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This paper presents an embedding framework for myocardial velocity processing with MRI based on a hollow, semi-spherical template. The relationship between vector bundle and manifold mapping is analysed and three different mapping methods that include tangent mapping, normal mapping, and normal-tangent mapping are assessed for their practical value of myocardial contractility analysis. The proposed method provides a basis for consistent volume matching and vector correspondence, in addition to the ease of calculating biomechanical indices such as radial, circumferential and longitudinal strain rates without the concern of boundary effects. Detailed analysis results with both synthetic and in vivo MR velocity data sets are provided. [ABSTRACT FROM AUTHOR]