Chaos theory, the mathematics of seemingly irregular behavior in deterministic systems, has been applied across a surprisingly wide range of medical fields, but a new systematic review concludes that the field remains fragmented, heterogeneous and hampered by poor reproducibility. The review, published in BMC Biomedical Engineering, screened 2,598 articles and included just 20 studies in its final analysis, spanning cardiology, neurology, oncology, epidemiology, health management, hematology, infectious diseases, pneumology, pharmacokinetics, physiotherapy, psychology, public health and telemedicine.
The systematic review was carried out under Cochrane’s international standards, with a search strategy using indexed terms from MeSH, DeCS and Emtree adapted to each database, including Embase, MEDLINE, SciELO and LILACS. The protocol was registered with PROSPERO under the identifier CRD42023491407. The search covered publications from January 1, 2010 to December 13, 2023, with no restrictions on study design or language. Two researchers independently and blindly screened titles and abstracts, with discrepancies resolved by a third reviewer, and the same procedure was applied during full-text screening and data extraction.
Chaos, as the authors describe it, is the non-periodic and seemingly irregular behavior of deterministic systems. A chaotic system is characterized by four main features: non-periodic behavior, strong sensitivity to initial conditions, dynamics that appear random despite being governed by deterministic rules, and intrinsic nonlinearity. Although such systems follow well-defined laws, their long-term behavior is difficult to predict, because it cannot be reliably extrapolated from observed trends. This makes chaos theory a powerful framework for analyzing data that might otherwise be dismissed as purely noisy or erratic, revealing underlying structures within apparent randomness.
These properties make the approach particularly suitable for studying biological systems, where variability, adaptation and multiscale interactions are fundamental. Physiological processes such as heart rate variability, neural activity and hormonal regulation often exhibit irregular fluctuations that cannot be adequately captured by linear models. The review’s authors note that healthcare systems themselves can be viewed as complex adaptive systems, further supporting the relevance of chaos-based approaches in medicine, although the application of chaos theory in medical sciences remains a subject of ongoing debate.
The methodologies used across the included studies were highly diverse, reflecting the algorithm-driven nature of the field. Studies relied on simulated data, observational data, or both, to quantify chaos in different settings. A variety of software tools were employed, including Python, R, Matlab, Benoit, Lyspect, Net Logo 5.3.1 and XPPAUT. Notably, only one study provided access to open-source code, a finding the review’s authors identify as a significant barrier to validation and wider adoption of these methods.
Most quantitative approaches were based on core concepts from chaos theory. Weissman and colleagues applied Poincaré plots and detrended fluctuation analysis to assess blood glucose dynamics, while Wurdeman and colleagues used the Lyapunov exponent to evaluate embedding dimensions and temporal dynamics of movement attractors. Oyama-Higa and colleagues employed the largest Lyapunov exponent to quantify instability in physiological signals related to the central nervous system, and Fang and colleagues applied the same measure to characterize pathological speech signals. Hewlett and colleagues used a binary box-counting method to perform fractal analysis of DNA sequences.
Additional techniques included the estimation of the Hurst exponent using wavelet-based methods to characterize nonlinear patterns in collective health behavior, and time-domain parameter estimation based on attractor and bifurcation theory. Pillai and colleagues combined adaptive chaos synchronization with grid search methods to estimate nonlinear parameters in pharmacological systems, while Dafilis and colleagues applied bifurcation analysis within a seasonally forced epidemiological model. Several studies focused on statistical testing for chaotic behavior: Schmidt and colleagues evaluated time reversibility and nonlinear prediction errors in cardiovascular signals, and Li and colleagues assessed power spectral density to explore chaotic dynamics in heart rate variability. Not all studies found evidence of chaotic behavior; Schmidt and colleagues, for instance, reported no such evidence in cardiovascular murmurs.
Network-based and machine learning approaches were also identified. Cheng and colleagues analyzed network entropy in cancer systems, Chiarucci and colleagues used a feed-forward neural network with the Levenberg–Marquardt algorithm, and Sarbaz and colleagues applied Elman networks and Petrosian’s algorithm to identify chaotic features in neurological signals. Yousefi and colleagues compared multiple machine learning models, including feedforward neural networks, adaptive neuro-fuzzy inference systems and recurrent neural networks, to optimize resource allocation in emergency departments, while Lee and colleagues developed a chaos-based authentication algorithm for telemedicine systems. On the practical side, Sarbaz and colleagues provided insights into the mechanisms underlying Parkinson’s disease symptoms and potential therapeutic approaches, Fang and colleagues contributed to improved detection of pathological speech, and Oyama-Higa and colleagues proposed real-time pulse-based indicators for mental health assessment.
The review also assessed methodological quality using the Strengthening the Reporting of Empirical Simulation Studies (STRESS) tool, adapted because many included studies relied on algorithmic and model-based approaches. The mean compliance across studies was 69 percent. All studies clearly described their modeling objectives, underlying assumptions and analytical results, but only 75 percent included schematic representations of their models, 90 percent reported data sources, and 95 percent described data preprocessing steps. While 90 percent specified their estimation methods, only 55 percent reported the software used. The lowest scores were observed in implementation and code availability, highlighting important limitations in reproducibility.
Looking forward, the authors argue that advancing this scientific paradigm requires not only demonstrating the presence of chaos, but also systematically linking these dynamics to clinically meaningful outcomes. They highlight the high computational demand of these methods, which require significant processing capacity, specialized expertise and time investment, as a barrier to broader adoption, though new computational techniques for estimating indicators such as Lyapunov exponents have shown improved performance over traditional methods. They also point to the integration of chaos theory with machine learning, including wavelet neural networks, convolutional neural networks, fuzzy systems and long short-term memory models, which have demonstrated improved predictive performance when applied to chaotic time series, and to reservoir computing as a promising framework for modeling complex nonlinear dynamics. The promotion of open-source development and reproducible research practices, they conclude, is essential for enabling researchers to replicate findings, compare methods and accelerate the translation of chaos-based approaches into clinical settings.
Subject of Research: Applications of chaos theory in medical sciences
Article Title: Recent applications of chaos theory in medical sciences: progress and challenges
Article References: Espinosa, O., Ordóñez, A., & Puentes, G. (2026). Recent applications of chaos theory in medical sciences: progress and challenges. BMC Biomedical Engineering, 8(1), Article 6. https://doi.org/10.1186/s42490-026-00111-0
Image Credits: AI Generated
DOI: 10.1186/s42490-026-00111-0
Keywords: chaos theory, systematic review, nonlinear dynamics, cardiology, neurology, oncology, Lyapunov exponent, machine learning, reproducibility, biomedical engineering, physiological signals, open-source code
News Source: Nathaniel Bowman. (October 29, 2026). Chaos theory finds footholds in cardiology, neurology and oncology, review finds. Scienmag.
