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 oh 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 estimata aortic flow curve and ventricular pressure volume loops non-invasively.

The pressure waveforms indicated on a catheter manometer system are subject to serious distortion due to the resonance of the catheter itself, or the compliance of a particular transducer. Although several methods have been proposed for improving those characteristics, they ahave never been put into practice. We have focused on the transfer function of the catheter manometer, and made a pilot system, using the natural observation method. This method has been suggested as a means of studying the structure of the instantaneous waveform. In this manner, we were able to increace the bandwidth in the ferquency domain and reduce the ringing in the time domain. Correction was performed automatically, using a step wave. Reproduction of the waveform with a flushing device, was a task of equal simplicity, that allowed us to estimate the system parameters so that the response waveform became step-like. In the experiment, our system provided distortion-free left-ventricular pressure waveform measurements and exact evaluation of the cardiac pumping system. The values obtained came much closer to the original figures arrived at by the catheter-tip manometer system.