Assessment of cardiopulmonary physiological modulation using multilayer visibility graph analysis of ECG and respiration signals

Objective. This study aimed to quantify cardiopulmonary physiological modulation in patients with hypertension (HTN) and ischaemic heart disease (IHD) using electrocardiogram (ECG) and respiration signals recorded before and after a 7 d Panchakarma-based integrative residential programme. Approach. Simultaneous 10 min ECG and respiration recordings were acquired before and after the programme. A predefined signal-quality pipeline was applied before graph construction. ECG-derived cardiac dynamics were based on normal-to-normal (NN) intervals after artefact and ectopy screening, while respiration cycles were screened for physiologically plausible breath intervals. From each acceptable recording, a clean 300 s segment was selected. NN-derived heart rate (HR) and respiration-rate series were interpolated to a common 4 Hz time base, detrended and standardised. Natural visibility graphs (VGs), weighted VGs and a two-layer multilayer VG (MLVG) were then constructed using synchronous HR-respiration interlayer coupling. Graph index complexity (GIC), average path length, assortativity and pulse-respiration quotient PRQ-derived features were analysed using paired Wilcoxon signed-rank tests with Hodges–Lehmann paired differences and false discovery rate correction. Main results. After quality control, alignment and graph-eligibility screening, paired graph-feature analysis included 20 HTN and 26 IHD subjects. The alignment procedure produced complete HR-respiration time series with negligible missing fractions. Post-program recordings showed measurable cardiopulmonary modulation. In HTN, PRQ decreased with false-discovery-rate-supported significance, while weighted GIC features showed descriptive post-program increases. In IHD, unweighted respiration-VG and MLVG GIC increased descriptively, whereas weighted and path-based metrics showed heterogeneous changes. Interlayer surrogate validation further quantified whether identity-coupled MLVG complexity exceeded shifted-coupling null networks. Significance. The proposed framework provides a reproducible ECG-respiration network-physiology workflow combining NN-based quality control, respiration-cycle screening, common-time-base alignment, unimodal and multilayer VG modelling, PRQ analysis and surrogate validation. The findings support objective quantification of post-program cardiopulmonary modulation while avoiding causal attribution to Panchakarma alone.