Propagación y activación de estímulos eléctricos en el músculo cardíaco
The interdisciplinary study of the flow of energy-matter-information in cardiac electrophysiology from the mathematical perspective and computational simulation, allowed to demonstrate characteristic aspects of complexity sciences and complex systems, such as non-linear dynamics, sensitivity of initial-conditions, autoorganization in non-equilibrium systems and emergence of patterns. This is particularly notable when considering a non-isotropic excitable medium, as occurs with the propagation and activation of electrical impulses in the heart, whose fibers not only change their orientation altering the speed depending on the thickness of the epicardium, myocardium and endocardium, but also present the properties of excitability, conductance, automatism, contractility and relaxation in the description of the normal and abnormal functioning of the heart when pumping blood to drive oxygen and other nutrients to tissues, remove waste products and transport substances, such as hormones, from one part of the body to another.
The objectives of this thesis can be summarized in three main chapters: i) Introduction to the complexity sciences and complex systems from the physiological foundations of wave propagation in excitable media at cellular level and from anisotropic heart tissue; ii) Mathematical modeling of electrical activity with temporary dynamic systems, discrete and continuous models, such as automata and specific ionic models at the cellular level, and for cardiac tissue, with reaction-diffusion systems such as the bidomain and monodomain model, respectively; iii) Mathematical formulation of anisotropic conduction to perform simulations of electrophysiological models with code development in the Matlab® environment. Application software designed for the UACM Master’s Degree in Complexity Sciences and, analysis of international standards for the exchange of information between mathematical-computer models of the organisms components: organs, cellular systems, biochemical and endocrine systems.
