Regression Analysis of the Left-ventricular Isochoric Pressure Decay of the Heart: Four or Five Model Parameters?

Abstract

IntroductionBiophysical models predicting the relaxation of cardiomyocytes 1 take into account a lot more variables than regression models analysing the left ventricular relaxation in human and animal hearts. These isochoric (isovolumic) pressure decay curves are often described by an exponential 2 or logistic 3 time constant. Both these three-parametric regression models are regarded unsatisfactory 4,5 . Consequently, a four-parametric extension of the logistic (or: hyperbolic tangent) model was introduced 4 ,(Langer model), estimating initial, P 0 , and asymptotic, P ∞ , pressure, asymptotic time constant,ττ∞, and a shape factor, γ. This model encompasses both the exponential (by γ = 0) and the logistic (γ = 0.5) model, and it yields fairly normally distributed regression residua 6 .A recent series of articles 7,8,9 proposes a five-parametric model according to the well known differential equation of a damped oscillation, (2) to describe the isochoric pressure decay (kinematic Chung model). This results in three types of pressure decays, where (Eq. 2A) holds if β 2 < E, undercritical damping, (Eq. 2B) if β 2 = E, critical damping, and (Eq. 2C) if β 2 > E, overcritical damping. We unify the parameters by introducing the initial pressure change velocity, P 0 , and obtain in the respective case: Abstract Background Isochoric (isovolumic) cardiac pressure decay data were previously described by a four-parametric logistic (tangens hyperbolicus) regression model (Langer model). However, a five-parametric kinematic model (Chung model), according to the differential equation of damped oscillation, was recently introduced to describe the isochoric pressure fall. The present study clarifies (a) whether these five parameters can be reliably estimated from empirical pressure decay data and if the model excels the four-parametric one, and (b) whether the kinematic Chung model validly describes these pressure decays.

Left-Ventricular Pressure Relaxation and Diastolic Function of Isolated Working Mammalian Hearts at Hypothermia

“…A recent study [3], most related to the present one, utilises two three-parametric models, exponential Ex3 and logistic Lg3. However, by reasons given before [9], four model parameters are necessary, and Lg4 covers the isochoric pressure fall properly. Present results confirm that even the individual heart changes its isochoric LVP shape during temperature or heart rate alteration.…”