Step response analyses of the cardiovascular system and their application to the measurement of systemic and pulmonary vein compliances

A theoretical analysis of the step response in the closed cardiovascular system induced by a sudden shift of the right cardiac output curve predicted that if the relations of the right heart output (COr) and the total systemic capillary flow (CFs) to the systemic venous pressure (Psv) are linear, then the time course of Psv change will become monexponential with a time constant T given by T=Csv/(Gr + Gs), where Csv is the systemic vein compliance and Gr and Gs are the conductances of the transient COr - Psv and CFs - Psv relationships. A similar prediction was obtained for the time constant T of the pulmonary vein pressure (Ppv) response to the step change in the left cardiac output (COl) curve, pulmonary vein compliance (Cpv) and the conductances of the Col curve, and the pulmonary capillary flow (CFp) curve against Ppv. The actual Psv or Ppv changes following sudden alteration of the COr or COl curve by inflation and deflation of the balloon in the right or left atrium revealed monoexponential time courses. Semilogarithmic plots of the transient vein pressure changes yielded correlation coefficients of -0.995 ± 0.006 (means ± SD) in 11 curves for Psv and 0.977 ± 0.017 in 16 curves for Ppv (P<0.01). The assumed linearity of dynamic COr and COl curves was confirmed by beat by beat COr - Psv and COl - Ppv relationships during the step responses, except for the first few beats immediately after the balloon maneuver. The linearity of the dynamic CFs curve was examined by measuring CFs with a double-step balloon maneuver so as to cause rapid equilibrium between COr and CFs at varied moments of the transient process. The correlation coefficient between CFs and Psv thus obtained was 0.98 ± 0.04 (P<0.01). A similar linearity of the dynamic CFp -Ppv relationship was suggested from their steady-state curves. The values of Csv calculated from the experimental data were 1.70 ± 0.12 ml/mmHg/kg body wt in 11 curves and those of Cpv were 0.13 ± 0.03 ml/mmHg/kg in 15 curves. These results are mostly consistent with those previously reported.