Physical determinants of left ventricular isovolumic pressure decline: model prediction with in vivo validation

The rapid decline in pressure during isovolumic relaxation (IVR) is traditionally fit algebraically via two empiric indexes: tau, the time constant of IVR, or tau(L), a logistic time constant. Although these indexes are used for in vivo diastolic function characterization of the same physiological process, their characterization of IVR in the pressure phase plane is strikingly different, and no smooth and continuous transformation between them exists. To avoid the parametric discontinuity between tau and tau(L) and more fully characterize isovolumic relaxation in mechanistic terms, we modeled ventricular IVR kinematically, employing a traditional, lumped relaxation (resistive) and a novel elastic parameter. The model predicts IVR pressure as a function of time as the solution of d(2)P/dt(2) + (1/mu)dP/dt + EkP = 0, where mu (ms) is a relaxation rate (resistance) similar to tau or tau(L) and E-k (1/s(2)) is an elastic (stiffness) parameter (per unit mass). Validation involved analysis of 310 beats (10 consecutive beats for 31 subjects). This model fit the IVR data as well as or better than tau or tau(L) in all cases (average root mean squared error for dP/dt vs. t: 29 mmHg/s for model and 35 and 65 mmHg/s for tau and tau(L), respectively). The solution naturally encompasses tau and tau(L) as parametric limits, and good correlation between tau and 1/mu E-k (tau = 1.15/mu E-k - 11.85; r(2) = 0.96) indicates that isovolumic pressure decline is determined jointly by elastic (E-k) and resistive (1/mu) parameters. We conclude that pressure decline during IVR is incompletely characterized by resistance (i. e., tau and tau(L)) alone but is determined jointly by elastic (Ek) and resistive (1/mu) mechanisms.