Estimation of Aortic Flow and Pressure Volume Loop by Optimal Control Theory (Special Section of Letters Selected from the 1995 Society Conference of IEICE)

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We have shown a non-invasive method for estimating transient changes in aortic flow and ventricular volume based on optimal control theory by using successful simulations of reported experimental data. The performance function to evaluate the optimality of the cardiovascular system was proposed based on physical, fluid mechanical and pathophysiological considerations. It involved the work of the ventricle, the rate of changes in the aortic flow and the ventricular pressure. We determined that the cardiovascular system operates optimally when the performance function has been minimized. The relative magnitudes of the reductions of changes in these terms were expressed by the weighting coefficients. The arterial system was described by the Wind Kessel model using arterial resistance, aortic compliance and aortic valvular resistance. We set boundary conditions and transitional conditions derived from the systolic and diastolic phases of the aortic flow and the arterial pressure. The optimized system equations were converted to 6 linear simultaneous differential equations with 6 boundary conditions. The optimal ventricular pressure and aortic flow rate that minimize the performance function were obtained by solving these differential equations. By alternating the weighting coefficients of the work of ventricle and the rate of change in the ventricular ejection pressure, successful simulations of the ventricular pressures recorded from human subjects and those from isolated canine ventricle were obtained. Once the sets of weighting coefficients had been determined by successful simulations of ventricular pressures, the calculated aortic flow curves and pressure volume loops by the present method coincided with the reported experimental data. The changes in ventricular pressure and aortic flow produced by alternating the weighting coefficients to simulate the reported ventricular pressures and aortic flow curves under the different afterload conditions were consistent with biophysical experimental data. The present method is useful to estimate aortic flow curve and ventricular pressure volume loops non-invasively.
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1996-05-25

Estimation of Aortic Flow and Pressure Volume Loop by Optimal Control Theory (Special Section of Letters Selected from the 1995 Society Conference of IEICE)

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