneous activation of the central nervous system that lasts seconds — the autonomic nervous system responds with an abrupt surge of sympathetic activity and a withdrawal of parasympathetic control, sending heart rate and blood pressure spiking. Researchers at TU Dresden have now shown that these fleeting arousals can be used as a physiological probe to measure how well information flows between the brain and the cardiovascular system, and that the answer changes measurably with sleep stage, age, and cardiovascular disease. The findings, published in Frontiers in Network Physiology, suggest that the autonomic response to sleep arousal could serve as a diagnostic marker of the health of the body’s regulatory networks.

The team, led by Richard Hohmuth, Jakob J. Müller, Hagen Malberg, and Martin Schmidt of the Institute of Biomedical Engineering at TU Dresden, tackled a long-standing technical problem in network physiology: how to calculate information transfer between physiological systems robustly enough to compare thousands of events across nearly two thousand people. Their tool of choice is transfer entropy, an information-theoretic quantity that measures directed predictive information — specifically, how much the past of a source signal, such as brain activity recorded by electroencephalography, improves prediction of a destination signal, such as heart rate variability derived from the electrocardiogram, beyond what the destination’s own past already contains. Unlike classical correlation, transfer entropy captures nonlinear dependencies and has a direction, making it well suited to mapping the dynamic networks that link organ systems as the body shifts between states.

Transfer entropy, however, is notoriously sensitive to noise, finite sample sizes, and a set of parameters known as the embedding. The embedding defines the information horizon of the calculation: how many past samples of the source and destination are included, the spacing between those samples, and the delay between the source and destination states. Conventional strategies for choosing these parameters, such as the Ragwitz criterion or approaches based on active information storage, optimize objectives related to — but not identical to — directed source-to-destination information transfer. The Ragwitz criterion minimizes prediction error for a single time series, while active information storage quantifies how much information a process keeps in its own past. Both can yield unstable parameter choices when applied event-by-event to short, noisy physiological windows, which is precisely the situation during a sleep arousal lasting only a few hundred seconds.

To overcome this, the Dresden group introduced a novel optimization strategy called maximum transfer entropy, or max. TE. Instead of optimizing each arousal independently, max. TE performs a grid search over embedding parameters — source history, source spacing, destination history, destination spacing, and source-to-destination delay, each varied from one to nine samples — and selects the parameters that yield the most stable group-level transfer entropy estimates for each sleep stage and each source-destination feature pair. The method was first developed and compared against three state-of-the-art auto-embedding strategies on a balanced development dataset of 400 arousals, 100 each from wake, light sleep, deep sleep, and REM sleep. When the strategies were compared using the coefficient of variation of the transfer entropy estimates as an empirical stability metric, max. TE achieved a mean coefficient of variation of 0.32, compared with 0.39 for the second-best strategy, Max. Corr. AIS + TE, 0.48 for Max. Corr. AIS, and 1.20 for the Ragwitz criterion — a 17.9 percent improvement in stability over the runner-up.

Robustness was assessed with four complementary criteria: empirical stability across repeated arousals, physiological surrogate reliability using iterative amplitude-adjusted Fourier transform surrogates that preserve each signal’s amplitude distribution and autocorrelation while destroying its temporal order, source-destination reliability screening, and delay-recovery robustness in simulated systems with known coupling. Across all 400 development arousals, the observed transfer entropy exceeded the surrogate expectations in every sleep stage, with mean IAAFT pass rates between 0.807 and 0.817, and no retained feature pair systematically failed the surrogate test. In a simulation benchmark on linear Gaussian systems with analytically computed ground truth, max. TE achieved the highest delay-recovery rate of all tested strategies, 0.652, while showing low variability across Monte Carlo repetitions. The authors are careful to note that max. TE is intended as a robust group-level embedding strategy, not as an unbiased estimator of absolute transfer entropy; the simulation showed a positive bias and a higher root mean square error than Max. Corr. AIS, and the method carried the highest computational cost.

With the optimized embedding in hand, the team turned to the physiological investigation, analyzing 8,136 sleep arousals from 1,956 subjects drawn from the follow-up visit of the Sleep Heart Health Study, one of the largest polysomnography cohorts ever assembled. Only arousals isolated from any other arousal by at least 400 seconds were included, ensuring that each analyzed event reflected a clean, uncontaminated autonomic response. From the electrocardiogram, the researchers extracted ten heart rate variability parameters and five QT interval variability parameters, assigned to sympathetic and parasympathetic branches of the autonomic nervous system; from the EEG, they derived band powers and Shannon entropy as markers of cortical activity. Transfer entropy was then calculated between all pairs of these parameters using nearest-neighbor estimators, with surrogate testing discarding the 9.2 percent of calculations that failed validation.

The results paint a vivid picture of the body’s regulatory networks in action. Information transfer was highest during arousals occurring in REM sleep and lowest during wake, with all sleep stages differing significantly from one another in a generalized linear mixed model that accounted for the nested structure of the data. This aligns with established autonomic physiology, in which parasympathetic dominance during non-REM sleep promotes cardiovascular rest while sympathetic activation during REM sleep produces surges in heart rate and blood pressure similar to waking states. The analysis also revealed a clear directionality: information transfer from autonomic nervous system parameters to central nervous system parameters averaged 105.7 milli-nats, exceeding the reverse direction at 81.4 milli-nats, with the maximum observed from sympathetic to cortical parameters at 110.3 milli-nats and the minimum within parasympathetic parameters at 45.2 milli-nats.

Most strikingly, cardiovascular disease left a measurable fingerprint on the network. Subjects diagnosed with cardiovascular disease showed significantly lower transfer entropy, averaging 85.4 plus or minus 0.8 milli-nats, than healthy controls at 87.9 plus or minus 0.5 milli-nats, indicating an impairment of regulatory control mechanisms. The authors hypothesize that disease disrupts information transfer within the autonomic nervous system while the central nervous system attempts to compensate, increasing transfer in the brain-to-body direction. Age also emerged as a powerful factor: transfer entropy decreased linearly with increasing age, at a slope of minus 0.1 milli-nats per year with an R-squared of 0.55, consistent with previous research showing that physiological networks weaken with age. Female subjects showed slightly higher information transfer than male subjects, and while apnea-hypopnea index and arousal index showed significant effects at the parameter-combination level, no linear trend was found across their severity categories.

The implications reach beyond sleep research. Cardiovascular disease is characterized by chronic sympathetic overdrive and reduced parasympathetic tone, which corrupts the bidirectional information flow between the brain and the autonomic nervous system. By using sleep arousals as a natural, repeatable stimulus, the information-theoretic approach can expose these disruptions at the level of the whole regulatory network, potentially offering a diagnostic window that conventional vital-sign analysis cannot. The authors emphasize that transfer entropy quantifies directed predictive information, not proof of direct mechanistic causation, and that the derived parameters are influenced by many physiological processes at once, so the observed effects reflect the sum of the underlying regulatory mechanisms rather than clearly isolated pathways.

Further research is needed to identify precisely which information pathways are disrupted by cardiovascular disease and to confirm that the observed relationships hold in other cohorts and settings. Once established, the methodology could address additional scientific questions and open new fields of application, ultimately enabling use in real-world scenarios. For now, the study demonstrates something remarkable: that the brief, spontaneous awakenings that punctuate every night’s sleep are not mere interruptions, but physiological stimuli that reveal the dynamic, sleep-stage-specific networks through which the brain and heart exchange the information needed to keep the body in balance — and that the strength of that exchange quietly records the toll of disease and age.

Subject of Research: Network Physiology

Article Title: Robust information transfer calculation reveals dynamic networks during sleep arousal

Article References: Hohmuth, R., Müller, J. J., Malberg, H., & Schmidt, M. (2026). Robust information transfer calculation reveals dynamic networks during sleep arousal. Frontiers in Network Physiology, 6, Article 1930617. https://doi.org/10.3389/fnetp.2026.1930617

Image Credits: AI Generated

DOI: 10.3389/fnetp.2026.1930617

Keywords: transfer entropy, sleep arousal, network physiology, cardiovascular disease, autonomic nervous system, heart rate variability, Sleep Heart Health Study, information dynamics, Robust, information, transfer, calculation