Abstract
Cortical thickness estimation in magnetic resonance imaging (MRI) is an important technique for research on brain development and neurodegenerative diseases. This paper presents a heat kernel based cortical thickness estimation algorithm, which is driven by the graph spectrum and the heat kernel theory, to capture the grey matter geometry information in the in vivo brain MR images. First, we use the harmonic energy function to establish the tetrahedral mesh matching with the MR images and generate the Laplace-Beltrami operator matrix which includes the inherent geometric characteristics of the tetrahedral mesh. Second, the isothermal surfaces are computed by the finite element method with the volumetric Laplace-Beltrami operator and the direction of the steamline is obtained by tracing the maximum heat transfer probability based on the heat kernel diffusion. Thereby we can calculate the cerebral cortex thickness information between the point on the outer surface and the corresponding point on the inner surface. The method relies on intrinsic brain geometry structure and the computation is robust and accurate. To validate our algorithm, we apply it to study the thickness differences associated with Alzheimer’s disease (AD) and mild cognitive impairment (MCI) on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. Our preliminary experimental results in 151 subjects (51 AD, 45 MCI, 55 controls) show that the new algorithm successfully detects statistically significant difference among patients of AD, MCI and healthy control subjects. The results also indicate that the new method may have better performance than the Freesurfer software.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clarkson, M.J., Cardoso, M.J., Ridgway, G.R., Modat, M., Leung, K.K., Rohrer, J.D., Fox, N.C., Ourselin, S.: A comparison of voxel and surface based cortical thickness estimation methods. Neuroimage 57(3), 856–865 (2011)
Mak-Fan, K.M., Taylor, M.J., Roberts, W., Lerch, J.P.: Measures of cortical grey matter structure and development in children with autism spectrum disorder. J. Autism Dev. Disord. 42(3), 419–427 (2012)
Fischl, B., Dale, A.M.: Measuring the thickness of the human cerebral cortex from magnetic resonance images. Proc. Natl. Acad. Sci. U.S.A. 97(20), 11050–11055 (2000)
Dahnke, R., Yotter, R.A., Gaser, C.: Cortical thickness and central surface estimation. Neuroimage 65, 336–348 (2013)
Cardoso, M.J., Clarkson, M.J., Ridgway, G.R., Modat, M., Fox, N.C., Ourselin, S.: LoAd: a locally adaptive cortical segmentation algorithm. Neuroimage 56(3), 1386–1397 (2011)
Scott, M.L., Bromiley, P.A., Thacker, N.A., Hutchinson, C.E., Jackson, A.: A fast, model-independent method for cerebral cortical thickness estimation using MRI. Med. Image Anal. 13(2), 269–285 (2009)
Das, S.R., Avants, B.B., Grossman, M., Gee, J.C.: Registration based cortical thickness measurement. Neuroimage 45(3), 867–879 (2009)
Jones, S.E., Buchbinder, B.R., Aharon, I.: Three-dimensional mapping of cortical thickness using Laplace’s equation. Hum. Brain Mapp. 11(1), 12–32 (2000)
Hyde, D.E., Duffy, F.H., Warfield, S.K.: Anisotropic partial volume CSF modeling for EEG source localization. Neuroimage 62(3), 2161–2170 (2012)
Jones, G., Chapman, S.: Modeling growth in biological materials. SIAM Review 54(1), 52–118 (2012)
Cassidy, J., Lilge, L., Betz, V.: Fullmonte: a framework for high-performance monte carlo simulation of light through turbid media with complex geometry, pp. 85920H-1–85920H-14 (2013)
Liu, Y., Xing, H.: A boundary focused quadrilateral mesh generation algorithm for multi-material structures. Journal of Computational Physics 232(1), 516–528 (2013)
Lederman, C., Joshi, A., Dinov, I.: Tetrahedral mesh generation for medical images with multiple regions using active surfaces. In: Proc. IEEE Int. Symp. Biomed. Imaging, pp. 436–439 (2010)
Liu, Y., Foteinos, P.A., Chernikov, A.N., Chrisochoides, N.: Mesh deformation-based multi-tissue mesh generation for brain images. Eng. Comput. 28(4), 305–318 (2012)
Zeng, W., Guo, R., Luo, F., Gu, X.: Discrete heat kernel determines discrete riemannian metric. Graph. Models 74(4), 121–129 (2012)
Chung, M.K., Robbins, S.M., Dalton, K.M., Davidson, R.J., Alexander, A.L., Evans, A.C.: Cortical thickness analysis in autism with heat kernel smoothing. NeuroImage 25(4), 1256–1265 (2005)
Bronstein, M.M., Bronstein, A.M.: Shape recognition with spectral distances. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 1065–1071 (2011)
Sharma, A., Horaud, R.P., Mateus, D.: 3D shape registration using spectral graph embedding and probabilistic matching. Image Processing and Analysing With Graphs: Theory and Practice, 441–474 (2012)
Lederman, C., Joshi, A., Dinov, I., Vese, L., Toga, A., Van Horn, J.D.: The generation of tetrahedral mesh models for neuroanatomical MRI. Neuroimage 55(1), 153–164 (2011)
Wang, Y., Gu, X., Chan, T.F., Thompson, P.M., Yau, S.T.: Volumetric harmonic brain mapping. In: IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2004, pp. 1275–1278 (2004)
Mueller, S.G., Weiner, M.W., Thal, L.J., Petersen, R.C., Jack, C., Jagust, W., Trojanowski, J.Q., Toga, A.W., Beckett, L.: The Alzheimer’s disease neuroimaging initiative. Neuroimaging Clin. N. Am. 15(4), 869–877 (2005)
Fischl, B., Sereno, M.I., Dale, A.M.: Cortical surface-based analysis II: Inflation, flattening, and a surface-based coordinate system. NeuroImage 9(2), 195–207 (1999)
Nichols, T., Hayasaka, S.: Controlling the familywise error rate in functional neuroimaging: a comparative review. Stat. Methods Med. Res. 12(5), 419–446 (2003)
Wang, Y., Shi, J., Yin, X., Gu, X., Chan, T.F., Yau, S.T., Toga, A.W., Thompson, P.M.: Brain surface conformal parameterization with the Ricci flow. IEEE Trans. Med. Imaging 31(2), 251–264 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Wang, G. et al. (2013). A Heat Kernel Based Cortical Thickness Estimation Algorithm. In: Shen, L., Liu, T., Yap, PT., Huang, H., Shen, D., Westin, CF. (eds) Multimodal Brain Image Analysis. MBIA 2013. Lecture Notes in Computer Science, vol 8159. Springer, Cham. https://doi.org/10.1007/978-3-319-02126-3_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-02126-3_23
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02125-6
Online ISBN: 978-3-319-02126-3
eBook Packages: Computer ScienceComputer Science (R0)