Validation of Equilibrated Warping—Image Registration with Mechanical Regularization—On 3D Ultrasound Images

Abstract

Image registration plays a very important role in quantifying cardiac motion from medical images, which has significant implications in the diagnosis of cardiac diseases and the development of personalized cardiac computational models. Many approaches have been proposed to solve the image registration problem; however, due to the intrinsic illposedness of the image registration problem, all these registration techniques, regardless of their variabilities, require some sort of regularization. An efficient regularization approach was recently proposed based on the equilibrium gap principle, named equilibrated warping. Compared to previous work, it has been formulated at the continuous level within the finite strain hyperelasticity framework and solved using the finite element method. Regularizing the image registration problem using this principle is advantageous as it produces a realistic solution that is close to that of an hyperelastic body in equilibrium with arbitrary boundary tractions, but no body load. The equilibrated warping method has already been extensively validated on both tagged and untagged magnetic resonance images. In this paper, we provide full validation of the method on 3D ultrasound images, based on the 2011 MICCAI Motion Tracking Challenge data.

Left Ventricular Torsion Obtained Using Equilibrated Warping in Patients with Repaired Tetralogy of Fallot

“…The assessment of torsion is based on the finite element method for image registration, and the equilibrium gap principle for problem regularization, known as equilibrated warping [2][3][4]. It has been shown to be able to predict global torsion in regular cine images as well in 3D tagged images, despite low contrast [2].…”

Translational Cardiovascular Modeling: Tetralogy of Fallot and Modeling of Diseases

“…Genet et al [65] described a novel motion tracking based on image registration, while imposing mechanical constraint of equilibrated gap regularization -the socalled equilibrated warping . It has been shown to successfully track the motion not only in the tagged MR images but also to extract global torsion in standard cine MR images [66]. The LV torsion in rTOF patients was previously studied, however, poor reproducibility was observed when using standard clinical commercial software [67].…”

“…The imaging model used by Škardová et al in [69] includes the 2D tagging and artifacts caused by a limited image spatial resolution. The image registration is regularized by the equilibrated warping, as described in [65,66]. We remark that the proposed method could be applied also for other medical imaging modalities.…”

Mechanical and Imaging Models-Based Image Registration

“…Many approaches have been proposed to regularize this ill-posed problem (Christensen, Rabbitt, and Miller, 1996;Veress, Gullberg, and Weiss, 2005;Mansi et al, 2011;Wang and Amini, 2012;Tobon-Gomez et al, 2013), which will not be discussed in details here. Specifically, details on the equilibrium gap regularization, an efficient mechanistic approach, can be found in (Claire, Hild, and Roux, 2004;Genet, C. Stoeck, et al, 2018;Lee and Genet, 2019).…”