Tissue-Based Affine Registration of Brain Images to form a Vascular Density Atlas Derek Cool, Dini Chillet, Jisung Kim, Mark Foskey, and Stephen Aylward Computer Aided Display and Diagnosis Laboratory, University of North Carolina at Chapel Hill, USA {cool, jisung, foskey, aylward}@unc.edu, [email protected] http://www.caddlab.rad.unc.edu Abstract. Anatomic brain atlases are widely used within the medical world and are important for identifying tissue and structural aberrations and inconsistencies within an individual. Unfortunately, there are many procedures and diseases that require examination of the brain’s vascular system, which is not easily identifiable in the anatomic atlases. We present a new concept of a brain atlas of vascular density, formed through tissue-based registration, to identify a standard vascular tree with expected variance. This density atlas can be used to assess the vascular variations within an individual and aid in diagnostics and presurgical planning. In this paper, a vascular density atlas is formed and validated for use as an effective measuring tool of human vasculature.

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Introduction

Creation of a 3-dimensional standardized brain atlas is important in both clinical and research fields. Numerous types of anatomical atlases have been formed to establish an average brain normal, with expected variance. Such atlases establish average structural brain forms, which can be used as statistical priors for effective assessment of individual anatomic aberrations. While effective for tissue-based analysis, anatomical atlases fail to illustrate the brain’s vasculature. The human vascular system, similar to skeletal structure, has well defined vessels and expected sub-epidermal locations common among the general populous. Researchers have shown that the vasculature of a brain actually forms prior to, and potentially drives the development of, tissue[5], making it a potential determinant of cranial anatomy. This paper proposes the formation of a vascular atlas as a valid and effective tool for measuring expected cerebral vessel distribution and illustrates its accuracy in estimating a societal average. Forming the average vascular matrix within brain matter could be useful for identifying subtle changes in vessel formation, not visible through standard tissue analysis. Construction of the proposed atlas involves the application of tissue-based anatomical registration transforms to corresponding individual vascular density maps, resulting in a mean vascular density atlas with expected variance. This approach is advantageous for the parallel formation of accurate, correlated anatomic and vascular atlases for tissuebased analysis.

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Establishment of a mean vascular atlas with expected deviation has numerous medical applications including pre-operative planning and diagnosis, identification of vascular anomalies, and assessment of an individual’s vascular changes over time. Such a tool might also aid in diagnosis of mental disorders, such as schizophrenia, that have a strong genetic component. With brain vasculature forming prior to tissue development[5], a vascular atlas may provide a more direct measure of the genetic component of such mental disorders. An atlas of vasculature could also be advantageous for stroke assessment— identifying affected areas, analyzing vascular malformation, and estimating arterial compensation. Finally, a vascular atlas could be used in conjunction with an anatomical atlas for additional verification and statistical validation.

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Methods

Various registration techniques could be used for vascular atlas formation. We present a solution built on tissue-based correlation of individual brains using affine, mutual-information registration [1, 4]. Resulting transforms are applied to corresponding vessel density maps to form a vascular mean. This approach focuses on the creation of a mean vascular brain resulting from anatomical brain alignment. Atlas formation requires a set of brain normals containing mutually aligned T2 MRIs and Magnetic Resonance Angiograms (MRA). For our experiment, a rigid body transformation of individuals T2 images onto their MRAs, ensured proper correlation between two images. Since both scans were acquired in one sitting, it is reasonable to expect a negligible amount of distortion between the images.

2.1

Vessel Extraction

Formation of the vascular density map requires extraction of all arterial vessels visible within a subject’s MRA. For our vessel segmentation solution we utilize a centerline traversal [2] approach. This method executes a multi-scale traversal of a vessel’s centerline, initiated from a point found on or near the tube. The radius of the vessel is then estimated using that centerline [6, 7]. During vessel modeling, only cerebral arteries, not veins, are gathered. This is done to improve the standardization of the vessel trees, since the image intensity of arterial vessels is more consistent across subjects’ MRAs, when compared to veins. It is acknowledged that visual extraction of arteries is not exhaustive nor guaranteed to draw all available vessels. However, with meticulous segmentation attention and averaging of multiple vascular trees, such limitations fall within a reasonable range of uncertainty. Clean MRA scans are essential for proper vascular tree collection.

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Formation of Density Map Images

After vascular tree segmentation, the Danielsson distance algorithm (DD) [3] is applied to the vessels, to generate a Euclidean distance field. The DD algorithm systematically generates an image for which each voxel contains the Euclidean distance to the nearest vessel.

2.3

Atlas Registration and Generation

The atlas is formed using tissue-based mutual-information registration . Using Parzen windows for estimating probability density distributions, the mutualinformation applies an affine transform to the T2 weighted image to align it with the atlas template. Initially, each T2 brain image is registered to a single brain that is used as the base template. An anatomical atlas is formed through summation of the registered images to form a mean. This procedure is repeated using the newly formed atlas as the base template in order to remove bias toward the originally templated individual. Repetition of this cycle, gradually moves toward a fully unbiased, general atlas. After satisfactory formation of a general atlas, the affine transformations from the tissue registration are applied to their corresponding vascular density map to align each field properly in the anatomical match. Combining the aligned fields forms the vascular mean and expected variance.

2.4

Assessment and Evaluation

To assess the validity of the vascular atlas for estimating intra-cranial vascular density, we compare individuals’ distance fields with the vascular atlas using voxel-by-voxel scoring. Evaluating on a per voxel basis allows regions of statistical deviation within an individual’s distance field to be localized. These scores are then used to quantify global differences through the subjects. To form the standard distribution, we use z-score analysis to estimate an individuals’ adherence to the atlas. Z-score is calculated using the following formula: zv =

χv −µv σv

where χv represents an individual’s brain intensity at location v, µv represents the mean atlas intensity for that location, and σv represents the standard deviation for that voxel. A large z-score value indicates a statistical anomaly at that voxel for an individual. Normally distributed populations can be assessed based on the zscore distibution within and across individuals. Computed for each individual, this process allows identification of outliers with subtle vascular variation.

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Fig. 1. Images of vascular density altas (From Left): coronal, axial, sagittal views

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Results

Figure 1 illustrates posterior axial, lateral axial and cranial views of the vascular density atlas formed through tissue-based mutual-information registration of nine subjects. The vascular cloud segments for the left and right hemispheres and medial arteries are clearly defined and distinct. Cranial shape is evident and locations of large structures, such as ventricles, are suggested within the vascular spaces. Table 1 shows the z-score results indicating the percentage of an individual’s voxels that deviate from the vascular atlas. The statistical expectation for normal distribution is indicated as well. Most subjects’ vascular maps fall within the expected normalized deviation the atlas. Two vascular outliers, subjects 09 and 04, illustrate the atlas capability of identifying subtle changes in vasculature and are illustrated in Figure 2 where deviation images highlighting deviant areas are compared with conforming subjects 5 and 8. Table 1. Percentage of voxels contained within z-score deviation of mean vascular density atlas Subject 01 02 03 04 05 06 07 08 09 Normal

0.2 14.98 14.95 15.11 13.16 15.50 16.19 15.16 15.31 11.68 15.9

0.6 44.29 44.05 45.84 39.46 46.35 46.92 44.68 45.64 34.43 45

1.0 68.54 68.05 72.50 63.08 72.31 72.44 69.63 71.11 55.61 68

1.4 85.90 86.05 89.38 81.98 89.65 89.37 87.81 88.58 74.08 84

1.6 91.52 92.02 94.21 88.67 94.46 94.29 93.31 93.56 81.85 89

2.0 97.79 98.33 98.78 97.16 99.07 98.61 98.67 98.84 93.41 95.4

2.4 99.82 99.71 99.99 99.85 99.97 99.43 99.90 99.95 99.19 98

2.8 100 100 100 100 100 100 100 100 100

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Table 2. Percentage of voxels contained within z-score deviation of mean anatomical atlas Subject 01 02 03 04 05 06 07 08 09 Normal

0.2 12.7 12.8 14.6 10.5 15.9 12.8 11.7 12.1 11.7 15.9

0.6 49.2 46.8 49.3 41.0 53.9 49.0 46.4 46.2 46.0 45

1.0 77.21 72.10 70.15 68.40 75.68 74.6 76.3 73.23 74.33 68

1.4 85.90 85.07 81.76 85.61 86.96 86.80 90.90 86.64 89.56 84

1.6 93.47 88.87 86.03 90.28 90.73 90.39 94.17 90.46 93.24 89

2.0 97.13 94.00 92.78 95.55 95.74 95.30 97.57 95.37 97.10 95.4

2.4 99.97 97.47 97.23 98.35 98.34 98.58 99.14 98.29 98.85 98

2.8 100 100 100 100 100 100 100 100 100

Fig. 2. Images of vascular density Z-score distributions (black = 0-0.9, gray = 1-1.9, white > 2) (Top Row): Deviatant individuals- 04 (left) and 09 (right) (Bottom Row): Conforming individuals- 05 (left) and 08 (right)

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Discussion

The vascular density atlas showed tight formation and distinct brain segments representing different lobe vasculature. While the vascular branches formed clouds of probable density as opposed to distinct vessels, the major branches and vascular structures, such as the Circle of Willis were clearly visible within the atlas. Additionally, structural anatomic silhouettes of the skull, ventricles, and spinal base were visible within the vascular atlas, which was to be expected as the atlas was formed through tissue registration. Qualitative results indicate a reasonable alignment of tissue and vascular tubes for formation of parallel creation. Quantitative validation of the vascular atlas through individual comparisons showed a normal deviation distribution for most subjects. Z-score analysis illustrated a largely normalized fit of subject vessels to the atlas. The deviation of individual vascular images from the calculated mean fell within a normalized distribution fit outside of 0.4 deviations. Inside of 0.4 deviations, the accuracy fell slightly below a normalized distribution, which can be expected for low range accuracy since the atlas registration is tissue-based, as opposed to vessel. It is interesting to note, however, that in almost all cases the vascular atlas had greater percentage estimation within 0.2 deviations than the mean tissue atlas. This is largely due to stark contrasts found within a tissue image, as opposed the gradient slopes formed in a Euclidean distance field. The vascular outliers, subject 04 and 09, indicate subtle variation from the general populous. In the case of subject 09, the anterior lobe of the brain showed heavy deviation and further examination verified that the vessel formation was less pronounced for that individual than others within the atlas. While many factors other than vessel depletion could have caused this anomaly, its nature caused it not to be visibly detected. A slight physical deformation in subject 4 had manifested in vascular shift, which was identified by heavy vascular deviation the vicinity of the aberration. Our experiment, while not conclusive, suggests formation of a brain vascular density atlas as a valid tool for estimating a societal norm. Conclusive results will require additional subjects to form a tighter fitting atlas representative of a larger portion of society. Regardless, our vascular atlas results indicate a correlation between the brain’s vasculature and tissue composition.

References 1. Viola, P. and Wells III, W.”Alignment by Maximization of Mutual Information” International Journal of Computer Vision, 1997, 24(2):137-154 2. Aylward, S., ”Vascular Image Registration for Intra-Operative 3D Ultrasound Annotation”, International Journal of Computer Vision, To Appear March 2003, pages 15 3. Danielsson, P. E., Euclidean Distance Mapping, Computer Graphics and Image Processing, 14, 1980, pp. 227-248 4. Hill, Derek. Medical Image Registration. 2000 5. C. Seydel ”Organs Await Blood Vessels’ Go Signal” Science, 2001, 291:2365

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6. S. Aylward, E. Bullitt, S.M. Pizer, D. Eberly, ”Intensity ridge and widths for tubular object segmentation and registration.” IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, 1996, 131-138 7. Aylward S, Bullitt E, ”A Comparison of Methods for Tubular-Object Centerline Extraction,” IEEE Transactions on Medical Imaging, 21(2), 2002, pp. 61-76