iLogDemons: A Demons-Based Registration Algorithm for Tracking Incompressible Elastic Biological Tissues

Abstract

Tracking soft tissues in medical images using non-linear image registration algorithms requires methods that are fast and provide spatial transformations consistent with the biological characteristics of the tissues. LogDemons algorithm is a fast non-linear registration method that computes diffeomorphic transformations parameterised by stationary velocity fields. Although computationally efficient, its use for tissue tracking has been limited because of its ad-hoc Gaussian regularisation, which hampers the implementation of more biologically motivated regularisations. In this work, we improve the logDemons by integrating elasticity and incompressibility for soft-tissue tracking. To that end, a mathematical justification of demons Gaussian regularisation is proposed. Building on this result, we replace the Gaussian smoothing by an efficient elasticlike regulariser based on isotropic differential quadratic forms of vector fields. The registration energy functional is finally minimised under the divergence-free constraint to get incompressible deformations. As the elastic regulariser and the constraint are linear, the method remains computationally tractable and easy to implement. Tests on synthetic incompressible deformations showed that our approach outperforms the original logDemons in terms of elastic incompressible deformation recovery without reducing the image matching accuracy. As an application, we applied the proposed algorithm to estimate 3D myocardium strain on clinical cine MRI of two adult patients. Results showed that incompressibility constraint improves the cardiac motion re-T. Mansi ( ) · X. Pennec · M. Sermesant · H. Delingette · N. Ayache covery when compared to the ground truth provided by 3D tagged MRI.

Benchmarking framework for myocardial tracking and deformation algorithms: An open access database

“…The incompressible log-domain demons algorithm described in Mansi et al (2011) (iLogDemons for short) is an optical-flow method for co-registering images that was adapted from the previous log-domain Demons algorithm (Vercauteren et al, 2008) for cardiac tissue tracking to impose physiological constraints in the myocardium such as incompressibility and elasticity.…”

“…The use of a fixed reference frame allows to define the mask of the myocardium once for the whole sequence. For more details on the sequence tracking pipeline, see Mansi et al (2011).…”

Statistical Atlas of Human Cardiac Fibers: Comparison with Abnormal Hearts

“…1 and has four steps. The myocardium is segmented [3] and its mask is used to guide the nonrigid pairwise registration [21,22,14]. All hearts are registered to an initial reference image, which is updated toward the morphological average of all hearts [7].…”

Variability of the Human Cardiac Laminar Structure

“…Heart Registration -Secondly, each myocardium is registered to a reference image using solely the B 0 images and the myocardial masks. The pairwise registrations are performed with the symmetric Log-domain diffeomorphic demons [29,19]. Construction of Healthy Atlas -Thirdly, the reference image is deformed toward the morphological average of all hearts by iterating until convergence the pairwise registrations and the heart averaging steps.…”