A PDE Approach for Thickness, Correspondence, and Gridding of Annular Tissues. In: Heyden A, Sparr G, Nielsen M, Johansen P, editors. Computer Vision — ECCV 2002. Berlin: Springer Berlin Heidelberg; 2002. pp. 575-89. [DOI: 10.1007/3-540-47979-1_39]

Investigation of outer cortical magnetisation transfer ratio abnormalities in multiple sclerosis clinical subgroups

BACKGROUND

Pathological abnormalities including demyelination and neuronal loss are reported in the outer cortex in multiple sclerosis (MS).

OBJECTIVE

We investigated for in vivo evidence of outer cortical abnormalities by measuring the magnetisation transfer ratio (MTR) in MS patients of different subgroups.

METHODS

Forty-four relapsing-remitting (RR) (mean age 41.9 years, median Expanded Disability Status Scale (EDSS) 2.0), 25 secondary progressive (SP) (54.1 years, EDSS 6.5) and 19 primary progressive (PP) (53.1 years, EDSS 6.0) MS patients and 35 healthy control subjects (mean age 39.2 years) were studied. Three-dimensional (3D) 1×1×1mm(3) T1-weighted images and MTR data were acquired. The cortex was segmented, then subdivided into outer and inner bands, and MTR values were calculated for each band.

RESULTS

In a pairwise analysis, mean outer cortical MTR was lower than mean inner cortical MTR in all MS groups and controls (p<0.001). Compared with controls, outer cortical MTR was decreased in SPMS (p<0.001) and RRMS (p<0.01), but not PPMS. Outer cortical MTR was lower in SPMS than PPMS (p<0.01) and RRMS (p<0.01).

CONCLUSIONS

Lower outer than inner cortical MTR in healthy controls may reflect differences in myelin content. The lowest outer cortical MTR was seen in SPMS and is consistent with more extensive outer cortical (including subpial) pathology, such as demyelination and neuronal loss, as observed in post-mortem studies of SPMS patients.

A hybrid Eulerian-Lagrangian approach for thickness, correspondence, and gridding of annular tissues

We present a novel approach to efficiently compute thickness, correspondence, and gridding of tissues between two simply connected boundaries. The solution of Laplace's equation within the tissue region provides a harmonic function whose gradient flow determines the correspondence trajectories going from one boundary to the other. The proposed method uses and expands upon two recently introduced techniques in order to compute thickness and correspondences based on these trajectories. Pairs of partial differential equations are efficiently computed within an Eulerian framework and combined with a Lagrangian approach so that correspondences trajectories are partially constructed when necessary. Examples are presented in order to compare the performance of this method with those of the pure Lagrangian and pure Eulerian approaches. Results show that the proposed technique takes advantage of both the speed of the Eulerian approach and the accuracy of the Lagrangian approach.