Formalism of Euler's Graph Theory is Suitable for Natural Etiopathogenetic Pathways and Clusters Mapping - Integrative Study of Pathophysiology

Leonard Euler (1707–1783) introduced the graph theory, a special part of geometry, as a tool to “… deal with relation dependent on position alone, and investigates properties of the position; it does not take magnitude into consideration, nor it does involve calculation …”. Graph theory is useful concept for nonlinear complex systems. As non‐numerical and non‐metric mathematical reasoning, it describes a complex system as a net of multiple events, seen as a whole. Similarly, graphic representation of physiological networks has an advantage in comparison with traditional narrative descriptions. We invented matrix guided analysis and re‐synthesis method to outline and visualize etiopathogenetic pathways and their natural interconnectivity. It is four steps method (consisting of a patient problem exposition, repetition of relevant knowledge, a design of algorithm and systematization) that enforces the horizontal, vertical and longitudinal integration of knowledge. The algorithmic pathways and networking of processes are crystallized out of plethora of clinical data (signs, symptoms, dysfunctions, outcomes, etc) and knowledge of sub‐systems (nano‐molecular, thermal, macromolecular, cellular phenomena, etc.), which are largely acquired via reductionistic methodologies. Algorithmic pathophysiology elaboration has revealed a natural tendency to form common crossing points of reactivity of heterogeneous pathways. The pathways spontaneously converge and form etiopathogenetic clusters (EPCs) . EPCs integrate multiple inputs and multiple exits. They look like natural integrators, the common “hubs” of human body response in various diseases. 91 EPCs have been identified at multiple levels of hierarchy of human body disease reactivity. EPCs are shared in natural development of heterogeneous conditions and they show tendency to form a network. Among the EPCs connecting pathways serve as “the EPC‐driving force”. Thus, the EPCs may be seen as “a new emerging feature” of pathophysiology foundation of disease. Following Euler’s strategy directed links in‐between elements of algorithm indicate a “physiological flux”, mutual oriented influence, and/or cause‐consequence. Physiological relations among acting elements have directionality of action, feedback and feed‐forward regulatory loops. Graphic maps outline the parallel pathways and easily put together relevant events of nano‐scale analyses with the clinical macro‐scale level. The (EPCs) are crossing and integrating points of complexity networks. The network visualization of physiology of disease and health underlying processes places individual mechanisms within the complex interconnectivity and may contribute to explanation of nonlinearity phenomena.