1 Mouse Imaging Centre, Hospital for Sick Children, 555 University Avenue, Toronto, Ontario, Canada M5G 1X8, 2 Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, Rm 315, 19 Russell Street, Toronto, Ontario, Canada M5S 2S2, 3 McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University, 3801 University Street, Montreal, Quebec, Canada H3A 2B4 and 4 Department of Medical Biophysics, University of Toronto, Toronto, Ontario, Canada
Address correspondence to X. Josette Chen, Mouse Imaging Centre, Hospital for Sick Children, 555 University Avenue, Toronto, Ontario, Canada M5G 1X8. Email: josette{at}sickkids.ca.
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Abstract |
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Key Words: central nervous system image processing magnetic resonance imaging phenotyping
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Introduction |
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Magnetic resonance imaging (MRI) has shown a substantial potential in this regard because of its ability to capture large amounts of anatomical information in a nondestructive manner. While the spatial resolution of this technique ranging from 20 to 60 µm for fixed samples (Benveniste et al., 2000; Johnson et al., 2002
) is not comparable to histology (
25 µm), detailed anatomical comparisons within murine systems can be made, such as in the central nervous system (CNS). In addition, this method allows the three-dimensional morphology of anatomical structures to be easily examined, thus providing significant advantages over serial histological sectioning techniques in analyzing complex structures (Dhenain et al., 2001
; Johnson et al., 1993
, 1997
). Several groups have made progress in the creation of MRI atlases of individual mouse brains (e.g. http://www.loni.ucla.edu/MAP; Van Essen, 2002
). Like conventional histological atlases (http://www.mbl.org/mbl_main/atlas.html, http://www.hms.harvard.edu/research/brain/atlas.html), these MRI-based atlases consist of high-resolution images of an individual specimen with anatomical labels. A crucial difference, however, is that both the data and the anatomical labels are three-dimensional and digital.
A critical step beyond obtaining the MR images is to analyze and compare the enormous amounts of data in an efficient and reliable manner. Current phenotypic assays require an average and standard deviation of the normal range of any measurement to allow identification of outliers. Likewise, we need equivalent analysis for three-dimensional images. One-dimensional metrics, such as heart rate, body weight or red blood cell count, can be averaged in a straightforward manner; however, the analogue for three-dimensional images requires more sophistication.
We propose to take the concept of an MRI atlas further by creating a variational atlas. The idea is to combine multiple three-dimensional images together to provide a representation of average anatomy and a range of anatomical variation within a particular population. Specifically, in this paper we register a number of genetically identical murine brains, which allows us to estimate the limits of natural variation in terms of anatomical structures, volumes, shapes and locations.
The fusing together of a set of individual images into a single image is the first component of our variational atlas, the average image. This average image extracts commonalities among individual brain anatomies and filters out idiosyncrasies. By manually delineating structures in the average image, we produce an annotated atlas. The second component of the variational atlas consists of a set of deformation fields, which is a measure of the anatomical variability across the set of individual brain images. This is the variational aspect of the atlas. Here, we capture and quantify precisely the differences that are removed in the process of creating the average image.
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Materials and Methods |
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Eight-week-old male inbred 129S1/SvImJ mice (Jackson Laboratory, Bar Harbor, ME) were acclimated for a period of 3 days. Animals were then anesthetized with an overdose of Avertin (2.5%) via intraperitoneal injection. Following lack of deep tendon responses, the thoracic cavity was opened and animals perfused through the left ventricle with 10 cm3 of 0.1 M phosphate-buffered (pH 7.4) 0.9% NaCl (PBS), followed by 4% formaldehyde in PBS. Solutions were infused at room temperature (25°C). Following perfusion, the heads were removed and allowed to postfix at room temperature for an additional 60 min, at which time the cranium was opened and the brain removed in its entirety. Brains were then postfixed for an additional 24 h in 4% paraformaldehyde in PBS at room temperature.
Magnetic Resonance Imaging
A 7.0 T, 40 cm bore magnet (Magnex Scientific, Oxford, UK) connected to a UnityINOVA console (Varian Instruments, Palo Alto, CA) with modified electronics for parallel imaging was used to acquire anatomical images of excised brains. Prior to imaging, the brains were removed from the fixative and placed into glass tubes filled with a proton-free susceptibility-matching fluid (Fluorinert FC-77, 3M Corp., St Paul, MN). We used two custom-built, 12 mm, non-uniform solenoid coils (Idzaiak and Haeberlen, 1982) to image two brains in parallel. The parameters used in the brain scans were as follows: T2-weighted, three-dimensional spin-echo sequence, with TR/TE = 1600/35 ms, single average, field-of-view = 12 x 12 x 24 mm and matrix size = 200 x 200 x 400 giving an image with (60 µm)3 isotropic voxels. The total imaging time was 18.5 h. The TR and TE settings were chosen for optimized contrast between grey matter and white matter in the mouse brain at 7 T as reported in previous studies (Guilfoyle et al., 2003
).
Algorithm for the Variational Atlas (Further Details in Appendix)
We used image registration to model the anatomical differences among the three-dimensional data sets. In image registration, two images are compared by performing a series of deformations in order to make one image identical to the other. The result of the process is stored in a deformation field, a vector field which records the magnitude and direction required to deform a point in the source image to come to the appropriate point in the target. In other words, the anatomical differences between the two images are encoded in the deformation field.
The algorithm takes a set of MR images acquired from a number (in this case nine) of excised brains and runs through six iterative steps. In the first step the images are registered and normalized in terms of global size, shape and MR intensity; we call these the globally normalized images. At this point only extrinsic, anatomically insignificant differences are removed. The remaining steps involve detailed matching of anatomical features starting from a coarse grid and ending at the resolution of the imaging voxels.
The final output consists of an average image and the deformation fields. The deformation fields encode local positional differences between the average image and the globally normalized images. The deformation fields represent a large body of data: number of images x number of voxels x three vector components, which is 1 GB of data. Therefore, to represent more simply and graphically the variability of the atlas, we calculate the mean positional distance (MPD) image between the average and the individuals.
We ran our implementation in parallel (a single thread corresponding to each dataset) on a 192-processor Origin 3000 supercomputer (Silicon Graphics, Inc., Mountain View, CA). We used nine processors (600 MHz each) to create the average image, which took 15 h.
Annotation
Structures that are clearly visible in the average image have been annotated by manual segmentation using the software package Display (Montreal Neurological Institute, Montreal, Canada). Every voxel of the average image has been assigned to a unique anatomical label, and the delineations were verified in three orthogonal directions. We delineated structures that were visible on MRI and nomenclature was adapted from the literature (Franklin and Paxinos, 1997). The resulting annotation is stored in the segmentation image, a three-dimensional image with the same size and coordinate system as the average image. Each voxel position of the segmentation image stores the anatomical label belonging to the corresponding voxel coordinate of the average image.
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Results |
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In Figure 1, we show the average image beside an individual brain (see Supplementary Material A for a full three-dimensional comparison). Because the average image is calculated nonlinearly and the noise is not well defined, we calculated the signal-to-noise ratio (SNR) to be the mean signal in a region of interest (ROI) in a homogeneous part of the brain divided by the standard deviation of the same ROI. On average, the individual brains had SNRs of 20 and the average brain of 50. We see that the contrast between grey and white matter is better than in the individual images, e.g. as seen in white matter structures like the corpus callosum, fimbria of the hippocampus and the anterior commissure. The average image on the whole exhibits greater definition than the individual images. In particular, the visibility and delineation of many anatomical structures is, on average, considerably improved (e.g. deep cerebellar structures, the globus pallidus and the lateral parabranchial nucleus). If one assumes that each of the individual specimens were identical, we would expect to see this effect as a result of averaging of repeated measurements. Thus, the improvement in the average image over that of individual specimens indicates successful alignment of all samples; clearly anatomical structures across the specimens have been stacked up; otherwise averaging would have produced a blurred image (see Appendix, Fig. A1). Some fine features, however, show the reverse trend of a reduction in their level of definition within the average image. For example, white matter tracks in the striatum and small blood vessels. The extreme variability of these regions cannot be resolved by our registration with topology-preserving transformations. This qualitative comparison between the average and individual images is not a proper assessment of the accuracy of our registration; quantitative validation is the subject of further study.
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Based on the average image, a three-dimensional stereotaxic coordinate system was defined (Fig. 2). The midsagittal plane that evenly divides left and right components of the brain along the anatomic midline is selected as the coordinate plane x = 0. Positive x-coordinates increase in the right lateral direction, while negative x-coordinates decrease in the left lateral direction. The brain was tilted so that horizontal and vertical directions are approximately the same as in the histological atlas of Franklin and Paxinos (1997). The coordinate origin was arbitarily selected within the midsagittal plane of the cerebrum as shown in Figure 2.
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The annotated structures can be explored in several ways. For example, slices from the average image can be taken at arbitrary angles and viewed overlaid with corresponding slices of the segmentation image (Fig. 3A). In particular, this type of visualization enables slicing in coronal, sagittal or transverse directions for comparison with classical two-dimensional histological atlases. More advanced visualization in three dimensions is obtained from surface renderings of individual structures. Using interactive visualization tools (e.g. Amira, TGS, San Diego, CA) the renderings can be easily manipulated; for example, the annotations can be rotated, individually coloured and switched on or off (Fig. 3B, also see Supplementary Material B and http://www.mouseimaging.ca/var_brain_atlas.html).
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Global Brain Size
In the first step of the atlas-creation algorithm, the individual brains were normalized to the average global size using the 12-parameter affine model. In order to estimate the true total brain sizes (before the normalization) we counted all brain voxels based on individual annotations of raw images. In doing so, we ensured a consistent definition across all input images of the total brain region being measured. The average ± standard deviation, minimum and maximum of the brain volume across the nine samples were 415 ± 24, 365 and 440 mm3 respectively.
Volumetric Measurement of Structures
The segmentation image enables volumetric measurement of the annotated structures. This is done by histogram counting, where the number of voxels with the same label determines the volume of the corresponding structure. For combined regions consisting of several structures the corresponding label counts are summed together. For example, the anterior comissure is represented as a sum of two labels, the pars anterior and the pars posterior. Table 1 shows volumes of selected structures based on the segmentation image. We estimated the variability of the calculated volumes based on the individualized annotations of the globally normalized images. Table 1 lists the standard deviation of said volumes evaluated from the nine individualized annotations.
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By construction, the deformation fields capture the anatomical differences among individual brains. From the arithmetic mean of the vectors, we have the mean positional distance (MPD) image as a representation of the spatial variability across all anatomical locations. Intensities in the MPD image represent distances in micrometres. The MPD image has the same size and coordinate system as the average image and is shown in Figure 4. Colour coding of the distances of the MPD image enables effective visualization of the variational component of the atlas. For example, it is immediately clear that most inner structures are coloured purple and have low variability; in contrast, the olfactory bulbs and the caudal end of the brain stem are yellow, red and white, indicating high variability.
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We have calculated 117 µm as the mean spatial variability across all locations. The majority of anatomical locations (91% of the brain) have variability <180 µm (three voxels). In fact, the deep interior structures (comprising 53% of the brain) typically show variability <120 µm (two voxels). The most pronounced exception to this rule is the central part of the corpus callosum, which shows variability of 200 µm. This is not surprising, given that the 129Sv inbred mouse strains are known to exhibit high callosal variability (Crawley, 2000
).
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Discussion |
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The anatomical variability within an inbred murine strain has been formalized and precisely quantified in three-dimensional space for the first time. The mathematical expression of normal variability the deformation fields represents a basis for detecting and quantifying subtle yet significant anatomical differences. For example, our techniques can be used to find differences between groups, such as different strains, hybrids or mutants. In this case, a variational atlas can be created for each group and comparisons between the atlases can be made. Image registration will allow precise quantification and characterization of anatomical differences.
The methodology introduced here also allows a rigorous approach to automatically detecting potential mutants. The deformation fields obtained after global normalization can be used for: (i) automated annotation and corresponding volumetric measurements and (ii) comparison with the normal average brain. A structure can be considered abnormal if found at stereotaxic locations with deformation magnitudes that are significantly larger than the corresponding MPD magnitudes. Not only will this type of analysis be useful for targeted mutagenesis, but it also has applications in screening for anatomical outliers in the context of random mutagenesis projects. In fact, coupled with the procedures we have developed for image acquisition, our image processing tools are ideally suited for high-throughput phenotypic screening. Further developments in parallel image acquisition techniques (Bock et al., 2003), combined with our fully automated algorithms, will enable unsupervised, high-throughput and highly sophisticated anatomical phenotyping.
MRI versus Histological Atlases
Despite having lower resolution than published histological atlases (5 µm versus 60 µm), our three-dimensional MRI atlas exhibits several important advantages with respect to the processing and subsequent analysis of the CNS structure. First, the MRI atlas captures a complete picture of spatial relationships within the brain. This is in contrast to histological atlases where the specimen is sliced at 150 µm intervals. In addition, histological atlases of the CNS are typically obtained from paraffin- or parlodion-embedded specimens in which the true spatial dimensions within a given section cannot be readily determined because of shrinkage during specimen dehydration and processing. Similarly, rehydration and staining following sectioning are difficult to reproduce precisely from section to section. All these factors complicate determination of true three-dimensional distances between CNS structures and make accurate three-dimensional reconstructions difficult, although there have been efforts to digitally reconstruct histological sections back into three-dimensional space (Taguchi and Chida, 2003
). Overall, an MRI-based atlas is superior for measuring volumes and analysis of long, distinct morphological features such as axon tracts.
Another advantage of MRI atlases over histological atlases relates to comparisons between sample specimens with a reference atlas. For example, if a brain specimen under investigation is significantly larger or smaller than the histological image, then the stereotaxic coordinates of a two-dimensional histological atlas will be difficult to compare. Such a situation is likely even in genetically identical lines of mice, as we have shown in the Results. Matching of the slicing angle to that of a two-dimensional atlas introduces further approximations. In contrast, our variational atlas enables much more accurate comparisons in three dimensions. After performing both linear and non-linear registrations, the resulting deformation field allows the sample brain to be fully annotated and measured in terms of structural volumes and shapes. Moreover, the variational component of the atlas allows us to estimate whether or not a sample brain is within the limits of natural variation.
Finally, three-dimensional MRI datasets can serve as a spatial backbone onto which higher-resolution histological sections can be overlaid. In this sense, the MR data is used as a three-dimensional organizer for histological sections. One group has started to create a mouse brain atlas based on MRI, histology as well as other imaging techniques (MacKenzie-Graham et al., 2004).
Comparison with MR Atlases Based on a Single Brain
The variational atlas overcomes many of the problems associated with atlases based on a single individual. A single MR image may have imaging artefacts, such as the magnetic field susceptibility arising from small air bubbles, which only become worse with increasing magnetic field strength (Benveniste and Blackband, 2002). The excision procedure can also cause variability among specimens. Most importantly, without a quantitative definition of normal anatomy it is not possible to ensure a choice of a valid single representative; any individual animal is a potential anatomical outlier. The methodology presented here provides means for creating an atlas that is representative of many individuals, is virtually free of artefacts and has an improved signal-to-noise ratio (Fig. 1).
Comparison with Other Atlases Based on Group Average
The atlas creation algorithm uses a novel approach for extracting the average anatomical representation from a group of images. It incorporates some of the techniques for image registration and probabilistic atlases that were originally developed for the study of anatomical variations in human brains (Collins and Evans, 1997; Grenander and Miller, 1998
; Woods et al., 1998; Guimond et al., 2000
; Kochunov et al., 2001
; Thompson and Toga, 2002
). Existing techniques for defining an average brain anatomy from a group of images can be loosely divided into two schools of thought. Methods from one group produce highly resolved, but biased average images because of dependencies on the choice of a particular subject as target for all registrations (Guimond et al., 2000
; Kochunov et al., 2001
). The methods from the other camp produce unbiased, but blurry average images because of the use of global, low-level registration models applied to genetically heterogeneous human populations (e.g. the dataset, MNI305, comprised of 305 individual human brains can be found at http://www.bic.mni.mcgill.ca/cgi/icbm_view/).
The novelty of our approach lies in using an evolving intensity average image as the source for nonlinear registrations of the individual images. In this way we avoid problems associated with other algorithms that attempt to fully localize anatomical differences of the individual images with respect to a single individual. Instead, we use a multi-resolution strategy to gradually reach an unbiased, yet highly resolved, consensus among individual images. By design, our atlas brain not only represents the average geometry, but is also located at the geometric centre of the individual brains. Consequently, the anatomical variability in three spatial dimensions is easily understood and visualized, reminiscent of one-dimensional measurements. For example, the average image and the mean positional distance image MPD can be viewed as estimates of the population mean and standard error respectively.
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Conclusions |
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Supplementary Material |
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Appendix |
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For affine registrations we used the methodology of Woods et al. (1998a,b
) and the corresponding software package AIR5.2.2 developed at the University of California, Los Angeles. We employed a 12-parameter affine transformation model with LevenbergMarquardt minimization of the ratio image uniformity cost fuction. Complete details of AIR methodology and validation have been given previously (Woods et al., 1998a
,b
).
For nonlinear registrations we used the multi-resolution, multi-scale ANIMAL methodology developed at the Montreal Neurological Institute (MNI) (Collins and Evans, 1997). Briefly, this methodology treats spatial transformations as deformation vector fields encoded as grid transforms. In the standard registration framework, where the source image deforms to align with the target image, grid transforms store the displacement vectors on regular three-dimensional grids of variable resolutions. In a low-resolution grid transform the displacement vectors are defined sparsely (e.g. for every 10th voxel coordinate); in this case the displacements of the remaining source voxels are obtained through interpolation. By contrast, a grid at the highest resolution records a unique displacement vector for every source voxel. The registration algorithm is designed to minimize the value of an objective function, which is constructed as a weighted sum of the similarity measure (a local correlation statistic) and a cost function, which constrains change in magnitude of the local deformation vectors. Continuity of deformation fields is achieved through moving window averaging. The multi-scale aspect of the methodology is implemented through the use of variable scale feature extraction (blurred image intensity and image gradient magnitude); the spatial scale of the extracted features is determined by the size of the convolving three-dimensional isotropic Gaussian kernel (full-width-half-maximum, FWHM = 2.35 x standard deviation). Complete details and validation of this technique have been given previously (Collins and Evans, 1997
).
Schedule of the Variational Atlas Algorithm
The schedule is graphically shown in Figure A1.
Step 0 (Affine Average)
In the initial step, the brains were first spatially normalized to share the same location, orientation and global size, and then intensity normalized to have equivalent brightness.
We arbitrarily selected one image, say In. The remaining images, I1,...,In1 were registered to In using a global affine transformation model. The unbiased common affine space was defined by matrix averaging and reconciliation (Woods et al., 1998a,b
).
We next performed intensity normalization of the images J1,...,Jn. We first corrected for image intensity non-uniformity, an MR artefact associated with radiofrequency field inhomogeneities, with an automated algorithm (Sled et al., 1998). We then used another automated algorithm (Kovacevic et al., 2002
) to estimate mean grey matter intensities in J1,...,Jn. The average value of the mean grey matter intensity across all images was calculated next. The images were normalized to the average grey matter peak using linear intensity rescaling. Figure A2 illustrates the effect of intensity normalization on image histograms.
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Step 1 (First Generation Nonlinear Average)
The purpose of this step is to account for large-scale nonlinear anatomical differences. We started with a two-step nonlinear registration of the average A0 to all individual images (steps 1.2 and 1.3 in Table A1). Using the corresponding inverse transforms, the indivdual images were resampled to produce images
This new set of individual images was then intensity averaged to produce a new average image A1.
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The remaining steps were similar to step 1: the most recent average image was nonlinearly registered to its constituents and an updated set of indivual images was produced. In order to avoid repeated resamplings that tend to accumulate interpolation error, we instead resampled the intial images using the concatenated transforms. In all resampling steps we used a windowed sinc interpolation with window size of 11 voxels in all three directions.
At the end of the last step, the concatenated individual deformation fields g1,...,gn were defined so that More precisely,
where
denotes the transform that was obtained in step i such that
The last average image A5 is an intensity average of
The registration throughout the nonlinear steps is scheduled so that the full resolution is reached at the end of step 5. Details of the registration parameters used in all non-linear steps (15) are given in Table A1. Note how each non-linear step contains two substeps to allow gradual progression in spatial matching. By the end of step 5, the full spatial normalization among individual images is achieved (Fig. A3).
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A5-space
The concatenated deformation fields were then used to produce
The intensity average of Aks was defined as the final atlas average image A. By construction, A is geometrically centred with respect to the individual images
For every anatomical location v in A, its n deformation vectors point towards homologous individual locations F1(v),...,Fn(v) in
in such a way that v is at the centroid of the individual locations (Fig. A4). As discussed in the main text, the arithmetic mean of the vector magnitudes
is the mean positional distance, mpd(v) (MPD in the main text). The sphere centred at v, with radius equal to mpd(v) represents the spatial variability' of the location v.
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Acknowledgments |
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