Complexity Measures in Biomedical Signal Analysis: A Clinically-Grounded Survey Across EEG, ECG, Intracranial Pressure, and Photoplethysmogram Modalities

Biomedical signals such as electroencephalogram (EEG), electrocardiogram (ECG), intracranial pressure (ICP), and photoplethysmogram (PPG) encode complex dynamical patterns that reflect the adaptive control of physiological systems. Complexity analysis—through entropy, compression, and causality metrics—has emerged as a critical tool for early diagnosis, risk prediction, and continuous monitoring in clinical and wearable settings. This review presents a clinically grounded synthesis of key complexity measures, including Sample Entropy (SampEn), Permutation Entropy (PE), Lempel–Ziv Complexity (LZC), and Effort-to-Compress (ETC), as well as causal inference techniques like Granger Causality, Transfer Entropy, and Compression–Complexity Causality (CCC). Applications across neurological and cardiovascular pathologies—such as epilepsy and sudden unexpected death in epilepsy (SUDEP)—are examined alongside signal-specific preprocessing, interpretability, and statistical validation strategies. We further evaluate the feasibility of deploying these measures in real-time on constrained hardware platforms—microcontrollers, FPGAs, and RISC–V-based SoCs—highlighting their suitability for embedded health systems and remote diagnostics. The review also explores synergistic integration with explainable machine learning, showing how complexity-informed features can enhance both performance and interpretability. By bridging signal complexity with hardware-aware deployment, ML transparency, and clinical translation, this work aims to guide the development of scalable, interpretable, and secure biomedical analytics for next-generation digital health systems.