RT info:eu-repo/semantics/bachelorThesis
T1 Modelización matemática de la fisiología cardíaca
A1 Mesa Gorrín, Gabriela
K1 Fisiología cardíaca
AB This study aims to explain, through a mathematical model, the physiology of the heart. Tothis end, the model proposed by Zeeman in 1972 has been chosen. It highlights threecharacteristics of the heartbeat cycle: it exhibits a state of equilibrium corresponding todiastole; it incorporates a triggering threshold of the electrochemical wave that emanatesfrom the pacemaker and causes the heart to contract in systole; and, finally, it reflects therapid return to the state of equilibrium.First, a local linearized model is obtained that explains the diastolic state through anautonomous system of differential equations. Next, in order to include the state of systolicequilibrium, some modifications are made to this system. To conclude the final form of themodel, the phase plane diagram associated with the resulting system is analyzed.Zeeman’s model is not the only one possible but, in addition to reflecting reasonably wellthe basic features of the heartbeat cycle, it has been quite successful in distinguishing someextreme forms of heartbeat behavior, such as the effects of high blood pressure or an excessof adrenalin in the bloodstream.The study concludes with a tentative modeling of the cardiac pacemaker firing mechanism.
YR 2019
FD 2019
LK http://riull.ull.es/xmlui/handle/915/17533
UL http://riull.ull.es/xmlui/handle/915/17533
LA es
DS Repositorio institucional de la Universidad de La Laguna
RD 09-nov-2024