A Comprehensive Framework for the Characterization of the Complete Mitral Valve Geometry for the Development of a Population-Averaged Model

Simulations of the biomechanical behavior of the Mitral Valve (MV) based on simplified geometric models are difficult to interpret due to significant intra-patient variations and pathologies in the MV geometry. Thus, it is critical to use a systematic approach to characterization and population-averaging of the patient-specific models. We introduce a multi-scale modeling framework for characterizing the entire MV apparatus geometry via a relatively small set of parameters. The leaflets and annulus are analyzed using a superquadric surface model superimposed with fine-scale filtered level-set field. Filtering of fine-scale features is performed in a spectral space to allow control of resolution, resampling and robust averaging. Chordae tendineae structure is modeled using a medial axis representation with superimposed filtered pointwise cross-sectional area field. The chordae topology is characterized using orientation and spatial distribution functions. The methodology is illustrated with the analysis of an ovine MV microtomography imaging data.