Multi-variate analysis: a tool for examining influences of mask and polynomial order on non-linear registration of T1-MRI volumes
Kelly Rehm1 , Stephen C Strother1 , Jon R Anderson2 , Roger P Woods3 , David A Rottenberg2
1Department of Radiology, University of Minnesota, Minneapolis, USA, 2Department of Neurology, University of Minnesota, Minneapolis, USA, 3Department of Neurology, University of California, Los Angeles, USA

Modeling & Analysis

Abstract
Spatial normalization of a structural MRI volume to a standard coordinate system is an essential preprocessing stage in inter-subject voxel-based analysis of functional neuroimaging data. Automated Image Registration (AIR5, [1]) is a widely used non-linear "warping" algorithm that achieves spatial normalization by employing high-order polynomials to co-register an MRI volume to a reference volume in the desired coordinate space. It is recommended that MRI volumes be spatially masked before registration by AIR; the design of the algorithm is such that variation in a spatial mask will affect the ultimate registration of volumes (to an unknown degree). Because registration problems are assumed to influence subsequent analysis it is desirable to examine the effects of polynomial warp order and mask quality on the process. Liow, et al [2] used Canonical Variable Analysis (CVA) to evaluate the effects of PET reconstruction algorithms on [15Owater] task activation. In this work we use CVA to evaluate the effects of polynomial warp order and mask quality on inter-subject registration.

We acquired T1-weighted MRI volumes from 16 normal subjects. Spatial masks for the volumes were computed automatically and later manually corrected; the Dice similarity metric [3] for the two sets of masks ranged from 0.96 to 0.98. AIR5 was used to register volumes to a masked reference volume. For each volume we created spatially-normalized volumes using polynomials of order 1 through 8 and the uncorrected mask; the process was repeated with the manually-corrected mask.

The 256 volumes (16 subjects x 8 polynomial orders x 2 masks) were submitted to a CVA analysis with 16 groups (8 orders x 2 masks). The results of the CVA are summarized in Figure 1. The first canonical variate accounted for 92.8% of the variance and demonstrates a strong influence of warp orders 1-5 on group registration with a small mask effect (greatest for polynomial order 3). Overall, using the corrected mask reduced the variance by 1.8% compared to using the uncorrected mask. For the second canonical variate use of the corrected mask resulted in similar group means but slightly tighter between-subject clustering when polynomials of orders 6-8 were used. For the third canonical variate there was a clear difference in polynomial warps due to mask choice when polynomials of order 5-8 were used.

Figure 2 depicts slices through the eigenvolumes associated with the first three canonical variates. The majority of highly-weighted voxels in the first and second eigenvolumes appear at ventricles and other high-contrast edges.
In the third eigenvolume the most influential voxels occur toward the periphery. Note that although the differences in spatial masks were restricted to the outer later of the volumes, their influences propagate well into the cortical mantle.

Multi-variate analysis of registration results for these 16 subjects clearly reveals that 1) the order of the polynomial warp was the dominant effect, 2) polynomial orders greater than 5 produced virtually the same result, and 3) mask choice had a negligible effect except for higher-order warps.

1. Woods RP, et al (1988). JCAT 22:153-165.

2. Liow J-S, Anderson JR, Strother SC (2000). IEEE Trans. Nuc. Sci. 47(3): 1136-1142.

3. Zijdenbos AP, et al (1994). IEEE Trans. Med. Img. 13(4):716-724.


This work was supported in part by NIH grant EB02013.




Figure 1. Canonical variates plotted as a function of polynomial order. Gold symbols (squares) represent the mean and one standard deviation of the canonical variate for 16 subjects co-registered using the uncorrected mask; blue symbols (diamonds) represent results from co-registrations using the corrected mask.




Figure 2. Canonical eigenvolumes. Axial slices through the eigenvolumes of canonical variates 1, 2, and 3 are presented, respectively, in the top, center and bottom rows. White voxels are those with the greatest positive and negative weights.