997-88 Ventricular Remodeling During Pacing Induced Congestive Heart Failure: The Logarithmic Model of Passive Properties is Physiologically and Mathematically Superior to the Exponential Model!

Ventricular remodeling is an important adaptation to both physiologic and pathologic stress and is accompanied by changes in passive myocardial and chamber properties. The analysis of remodeling and its subsequent effect on the dynamics of both systolic and diastolic function, requires the use of an appropriate mathematical characterization. We compared the exponential and logarithmic models in a study of ventricular dilatation following four weeks of rapid ventricular pacing (240/min) in dogs. We start by rejecting the relation, P = Ae kV , because it does not allow for a positive value of the equilibrium volume, V o , ie, the volume at zero transmural pressure, and we use: P = P ∞ [e k(V-Vo) -1], so that stiffness is given by: dP/dV = k(P + P ∞ ). Thus, both k and P ∞ (the pressure asymptote) determine chamber stiffness. It is important to note the mathematical limitations of an exponential: because P ∞ is small and because the equation is asymptotic to the volume axis, there is a strong tendency to underestimate V o , often giving negative values when using nonlinear regression analyses. These mathematical and physiological problems are overcome by the logarithmic model: P = –SpIn[(V m –– V)/(V m –– V o )]; dP/dV = Sp/(V m — V), where Sp is a stiffness parameter in the positive plane, and V m is the maximum physiologic volume that the ventricle can tolerate. Vo, an important parameter in remodeling, is accurately determined because the equation is not asymptotic to the volume axis. Furthermore, Sp has the units of stress and thus characterizes the myocardium, and, when normalized by the operating volume, V m –– V o , the chamber. S p (mmHg) V m (ml) V o (ml) P ∞ (mmHg) α (l/ml) C 9 ± 4 80 ± 15 39 ± 11 7 ± 3 0.03 ± 0.01 HF 6 ± 2 159 ± 31 97 ± 15 2 ± 1 0.04 ± 0.02 pg 0.03 0.0001 0.0001 0.0001 NS Thus, in this model of heart failure, chronic depression of contractility requires constant use of the Frank-Starling mechanism to maintain cardiac output, and the ventricle remodels by dilating (both V m and V o increased) as well as by increasing compliance (Sp decreased). This growth pattern is adaptive, although it may not allow regression. The exponential model failed to show a change in stiffness. The logarithmic approach is both physiologically and mathematically superior.