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BUAN 2.0, streamlines as functions, nonlinear registration, and subdivision of bundles for advanced tractometry
Bramsh Qamar Chandio1,2, Sophia I Thomopoulos1, Paul M Thompson1, Jaroslaw Harezlak3, and Eleftherios Garyfallidis2
1Mark and Mary Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Marina del Rey, CA, United States, 2Department of Intelligent Systems Engineering, Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington, Bloomington, IN, United States, 3Department of Epidemiology and Biostatistics, Indiana University Bloomington, Bloomington, IN, United States

Synopsis

Keywords: Software Tools, Diffusion/other diffusion imaging techniques, Tractography, tractometry, bundle segmentation, white matter tracts, group analysis

We propose BUAN 2.0, which adds new advancements to its predecessor BUAN. It sub-segments bundles with varying substructures in them. It uses nonlinear registration of bundles to find accurate correspondences among bundle segments across subjects. The number of horizontal segments is decided based on the bundle and data specifications. More importantly, in BUAN 2.0, instead of treating each point on the streamline as an independent observation, we treat each streamline as a complete entity, as a function. Streamlines are analyzed by deploying functional data analysis (FDA) methods for studying group differences in populations along the length of the tracts.

Introduction

Tractometry methods aim to quantify microstructural differences in populations along the length of the tracts. Current tractometry methods do not consider substructures within bundles. An arbitrary number of nodes/segments are created along the length of the tracts. Furthermore, data per streamline node/segment coming from groups are analyzed independently without considering the neighborhood information on the streamlines. In BUAN 2.0, we address the above-mentioned limitations for advancing the tractometric analysis. BUAN 2.0 adds new advancements to its predecessor, BUAN1. BUAN 2.0 introduces an approach for the vertical sub-segmentation of those bundles with varying substructures. It uses nonlinear registration of bundles to find accurate correspondences among bundle segments across subjects. The number of horizontal segments is decided based on the average length of the bundle and the voxel size of the diffusion data. More importantly, in BUAN 2.0, we treat an entire streamline as a curve, a function. Streamlines are analyzed by deploying functional data analysis (FDA)2 methods for studying group differences in populations along the length of the tracts. Final statistical analysis always takes place in the subjects’ native diffusion space without any impact of linear or nonlinear registration on streamlines or microstructural measures. Results are presented using the publicly available Alzheimer’s Disease Neuroimaging Initiative phase 3 (ADNI3)3,4 dataset.

Methods

BUAN 2.0 adds four new additions/enhancements to BUAN1 after the bundle extraction step. Bundle extraction steps in BUAN 2.0 are the same as in BUAN. Briefly, we start by registering whole-brain tractograms of subjects to HCP-842 atlas tractogram in MNI space. Bundles are extracted from registered tractograms using auto-calibrated RecoBundles (aRB)1,6. aRB returns bundles in both native space and common space (i.e., MNI).

Below is the summary of the new steps introduced in BUAN 2.0:

  • Nonlinearly register subject's bundles to model bundles using deformable BundleWarp registration7,8.
  • Create vertical segments (sub-division) on bundles, if necessary (Fig.1.A). MDF9 distance is calculated among the subject’s streamlines and model bundle centroid streamlines, streamlines are assigned to the vertical segment based on the closest distance to the centroid streamline (Fig.3.B). Model bundle centroids are always kept the same for all subjects.
  • Create n horizontal segments based on the length and voxel size of the diffusion data (Fig.1.B, Fig.3.C). Calculated by $$\text{Number of horizontal segments} = \frac{\text{Average Euclidean length of the bundle}}{voxel\_size+0.5}$$ Project microstructural measures onto segments in the native space.
  • Run function-on-scalar (fosr) regression10 to find group differences along the length of the bundles (Fig.1.C). Functional responses are recorded for observations over time or location in our case. The functional regression method gives us a smooth functional response, Y(t), to known covariates, X, by a linear combination of parameter functions, β(t). β(t) are to be estimated. A linear function-on-scalar regression10 in a matrix form2 is given by:
    • Y(t) = β(t)X +ε(t)
      • Y(t)Nxm is a matrix of functional responses such as fractional anisotropy (FA) curves. N is the number of streamlines, and m is equal to the number of horizontal segments on a bundle.
      • XNxq is a design matrix.
      • β is a matrix of functions of t and characterizes the association between Y (e.g., FA) with covariate of interest such as group.
      • ε(t) is an error term.

Results

We multi-shell diffusion MRI (dMRI) data from 131 ADNI33 participants (age: 55-91 years, 74F, 57M) scanned on 3T Siemens scanners. dMRI consisted of 127 volumes; 13 b0, 48 b=1,000, 6 b=500 and 60 b=2,000 s/mm2 volumes with an isometric 2-mm voxel size. Participants included 44 with mild cognitive impairment (MCI) and 87 cognitively normal controls (CN). dMRI were pre-processed using the ADNI3 dMRI 4, correcting for artifacts including noise, Gibbs ringing, eddy currents, bias field inhomogeneity, and echo-planar imaging distortions. We applied multi-shell multi-tissue constrained spherical deconvolution11 and probabilistic particle filtering tracking12 to generate whole-brain tractograms using DIPY13. BUAN 2.0 was run to extract 18 bundles per subject and analyze them to find group differences on the FA metric.

Group differences are considered significant if β1(t) diverges +/- 0.02 from zero slope. BUAN 2.0 generates smooth β1(t) curves incorporating neighborhood information on streamlines. Fig 4. Shows results on corticospinal tracts (CST). BUAN 2.0 is able to highlight specific regions on bundles that are significant. Fig 5. Shows results on all 18 tracts along with mean group FA differences plots. Overall, we see a similar trend of FA being lower in the MCI group for tracts with significant group differences.

Discussion and Conclusion

We introduce BUAN 2.0, which brings new advancements to the BUAN tractometry pipeline. BUAN 2.0 adds the vertical sub-segmentation of those bundles that have differing substructures within them. It uses BundleWarp nonlinear registration of bundles to find better correspondences among different subjects' bundles. The number of horizontal segments is decided based on the average length of the bundle and the voxel size of the diffusion data. BUAN 2.0 addresses the most significant limitation of current tractometry methods, where points on the streamlines are treated as independent variables in the statistical analysis step without considering that points are connected with neighboring points on a streamline. BUAN 2.0 treats each streamline as a function. It deploys FDA methods to study group differences in populations along the length of the tracts.

Acknowledgements

This research was supported by the NIH National Institute of Biomedical Imaging and Bioengineering under award number R01EB027585 and the NIH (National Institutes of Health) 2R01EB017230-05A1 grant. It was also supported by the NIH under the AI4AD project grant U01 AG068057, grant numbers P41 EB015922, and RF1 AG057892.

References

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[2] Ramsay, JO., Functional data analysis. Encyclopedia of Statistical Sciences, 4, 2004.


[3] Zavaliangos-Petropulu, A., Nir, T.M., Thomopoulos, S.I., Reid, R.I., Bernstein, M.A., Borowski, B., Jack Jr, C.R., Weiner, M.W., Jahanshad, N. and Thompson, P.M., 2019. Diffusion MRI indices and their relation to cognitive impairment in brain aging: the updated multi-protocol approach in ADNI3. Frontiers in Neuroinformatics, 13, p.2.


[4] Thomopoulos, S.I., Nir, T.M., Villalon-Reina, J.E., Zavaliangos-Petropulu, A., Maiti, P., Zheng, H., Nourollahimoghadam, E., Jahanshad, N., Thompson, P.M., for the Alzheimer’s Disease Neuroimaging Initiative. Diffusion MRI Metrics and their Relation to Alzheimer’s Disease Severity: Effects of Harmonization Approaches. SIPAIM 2021, Campinas, Brazil. 2021.


[5] Yeh, F.C., Panesar, S., Fernandes, D., Meola, A., Yoshino, M., Fernandez-Miranda, J.C., Vettel, J.M. and Verstynen, T., 2018. Population-averaged atlas of the macroscale human structural connectome and its network topology. NeuroImage, 178, pp.57-68.


[6] Garyfallidis, E., Côté, M.A., Rheault, F., Sidhu, J., Hau, J., Petit, L., Fortin, D., Cunanne, S. and Descoteaux, M., 2018. Recognition of white matter bundles using local and global streamline-based registration and clustering. NeuroImage, 170, pp.283-295.


[7] Chandio, B.Q. and Garyfallidis, E., 2020. StND: Streamline-based non-rigid partial-deformation tractography registration. Medical Imaging Meets NeurIPS.


[8] Chandio, B.Q., 2022. Advancing White Matter Tractometry of the Brain Using Diffusion MRI and Machine Learning, PhD thesis, Indiana University.


[9] Garyfallidis, E., Brett, M., Correia, M.M., Williams, G.B. and Nimmo-Smith, I., 2012. Quickbundles, a method for tractography simplification. Frontiers in Neuroscience, 6, p.175.


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Figures

BUAN 2.0 overview. (A) shows input bundle Arcuate Fasciculus in the Left hemisphere (AF_L) divided into two vertical segments. Vertical segments and horizontal segments per vertical segment are visualized in (B). (C) shows the process of analyzing vertical segments on AF_L from different subjects and groups using function-on-scalar regression (fosr).

Visualization of bundles with and without vertical segments that are used in BUAN 2.0. Each box represents a bundle type with right and left hemispheric bundles visualized in that order. Some bundles are divided into vertical segments based on substructures present in them, such as Corticospinal Tract (CST), Occipito-Pontine Tract (OPT), Inferior Longitudinal Fasciculus (ILF) bundles, and Arcuate Fasciculus Left (AF_L), and Extreme Capsule Left (EMC_L). Others are kept as whole bundles. Different colors within a bundle represent a vertical segment (substructure in a bundle).

BUAN 2.0 process of creating horizontal segments per vertical segment. (A) shows three vertical segments visualized in different colors. (B) Each vertical segment gets a model bundle centroid visualized in yellow color. (C) Shows horizontal segments created per vertical segment based on points on streamlines belonging to the closest centroid point of its vertical segment centroid.

BUAN 2.0 results on CST_L (top) and CST_R (bottom) bundles with FA metric. From left to right, bundles with vertical segments, fosr results per vertical segment, and significant group differences highlighted on bundles with red color are visualized.

BUAN 2.0 results on 18 bundles with FA metric. Each box has a bundle type with the results plotted inside. In each box, the top row has β1(t) plots, and the bottom row has the mean FA(t) of the two groups plotted. In both plots, the x-axis has segment/location 't' along the length of the bundles.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)
3965
DOI: https://doi.org/10.58530/2023/3965