  Learning spatial-temporal correspondences in cardiac motion from images is
important for understanding the underlying dynamics of cardiac anatomical
structures. Many methods explicitly impose smoothness constraints such as the
$\mathcal{L}_2$ norm on the displacement vector field (DVF), while usually
ignoring biomechanical feasibility in the transformation. Other geometric
constraints either regularize specific regions of interest such as imposing
incompressibility on the myocardium or introduce additional steps such as
training a separate network-based regularizer on physically simulated datasets.
In this work, we propose an explicit biomechanics-informed prior as
regularization on the predicted DVF in modeling a more generic biomechanically
plausible transformation within all cardiac structures without introducing
additional training complexity. We validate our methods on two publicly
available datasets in the context of 2D MRI data and perform extensive
experiments to illustrate the effectiveness and robustness of our proposed
methods compared to other competing regularization schemes. Our proposed
methods better preserve biomechanical properties by visual assessment and show
advantages in segmentation performance using quantitative evaluation metrics.
The code is publicly available at
\url{https://github.com/Voldemort108X/bioinformed_reg}.
