||Impairment of left ventricular (LV) contractility due to cardiovascular diseases is reflected in LV motion patterns. The mechanics of any muscle strongly depends on the spatial orientation of its muscular fibers since the motion that the muscle undergoes mainly takes place along the fiber. The helical ventricular myocardial band (HVMB) concept describes the myocardial muscle as a unique muscular band that twists in space in a non homogeneous fashion. The 3D anisotropy of the ventricular band fibers suggests a regional analysis of the heart motion. Computation of normality models of such motion can help in the detection and localization of any cardiac disorder. In this paper we introduce, for the first time, a normalized parametric domain that allows comparison of the left ventricle motion across patients. We address, both, extraction of the LV motion from Tagged Magnetic Resonance images, as well as, defining a mapping of the LV to a common normalized domain. Extraction of normality motion patterns from 17 healthy volunteers shows the clinical potential of our LV parametrization.