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Stiffness and relaxation components of the exponential and logistic time constants may be used to derive a load-independent index of isovolumic pressure decay

Cardiovascular Biophysics Laboratory, Cardiovascular Division, ¹Department of Internal Medicine, ²Department of Physics, College of Arts and Sciences, ³Division of Biology and Biomedical Sciences, Washington University School of Medicine, Saint Louis, Missouri

Submitted 24 July 2008 ; accepted in final form 17 October 2008

In current practice, empirical parameters such as the monoexponential time constant or the logistic model time constant _L are used to quantitate isovolumic relaxation. Previous work indicates that and _L are load dependent. A load-independent index of isovolumic pressure decline (LIIIVPD) does not exist. In this study, we derive and validate a LIIIVPD. Recently, we have derived and validated a kinematic model of isovolumic pressure decay (IVPD), where IVPD is accurately predicted by the solution to an equation of motion parameterized by stiffness (E_k), relaxation (_c), and pressure asymptote (P) parameters. In this study, we use this kinematic model to predict, derive, and validate the load-independent index M_LIIIVPD. We predict that the plot of lumped recoil effects [E_k·(P*_max – P)] versus resistance effects [_c·(dP/dt_min)], defined by a set of load-varying IVPD contours, where P*_max is maximum pressure and dP/dt_min is the minimum first derivative of pressure, yields a linear relation with a constant (i.e., load independent) slope M_LIIIVPD. To validate the load independence, we analyzed an average of 107 IVPD contours in 25 subjects (2,669 beats total) undergoing diagnostic catheterization. For the group as a whole, we found the E_k·(P*_max – P) versus _c·(dP/dt_min) relation to be highly linear, with the average slope M_LIIIVPD = 1.107 ± 0.044 and the average r² = 0.993 ± 0.006. For all subjects, M_LIIIVPD was found to be linearly correlated to the subject averaged (r² = 0.65), _L(r² = 0.50), and dP/dt_min (r² = 0.63), as well as to ejection fraction (r² = 0.52). We conclude that M_LIIIVPD is a LIIIVPD because it is load independent and correlates with conventional IVPD parameters. Further validation of M_LIIIVPD in selected pathophysiological settings is warranted.

isovolumic relaxation; mathematical modeling; hemodynamics