A Point-Wise Quantification of Asymmetry Using Deformation Fields: Application to the Study of the Crouzon Mouse Model

Abstract

This paper introduces a novel approach to quantify asymmetry in each point of a surface. The measure is based on analysing displacement vectors resulting from nonrigid image registration. A symmetric atlas, generated from control subjects is registered to a given subject image. A comparison of the resulting displacement vectors on the left and right side of the symmetry plane, gives a point-wise measure of asymmetry. The asymmetry measure was applied to the study of Crouzon syndrome using Micro CT scans of genetically modified mice. Crouzon syndrome is characterised by the premature fusion of cranial sutures, which gives rise to a highly asymmetric growth. Quantification and localisation of this asymmetry is of high value with respect to surgery planning and treatment evaluation. Using the proposed method, asymmetry was calculated in each point of the surface of Crouzon mice and wild-type mice (controls). Asymmetry appeared in similar regions for the two groups but the Crouzon mice were found significantly more asymmetric. The localisation ability of the method was in good agreement with ratings from a clinical expert. Validating the quantification ability is a less trivial task due to the lack of a gold standard. Nevertheless, a comparison with a different, but less accurate measure of asymmetry revealed good correlation.

New Algorithms to Map Asymmetries of 3D Surfaces

“…It must be noted that the measured errors include the imprecision of the manual delineation of the landmarks. Second, our algorithm has a mean accuracy of 0.6mm ± 0.5mm when recovering ground truth asymmetries, and proves to be superior to the competitive algorithm [7]. This is not surprising, as in this last method the individual asymmetry mapping is based on the registration of the two sides of the surface with the template, which is less precise than registering the two sides of the same surface together.…”

“…First, the mean error in the first experiment (2.63mm ± 0.59mm) is larger than the error in the second (0.67mm ± 0.13mm), From left to right: a deformation field is applied to a perfectly symmetrical face; estimated asymmetry map by our method; normalised asymmetry map on the template; template-based asymmetry map as estimated by another method [7].…”

“…2). We also map the asymmetries of the surface using the approach ofÓlafsdóttir et al (performing the registration task with our tool for fair comparison) [7].…”

“…A first approach consists in registering a template, perfectly symmetrical surface, to the surface of interest in a nonlinear way. The difference between the two displacement vectors needed to map bilateral points of the template with points of the surface is used to quantify the local asymmetry at these points [7]. A second approach normalises the surface of interest in a reference frame using several manually selected bilateral landmarks.…”

A New Landmark-Independent Tool for Quantifying and Characterizing Morphologic Variation

“…A similar method was applied byÓlafsdóttir et al [27] to assess craniofacial symmetry in a mouse model. A symmetric atlas was generated by mirroring an average image across the midsaggital plane.…”