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Abstract

A correlation function of cardiac output and mean arterial pressure is presented for the human cardiovasular system. The function is developed using an energy transfer balance for a unit volume of blood which flows in the vascular system between the aorta and the vena cava. The energy transfer balance equates the energy utilized in the vascular system to the algebraic sum of the pulse energy, the kinetic energy and the potential energy in the vascular system. Each of these energies is defined in terms of the physiology of the cardiovascular system. Pulse energy is defined in terms of the work done by the heart on the aorta. Kinetic energy is defined in terms of the cardiac output and the potential energy is defined in terms of the diastolic pressure in the aorta. The utilization energy is equivalent to the energy transfer in the work done by the blood on the viscoelastic blood vessels, and to the frictional energy loss due to drag on the blood mass as it flows through the vascular system.The correlation function of cardiac output with mean arterial pressure demonstrates that the cardiac output is a double-valued function of the mean arterial pressure. The function also varies with the ratio of the fourth power of the Shear Modulus of the blood vessels to the third power of Young's Modulus. The function shows that mean arterial pressure minimizes for a cardiac output of approximately 51 per min when one holds the ratio of the elastic moduli constant. Further discussion indicates how clinicians can use the function, developed in this research, to interpret the experimental data obtained from cardiac output studies.