AJP - Heart and Circulatory Physiology, Vol 258, Issue 5 1300-H1311, Copyright © 1990 by American Physiological Society
Approximation of various canine left ventricular end-systolic relations by a cylinder model
K. Takeda, M. Takeda, T. Shimizu and S. Yagi
Department of Medicine, Dokkyo University School of Medicine, Japan.
Assuming a linear end-systolic force-length relation and a cylindrical
geometry of the left ventricle (LV), we have developed a mathematical model
(cylinder model) and derived formulas for LV end-systolic force-diameter
(Fes-Des), stress-diameter (Ses-Des), pressure-diameter (Pes-Des), and
pressure-cylinder volume (Pes-Ves) relations. To assess the validity of
this model for the study of the intact LV, eight healthy beagles were
instrumented with ultrasonic crystals to measure LV diameter and wall
thickness and a micromanometer to measure LV pressures. Preload was altered
by vena caval occlusion. Contractility was increased by addition of Ca2+.
Fes-Des relation was nearly linear under control contractility, whereas
after addition of Ca2+ this relation became concave toward the diameter
axis. Linear approximation was more accurate for this relation than for the
Pes-Des and Pes-Ves relations in control contractility. Predictions from
the model formulas more accurately reproduced observed data in the Pes-Des
(P less than 0.01) and Pes-Ves (P less than 0.001) relations than those
from linear regression equations, whereas the model predictions for the
Ses-Des relation were as accurate as those of a linear regression equation.
Although the slope of the Fes-Des relation increased with inotropic
stimulation, diameter intercepts of this relation did not change. Thus the
present results obtained under control contractility were consistent with
assumptions of the model. This cylinder model might provide reasonable
approximations for various canine LV end-systolic relations.
