Determinants of stroke volume and systolic and diastolic aortic pressure

We investigated how parameters describing the heart and the arterial system contribute to the systolic and diastolic pressures (Ps and Pd, respectively) and stroke volume (SV). We have described the heart by the varying-elastance model with six parameters and the systemic arterial tree by the three-element windkessel model, leading to a total of nine parameters. Application of dimensional analysis led to a total of six dimensionless parameters describing dimensionless Ps and Pd, i.e., pressures with respect to venous pressure (Ps/Pv and Pd/Pv). SV was normalized with respect to unloaded ventricular volume (Vd). Sensitivity analysis showed that Ps/Pv, Pd/Pv, and SV/Vd could be accurately described by four, three, and three dimensionless parameters, respectively. With this limited number of parameters, it was then possible to obtain empirical analytical expressions for Ps/Pv, Pd/Pv, and SV/Vd. The analytic predictions were tested against the model values and found to be as follows: Ps predicted = (1.0007 +/- 0.0062) Ps, r = 0.987; Pd predicted = (1.016 +/- 0.0085) Pd, r = 0.992; and SV predicted = (0.9987 +/- 0.0028) SV, r = 0.996. We conclude that aortic Ps, Pd, and SV can be accurately described by a limited number of parameters and that, for any condition of the heart and the arterial system, Ps, Pd, and SV can be presented in analytical form.