Abstract
Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer’s Disease (AD; 26 subjects), lateral ventricular surface morphometry in HIV/AIDS (19 subjects) and cortical surface morphometry in Williams Syndrome (WS; 80 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.
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References
Dale, A.M., Fischl, B., Sereno, M.I.: Cortical surface-based analysis I: segmentation and surface reconstruction. Neuroimage 9, 179–194 (1999)
Ashburner, J., Hutton, C., Frackowiak, R., Johnsrude, I., Price, C., Friston, K.: Identifying global anatomical differences: deformation-based morphometry. Human Brain Mapping 6(5-6), 348–357 (1998)
Chung, M., Dalton, K., Davidson, R.: Tensor-based cortical surface morphometry via weighted spherical harmonic representation. IEEE Trans. Med. Imag. 27(8), 1143–1151 (2008)
Guggenheimer, H.W.: Differential Geometry. Dover Publications (1977)
Wang, Y., Gu, X., Hayashi, K.M., Chan, T.F., Thompson, P.M., Yau, S.-T.: Brain surface parameterization using riemann surface structure. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 657–665. Springer, Heidelberg (2005)
Wang, Y., Gu, X., Chan, T.F., Thompson, P.M., Yau, S.T.: Conformal slit mapping and its applications to brain surface parameterization. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 585–593. Springer, Heidelberg (2008)
Leporé, N., Brun, C., Chou, Y.Y., Chiang, M.C., Dutton, R.A., Hayashi, K.M., Luders, E., Lopez, O.L., Aizenstein, H.J., Toga, A.W., Becker, J.T., Thompson, P.M.: Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors. IEEE Trans. Med. Imag. 27(1), 129–141 (2008)
Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Reson. Med. 56, 411–421 (2006)
Thompson, P.M., Hayashi, K.M., de Zubicaray, G.I., Janke, A.L., Rose, S.E., Semple, J., Hong, M.S., Herman, D.H., Gravano, D., Doddrell, D.M., Toga, A.W.: Mapping hippocampal and ventricular change in Alzheimer’s disease. NeuroImage 22(4), 1754–1766 (2004)
Thompson, P.M., Lee, A.D., Dutton, R.A., Geaga, J.A., Hayashi, K.M., Eckert, M.A., Bellugi, U., Galaburda, A.M., Korenberg, J.R., Mills, D.L., Toga, A.W., Reiss, A.L.: Abnormal cortical complexity and thickness profiles mapped in Williams syndrome. J. Neuroscience 25(16), 4146–4158 (2005)
Thompson, P.M., Dutton, R.A., Hayashi, K.M., Lu, A., Lee, S.E., Lee, J.Y., Lopez, O.L., Aizenstein, H.J., Toga, A.W., Becker, J.T.: 3D mapping of ventricular and corpus callosum abnormalities in HIV/AIDS. NeuroImage 31(1), 12–23 (2006)
Thompson, P.M., Woods, R.P., Mega, M.S., Toga, A.W.: Mathematical/computational challenges in creating population-based brain atlases. Human Brain Mapping 9(2), 81–92 (2000)
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Wang, Y., Chan, T.F., Toga, A.W., Thompson, P.M. (2009). Multivariate Tensor-Based Brain Anatomical Surface Morphometry via Holomorphic One-Forms. In: Yang, GZ., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009. MICCAI 2009. Lecture Notes in Computer Science, vol 5761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04268-3_42
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DOI: https://doi.org/10.1007/978-3-642-04268-3_42
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