Utility and limitations of linear models for echocardiographic estimation of left ventricular ejection fraction by segmental wall-motion scoring. A geometric analysis.
Although the geometric relation between left ventricular (LV) volume and its internal dimensions is nonlinear, recent clinical study has shown that LV ejection fraction (EF) predicted by a linear combination of segmental contraction scores correlates well with the EF by radionuclide angiography. To determine whether the linear coefficients found by empirical study are consistent with basic geometric principles, we compared the LV EF obtained by exact geometric calculation to the EF predicted using a simple linear combination of segmental contraction scores over a wide range of segmental function, from marked dyskinesis to marked hyperkinesis. We found that an optimal linear equation for global EF on geometric grounds is: Global EF = 4 + 0.28xC1 + 0.24xC2 + 0.12xC3, where C1, C2, and C3 are the mean segmental contraction scores at the base, mid-left ventricle, and the apex, respectively. The EF predicted by this formula differs by less than 6 percentage points from the EF predicted by exact geometry when segmental contraction ranges from normal to akinetic, and the coefficients are in close accord with those found empirically by regression of linearly-derived EFs against the radionuclide EFs in 50 patients. However, when segmental contraction is significantly hyperkinetic or dyskinetic, agreement with the exact geometric formula is poor. We conclude that: (1) a linear combination of segmental contraction scores can provide reasonable estimates of LV EF over a broad range of contraction; (2) previous, empirically determined linear coefficients are consistent with geometric principles; and (3) exact, nonlinear formulas may be required for ventricles with significant degrees of hyperkinesis or dyskinesis.