Coordination-dynamics invariants from simultaneous vagus nerve electroneurogram and ECG: a Python pipeline applied to neonatal piglet endotoxaemia
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HRV complexity metrics track the systemic cytokine response across mammalian inflammation models, but the dynamical mechanism translating molecular inflammation into HRV structure has remained unresolved, and no existing tool jointly extracts coordination-dynamics signatures from simultaneous vagus nerve electroneurogram (VENG) and ECG. We describe a modular open-source Python pipeline that (i) detects spectrally distinct latent states in 20 kHz whole-trunk VENG using a symmetric-Kullback–Leibler scan-statistic changepoint detector ported from earthquake seismology and verified against its R progenitor; (ii) places the inter-changepoint-interval series in the Haken–Kelso–Bunz coupled-oscillator framework, computes the Kuramoto order parameter R , fits the bistable potential V ( φ ) = − a cos φ − b cos 2 φ , and maps each timepoint into the Arnold-tongue (Ω, K ) plane; contrasts compound-action-potential band power between successive latent states; and (iii) couples the VENG analysis to a CIMVA HRV pipeline driven by a 5-algorithm Pro-MAC R-peak ensemble. Applied to a previously published two-animal neonatal piglet endotoxaemia cohort (Castel et al., 2020, 2024), the pipeline recovers known features of the (iv) preparation and surfaces three case-series observations that we frame as hypotheses for prospective replication: (1) a 6–8 s VENG state-switching period coincident with the HRV LF/HF spectral boundary; (2) qualitatively divergent coordination-dynamics trajectories under LPS versus LPS + VNS (Kuramoto R collapses from 0.69 to 0.12 without VNS, undergoes biphasic recovery to 0.99 with VNS, the two trajectories crossing at 60–75 min); (3) a regime-dependent empirical coupling between R and the HRV embedding scaling exponent eScalE ( R · eScalE ≈ 0.33 during moderate challenge, doubling to ≈0.80 during VNS overshoot). Pre-specified null comparisons (Poisson and bootstrap surrogates) demonstrate that R and the critical-slowing-down indicators carry information beyond their most obvious null alternatives. With N = 2 animals no inferential statistics are possible, so these findings are reported as hypothesis-generating; the manuscript closes with a pre-registered prospective protocol designed specifically to falsify them.
Graphical Abstract
Key Points
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We present an open-source Python pipeline that extracts coordination-dynamics invariants (Kuramoto phase coherence, Haken–Kelso–Bunz potential parameters, Arnold-tongue position, critical-slowing-down indicators) from simultaneously recorded vagus nerve electroneurogram (VENG) and ECG, starting from a spectral-KL scan-statistic changepoint detector ported from earthquake seismology.
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Applied to a previously published two-animal cohort (Castel et al., 2024), the pipeline reveals that VENG alternates between two spectrally distinct latent states at a baseline period of 6–8 s that coincides with the HRV low-frequency/high-frequency spectral boundary (∼0.15 Hz). We propose the VENG latent-state oscillator as a candidate mechanistic generator of vagal LF HRV; this is a hypothesis motivated by the timescale match and is not established by the present data.
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In this cohort, LPS endotoxaemia and vagus nerve stimulation drove qualitatively divergent trajectories in the coordination-dynamics phase space (Kuramoto R : 0.69 → 0.12 without VNS; biphasic to R → 0.99 with VNS at the IL-6/IL-8 cytokine peak). Because the design provides one animal per arm, these are case-series observations and not a between-arm statistical comparison.
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Inter-changepoint-interval variance rose >100-fold roughly 15 min before overt state-switching collapse in the unmitigated animal. Bootstrap nulls drawn from the same animal’s pre-collapse ICI pool reject the same-distribution alternative (§2.6), motivating a critical-slowing-down early-warning hypothesis that requires prospective replication before any clinical use is warranted.
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The pipeline surfaces a regime-dependent empirical coupling between VENG phase coherence ( R ) and HRV embedding scaling exponent (eScalE) in the VNS-treated animal: during moderate challenge R · eScalE ≈ 0.33 (CV ≈ 0.20), during VNS-enhanced overshoot (45, 90, 105 min) the product doubles to ≈0.80. The product is a post-hoc empirical construct, not a derived conservation law; we propose it as a falsification target for prospective cohorts (§6).
