Reduced Order Modeling And Analysis Of Cardiac Chaos

Numerous physiological processes are functioning at the level of cells, tissues and organs in the human body, out of which some are oscillatory and some are non-oscillatory. Networks of coupled oscillators are widely studied in the modeling of oscillatory or rhythmical physiological processes. Phase-isostable reduction is an emerging model reduction strategy that can be used to accurately replicate nonlinear behaviors in dynamical systems for which standard phase reduction techniques fail. We apply strategies of phase reduction, or isostable reductions in biologically motivated problems like eliminating cardiac alternans to alleviate arrhythmia by applying energy-optimal, non-feedback type control solutions.

Cardiac fibrillation caused by self-sustaining spiral may occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. Phase-based reduction techniques can be implemented to formulate and solve optimal control problems to yield time varying external voltage gradients that can synchronize a collection of spiral waves pinned to a collection of heterogeneous obstacles.

Teleportation is a universal mechanism that can work as a potential low energy tool to terminate the spiral wave in excitable media. This concept is a fusion of dynamics of limit cycle and the study of excitable media which generates phase singularities of opposite chirality to consume its pair, which is the primary cause of such cardiac chaos.

Designing an optimal stimulus is an optimal control problem which relies on extensive mathematical computation and arduous in nature. Computations tend to become more complex as the system shows more nonlinearity and heterogeneity, as its degree of freedom increases. Data driven neural network models and deep learning techniques can be a good choice to extract the optimal solution without going through the underlying dynamics. The designed low energy optimal stimulus is equally effective to alleviate spiral waves.