Medical Diagnostics Using Nonlinear Dynamical Analysis

Medical diagnostics is a vital endeavor in which one studies the symptoms and causes of diseases in order to facilitate better healthcare outcomes. The medical diagnostic process is a complex and collaborative activity that involves clinical reasoning and information gathering to determine a patient's health problem.

One of the big questions in physiology is: what are the intrinsic differences between healthy (normal) and abnormal (pathological) functions/ systems in the human body? We can translate this physiological question to the nonlinear dynamics language as identifying the disparities between nonlinear dynamic-based features of healthy and pathological systems. Then, we can use nonlinear dynamics-based tools such as Largest Lyapunov exponent, fractal dynamics, network science, reconstructed phase space analysis, correlation dimension, detrended fluctuation analysis, recurrence plot, Poincaré plot, approximate entropy, multiscale entropy, sample entropy and many other sub-fields of nonlinear dynamics to explore the problem domain.

Looking at above figures, we can observe that at the smaller spatial scales, the time scales are also smaller (there is a correlation between spatial and temporal scales of the system). Arguably, the brain operates on multiple spatial and temporal scales more than any other organ.

The medical field is undergoing a transformation with the rise of personalized medicine. This approach focuses on individualized and tailored treatments, rather than broad population-based methods. The utilization of nonlinear system dynamics is seen as a crucial tool in advancing personalized medicine, with growing evidence supporting its use. The integration of computational methods like nonlinear dynamics, complexity science, AI, and ML will greatly aid in this effort. Related to the personalized medicine paradigm are the concepts of “digital twins" and “virtual physiological human". “Digital twin" or DT (also known as “the algorithm of you” or “the other digital me”) is a well-established concept. It is defined as a digital alter ego (extension) of each individual, based on the engineering concept of twinning complex machines, by modeling their functions, to monitor their past and present behavior. The “virtual physiological human" (VPH), or “in silico medicine", is defined as the use of individualized physiology-based computer simulations in all aspects of the prevention, diagnosis, prognostic assessment, and treatment of a disease and development of a biomedical product.