  Image registration is an ill-posed inverse problem which often requires
regularisation on the solution space. In contrast to most of the current
approaches which impose explicit regularisation terms such as smoothness, in
this paper we propose a novel method that can implicitly learn
biomechanics-informed regularisation. Such an approach can incorporate
application-specific prior knowledge into deep learning based registration.
Particularly, the proposed biomechanics-informed regularisation leverages a
variational autoencoder (VAE) to learn a manifold for biomechanically plausible
deformations and to implicitly capture their underlying properties via
reconstructing biomechanical simulations. The learnt VAE regulariser then can
be coupled with any deep learning based registration network to regularise the
solution space to be biomechanically plausible. The proposed method is
validated in the context of myocardial motion tracking on 2D stacks of cardiac
MRI data from two different datasets. The results show that it can achieve
better performance against other competing methods in terms of motion tracking
accuracy and has the ability to learn biomechanical properties such as
incompressibility and strains. The method has also been shown to have better
generalisability to unseen domains compared with commonly used L2
regularisation schemes.
