Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging
Cheng G. Koay1,2, Ping-Hong Yeh2,3, John M. Ollinger2, M. Okan İrfanoğlu1,3, Carlo Pierpaoli1, Peter J. Basser1, Terrence R. Oakes2, and Gerard Riedy2

1Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, United States, 2National Intrepid Center of Excellence, Walter Reed National Military Medical Center, Bethesda, MD, United States, 3The Henry M. Jackson Foundation for the Advancement of Military Medicine, Bethesda, MD, United States

Synopsis

The purpose of the proposed framework is to carry out single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI). It is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests (orientation and shape tests) based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor.

Purpose

To develop a framework for single-subject analysis of diffusion tensor imaging1 (DTI) data.

Methods

This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion2,3 are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty, Fig. 1, formed by a collection of elliptical cones of uncertainty, Fig. 2. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures3 (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate4,5 (FDR) and False Non-discovery Rate6 (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. We illustrate the application of the proposed framework by testing the data of two TBI patients and one single non-TBI subject against a control group of 45 non-TBI subjects. The TBI patients were volunteers in the National Capital Neuroimaging Consortium (NCNC) Neuroimaging Core project. Non-TBI subjects (45 for the control group and 1 for the non-TBI single subject) consisted of active-duty service members or dependents with no diagnosis of TBI and no history of other major neurologic disorders. All scans were conducted with approval and according to the guidelines of the Walter Reed National Military Medical Center IRB. Each TBI patient was scanned in four separate occasions within a 3-year period. While some of the non-TBI subjects were scanned multiple times, we used only one session from each of the non-TBI subjects as our control group. Note that the single non-TBI subject used in this study is not part of the control group (N=45). Images were acquired on a 3T scanner (GE MR750, Milwaukee WI) with a 32-channel head coil. DWIs had the following parameters: TR≈10s, TE≈85ms, 2 mm3 resolution, 49 diffusion-weighted gradient directions at b=1000 s/mm2 and 6 non-DWI at b=0 s/mm2, approximately 65 slices with data matrix of 128x128. A field map was collected for B0 distortion correction, and cardiac gating was used to minimize cardiac motion artifacts. DTIPrep, HI-SPEED software packets and DTITK were used for preproceesing, constrained tensor estimation, and tensor registration.

RESULTS

The results of the FDR-FNR-based Orientation Deviation Indicator based on the clinical data of two TBI patients and one non-TBI subject against the chosen group of 45 controls are shown in Figures 3A, 3B and 3C, respectively (Both FDR and FNR were set at 1.0x10-10). These results have been treated with cluster thresholding10. Only cluster of sufficient size (128 voxels) are shown in Figure 3. In the case of the Shape Deviation Indicator, the FDR was set at 0.0005 and the results for the two TBI patients are shown in Figures 3D and 3E. Similarly, cluster thresholding was applied to the results shown in Figures 3D-E. Interestingly, the Shape Deviation Indicator of the single non-TBI subject did not have any voxel that was statistically significant at this FDR threshold. Note that no statistically significant voxel was found before the application of cluster thresholding.

DISCUSSION

The salient features of the proposed framework are rigorous statistical quantification of orientation or shape deviation on a per-voxel basis, the incorporation of FDR and FNR methods for controlling the proportions of false positives and false negatives for an orientation deviation test and a nonparametric approach to testing shape deviation of the elliptical cones of uncertainty.

The most interesting preliminary biological finding from our clinical data is that the frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as being significantly different from that of the control group. Another interesting result is that the Shape Deviation Indicator was able to separate the TBI patients from the single non-TBI subject at the chosen FDR level. The most puzzling result of this pilot study is that statistically significant voxels were found in the non-TBI subject under the orientation deviation test. Based on this preliminary test, we learned that the proposed orientation deviation test may be more sensitive to orientation changes in white matter tracts and perhaps at the cost of encountering more false positives.

Acknowledgements

C.G. Koay dedicates this work to the memory of Madam Oh Soo See. The authors would like to thank Drs Connie Duncan and Louis French for sharing TBI patients' imaging data. The authors would also like to thank Ms. Elyssa Sham for coordinating the recruitment of patients and volunteers, Mr. John A. Morissette for acquiring the clinical data, Mr. Justin S. Senseney for managing the clinical data.

References

1. Basser, P.J., Mattiello, J., Le Bihan, D., 1994b. MR diffusion tensor spectroscopy and imaging. Biophys. J. 66, 259-267.

2. Koay, C.G., Chang, L.C., Pierpaoli, C., Basser, P.J., 2007. Error propagation framework for diffusion tensor imaging via diffusion tensor representations. IEEE Transactions on Medical Imaging 26, 1017-1034.

3. Koay, C.G., Nevo, U., Chang, L.C., Pierpaoli, C., Basser, P.J., 2008. The elliptical cone of uncertainty and its normalized measures in diffusion tensor imaging. IEEE Transactions on Medical Imaging 27, 834-846.

4. Benjamini, Y., Hochberg, Y., 1995. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological) 57, 289-300.

5. Genovese, C.R., Lazar, N.A., Nichols, T., 2002. Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate. NeuroImage 15, 870-878.

6. Genovese, C., Wasserman, L., 2002. Operating characteristics and extensions of the false discovery rate procedure. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64, 499-517.

7. Oguz, I., Farzinfar, M., Matsui, J., Budin, F., Liu, Z., Gerig, G., Johnson, H.J., Styner, M.A., 2014. DTIPrep: Quality Control of Diffusion-Weighted Images. Frontiers in Neuroinformatics 8.

8. Koay, C.G., 2009. URL: http://sites.google.com/site/hispeedpackets/. Highly specific but edgily effective data-processing (HI-SPEED) software packets.

9. Zhang, H., Yushkevich, P.A., Alexander, D.C., Gee, J.C., 2006. Deformable registration of diffusion tensor MR images with explicit orientation optimization. Medical Image Analysis 10, 764-785.

10. Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., Smith, S.M., 2012. FSL. NeuroImage 62, 782-790.

Figures

(A) The Gnomonic projection maps a point, s, on the unit sphere to a point, p, on the u-v plane in which the line connecting both points also passes through the center of the unit sphere. The u-v plane is tangent to the unit sphere at (0,0,1). The inverse Gnomonic projection is the inverse of the Gnomonic projection. (B) An ellipse on the u-v plane and its inverse Gnomonic projection on the unit sphere. (C) The elliptical cone of uncertainty with its center aligned along the z-axis.

Given two distinct centers (control group [red] and individual subject [blue]) of the elliptical COUs, two scenarios are possible. (A) has a lower Type II error than (B) because the center of the control group is also deemed significantly different from that of the individual subject. In (B), the center of the control group is not significantly different from that of the individual subject because it is located within the confidence cone of the individual subject.

Results of statistically significant deviation in orientation shown in (A) red, (B) blue and (C) yellow for TBI patient I, TBI patient II and single non-TBI subject, respectively. Results of statistically significant deviation in shape of the elliptical COU shown in (D) red and (E) blue for TBI patient I and TBI patient II, respectively. No voxel was found to be statistically significant under the shape deviation test for the non-TBI subject (F).



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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