The research team, led by Nikolay Syrov of Ruhr University Bochum together with colleagues from the Skolkovo Institute of Science and Technology and Lomonosov Moscow State University, set out to fill a conspicuous gap in neuroscience. Over the past two decades, scientists have meticulously mapped how cortical excitability fluctuates across the heartbeat, revealing that the brain’s response to transcranial magnetic stimulation varies with cardiac phase. Yet the spinal cord, the critical relay between brain and body, had remained largely unexplored in this respect. Because the spinal cord hosts the final common pathway for all voluntary movement, understanding how its excitability is modulated by the heart carries direct implications for rehabilitation medicine and neurostimulation therapies.

To probe this relationship, the researchers recruited twenty healthy volunteers and employed trans-spinal magnetic stimulation, or TSMS, a technique in which a magnetic coil placed over the cervical spine induces electric currents that activate spinal motor neurons and their incoming pathways. The key methodological innovation was real-time adaptation: the stimulation system continuously monitored the electrocardiogram and triggered each single pulse at a defined fraction of the individual’s RR interval, the time between two consecutive R-wave peaks of the ECG. Pulses were delivered at five cardiac phases, corresponding to 0, 15, 30, 60, and 85 percent of the RR interval, a range that spans both systole, the contraction phase, and diastole, the relaxation phase.

The outcome measure was the amplitude of the motor-evoked potential, or MEP, recorded from hand muscles with electromyography. When a magnetic pulse excites spinal circuitry, a small electrical volley travels down the peripheral nerves and produces a measurable twitch-related potential in the target muscle. Larger MEPs indicate a more excitable spinal cord at the moment of stimulation. By comparing MEP amplitudes across the five cardiac phases, the team could reconstruct a fine-grained temporal profile of cardiac influence on spinal motor excitability.

The results were unambiguous. MEP amplitudes varied significantly across the cardiac cycle, with maximal facilitation occurring at 60 percent of the RR interval, deep in mid-diastole. This temporal profile stands in sharp contrast to the pattern previously documented for the cerebral cortex, where excitability tends to be facilitated during systole, when arterial pressure surges and baroreceptors in the great vessels fire most vigorously. The dissociation is scientifically tantalizing: it suggests that the heart’s grip on the spinal cord is governed by different timing and possibly different mechanisms than its grip on the cortex, even though both structures are exposed to the same rhythmic cardiovascular signals.

To analyze the data rigorously, the authors turned to linear mixed-effects models, a statistical framework well suited to repeated-measures designs in which multiple observations are nested within each participant. Crucially, the models controlled for two potential confounds: the duration of the preceding RR interval, which reflects moment-to-moment heart rate variability, and the respiratory phase, since breathing is known to modulate neural excitability in its own right. The analysis confirmed the cardiac-phase effect on spinal excitability and added an intriguing secondary finding: the length of the preceding RR interval was itself significantly associated with spinal excitability, whereas respiratory phase was not. In other words, the recent history of the heartbeat, not the breath, carried the predictive weight for how responsive the spinal cord would be.

What mechanism could explain a diastolic peak in spinal excitability? The authors advance two non-exclusive hypotheses. The first is physiological and centers on the baroreflex, the homeostatic loop through which pressure sensors in the carotid arteries and aortic arch relay information to the nucleus tractus solitarius in the brainstem. Baroreceptor firing peaks during systole, and the downstream autonomic adjustments ripple through the nervous system with characteristic delays. A delayed, reflex-mediated modulation of spinal motor circuits could plausibly produce facilitation in diastole, after the systolic pressure wave has been sensed and processed. The second hypothesis is strikingly mechanical: the spinal cord does not sit motionless in the vertebral canal but is bathed in cerebrospinal fluid and subjected to pressure pulses synchronized with the heartbeat. With each cardiac cycle, the cord may undergo small displacements within the spinal canal, altering the geometric relationship between the stimulation coil, the induced electric field, and the excitable neural tissue. If the cord drifts closer to the coil or into a more favorable orientation during certain phases, the effective stimulation strength would fluctuate, masquerading as genuine neurophysiological modulation.

The authors are careful to note that these mechanisms are not mutually exclusive, and that disentangling them is a priority for future work. The distinction matters enormously for translational science. If baroreflex-related physiology drives the effect, then cardiac-timed spinal stimulation could be harnessed to deliver neuromodulation when spinal circuits are naturally most receptive, potentially amplifying the efficacy of rehabilitation protocols for spinal cord injury, stroke, and other motor disorders. If mechanical displacement is the dominant factor, then apparent phase-dependent effects must be corrected for in experimental designs, lest researchers mistake coil-to-cord geometry for neural plasticity. Either way, the study delivers a clear methodological warning: experiments and clinical protocols involving spinal stimulation should record and account for the cardiac phase of each pulse, just as the field has learned to control for respiratory phase and cortical state.

The work also enriches the broader and rapidly growing field of heart-brain interaction research. Cardiac-phase effects have now been documented in perception, cognition, and cortical physiology, feeding into theories that frame the heartbeat as a fundamental rhythm shaping information processing in the nervous system. Extending this framework to the spinal cord closes the loop in a satisfying way: the structure that ultimately commands every movement is itself modulated by the organ that powers it. The finding that spinal excitability peaks in mid-diastole, a window when the heart is at rest, hints at an elegant temporal architecture in which the motor machinery of the body is primed during the cardiovascular system’s quietest moment.

For a field racing toward closed-loop neuromodulation, in which stimulation devices read physiological signals and fire only at optimal moments, the study offers a concrete and immediately actionable parameter. Real-time, ECG-triggered stimulation is technically feasible, as this experiment demonstrates, and the identified diastolic window provides a natural target for such algorithms. As the authors emphasize, a more complete understanding of how the heart shapes the nervous system, through both reflex pathways and mechanical forces, will be essential for building the next generation of neurostimulation-based treatments. The heartbeat, it turns out, is not merely background noise for the spinal cord; it is part of the score to which the cord plays.

Subject of Research: Cardiac-cycle modulation of human spinal cord excitability measured with heart-rate-adapted trans-spinal magnetic stimulation

Article Title: Cardiac cycle shapes spinal cord excitability

Article References: Syrov, N., Morozova, P., Popova, A., Melashenko, E., Takhirov, R., Mustafina, A., Benachour, A., Yakovlev, L., Knyshenko, M., & Kaplan, A. (2026). Cardiac cycle shapes spinal cord excitability. BMC Biology. https://doi.org/10.1186/s12915-026-02752-y

Image Credits: AI Generated

DOI: 10.1186/s12915-026-02752-y

Keywords: cardiac cycle, spinal cord excitability, trans-spinal magnetic stimulation, motor evoked potential, heart-brain interaction, baroreflex, diastole, systole, neurostimulation, electrophysiology, RR interval, cerebrospinal fluid

The study, conducted by Thomas Murchie, tackles the question with analytical mathematics rather than new animal or human experiments. Its starting point is the three-element Windkessel model, in which the arterial system is represented by a peripheral resistance, a characteristic impedance of the proximal aorta, and a compliance that stores blood during systole and releases it during diastole. In that framework, Ea depends on total systemic resistance, on arterial compliance through the time constant tau, and critically on the durations of systole and diastole. Clinicians, however, rarely measure Ea that way. Instead they use a convenient surrogate, the ratio of end-systolic pressure to stroke volume, which tracks the Windkessel value closely in living subjects but hides the separate contributions of resistance and compliance beneath a single ratio.

Over the years, several laboratories have proposed a compromise: a linear approximation of the form Ea equals R plus k divided by C, where R is a resistance term, C is compliance, and k is a coefficient that must be fitted to data. Empirical studies produced values of k around 0.314 in work by Segers and colleagues in 2002 and 0.42 in work by Chemla and colleagues in 2003. More provocatively, other analyses concluded that compliance contributes almost nothing at all, effectively setting k near zero and reducing Ea to roughly total resistance divided by cycle length. The physiological determinants of k were never described analytically, leaving the field with a scatter of numbers and no principled way to choose among them.

The new paper resolves the ambiguity with a higher-order approximation. By replacing the exponential term in the Windkessel equation with a polynomial expansion and carrying the algebra one step beyond the truncation that yields the k-equals-zero result, Murchie derives a closed-form expression: Ea is approximately total resistance divided by the cardiac cycle length, plus a compliance term whose coefficient k equals one half multiplied by the square of the ratio of diastolic duration to total cycle duration. In other words, k is not a universal constant at all. It is a timing factor, growing as diastole occupies a larger share of the heartbeat, which happens characteristically when the heart rate is low. At high heart rates, where diastole is squeezed short, the compliance term shrinks toward irrelevance, which is precisely why some studies concluded that compliance barely matters.

To test the approximation, the analysis first compared it against the parent Windkessel equation across a deliberately broad parameter space: 693 evenly distributed combinations of total resistance, compliance, and heart rate, spanning values seen in healthy adults and in patients treated for septic and cardiogenic shock. Heart rates of 60, 80, and 100 beats per minute were used, with ejection times adjusted according to the relationship observed during exercise by Mertens and colleagues. The agreement was essentially exact for practical purposes, with a coefficient of determination above 0.9999 and a mean absolute percentage error of just 0.51 percent. The worst-case error, arising only when heart rate, resistance, and compliance were simultaneously low, was 3.96 percent, a deviation traced to the limits of the truncated Taylor series at large values of the ratio of diastolic duration to the Windkessel time constant.

The second validation was more demanding, because it pitted the formula against a completely independent model of the circulation. Using a publicly available database of 4,374 simulated adults generated by Charlton and colleagues with a one-dimensional vascular model reproducing age-appropriate cardiovascular distributions from 25 to 75 years, the study compared the new approximation against the clinical surrogate of end-systolic pressure divided by stroke volume, sampled carefully at the end of the small end-systolic flow reversal in the aortic root. The new timing-dependent formula achieved a coefficient of determination of 0.9980 with a mean absolute percentage error of 0.87 percent. Segers’ fixed-coefficient regression, by contrast, yielded 0.9903 with errors up to nearly 15 percent, and the k-equals-zero simplification fell to 0.9610 with maximum errors above 25 percent. The ordering was unambiguous: retaining compliance with a timing-scaled coefficient beats ignoring it outright.

Beyond the curve-fitting, the paper offers a physical intuition for what the coefficient k actually represents. Since Ea approximates end-systolic pressure over stroke volume, and resistance over cycle length approximates mean arterial pressure over stroke volume, the compliance term corresponds to the excess of end-systolic pressure over mean pressure, per unit of stroke volume. That excess depends on two timing-dependent factors. The first is the fraction of the stroke volume still stored in the arterial compartment at the end of systole rather than already run off through the peripheral resistance, which vanishes as diastole shrinks. The second is the fraction of the resulting arterial pressure change that sits above mean arterial pressure, which depends on how the arterial pressure decay is weighted in time. Both factors converge to zero as diastole occupies an ever-smaller slice of the cycle, which is exactly the behavior captured by the squared ratio of diastolic to total cycle duration.

The implications reach beyond theory into the design of empirical studies. Because the ratio of diastolic duration to cycle length varies substantially with heart rate, the apparent relationship between compliance and Ea measured across a population with natural heart-rate variation may not reflect the true contribution of compliance within any single individual. If diastolic fraction happens to covary systematically with compliance across a cohort, the compliance-dependent term could appear nearly constant even though Ea physically depends on compliance in every subject. That mechanism, the paper argues, offers a coherent explanation for the divergent empirical estimates of k that have accumulated since the early 2000s: analyses that reduce Ea to resistance over cycle length and analyses that fit a constant k are simply working at different orders of approximation of the same underlying exponential expression.

The author is careful to delineate the limits of the work. The analysis addresses the interpretation of Windkessel parameters in the systemic circulation only, does not tackle the uncertainty inherent in estimating those parameters from clinical data, excludes the pulmonary circulation, and does not examine how the derived load expressions relate to pressure-flow behavior in living vessels. No new human or animal data were collected, so ethics approval was not required. Even so, the central message is likely to resonate widely among physiologists and clinicians who use Ea to gauge ventricular afterload: the stiffness of the arteries and the rhythm of the heart are not independent contributors to cardiac load but are woven together by the clock of the cardiac cycle, and any formula that ignores that coupling risks misreading how hard the heart truly works.

Subject of Research: The dependence of effective arterial elastance on arterial compliance and cardiac cycle timing in a Windkessel model of the systemic circulation

Article Title: Cardiac timing modulates the contribution of compliance to effective arterial elastance

Article References: Murchie, T. (2026). Cardiac timing modulates the contribution of compliance to effective arterial elastance. Physiological Reports, 14(19), Article e71112. https://doi.org/10.14814/phy2.71112

Image Credits: AI Generated

DOI: 10.14814/phy2.71112

Keywords: effective arterial elastance, arterial compliance, Windkessel model, cardiac timing, diastole, heart rate, ventricular afterload, end-systolic pressure, stroke volume, hemodynamics, cardiovascular physiology, mathematical modeling