A unified method for assessing the observability of dynamic complex systems.

PROBLEM: Systems theory applied to biology and medicine assumes that the complexity of a system can be described by quasi-generic models to predict the behavior of many other similar systems. To this end, the aim of various research works in systems theory is to develop inductive modeling (based on data-intensive analysis) or deductive modeling (based on the deduction of mechanistic principles) to discover patterns and identify plausible correlations between past and present events, or to connect different causal relationships of interacting elements at different scales and compute mathematical predictions. Mathematical principles assume that there are constant and observable universal causal principles that apply to all biological systems. Nowadays, there are no suitable tools to assess the soundness of these universal causal principles, especially considering that organisms not only respond to environmental stimuli (and inherent processes) across multiple scales but also integrate information about and within these scales. This implies an uncontrollable degree of uncertainty.

METHODOLOGY: A method has been developed to detect the stability of causal processes by evaluating the information contained in the trajectories identified in a phase space. Time series patterns are analyzed using concepts from geometric information theory and persistent homology. In essence, recognizing these patterns in different time periods and evaluating their geometrically integrated information leads to the assessment of causal relationships. With this method, and together with the evaluation of persistent entropy in trajectories in relation to different individual systems, we have developed a method called Φ-S diagram as a complexity measure to recognize when organisms follow causal pathways leading to mechanistic responses.

RESULTS: We calculated the Φ-S diagram of a deterministic dataset available in the ICU repository to test the method's interpretability. We also calculated the Φ-S diagram of time series from health data available in the same repository. This includes patients' physiological response to sport measured with wearables outside laboratory conditions. We confirmed the mechanistic nature of both datasets in both calculations. In addition, there is evidence that some individuals show a high degree of autonomous response and variability. Therefore, persistent individual variability may limit the ability to observe the cardiac response. In this study, we present the first demonstration of the concept of developing a more robust framework for representing complex biological systems.