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: τ, the time constant of IVR, or τ_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 τ and τ_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 ²P/dt2² + (1/μ)dP/dt + E_kP = 0, where μ (ms) is a relaxation rate (resistance) similar to τ or τ_L and E_k (1/s²) 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 τ or τ_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 τ and τ_L, respectively). The solution naturally encompasses τ and τ_L as parametric limits, and good correlation between τ and 1/μE_k (τ = 1.15/μE_k - 11.85; r² = 0.96) indicates that isovolumic pressure decline is determined jointly by elastic (E_k) and resistive (1/μ) parameters. We conclude that pressure decline during IVR is incompletely characterized by resistance (i.e., τ and τ_L) alone but is determined jointly by elastic (E_k) and resistive (1/μ) mechanisms.