Predicting systolic and diastolic aortic blood pressure and stroke volume in the intact sheep
We developed a mathematical model describing the interaction between the heart and the arterial system. The model was constructed and tested on basis of invasive hemodynamic data in six sheep. Data from a first group of three animals (49 cardiac cycles) were used to assess a template time-varying elastance curve for the left ventricle, while the baseline steady-state data of a second group of three animals were used to assess reference cardiac and arterial parameters in sheep. The model is fully characterized by nine parameters, which were converted into 6 dimensionless numbers using the Buckingham pi theorem. The model was then used to generate LV pressure and volume and aortic pressure and flow for 86 conditions obtained by varying parameters 50 to 200% of their reference value. Systolic (SBP) and diastolic (DBP) blood pressure and stroke volume (SV) were determined from these model-generated curves and multiple linear regression analysis yielded the following expressions: SBP = Pisovolumic [0.638 - 0.0773 Emax C + 0.0507 RC/T] (r2 = 0.89); DBP = Pisovolumic [0.438-0.0712 Emax C + 0.0655RC/T] (r2 = 0.88) and SV = LVEDV [1.265-1.040 LVEDV/(LVEDV - Vd) + 0.125 Emax C-0.0777RC/T] (r2 = 0.93) with Pisovolumic = Emax (LVEDV - Vd), Emax and Vd being the slope and intercept of the end-systolic pressure-volume relation, R and C the total peripheral resistance and compliance, LVEDV the left ventricular end-diastolic volume, and T the cardiac cycle length. These expressions were validated using data from the second group of three animals obtained during vena cava occlusion at baseline and during administration of dobutamine (61 cycles). The correlation between measured and predicted values was 0.98, 0.97 and 0.92 for SBP, DBP and SV, respectively. Compared to the measured values, SBP and DBP were, on average, underestimated by 5 and 6mmHg, respectively, and SV overestimated by 1.4 ml. We conclude that the derived expressions for blood pressure and stroke volume remain valid in the intact sheep for various hemodynamic conditions, and, taking into account their dimensionless form, may hold in other species and in humans.