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. 2009 Apr 15;45(3):867-79.
doi: 10.1016/j.neuroimage.2008.12.016. Epub 2008 Dec 25.

Registration based cortical thickness measurement

Sandhitsu R Das  1 , Brian B Avants, Murray Grossman, James C Gee
Affiliations

Registration based cortical thickness measurement

Sandhitsu R Das et al. Neuroimage. .

Abstract

Cortical thickness is an important biomarker for image-based studies of the brain. A diffeomorphic registration based cortical thickness (DiReCT) measure is introduced where a continuous one-to-one correspondence between the gray matter-white matter interface and the estimated gray matter-cerebrospinal fluid interface is given by a diffeomorphic mapping in the image space. Thickness is then defined in terms of a distance measure between the interfaces of this sheet like structure. This technique also provides a natural way to compute continuous estimates of thickness within buried sulci by preventing opposing gray matter banks from intersecting. In addition, the proposed method incorporates neuroanatomical constraints on thickness values as part of the mapping process. Evaluation of this method is presented on synthetic images. As an application to brain images, a longitudinal study of thickness change in frontotemporal dementia (FTD) spectrum disorder is reported.

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Figures

Fig. 1
Fig. 1
Overview of proposed methodology. The original gray matter and white matter images are shown in (a). In (b), M is the initial cortical model, a thin (one voxel thick) sheet, with the inner edge at the gray/white interface, and the outer edge within gray matter. The region enclosed in red is zoomed in to show the initial model (also in (c)), in which M is represented as a gray dotted line. Panel (d) shows how the initial model is deformed to find the estimated gray/csf interface, and establish point-to-point correspondences (green arrows). Gray levels at the gray/white interface denote the distance between corresponding points, which is the measure of thickness. The thickness values are propagated to the GM volume to generate the volumetric thickness map shown in (e), where C denotes the estimated location of gray/csf interface.
Fig. 2
Fig. 2
Examples of probability map image. WM probability map image in (a) is added to GM probability map in (b) to create combined WM and GM probability map image in (c). Correspondence is found by registering images in (a) and (c).
Fig. 3
Fig. 3
(a) and (b) show two Diffeomorphic measurements of thickness that fit the model in Figure 1 to the gray matter. Both measurements minimize the image difference term with approximately the same level of quality, but with two very different levels of deformation. Model (a) uses no explicit regularization of the deformation, and yields a more deforming thickness solution with similarity value of 242 and a first derivative based deformation value of 1.74. Model (b), on the other hand, uses Diffeomorphic regularization and produces a continuous thickness solution with similarity value of 250 and a deformation value of 0.93. The solution in (a) requires 1.86 times the deformation of the solution in (b) but gains only 3 percent improvement in similarity, when similarity is measured in the continuous domain, implying “infinitesimal” proximity of the neighboring gray matter banks. Solution (a) is also much more computationally expensive to generate and greatly violates expected thickness values. Neither solution is perfect, because the true solution is unknown within the closed sulcus – but both represent optimal solutions given the respective models.
Fig. 4
Fig. 4
(a) Ribbon shaped phantom. (b) Ribbon with sulcus phantom. Color represents measured thickness values on the surface.
Fig. 5
Fig. 5
Deformation fields showing correspondences found by Diffeomorphic mapping in a spherical phantom with no noise. A 2D slice is shown here with the solid colors representing WM (white) and GM (gray). Resolution increases from left to right. Color represents norm of the deformation field which is the estimated thickness (in mm). Histogram of measured thickness values are shown in each case.
Fig. 6
Fig. 6
Deformation fields showing correspondences defined in different ways in a ribbon shaped phantom with no noise. A 2D slice is shown here with the gray levels representing WM (light gray) and GM (gray). Color represents norm of the deformation field which is the estimated thickness. (a) Closest point-based correspondence. Notice that some correspondence lines do not seem to map to GM boundary points since many of them point to boundary locations at a different slice in 3D. (b) Radial direction based correspondence – by construction, deformation norms are tightly clustered around 3 mm –the variation around the theoretical value is only due to discretization. (c) Correspondence based on Diffeomorphic mapping – this captures the visible variation in thickness along the surface.
Fig. 7
Fig. 7
Left: No noise, Middle: Low noise, and Right: High noise – the same slice at different levels of noise and at the same spatial resolution. Top row shows slices through 3D phantom with noise added. Bottom row shows deformation fields extracted from phantoms with corresponding noise levels as well as histogram of thickness distribution in each case.
Fig. 8
Fig. 8
Results of running the proposed algorithm on a 2D high resolution brain slice. Left column: original slice (top) and the zoomed in section of cortex in inset (bottom). (a) Segmentation of the portion of the cortex in inset with all sulci resolved. (b) DiReCT correspondence from segmentation in (a). (c) Segmentation with only a few pixels of CSF resolved in the fundus. (d) DiReCT correspondence from segmentation in (c). (e) Segmentation with closed sulcus. (f) DiReCT correspondence from segmentation in (e) with a high prior making measurements unconstrained. (g) DiReCT correspondence from segmentation in (e) with a prior = 18. (h) DiReCT correspondence from segmentation in (e) with spatially varying prior, with a prior 6 on the lower bank of the closed sulcus and unconstrained elsewhere as in (f). (i) Segmentation with closed sulcus as in (e) and gyri touching each other in the middle. (j) DiReCT correspondence from segmentation in (i) with σ ≈ one voxel length. (k) DiReCT correspondence from segmentation in (i) with σ double that of (j). (l) DiReCT correspondence from segmentation in (i) with σ double that of (k). All quantities are measured in voxel units. See text for discussion.
Fig. 9
Fig. 9
Top: (a) Axial slice of skull-stripped brain. (b) Segmentation and (c) thickness map of slice in (a). Colorbar is in mm. Yellow is higher, blue is lower. Bottom Left: DiReCT maps in the template space for the same slice at (d) earlier and (e) later time points. Bottom Right: Examples of recovery of deep sulci in (f) and (g). Upper panels show original segmentation: black = background, white = WM, gray = GM, dark gray = CSF. Lower panels show recovered CSF in red.
Fig. 10
Fig. 10
Top: Mean annual decrease in thickness in different Brodmann regions. Colormap corresponds to annual thickness change in mm. Bottom: FDR corrected (p < 0.05) regions with significant reduction in thickness in 20 patients with FTD spectrum disorder. Colormap corresponds to pairwise t-statistic.
Fig. 11
Fig. 11
Voxelwise average annual thickness reduction map across subjects.
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References

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