Can the sagittal lumbar curvature be closely approximated by an ellipse?

Abstract

For the sagittal lumbar curvature, existing spinal models are based only on the anthropomorphic radiographic characteristics of one individual, or, at best, of only a few individuals. This raises questions of applicability of the modeling results to clinical situations. Because spinal coupling and loads on spinal tissues have been shown to be functions of the initial static posture, a rigorously derived neutral lumbar lordosis would be important for clinicians and spine researchers. This study presents modeling of the sagittal lumbar spine in the shape of an ellipse. Vertebral body and disc heights, derived from digitized lateral lumbar radiographs of 50 normal subjects, were used to create an ellipse along the posterior body margins from the inferior of T12 to the superior sacral base. Additional data to create an elliptical lumbar model were determined from a least-squares analysis of passing ellipses through the digitized posterior body points. This confirmed that an elliptical model closely fit the lumbar curvature with a least-squares error of 1.2 mm per digitized point. The elliptical model is approximately an 85 degrees portion of a quadrant. The semi-major and semi-minor axes, a and b, are parallel to the posterior body margin of T12 and parallel to the inferior body endplate of T12, respectively, with a semi-minor to semi-major radio of b/a=0.39. The elliptic model has a height-to-length ratio of H/L=0.963, where height is the vertical distance from inferior T12 to superior S1 and length is the arc length along George's line (along the posterior longitudinal ligament) from T12 to S1.