References:[1] S.M. Smith et al. (2004) Advances in functional and structural MR image analysis and implementation in FSL. Neuroimage 23:208-219

[2] S.M. Smith et al. (2006) Tract-based spatial statistics: Voxelwise analysis of multi-subject diffusion data. Neuroimage 31:1487-1505

[3] C. Pierpaoli, P.J. Basser (1996) Toward a quantitative assessment of diffusion anisotropy. Magnetic Resonance in Medicine 36:893-906

Acknowledgement:

Work supported by NINDS grant 48299 (JASK).

Methods:

DTI scans from College football players who suffered a concussion were taken within 24h of the injury with follow up scans about one and two weeks later;

Eigenvalues and eigenvectors of the diffusion tensor were calculated for each voxel using FSL [1] and the three scans were co-registered using TBSS [2];

The lattice index together with a color component encoding scheme (see below) was used to identify regions where the scans show differences in the integrity of the white matter. In such a scheme the scans in the sequence are encoded by different colors thereby highlighting brain regions where structural changes over time take place as colored whereas areas that do not change appear gray;

In these regions additional analysis was performed by investigating the vector field that corresponds to the dominating eigenvalue.

Introduction:Diffusion tensor imaging (DTI) has been applied to a great variety of neurological diseases and brain injuries. One of the problems that still faces this technology originates from the fact that tensors are difficult to visualize and the various scalar quantities that can be derived from the tensors’ eigenvalues and eigenvectors, like fractional anisotropy (FA), mean diffusivity (MD) or the linear, planar and spherical coefficient (see fig. 1), may or may not be appropriate for a given application. Here we extend DTI into the temporal domain by comparing such measures within sequences of scans obtained from subjects who suffered a concussion. In such scans we expect to find differences in the structural integrity of the white matter during the recovery period. We also propose an analysis technique that can lead to a better diagnosis and classification of the severity of mild traumatic brain injuries (MTBI).

Fig. 1: Scalar quantities derived from the diffusion tensor that allow for quantifying the degree of anisotropy.

1 2l

1

λ - λc =

λ

linear coefficient

2 3p

1

λ - λc =

λ

planar coefficient

3s

1

λc =

λ

spherical coefficient

2 2 21 2 1 3 2 3

2 2 21 2 3

(λ - λ ) + (λ - λ ) + (λ - λ )FA =

λ + λ + λ1 2 3λ + λ + λ

MD =3

fractional anisotropy

mean diffusivity

Fig. 3: Vector field that corresponds to the dominating eigenvalue with red, green and blue indicating the components in the x-, y- and z-direction, respectively (left). Overlay of three vector fields where red, green and blue represent the different scans (right).

Lattice Index and Color Component Encoding:

The lattice index (LI) is a scalar measure, which is derived from a tensor field [3]. It quantifies the degree of similarity of tensors and therefore the structural integrity of white matter in a given region. First, a product between two tensors is defined as

from which the isotropic part, given by the product of the traces, is subtracted

Properly normalized such that LI=0 for an isotropic region and LI=1 for a region with linear diffusion the lattice index reads

Finally, the lattice index for a small spatial region is obtained by averaging the indices between a center voxel and all its 18 neighboring voxels weighted by spatial distances

Now for each voxel the lattice index is interpreted as the red, green and blue component for the first, second and third scan, respectively. Thus, if the structural organization in a given region is the same for all the scans it will appear gray. A colored area indicates a difference between the scans. Results from this procedure for two subjects are shown in fig. 2.

18

1

nr

n n

LILI

d

3 : ' 3 : '

8 4

D D D DLI

D : D' D : D D' : D'

1: ' ( ) ( )

3 race raceD D t t D : D' D D'

3 3( ) ( ) 2

1 1

{ }i ji j

i j

D : D' v v

398.1

Fig. 2: Lattice indices for three sequential scans color coded such that the first, second and third scan correspond to the red, green and blue component of a voxel, respectively. Regions where there are no differences appear gray, colored areas indicate differences. Blue means that the LI for the third scan is larger than for the first two, whereas yellow indicates a bigger LI during the first two scans compared to the third.

S1 S2

Conclusions:Reorganization in the white matter is found in sequences of DTI scans taken within 24h of a concussion and about one and two weeks later;The lattice index is a compelling measure for the comparison of the white matter integrity as is allows for a comparison of tensor properties in regions (not single voxels) therefore increasing the S/N ratio;Color component encoding is a powerful tool to identify brain regions where the white matter integrity in a sequence of scans differs and may be a powerful diagnosic technique for detecting MTBI and recovery from MTBI.

For closer investigation, the vector fields corresponding to the dominating eigenvalue for the three scans in regions with LI>0.2 are shown in fig. 3 (right). Vectors plotted on top of each other in red, green and blue show clear differences in the region where the colors appear in fig. 2, indicating a reorganization of the white matter integrity over the time span of two weeks.