Oscillatory Components of Bidirectional Cardio-Respiratory Coupling in Depression and Suicidal Ideation: Insights from Swarm Decomposition and Entropy Analysis

Herbert F Jelinek^1*Mohanad Alkhodari²Ahsan H Khandoker¹Leontios J Hadjileontiadis¹

• ¹Khalifa University, Abu Dhabi, United Arab Emirates
• ²Oxford University, Oxford, United Kingdom

Introduction Major depressive disorder (MDD) and MDD with suicidal ideation (MDDSI) present with heterogeneous symptoms, complicating diagnosis and treatment. Precision psychiatry addresses this challenge by applying computational methods and digital biomarkers to objectively distinguish psychiatric states. While psychiatric research has traditionally focused on neural activity, increasing evidence highlights the value of autonomic indices, particularly heart rate variability (HRV), in capturing clinically relevant dysregulation. Cardio-respiratory coupling (CRC), which reflects bidirectional interactions between cardiovascular and respiratory systems, represents a physiologically grounded extension of this approach. Although less frequently applied in psychiatry compared to HRV, CRC offers a sensitive window into autonomic network dynamics and holds promise for differentiating between MDD and MDDSI. Methods A total of 74 participants were assigned to Control (n=35), MDD (n=21), or MDDSI (n=18) groups. ECG, PPG, and respiratory signals were recorded at rest and segmented into two-minute intervals. Swarm Decomposition (SwD) was applied to extract four oscillatory components (OC1–OC4) from each signal that go from low to high frequency, respectively. Fractal dimension (Higuchi, Katz) and Shannon entropy quantified coupling complexity. Bidirectional (λbi) and unidirectional (λ) coupling measures and phase angles were computed between respiratory signals and cardiovascular markers: pulse wave amplitude (PWA), pulse transit time (PTT), and pulse rate (PR). Group differences were evaluated using Kruskal-Wallis and post-hoc tests (p < 0.05). Results Bidirectional PR coupling in OC3 showed significant group differences (p < 0.01). Higuchi fractal dimension of PTT in OC3 was reduced in MDDSI compared to MDD and controls (p = 0.018), suggesting diminished complexity. For PWA in OC4, high-frequency power significantly differed between controls and MDDSI (p = 0.004). Directional coupling entropy also distinguished MDD from MDDSI (p = 0.039). Conclusion This study reveals that frequency-specific disruptions in bidirectional cardiorespiratory coupling, along with reduced signal complexity and entropy, are characteristic of MDDSI. These features may reflect impaired autonomic adaptability and emotional regulation. Phase-based coupling metrics and SwD show promise as physiological biomarkers for early identification of high-risk depressive states in digital psychiatry.