Radial and Axial Fractional Shortening for Rapid Estimation of Left Ventricular Ejection Fraction: A Computational Analysis

Abstract

BACKGROUND AND PURPOSE: Simpson Rule based planimetry remains the gold standard for left ventricular (LV) ejection fraction (EF) but due to sub-optimal endocardial delineation, planimetry is not feasible in many cases. The purpose of this study was to derive and to analytically evaluate the theoretical accuracy of several simple novel formulas for estimating EF in ventricles with uniform wall motion using only the radial diameter and axial length LV fractional shortening (FD and FL respectively), which are less subject to image quality limitations than planimetry. METHODS: A truncated ellipsoidal model of the LV at end-diastole and end-systole was assumed leading to a novel compact formula for directly calculating an exact EF that is identical to the Simpson Rule EF when the ventricle has ellipsoidal end-diastolic (ED) and end-systolic (ES) shapes. EFexact = 1− (1−FD)exp(2)×(1−FL) Three linear formulas were then developed to directly calculate an approximation to the exact EF without intermediate calculation of volumes. To avoid population selection bias in this initial investigation the linear coefficients were determined by an analytic graphical optimization procedure that minimized the EF errors compared to the exact EF over the full range of exact EFs from 0 to 80% (FD and FL in percent). #1) EF = 2×FD, #2) EF = 1.8×FD+4 #3) EF = 1.5×FD+0.6×FL+5 RESULTS: In single factor linear approximations #1 and #2, the EF difference from the exact EF was dependent on the ratio FL/FD, which is normally between 40 and 50%. Subject to the assumption of ellipsoidal LV shape at ED and ES, for ratios of FL/FD between 20% and 80%, and over EFs ranging from 0 to 55%, the calculated differences from the exact EF were less than 6 EF points. At extremes of the ratio, less than 20% or over 80%, or for EFs over 55%, the difference could reach or exceed 10 points. Formula #2 produced slightly smaller differences than formula #1. Formula #3 reduced the difference error substantially to less than 4 EF percentage points regardless of the FL/FD ratio except at EFs over 75%. CONCLUSIONS In uniformly contracting ventricles, simple linear formulas could provide rapid estimation of EF and may be helpful when image quality degrades planimetric EF accuracy, as well as in point-of-care echocardiography where planimetry is not feasible. Validation of these formulas through empirical testing is warranted.