Using ellipsoidal shell models without empirical corrections, calculated endocardial R in end-systole underestimated measured R by 12%, and calculated epicardial R overestimated measured R by 4%.
A mathematical model of the left ventricle using nested ellipsoidal shells provides a framework for analyzing fiber orientation, though it slightly misestimates systolic dimensions without empirical corrections.
The relations between end-diastolic ( D ) and end-systolic (S) cavitary volumes ( V c ), wall volumes ( V 10 ), and cavitary dimensions have been studied in the canine and human left ventricle. However, the models selected for left ventricular myocardium do not represent the real heart adequately for a fiber-by-fiber analysis of fiber orientation and sarcomere length during successive states of the ejection cycle. In this study, the endocardial and epicardial surfaces were postulated to be a nested set of truncated ellipsoidal shells of revolution where wall volumes were preserved from D to S. Shell dimensions on the semiminor and semimajor axes, R and Z , respectively, were related to V c and V w by two representations: confocal and nonconfocal. If the focal length C = ) 1/2 and C is the same for each shell, then the shells are confocal, otherwise they are nonconfocal. From measured V c , V w , and epicardial Z in D , shell dimensions were calculated for states D and S, using both confocal and nonconfocal representations, and compared with the measured dimensions. When no empirical corrections were made, the calculated endocardial R in S underestimated the measured R in S by 12%; moreover, the calculated epicardial R in S overestimated the measured R in S by 4%. Endocardial and epicardial C measured 3.73 ± 0.33 (SE) cm and 3.79 ±0.34 cm, respectively, in D and 3.77±0.11 cm and 3.71 ±0.10 cm, respectively, in S.
Streeter et al. (1973) studied Left ventricular myocardium mechanics. Confocal and nonconfocal representations of truncated ellipsoidal shells vs. Measured dimensions was evaluated on Shell dimensions (endocardial and epicardial R and C) in end-diastolic and end-systolic states. Using ellipsoidal shell models without empirical corrections, calculated endocardial R in end-systole underestimated measured R by 12%, and calculated epicardial R overestimated measured R by 4%.