Physically-constrained modeling of a heart is provided. Patient-specific data may be used to estimate heart anatomy locations. A model is applied to the data for estimation. For increased accuracy of estimation, the biomechanics of the heart, such as the valve, may be used to constrain the estimation. By applying a dynamic system between estimated anatomy locations of different times, the locations may be deformed or refined. The modeled heart and/or valve may be used to estimate hemodynamics. The resulting velocities or other motion information may be used to emulate ultrasound Doppler imaging for comparing with acquired ultrasound Doppler data. The comparison may validate the modeling.