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<strong>European</strong> <strong>Conference</strong> on Ma<strong>th</strong>ematical and Theoretical Biology 2011 Keywords: endocytosis, Rab GTPAses, reaction-diffusion system, travelingwave solutions, cut-out switch, toggle switch 136
<strong>European</strong> <strong>Conference</strong> on Ma<strong>th</strong>ematical and Theoretical Biology 2011 Heart rate dynamics: models and measures <strong>of</strong> complexity (part II); Wednesday, June 29, 17:00 Teodor Buchner Cardiovascular Physics Group, Faculty <strong>of</strong> Physics, Warsaw University <strong>of</strong> Technology e-mail: buchner@if.pw.edu.pl Oscillations and synchronization in human circulatory system Human cardiovascular system exhibits interesting dynamics, which is expressed in beat-by-beat changes <strong>of</strong> such variables as heart rate (interbeat interval) and blood pressure. As <strong>th</strong>e system is complex, <strong>th</strong>e origin <strong>of</strong> <strong>th</strong>is dynamics is complex as well. Part <strong>of</strong> <strong>th</strong>e dynamics is <strong>of</strong> neural or electrophysiological nature, depending on <strong>th</strong>e functional state <strong>of</strong> <strong>th</strong>e heart muscle, which is an example <strong>of</strong> an active medium, subject to neural control. Ano<strong>th</strong>er part <strong>of</strong> <strong>th</strong>e dynamics is related wi<strong>th</strong> <strong>th</strong>e vascular response to <strong>th</strong>e hemodynamic heart action. This response depends on vascular resistance and on elastic properties <strong>of</strong> <strong>th</strong>e vascular wall. The resulting blood pressure and chemical properties (pH) are constantly monitored by specific receptors <strong>th</strong>at initiate neural reflexes, which applies neural control to specific variables. There are many independent mechanisms <strong>th</strong>at may be activated in order to respond to certain fluctuations. Moreover, <strong>th</strong>e characteristic times <strong>of</strong> different control loops may differ by order <strong>of</strong> magnitude. Ano<strong>th</strong>er source <strong>of</strong> complex oscillations, crucially important for homeostasis is <strong>th</strong>e respiratory system. All <strong>th</strong>e systems are interrelated in a complex way and give rise to <strong>th</strong>e complex cardiovascular dynamics. One <strong>of</strong> interesting phenomena <strong>th</strong>at arises in such a system is <strong>th</strong>e cardiorespiratory synchronization and <strong>th</strong>e related phenomenon <strong>of</strong> <strong>th</strong>e interdependence between short-term dynamics <strong>of</strong> blood pressure, heart rate and brea<strong>th</strong>ing. Bo<strong>th</strong> problems will be addressed in <strong>th</strong>e talk. 137
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