The mitral valve plays a critical role in unidirectional blood flow within the heart, but is prone to pathologies requiring surgical intervention. Computational modeling offers promising solutions to improve surgical outcomes. However, challenges remain due to its computing time and difficult patient-specific data integration. This study introduces a parameterized framework for modeling the mitral valve, incorporating a universal coordinate system to standardize geometry across datasets. An initial feasibility study of this framework was demonstrated through dynamic mitral valve simulations using an immersed boundary method. These results highlight the potential of this parameterization approach to be used for deep learning or to enhance segmentation, particularly in cases of incomplete or noisy data.