Approximation of various canine left ventricular end-systolic relations by a cylinder model

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.