a statistical study on DT-MRI data - CiteSeerX

Variation in fiber spreading from the human corpus callosum: a statistical study on DT-MRI data P. Hagmann1,2, S. Clarke3, J-P. Thiran1, P. Maeder2, R. Meuli2 Department of Radiology2, Division of Neuropsychology3 University Hospital, Lausanne

Signal Processing Institute1 Swiss Federal Institute of Technology, Lausanne Introduction The main potential of diffusion weighted MR imaging resides certainly in its capability to give information about nerve fibre tract orientation in the brain. To isolate fibre-tracts on a 3D tensor field deterministic as well as probabilistic approaches are possible. Here a stochastic approach is implemented and used to tackle a morphological question. Histological corpus callosum (CC) studies in cat brain [1, 2] showed a: • rostro-caudal topographical order of axonal projection from the CC into the hemispheres • posterior parts of the cortex send axons though the splenium • axons coming from more rostral parts of the cortex travel through more rostral parts of the CC • axonal spreading from CC • axons travel in tight parallel bundles from the midline of the CC • reaching lateral border of lateral ventricle they spread rostrocaudally In the human our knowledge is more restricted but it seems that as far as those observations are concerned the topography remains identical. We will investigate callosal connectivity on a healthy subject with diffusion tensor (DT) MRI and fibre-tracking. Some of the results will be compared to histological studies in the cat [1,2] and human brain.

Axonal spreading from CC in human brain If we look at histological slices of a human corpus callosum, one can see that close to the midline axons run parallel to each other in tight bundles. While approaching the lateral wall of the lateral ventricle, the bundles of fibres spread ventro-dorsally. This phenomenon is also observed on the simulated trajectories inferred from our fibre-tracking algorithm.

As in cat brains rostro-caudal spreading can also be demonstrated with this algorithm.

Material, Methods and Results Acquisition The brain imaging was performed on a 1.5 Tesla MAGNETOM Symphony Scan from Siemens with a 30mT/m field gradient. 1 normalising and 6 non-collinear diffusion weighted single shot EPI images were acquired with the following parameters: • TR=10’000 s, TE=120 s, b=1000 s/mm2, 8 averaging • Voxel size: 1.64 x 1.64 x 3.3 mm, volume: 128 x 128 x 34 Tensor field was reconstructed according to Basser [3]. Fibre-tracking Fibre-tracking is based on a Monte-Carlo simulation. Axonal trajectories are modelled by the random walk of virtual particles diffusing in the tensor field. Curves are initiated in each white matter voxel. The connectivity of the whole brain is simulated by about 100’000 curves. Virtual dissection by selection of region of interest (ROI) is then performed in order to extract the tracts of interest. Connectivity can be represented in different ways. Classically the axons or fibre-tracts trajectories are represented by curves. Alternatively a “fibre density map” or a “probability of connection map” can also adequately represent brain connectivity. In such maps the brightness of the colour is proportional to the density of the fibres passing through the ROI and a given voxel.

Divergence of fibres passing through the CC In order to obtain a measure of the divergence of the fibres passing by a ROI in the corpus callosum and spreading in both hemispheres, a parameterized plane of finite dimension is place at a distance defined as the mean distance the particles have travelled when passing through the centre of the distribution and oriented so that the spreading is minimal (this means approximately orthogonal to the particle main stream). The particles that pass through the surface define a 2D probability density function (pdf) from which we can infer the covariance matrix. This covariance matrix is a good measure of the spreading of the fibres at a given distance. To have a even simpler measure of spreading one can take the first eigenvalue of this matrix. If this “spreading coefficient” (the first eigenvalue) is plotted as a function of the rostro-caudal position of the region of interest in the midline of the CC, several observations can be made: • projections in the rostral and caudal extremes of the CC remain pact in tight bundles whereas fibres leaving the body of the CC tend to diverge a lot more. • the divergence coefficient at position ten drops suddenly. The reason is not very clear. It might be linked to the natural thickness decrease of the CC at that position. 17

Rostro-caudal topographical order of callosal projections in human brain Eight-teen ROI (0 to 17) are placed all along the midline of the corpus callosum. The corresponding hemispheric fibre-projections are studied. 0

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A statistical approach towards fibre-tracking seem to be valuable. The confrontation of the traced axonal trajectories with histological data shows a good correlation in as complex structures as the CC. Nevertheless as all other recent fibre-tracking algorithms, the exact mapping of the corpus callosum still remains impossible. This seems to be inherent to the acquisition methodology: DTI hasn’t got enough angular resolution to solve fibre crossings. Newer imaging modalities, so called High Angular Resolution Imaging [4] should overcome this limitation. The presented fibre-tracking algorithm should be adaptable to such imaging modality.

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It can be shown, using fibre density maps, that there is a strong correlation between the area where the fibres decussate in the corpus callosum and their respective projections. Fibre decussating rostrally project also more rostrally than fibre decussating more caudally. We can observe topographical matching.

Bibliography [1] Nakamura H et al. Topography of the corpus callosum in the cat. Brain Res. 1989;485:171175. [2] Clarke S et al. The auditory pathway in cat corpus callosum. Exp Brain Res 1995;104:534540. [3] Basser PJ et al. A simplified method to measure the diffusion tensor from seven MR images. Magn Reson Med 1998;39:928-934. [4] Frank LR. Anisotropy in High Angular Resolution Diffusion-Weighted MRI. Magn Reson Med. 2001;45:935-939.