A mathematical model of the dynamic geometry of the intact left ventricle and its application to clinical data

In this paper we examine the relations that may exist between the geometric variables most frequently used to describe left ventricular contraction. The left ventricle is represented by a thick-walled cylinder contracting both radially and longitudinally. For this model, wall thickening, mid-wall radius shortening and longitudinal axis shorteining can be shown to be uniquely related during contraction, whereas it can be demonstrated that internal radius shortening is not uniquely related to these variables, but is also determined by the specific geometry of the cylinder, expressed in terms of the mid-wall radius-to-wall thickness (R/h) ratio of the cylinder. Detailed analysis of the same variables in 44 normal subjects, 32 patients with aortic stenosis and 54 patients with valvular regurgitation (33 aortic and 21 mitral), strongly suggests that the same relations are also clinically applicable. For instance, ventricular longitudinal axis shortening can be estimated with some accuracy from the standard M-mode echocardiogram. Also, wall thickening can be viewed as the direct reflection of the shortening that occurs in the circumferential and longitudinal directions, whereas internal radius shortening is significantly influenced by the R/h ratio of the ventricle, a consideration which becomes important when analyzing results in patients with left ventricular hypertrophy.