Mathematical model that characterizes transmitral and pulmonary venous flow velocity patterns. 1995

Y Sun, and B J Sjöberg, and P Ask, and D Loyd, and B Wranne
Department of Electrical Engineering, University of Rhode Island, Kingston 02881.

The transmitral and pulmonary venous flow velocity (TMFV and PVFV, respectively) patterns are related to the physiological state of the left heart by use of an electrical analog model. Filling of left ventricle (LV) through the mitral valve is characterized by a quadratic Bernoulli's resistance in series with an inertance. Filling of the left atrium (LA) through the pulmonary veins is represented by a lumped network of linear resistance, capacitance, and inertance. LV and LA are each represented by a time-varying elastance. A volume dependency is incorporated into the LV model to produce physiological pressure-volume loops and Starling curves. The state-space representation of the analog model consists of 10 simultaneous differential equations, which are solved by numerical integration. Model validity is supported by the following. First, the expected effects of aging and decreasing LV compliance on TMFV and PVFV are accurately represented by the model. Second, the model-generated TMFV and PVFV waveforms fit well to pulsed-Doppler recordings in normal and postinfarct patients. It is shown that the TMFV deceleration time is prolonged by the increase in LV compliance and, to a lesser extent, by the increase in LA compliance. A shift from diastolic dominance to systolic dominance in PVFV occurs when LA compliance or pulmonary perfusion pressure increases or when LV compliance or mitral valve area decreases. The present model should serve as a useful theoretical basis for echocardiographic evaluation of LV and LA functions.

UI MeSH Term Description Entries
D008955 Models, Cardiovascular Theoretical representations that simulate the behavior or activity of the cardiovascular system, processes, or phenomena; includes the use of mathematical equations, computers and other electronic equipment. Cardiovascular Model,Cardiovascular Models,Model, Cardiovascular
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D009131 Muscle, Smooth, Vascular The nonstriated involuntary muscle tissue of blood vessels. Vascular Smooth Muscle,Muscle, Vascular Smooth,Muscles, Vascular Smooth,Smooth Muscle, Vascular,Smooth Muscles, Vascular,Vascular Smooth Muscles
D011652 Pulmonary Circulation The circulation of the BLOOD through the LUNGS. Pulmonary Blood Flow,Respiratory Circulation,Circulation, Pulmonary,Circulation, Respiratory,Blood Flow, Pulmonary,Flow, Pulmonary Blood,Pulmonary Blood Flows
D011667 Pulmonary Veins The veins that return the oxygenated blood from the lungs to the left atrium of the heart. Pulmonary Vein,Vein, Pulmonary,Veins, Pulmonary
D001783 Blood Flow Velocity A value equal to the total volume flow divided by the cross-sectional area of the vascular bed. Blood Flow Velocities,Flow Velocities, Blood,Flow Velocity, Blood,Velocities, Blood Flow,Velocity, Blood Flow
D001794 Blood Pressure PRESSURE of the BLOOD on the ARTERIES and other BLOOD VESSELS. Systolic Pressure,Diastolic Pressure,Pulse Pressure,Pressure, Blood,Pressure, Diastolic,Pressure, Pulse,Pressure, Systolic,Pressures, Systolic
D003971 Diastole Post-systolic relaxation of the HEART, especially the HEART VENTRICLES. Diastoles
D006321 Heart The hollow, muscular organ that maintains the circulation of the blood. Hearts
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man

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