The heart’s left ventricle (LV) has an intrinsically optimal ellipsoidal shape that efficiently contributes to its contractility. We start with this below figure,depicting the LV simulating geometrical model, as a prolate ellipsoid truncated 50% of the distance from equator to base. Based on this figure, we define:
LV shape factor: S = SA/LA (1)
Figure. LV ellipsoidal model geometry: SA = AP/2 and LA = BA/1.5, where AP and BA are the major and minor axes of the LV ellipsoid.
The values of SA and LA can be determined from the echocardiographic monitored values of the LV volume (V) and myocardium volume (VM), given by: VM = 9 π [2 LA x SA² + SA²]h/8 (2) V = 9 π SA² LA/8 (3) wherein V is LV volume, VM is myocardial volume, h is wall-thickness, LA and SA are endocardial major and minor radii. We then define V*= VM /V. Based on the left ventricular ellipsoidal shell model, we can express the circumferential pressure-normalized LV wall stress * (= /P), at the waist of the LV ellipsoidal model, as: (4) This equation provides *as a function of shape factor S, for a given V*. Then the LV contractility index is given by d*/dtmaxwhich is a function of both S and V* (= VM /V). We can thereby employ this LV contractility index which is also shown to be closely related to the conventional contractility index dP/dtmax. Now, based on the 3-d reconstructed surface images of normal LV and ischemic cardiomyopathic (ICM) LV, we have noted that a normal LV is more ellipsoidal in shape compared to the ICM LV. We have also noted that (i) the normal LV becomes more ellipsoidal from end-diastole (ED) to end-systole (ES)with greater reduction in shape factor (S), and (ii) also smaller in size (i.e. greater decrease V and hence greater increase in V*, compared to the ICM LV. In other words, the shape & size factor (S/ V*) decreases far more from the start of ejection (se) to the end of ejection (ee) in the normal LV compared to the ICM LV. So, then based on all these findings, we can now define a simplistic and yet very effective LV Shape &Size Factor-based nondimensional Contractility Index (LVSCI): LVSCI = [(S/ V*)se - (S/ V*)ee ]/ (S/ V*)se x 100 % (5) where se denotes start of ejection and ee denotes end of ejection. Based on thclinical studies data, it is shown that (i) for Group 1 with normal contractility, LVSCI = 70 and the traditional contractility indexdP/dtmax= 1406 mmHg/s, whereas (ii) for Group 3, with poor contractility LVSCI = 47 and dP/dtmax= 948 mmHg/s. This represents a big testimony of the validity and novelty of our LV shape & size based nondimensional contractility Index LVSCI. which can be totally based on LV echocardiographic imaging of LV volume and its myocardial volume only.
