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Hierarchical Geodesic Modeling on the Diffusion Orientation Distribution Function for Longitudinal DW-MRI Analysis

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 12267)

Abstract

The analysis of anatomy that undergoes rapid changes, such as neuroimaging of the early developing brain, greatly benefits from spatio-temporal statistical analysis methods to represent population variations but also subject-wise characteristics over time. Methods for spatio-temporal modeling and for analysis of longitudinal shape and image data have been presented before, but, to our knowledge, not for diffusion weighted MR images (DW-MRI) fitted with higher-order diffusion models. To bridge the gap between rapidly evolving DW-MRI methods in longitudinal studies and the existing frameworks, which are often limited to the analysis of derived measures like fractional anisotropy (FA), we propose a new framework to estimate a population trajectory of longitudinal diffusion orientation distribution functions (dODFs) along with subject-specific changes by using hierarchical geodesic modeling. The dODF is an angular profile of the diffusion probability density function derived from high angular resolution diffusion imaging (HARDI) and we consider the dODF with the square-root representation to lie on the unit sphere in a Hilbert space, which is a well-known Riemannian manifold, to respect the nonlinear characteristics of dODFs. The proposed method is validated on synthetic longitudinal dODF data and tested on a longitudinal set of 60 HARDI images from 25 healthy infants to characterize dODF changes associated with early brain development.

Keywords

Diffusion weighted imaging Longitudinal analysis Hierarchical geodesic modeling 

Notes

Acknowledgements

This work was supported by the NIH grants R01-HD055741-12, 1R01HD089390-01A1, 1R01DA038215-01A1 and 1R01HD088125-01A1.

Conflict of Interest Statement

The authors declare that there are no conflicts or commercial interest related to this article.

Supplementary material

505220_1_En_31_MOESM1_ESM.pdf (147 kb)
Supplementary material 1 (pdf 147 KB)

Supplementary material 2 (mp4 6718 KB)

References

  1. 1.
    Allassonnière, S., Chevallier, J., Oudard, S.: Learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data. In: Advances in Neural Information Processing Systems, pp. 1152–1160 (2017)Google Scholar
  2. 2.
    Bône, A., Colliot, O., Durrleman, S.: Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 9271–9280 (2018)Google Scholar
  3. 3.
    Chen, Y., et al.: Longitudinal regression analysis of spatial-temporal growth patterns of geometrical diffusion measures in early postnatal brain development with diffusion tensor imaging. Neuroimage 58(4), 993–1005 (2011)CrossRefGoogle Scholar
  4. 4.
    Cohen-Adad, J., Descoteaux, M., Wald, L.L.: Quality assessment of high angular resolution diffusion imaging data using bootstrap on q-ball reconstruction. J. Magnetic Resonance Imag. 33(5), 1194–1208 (2011)CrossRefGoogle Scholar
  5. 5.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical q-ball imaging. Magnetic Resonance Med. Official J. Int. Soc. Magnetic Resonance Med. 58(3), 497–510 (2007)CrossRefGoogle Scholar
  6. 6.
    Du, J., Goh, A., Kushnarev, S., Qiu, A.: Geodesic regression on orientation distribution functions with its application to an aging study. NeuroImage 87, 416–426 (2014)CrossRefGoogle Scholar
  7. 7.
    Dubois, J., Dehaene-Lambertz, G., Kulikova, S., Poupon, C., Hüppi, P.S., Hertz-Pannier, L.: The early development of brain white matter: a review of imaging studies in fetuses, newborns and infants. Neuroscience 276, 48–71 (2014)CrossRefGoogle Scholar
  8. 8.
    Durrleman, S., Pennec, X., Trouvé, A., Braga, J., Gerig, G., Ayache, N.: Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data. Int. J. Comput. Vis. 103(1), 22–59 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fitzmaurice, G.M., Laird, N.M., Ware, J.H.: Applied longitudinal analysis, vol. 998. John Wiley & Sons (2012)Google Scholar
  10. 10.
    Fletcher, P.T.: Geodesic regression and its application to shape analysis. In: Innovations for Shape Analysis, pp. 35–52. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-34141-0_2
  11. 11.
    Garyfallidis, E., et al.: Dipy, a library for the analysis of diffusion MRI data. Front. Neuroinform. 8, 8 (2014)CrossRefGoogle Scholar
  12. 12.
    Gerig, G., Fishbaugh, J., Sadeghi, N.: Longitudinal modeling of appearance and shape and its potential for clinical use. Med. Image Anal. 33, 114–121 (2016)CrossRefGoogle Scholar
  13. 13.
    Goh, A., Lenglet, C., Thompson, P.M., Vidal, R.: A nonparametric riemannian framework for processing high angular resolution diffusion images (hardi). In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2496–2503. IEEE (2009)Google Scholar
  14. 14.
    Guizard, N., Fonov, V.S., García-Lorenzo, D., Nakamura, K., Aubert-Broche, B., Collins, D.L.: Spatio-temporal regularization for longitudinal registration to subject-specific 3d template. PLoS ONE 10(8), 10 (2015)Google Scholar
  15. 15.
    Hong, S., Fishbaugh, J., Wolff, J.J., Styner, M.A., Gerig, G.: Hierarchical multi-geodesic model for longitudinal analysis of temporal trajectories of anatomical shape and covariates. In: Shen, D., et al. (eds.) MICCAI 2019. LNCS, vol. 11767, pp. 57–65. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-32251-9_7CrossRefGoogle Scholar
  16. 16.
    Kim, H., Styner, M., Piven, J., Gerig, G.: A framework to construct a longitudinal dw-mri infant atlas based on mixed effects modeling of dodf coefficients. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer (2019)Google Scholar
  17. 17.
    Kim, H.J., Adluru, N., Suri, H., Vemuri, B.C., Johnson, S.C., Singh, V.: Riemannian nonlinear mixed effects models: analyzing longitudinal deformations in neuroimaging. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2540–2549 (2017)Google Scholar
  18. 18.
    Kim, J., Chen, G., Lin, W., Yap, P.-T., Shen, D.: Graph-constrained sparse construction of longitudinal diffusion-weighted infant atlases. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10433, pp. 49–56. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66182-7_6CrossRefGoogle Scholar
  19. 19.
    Pietsch, M., et al.: A framework for multi-component analysis of diffusion mri data over the neonatal period. NeuroImage 186, 321–337 (2019)CrossRefGoogle Scholar
  20. 20.
    Reynolds, J.E., Grohs, M.N., Dewey, D., Lebel, C.: Global and regional white matter development in early childhood. Neuroimage 196, 49–58 (2019)CrossRefGoogle Scholar
  21. 21.
    Rutherford, M.A.: MRI of the Neonatal Brain. Elsevier Health Sciences (2002)Google Scholar
  22. 22.
    Sadeghi, N., Prastawa, M., Fletcher, P.T., Wolff, J., Gilmore, J.H., Gerig, G.: Regional characterization of longitudinal dt-mri to study white matter maturation of the early developing brain. Neuroimage 68, 236–247 (2013)CrossRefGoogle Scholar
  23. 23.
    Schiratti, J.B., Allassonniere, S., Colliot, O., Durrleman, S.: A bayesian mixed-effects model to learn trajectories of changes from repeated manifold-valued observations. J. Mach. Learn. Res. 18(1), 4840–4872 (2017)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Serag, A., et al.: Construction of a consistent high-definition spatio-temporal atlas of the developing brain using adaptive kernel regression. NeuroImage 59(3), 2255–2265 (2012)CrossRefGoogle Scholar
  25. 25.
    Singh, N., Hinkle, J., Joshi, S., Fletcher, P.T.: Hierarchical geodesic models in diffeomorphisms. Int. J. Comput. Vis. 117(1), 70–92 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Srivastava, A., Jermyn, I., Joshi, S.: Riemannian analysis of probability density functions with applications in vision. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8. IEEE (2007)Google Scholar
  27. 27.
    Van Hecke, W., Emsell, L., Sunaert, S.: Diffusion Tensor Imaging: A Practical Handbook, Springer, New York (2015).  https://doi.org/10.1007/978-1-4939-3118-7
  28. 28.
    Zhang, M., Fletcher, T.: Probabilistic principal geodesic analysis. In: Advances in Neural Information Processing Systems, pp. 1178–1186 (2013)Google Scholar
  29. 29.
    Zhang, Y., Shi, F., Wu, G., Wang, L., Yap, P.T., Shen, D.: Consistent spatial-temporal longitudinal atlas construction for developing infant brains. IEEE Trans. Med. Imag. 35(12), 2568–2577 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringNew York UniversityNew YorkUSA
  2. 2.Department of NeurologyMGH, Harvard Medical SchoolBostonUSA
  3. 3.Department of PsychiatryUniversity of North CarolinaChapel HillUSA
  4. 4.Department of Computer ScienceUniversity of North CarolinaChapel HillUSA
  5. 5.Department of PsychiatryWashington UniversitySt. LouisUSA

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