Modelos matemático-computacionais do sistema cardiovascular humano a parâmetros condensados e aplicações

Abstract

Advances in computing performance in last decades have led to increasing developments in Mathematical and Computational Modeling. The main advantage of mathematical-computational models is the ability to represent and simulate reality, generating descriptive and predictive results about the modeled phenomenon. Following this trend of recent decades, the application of mathematical models has been increasingly intense in medicine and other health sciences. Mathematical-computational models act as auxiliary tools in the medical field, both in clinical and surgical decision making, as well as in teaching and research. In particular, mathematical models of blood flow in the Human Cardiovascular System (HCVS) have been developed and improved. This Course Conclusion Paper addresses mathematical models of HCVS to condensed parameters, that is, mathematical descriptions of hemodynamic quantities by ordinary differential equations that take into account the temporal evolution of physical variables present in the circulation. These models were used in two applications: in the elaboration of an HCVS simulator - SimulCárdio - for educational purposes for undergraduate medical students and in an inverse problem study to estimate hemodynamic parameters in order to more accurately simulate cardiovascular pathologies.