Local tests for identifying anisotropic diffusion areas in human brain with DTI. (English) Zbl 1454.62426

Yu, Tao; Zhang, Chunming; Alexander, Andrew L.; Davidson, Richard J.

Ann. Appl. Stat. 7, No. 1, 201-225 (2013).

Summary: Diffusion tensor imaging (DTI) plays a key role in analyzing the physical structures of biological tissues, particularly in reconstructing fiber tracts of the human brain in vivo. On the one hand, eigenvalues of diffusion tensors (DTs) estimated from diffusion weighted imaging (DWI) data usually contain systematic bias, which subsequently biases the diffusivity measurements popularly adopted in fiber tracking algorithms. On the other hand, correctly accounting for the spatial information is important in the construction of these diffusivity measurements since the fiber tracts are typically spatially structured. This paper aims to establish test-based approaches to identify anisotropic water diffusion areas in the human brain. These areas in turn indicate the areas passed by fiber tracts. Our proposed test statistic not only takes into account the bias components in eigenvalue estimates, but also incorporates the spatial information of neighboring voxels. Under mild regularity conditions, we demonstrate that the proposed test statistic asymptotically follows a \(\chi ^{2}\) distribution under the null hypothesis. Simulation and real DTI data examples are provided to illustrate the efficacy of our proposed methods.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62J15	Paired and multiple comparisons; multiple testing
92C55	Biomedical imaging and signal processing

Keywords:

brain tissue; diffusion tensor; eigenvalue; fiber tracts; local test; quantitative scalar

Software:

dti

References:

[1]	Alexander, D., Gee, J. and Bajcsy, R. (1999). Similarity measures for matching diffusion tensor images. In Proceedings of the 10 th British Machine Vision Conference , 13 - 16 September 1999, University of Nottingham 93-102.
[2]	Anderson, A. W. (2001). Theoretical analysis of the effects of noise on diffusion tensor imaging. Magn. Reson. Med. 46 1174-1188.
[3]	Basser, P. J., Mattiello, J. and Lebihan, D. (1994). Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B 103 247-254.
[4]	Basser, P. J. and Pierpaoli, C. (1996). Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. B 111 209-219.
[5]	Behrens, T. E. J., Berg, H. J., Jbabdi, S., Rushworth, M. F. S. and Woolrich, M. W. (2007). Probabilistic dissusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34 144-155.
[6]	Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289-300. · Zbl 0809.62014
[7]	Chang, L.-C., Jones, D. K. and Pierpaoli, C. (2005). RESTORE: Robust estimation of tensors by outlier rejection. Magn. Reson. Med. 53 1088-1095.
[8]	Conturo, T. E., Lori, N. F., Cull, T. S., Akbudak, E., Snyder, A. Z., Shimony, J. S., McKinstry, R. C., Burton, H. and Raichle, M. E. (1999). Tracking neuronal fiber pathways in the living human brain. Proc. Natl. Acad. Sci. USA 96 10422-10427.
[9]	Dalton, K. M., Nacewicz, B. M., Johnstone, T., Schaefer, H. S., Gernsbacher, M. A., Goldsmith, H. H., Alexander, A. L. and Davidson, R. J. (2005). Gaze fixation and the neural circuitry of face processing in autism. Nat. Neurosci. 8 519-526.
[10]	Douek, P., Turner, R., Pekar, J., Patronas, N. and Bihan, D. L. (1991). MR color mapping of myelin fiber orientation. J. Comput. Assist. Tomogr. 15 923-929.
[11]	Gössl, C., Fahrmeir, L., Pütz, B., Auer, L. M. and Auer, D. P. (2002). Fiber tracking from DTI using linear state space models: Detectability of the pyramidal tract. NeuroImage 16 378-388.
[12]	Grigis, A., Renard, F., Noblet, V., Heinrich, C., Heitz, F. and Armspach, J. (2011). A new high order tensor decomposition: Application to reorientation. In ISBI 2011, Chicago , 8 th IEEE International Symposium on Biomedical Imaging 258-261.
[13]	Hasan, K. M., Parker, D. L. and Alexander, A. L. (2001). Comparison of gradient encoding schemes for diffusion-tensor MRI. Journal of Magnetic Resonce Imaging 13 769-780.
[14]	Heim, S., Fahrmeir, L., Eilers, P. H. C. and Marx, B. D. (2007). 3D space-varying coefficient models with application to diffusion tensor imaging. Comput. Statist. Data Anal. 51 6212-6228. · Zbl 1445.62193
[15]	Henkelman, R. M. (1985). Measurement of signal intensities in the presence of noise in MR images. Medical Physics 12 232-233.
[16]	Johansen-Berg, H. and Behrens, T. E. J. (2009) Diffusion MRI : From Quantitative Measurement to in-vivo Neuroanatomy . Academic Press, London.
[17]	Jones, D. K. (2003). Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magn. Reson. Med. 49 7-12.
[18]	Lazar, M. and Alexander, A. L. (2003). An error analysis of white matter tractography methods: Synthetic diffusion tensor field simulations. NeuroImage 20 1140-1153.
[19]	Li, Y., Zhu, H., Shen, D., Lin, W., Gilmore, J. H. and Ibrahim, J. G. (2011). Multiscale adaptive regression models for neuroimaging data. J. R. Stat. Soc. Ser. B Stat. Methodol. 73 559-578. · Zbl 1226.62063
[20]	Mangin, J. F., Poupon, C., Clark, C., Le Binhan, D. and Bloch, I. (2002). Distortion correction and robust tensor estimation for MR diffusion imaging. Medical Image Analysis 6 191-198. · Zbl 1041.68681
[21]	Moseley, M. E., Cohen, Y., Kucharczyk, J., Mintorovitch, J., Asgari, H. S., Wendland, M. F., Tsuruda, J. and Norman, D. (1990). Diffusion-weighted MR imaging of anisotropic water diffusion in cat central nervous system. Radiology 176 439-445.
[22]	O’Donnell, L. J. and Westin, C.-F. (2007). Automatic tractography segmentation using a high-dimensional white matter atlas. IEEE Trans. Med. Imaging 26 1562-1575.
[23]	Pepe, M. S. (2003). The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford Statistical Science Series 28 . Oxford Univ. Press, Oxford. · Zbl 1039.62105
[24]	Pierpaoli, C. and Basser, P. J. (1996). Toward a quantitative assessment of diffusion anisotropy. Magn. Reson. Med. 36 893-906.
[25]	Pierpaoli, C., Jezzard, P., Basser, P. J., Barnett, A. and Chiro, G. D. (1996). Diffusion tensor MR imaging of the human brain. Radiology 201 637-648.
[26]	Polzehl, J. and Tabelow, K. (2009). Structural adaptive smoothing in diffusion tensor imaging: The R package dti. Journal of Statistical Software 31 1-24.
[27]	Salvador, R., Peña, A., Menon, D. K., Carpenter, T. A., Pickard, J. D. and Bullmore, E. T. (2005). Formal characterization and extension of the linearized diffusion tensor model. Hum. Brain Mapp. 24 144-155.
[28]	Stejskal, E. O. and Tanner, J. E. (1965). Spin diffusion measurements: Spin echoes in the presence of a time-depend field gradient. Journal of Chemical Physics 42 288-292.
[29]	Storey, J. D. (2002). A direct approach to false discovery rates. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 479-498. · Zbl 1090.62073
[30]	Storey, J. D., Taylor, J. E. and Siegmund, D. (2004). Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: A unified approach. J. R. Stat. Soc. Ser. B Stat. Methodol. 66 187-205. · Zbl 1061.62110
[31]	Tabelow, K., Polzehl, J., Spokoiny, V. and Voss, H. U. (2008). Diffusion tensor imaging: Structural adaptive smoothing. NeuroImage 39 1763-1773.
[32]	van Gelderen, P., de Vleeschouwer, M. H., DesPres, D., Pekar, J., van Zijl, P. C. and Moonen, C. T. (1994). Water diffusion and acute stroke. Magn. Reson. Med. 31 154-163.
[33]	Xu, D., Mori, S., Solaiyappan, M., van Zijl, P. C. M. and Davatzikos, C. (2002). A framework for callosal fiber distribution analysis. NeuroImage 17 1131-1143.
[34]	Yu, T. (2009). Local tests for detecting human brain isotropy-anisotropy areas on DT-MRI. Ph.D. thesis, Univ. Wisconsin-Madison.
[35]	Yu, T., Zhang, C. M., Alexander, A. L. and Davidson, R. J. (2013). Supplement to “Local tests for identifying anisotropic diffusion areas in human brain with DTI.” . · Zbl 1454.62426
[36]	Zhang, C., Fan, J. and Yu, T. (2011). Multiple testing via \(\operatorname{FDR}_{L}\) for large-scale imaging data. Ann. Statist. 39 613-642. · Zbl 1209.62166
[37]	Zhu, H., Xu, D., Amir, R., Hao, X., Zhang, H., Alayar, K., Bansal, R. and Peterson, B. (2006). A statistical framework for the classification of tensor morphology in diffusion tensor images. Magnetic Resonance Imaging 24 569-582. · Zbl 1332.62222
[38]	Zhu, H., Zhang, H., Ibrahim, J. G. and Peterson, B. S. (2007). Statistical analysis of diffusion tensors in diffusion-weighted magnetic resonance imaging data. J. Amer. Statist. Assoc. 102 1085-1102. · Zbl 1332.62222