Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain

Abstract

One of the most challenging problems in modern neuroimaging is detailed characterization of neurodegeneration. Quantifying spatial and longitudinal atrophy patterns is an important component of this process. These spatiotemporal signals will aid in discriminating between related diseases, such as frontotemporal dementia (FTD) and Alzheimer’s disease (AD), which manifest themselves in the same at-risk population. Here, we develop a novel symmetric image normalization method (SyN) for maximizing the cross-correlation within the space of diffeomorphic maps and provide the Euler–Lagrange equations necessary for this optimization. We then turn to a careful evaluation of our method. Our evaluation uses gold standard, human cortical segmentation to contrast SyN’s performance with a related elastic method and with the standard ITK implementation of Thirion’s Demons algorithm. The new method compares favorably with both approaches, in particular when the distance between the template brain and the target brain is large. We then report the correlation of volumes gained by algorithmic cortical labelings of FTD and control subjects with those gained by the manual rater. This comparison shows that, of the three methods tested, SyN’s volume measurements are the most strongly correlated with volume measurements gained by expert labeling. This study indicates that SyN, with cross-correlation, is a reliable method for normalizing and making anatomical measurements in volumetric MRI of patients and at-risk elderly individuals.

Introduction

Frontotemporal dementia (FTD) prevalence may be higher than previously thought and may rival Alzheimer’s disease (AD) in individuals younger than 65 years (Ratnavalli et al., 2002). Because FTD can be challenging to detect clinically, it is important to identify an objective method to support a clinical diagnosis. MRI studies of individual patients are difficult to interpret because of the wide range of acceptable, age-related atrophy in an older cohort susceptible to dementia. This has prompted MRI studies that look at both the rate and the anatomic distribution of change (Chan et al., 2001, Fox et al., 2001, Studholme et al., 2004, Kertesz et al., 2004, Avants et al., 2005a, Ballmaier et al., 2004).

Manual, expert delineation of image structures enables in vivo quantification of focal disease effects and serves as the basis for important studies of neurodegeneration (Studholme et al., 2004). Expert structural measurements from images also provide the gold-standard of anatomical evaluation. The manual approach remains, however, severely limited by the complexity of labeling 256³ or more voxels. Such labor is both time consuming and expensive to support, while the number of individual experts available for such tasks is limited. A third significant difficulty is the problem of inter-rater variability which limits the reliability of manual labeling (Sparks et al., 2002). While rarely available for large-scale data processing, an expert eye remains valuable for limited labeling tasks that give a basis for algorithmic evaluation.

Deformable image registration algorithms are capable of functioning effectively in time-sensitive clinical applications (Dawant et al., 2003) and high-throughput environments and are used successfully for automated labeling and measurement research tasks. One challenge is reliable performance on non-standard data, as in studies of potentially severe neurodegenerative disorders. These types of images violate the basic assumptions of small deformations and/or simple intensity relationships used in many existing image registration methods.

Diffeomorphic image registration algorithms hold the promise of being able to deal successfully with both small (Bajcsy et al., 1983, Gee et al., 1993, Gee and Bajcsy, 1999, Peckar et al., 1998, Rueckert et al., 1999, Rogelj and Kovacic, 2006, Ashburner et al., 2000) and large deformation problems (Trouv’e, 1998, Christensen et al., 1997, Dupuis et al., 1998, Younes, 1998, Joshi and Miller, 2000, Miller et al., 2002, Beg et al., 2005, D’Agostino et al., 2003, Lorenzen et al., 2006, Vaillant et al., 2004). State of the art methods also give full space–time optimizations, are symmetric with respect to image inputs and allow probabilistic similarity measures (Avants et al., 2005b). Inverse consistent image registration (ICIR) is an additional common alternative to diffeomorphic mapping. Inverse consistency was first introduced by Thirion as an extension to his Demons algorithm (Thirion, 1998) but was popularized by Christensen and Johnson (2001) and others (Shen and Davatzikos, 2002). Symmetric methods are distinct from ICIR in that symmetric algorithms, first, guarantee that results are identical regardless of the order of input data and, second, use exact inverse transformations guaranteed by diffeomorphisms. Inverse consistency approximates symmetry by including variational penalties in the normalization optimization algorithm. Depending on the weights of the various data, regularization and inverse consistency terms, consistency may be satisfied (or not) at the expense of the other matching criterion. Furthermore, inverse consistent algorithms use approximate inverse transformations (Christensen and Johnson, 2001). Because the inverse transformations themselves are approximate, the consistency term, as well, is compromised.

Here, we develop a novel symmetric diffeomorphic optimizer for maximizing the cross-correlation in the space of topology preserving maps. The cross-correlation measure has been used in medical image registration before (Bajcsy et al., 1983, Gee et al., 1993, Hermosillo et al., 2002) and more extensively in computer vision. However, this measure has not been investigated for the diffeomorphic case. Furthermore, it has not been used in symmetric normalization or “inverse consistent” studies. Applying our novel normalization formulation to cross-correlation provides the advantage (or option) of symmetrizing the cross-correlation Euler–Lagrange equations. We show that these symmetric Euler–Lagrange equations can be computed with only minor additional computational costs. We then give a careful evaluation of the performance of our symmetric diffeomorphic algorithm for high dimensional normalization of elderly and neurodegenerative cortical anatomy. We compare the method to an elastic cross-correlation optimizer as well as the Demons algorithm which was shown to outperform other methods in a careful evaluation of inter-subject brain registration (Hellier et al., 2003).