A new method for improving functional-to-structural MRI alignment using local Pearson correlation
Introduction
In Blood Oxygenation Level Dependent (BOLD) Functional Magnetic Resonance Imaging (FMRI), T2⁎-weighted volumes (E) are acquired to create maps of brain activity. Because T2⁎-weighted volumes are low-resolution and have poor anatomical contrast, these activation maps are almost always overlaid on a separate, high-resolution T1-weighted structural volume (S) collected in the same subject. Inferring any neuroscience conclusion from the activation map therefore depends on a close spatial correspondence between the T2⁎- and T1-weighted volumes; high precision in this correspondence is particularly critical for pre-surgical mapping (Hirsch et al., 2000, O'Shea et al., 2006, Sunaert, 2006, Yetkin et al., 1996) and cortical surface based analyses (Argall et al., 2006, Dale et al., 1999, Fischl et al., 1999, Van Essen et al., 2000, Van Essen et al., 2001). In order to ensure the correspondence between anatomy and function, most neuroimaging data analysis packages perform cross-modality registration. Ensuring that E is well aligned with S is very important.
Because the T2⁎- and T1-weighted images have very different contrasts, registering them is considered to be “cross-modality” registration (although both volumes are collected using MRI). Automated pair-wise image alignment tools seek improved alignment by minimizing a cost functional that measures the mismatch between the two volumes (or whose negative measures the correspondence between the images). Optimization routines are used to seek the spatial transformation that minimizes the cost functional between the transformed volume and its pair. Achieving alignment is consigned to the successful reduction of the cost functional while avoiding local minima; however, it is known that for many cost functionals, this reduction does not necessarily translate into better alignment. An extreme example is that the Mutual Information (MI) cost of two volumes which are completely out of alignment might be better (lower) than the cost when they were somewhat aligned (Studholme et al., 1999). Such problems, readily detected by a cursory visualization of the results, are addressed in software by using more robust cost functionals and heuristics to restrict the transformation parameter space.
Most current image registration packages use generic cost functionals that do not rely on a specific model of the signal intensity between the volume pair. For example, AFNI's 3dAllineate and FSL's FLIRT have variants of MI and Correlation Ratio (CR) cost functionals. As developers of the AFNI neuroimaging data analysis package, our initial impetus for the developments reported herein was a collection of Echo Planar Imaging (EPI) and structural volumes, presented to us by several FMRI researchers who had great difficulty in obtaining decent alignments between their functional time series and their anatomical reference volumes. These datasets had been processed in AFNI (http://afni.nimh.nih.gov) (Cox, 1996, Cox and Jesmanowicz, 1999), FSL (http://www.fmrib.ox.ac.uk) (Jenkinson and Smith, 2001), and SPM (http://www.fil.ion.ucl.ac.uk/spm/) (Collignon et al., 1995), and none of these packages had produced satisfactory results, despite numerous attempts at adjusting the available algorithmic parameters.
Because of the failure of these routines, we developed a specialized cost functional that is optimized for T2⁎- to T1-weighted image alignment. During this process, we addressed the following questions: do the transformations obtained by minimizing general purpose cross-modality cost functionals reliably result in good alignment of EPI and structural MRI volumes? How can we assess the quality of the alignment over an entire volume, without an objectively computable figure of merit, and considering the minimal anatomical contrast in the EPI data? Answering such questions for real data is difficult. Using simulated data, where the proper alignment is known, does not fully take into account the complex variations in noise, contrast, signal dropouts, and image distortion that occur in practice. In our examination of the registration results, we rely on meticulous visual inspections of the detailed anatomical overlap between the image pairs, facilitated by automatically creating edge-enhanced versions of the volumes and displaying them in a way that allows one to compare alignment results obtained with a variety of cost functionals. While this methodology does not easily allow for precise quantification of misalignment, it does allow for a coarse scale rating of different alignment results.
In the Methods section, we first describe a new cost functional designed for the specific purpose of T2⁎-to-T1 alignment. We then describe our visual examination methodology for assessing and rating the results of different alignment algorithms, including our statistical approach for interpreting the scores. In the Results section, we illustrate the types of displays the raters used in assessing the registration results, and then present the results of the statistical analysis. We conclude with a discussion of two non-controversial but under-appreciated points: generic image analysis algorithms can often be improved by modality-specific enhancements, and visual examination of transformed images is vital to ensure the integrity of the FMRI data processing stream.
Section snippets
Generic cross-modality cost functionals
We denote a single T2⁎-weighted EPI volume by E(x) and a T1-weighted structural volume by S(x), where x is the (discretized) spatial coordinate vector. Volume pair registration is generically performed by minimizing some real-valued cost functional C[E(T(x;θ)),S(x)] over a subset of proper affine transformations parameterized by a vector θ: {T(•,θ) ∋ det[T] > 0 and θ is “reasonable”}. Ad hoc constraints are usually placed on the parameter vector θ to limit the search space for the sake of
Comparisons of generic functionals to LPC
Fig. 2 shows melded images for the data as acquired (ORIG), and after alignment with CR, LPC, and MI cost functionals, respectively. The scores given by the three raters are shown in white under the alignment cost functional label. Examination of the edge-highlighted views clearly shows that LPC resulted in an improved alignment from the ORIG case; improvement is evident at internal structures such as the ventricles, and at sulcal edges. Red arrows point to corresponding central and peripheral
Conclusions
We emphasize that our 27 primary test cases all posed difficult registration problems: it was reports of these recurring troubles that led us to examine the EPI-structural alignment problem closely. However, these datasets are representative of the quality of data often acquired at different centers. With this real data, the problem with improving alignment between EPI and structural volumes is not one of implementation or of the optimization algorithm. Rather, generic histogram-based methods
Acknowledgments
This research was supported by the NIMH and NINDS Intramural Programs of the NIH. MSB was supported by NSF grant 0642532 (PI Michael Beauchamp); RD was supported by NIH/NIDCD grant 5R03DC008416-02 (PI Rutvik Desai) and NIH/NINDS grant 2R01NS33576-11 (PI Jeffery Binder).
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