Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Podsumowanie

Diffusion tensor imaging (DTI) basically serves as an MRI-based tool to identify in vivo the microstructure of the brain and pathological processes due to neurological disorders within the cerebral white matter. DTI-based analyses allow for application to brain diseases both at the group level and in single subject data.

Streszczenie

Diffusion tensor imaging (DTI) techniques provide information on the microstructural processes of the cerebral white matter (WM) in vivo. The present applications are designed to investigate differences of WM involvement patterns in different brain diseases, especially neurodegenerative disorders, by use of different DTI analyses in comparison with matched controls.

DTI data analysis is performed in a variate fashion, i.e. voxelwise comparison of regional diffusion direction-based metrics such as fractional anisotropy (FA), together with fiber tracking (FT) accompanied by tractwise fractional anisotropy statistics (TFAS) at the group level in order to identify differences in FA along WM structures, aiming at the definition of regional patterns of WM alterations at the group level. Transformation into a stereotaxic standard space is a prerequisite for group studies and requires thorough data processing to preserve directional inter-dependencies. The present applications show optimized technical approaches for this preservation of quantitative and directional information during spatial normalization in data analyses at the group level. On this basis, FT techniques can be applied to group averaged data in order to quantify metrics information as defined by FT. Additionally, application of DTI methods, i.e. differences in FA-maps after stereotaxic alignment, in a longitudinal analysis at an individual subject basis reveal information about the progression of neurological disorders. Further quality improvement of DTI based results can be obtained during preprocessing by application of a controlled elimination of gradient directions with high noise levels.

In summary, DTI is used to define a distinct WM pathoanatomy of different brain diseases by the combination of whole brain-based and tract-based DTI analysis.

Wprowadzenie

Diffusion tensor imaging in the human brain

The white matter (WM) tracts in the central nervous system consist of densely packed axons in addition to various types of neuroglia and other small populations of cells. The axonal membrane as well as the well-aligned protein fibers within an axon restricts water diffusion perpendicular to the fiber orientation, leading to anisotropic water diffusion in brain WM ¹. Myelin sheaths around the axons may also contribute to the anisotropy for both intra- and extracellular water ².

The quantitative description of this anisotropy could be detected by diffusion tensor imaging (DTI). DTI produces images of tissues weighted with the local microstructural characteristics of water diffusion. The image-intensities at each position are attenuated, depending on the strength and direction of the so-called magnetic diffusion gradient (represented in the b-value), as well as on the local microstructure in which the water molecules diffuse ³, the diffusion coefficient D, a scalar value:

However, in the presence of anisotropy in WM, diffusion can no longer be characterized by a single scalar coefficient, but requires a tensor which in first approximation describes molecular mobility along each direction and correlation between these directions ⁴. Diffusion anisotropy is mainly caused by the orientation of fiber tracts in WM and is influenced by its micro- and macrostructural features. Of the microstructural features, intraaxonal organization appears to be of greatest influence on diffusion anisotropy, besides the density of fiber and cell packing, degree of myelination, and individual fiber diameter. On a macroscopic scale, the variability in the orientation of all WM tracts in an imaging voxel influences its degree of anisotropy ⁵.

In typical DTI measurements, the voxel dimensions are in the order of millimeters. Thus, a voxel always contains the averaged information of the water molecules inside the detected volume that usually covers several axons as well as the surrounding water molecules. Despite this multidirectional environment, DTI is sensitive to the orientation of the largest principal axis which aligns to the predominant axonal direction, i.e. the axonal contribution dominates the measured signal ².

DTI provides two types of information about the property of water diffusion: first, the orientation-independent extent of diffusion anisotropy ⁵ and second, the predominant direction of water diffusion in image voxels, i.e. the diffusion orientation ⁶.

The current protocols are supposed to provide a framework of DTI analysis techniques for quantitative comparison of subject groups at the group level, as outlined in the following.

Quantification of diffusion properties - analysis parameters

The elements of the symmetric tensor can be measured by diffusion gradients along at least six non-collinear and non-coplanar directions so that b (Equation 1) has become a tensor, resulting in signal attenuation

This equation requires accounting for possible interactions between imaging and diffusion gradients that are applied in orthogonal directions (cross terms) and even between imaging gradients that are applied in orthogonal directions ⁴.

The second-rank diffusion tensor can always be diagonalized leaving only three non-zero elements along the main diagonal of the tensor, i.e. the Eigenvalues ( ). The Eigenvalues reflect the shape or configuration of the ellipsoid. The mathematical relationship between the principal coordinates of the ellipsoid and the laboratory frame is described by the Eigenvectors

Since there are several challenges in displaying tensor data, the concept of diffusion ellipsoids has been proposed ³. The Eigendiffusivities of these ellipsoids represent the unidimensional diffusion coefficients in the main direction of diffusivities of the medium, i.e. the main axis of the ellipsoid represents the main diffusion direction in the voxel which coincides with the direction of the fibers, while the eccentricity of the ellipsoid provides information about the degree of anisotropy and its symmetry. Therefore, diffusion anisotropy metrics such as the fractional anisotropy (FA) could be defined ⁷.

is the arithmetic average of all Eigenvalues.

An additional approach is to use the principal direction of the diffusion tensor to address the WM connectivity of the brain, corresponding to the tractography approach which has the intention to investigate which parts of the brain are connected to each other. Assuming that the orientation of the major component of the diffusion tensor represents the orientation of the dominant axonal tracts, a 3-D vector field is provided in which each vector represents the fiber orientation. Currently, there are several different approaches to reconstruct WM tracts which could be divided into two types: the first category is based on line propagation algorithms using the local tensor information for each step of the fiber tract propagation ^2,8,9. The second category is based on global energy minimization to find the energetically most favorable path between two WM regions, resulting in the approach of tract-based spatial statistics (TBSS) ¹⁰ which has been used in other algorithms such as tractwise fractional anisotropy statistics (TFAS - see protocol text, section 2.4.).

Transformation into stereotaxic standard space

Like in other advanced MRI methods, DTI- and FT-based studies in a clinical context pursue the ultimate goal to categorize individual patient's brain morphology in order to facilitate the diagnostic process based on some discrimination metric ¹¹. Studies at the group level are most relevant if the common clinical phenotype is supposed to be due to damage to one or more specific brain areas or a specific neuroanatomical network. Here, averaging of results for different subjects is useful in order to assess common patterns of microstructural alterations. Each individual brain has to be transferred into stereotaxic space so that, in a second step, the arithmetic averaging of the results at a voxel-by-voxel level is possible. Spatial normalization allowed for arithmetic averaging of the results obtained from different subjects in order to improve the signal-to-noise ratio (SNR) and to perform a comparison of samples of patients and controls in order to analyze the computational pathoanatomy of a specific disorder, e.g. a neurodegenerative disease which is associated with the affectation of a specific brain system.

The early approach of normalization to a standardized stereotaxic space by ¹² suggested a transformation algorithm to a standard atlas involving the identification of various brain landmarks and piecemeal scaling of brain quadrants. Nowadays, most of the advanced MRI data analysis packages use normalization to the Montreal Neurological Institute (MNI) stereotaxic space ¹³. For this transformation, semiautomatic and automated brain registration algorithms using study specific templates were developed ^14,15. In DTI, special attention has to be drawn to preserve the directional information during the normalization process ^16,17. The application of spatial transformations to DT-MR images which are required for spatial normalization of collections of data sets is, in contrast to warping scalar images, complicated by the fact that DTs contain orientational information which is again affected by the transformation. This effect must be accounted for in order to ensure the anatomical correctness of the transformed image. Here, techniques for applying affine transformations to DTI data sets are presented.

Application of DTI to brain diseases

The comparison of longitudinal DTI data requires an alignment/registration of one subject's data among each other. In that context, preservation of the directional information is necessary (i.e. rotation of the diffusion tensor during affine transformations). Possible applications to neurodegenerative disorders have been reported previously (e.g. ^18,19).

DTI has been established as a robust non-invasive technical tool to investigate in vivo neuropathology of WM neuronal tracts (e.g. ^11,20,21,22). DTI-based quantitative metrics of the diffusion process, e.g. the FA, have already been shown to be sensitive markers for studying a wide range of WM pathologies, such as stroke ²⁰, multiple sclerosis ²³, amyotrophic lateral sclerosis ^{24, 25}, Alzheimer's disease ²⁶, and several other WM disorders ^27,28.

Additionally, DTI with FT can be used to identify WM tracts ²³. This technique, while still not in routine clinical use, is emerging as a powerful instrument for the assessment of pathway-specific abnormalities in neurological disease. Within the identified tracts, various quantitative MRI indices derived from DTI and additional acquisitions (e.g. T2-weighted images and/or magnetization transfer (MT) imaging) that are anatomically coregistered to the DTI data could be measured. Hereby, each index could be calculated as a function of position within the tract, referring to plots depicting their spatial variation as tract profiles.

In the following, human DTI scans which were performed on 1.5 Tesla MRI-scanners (Siemens Medical, Erlangen, Germany) were used to investigate the potential of various analysis techniques for detecting white matter abnormalities in patient groups as well as in individuals. After an automated quality check for the elimination of motion-corrupted volumes and volumes with other kinds of artifacts, standardized postprocessing procedures prepare the DTI data for the consecutive analysis. Different analysis approaches will be illustrated in the following, i.e. first, whole brain based spatial statistics (WBSS), second, FT, and third, Tractwise fractional anisotropy statistics (TFAS). WBSS is a method that runs in analogy to voxel-based morphometry (VBM) which is usually known as voxel-based morphometry/statistics on DTI data (VBM/DTI). VBM is a method that originally runs on contrast images where contrast differences in separate scans have to be resolved while WBSS is a method that uses the voxelwise comparison of a physical parameter. Therefore, although algorithmically similar, a terminology which is differentiating WBSS and VBM will be used in the following.

Protokół

Analysis Methods: Pre- and Postprocessing

The task of the following protocol is to analyze diffusion properties voxelwise within white matter tracts which could be - due to the voxelwise detection - either isotropic or anisotropic, resulting in prolate or oblate diffusion tensors for the respective voxels. The parameterization of the voxel tensors is used for either the calculation of FA-maps or the identification of fibertracts (Figure 1).

In order to obtain analysis results as shown in the following, use the software package Tensor Imaging and Fiber Tracking (TIFT) ¹⁷. TIFT provides analysis tools for the following requirements:

• analysis in terms of DTI metrics, e.g. FA-maps,
• stereotaxic normalization
• group comparison in terms of FA or other DTI metrics
• various analysis approaches of FT
• FT on group averaged DTI data and the corresponding statistical analysis.

These features allow a variety of analyses in one software environment ^17,29,30,31. The TIFT software is constantly under development for new options in DTI data analysis.

Figure 2 gives a schematic overview how to analyze DTI data at the group level after spatial normalization by two complementary approaches, i.e. both by WBSS and by TFAS to finally obtain differences between subject samples at the group level, e.g. diseased brains versus healthy controls. Here, WBSS aims at a voxelwise unbiased detection of areas with differences at the group level, whereas TFAS is based upon pre-defined fibertracts; the TFAS starting areas can either be freely chosen or can be derived from the WBSS results (`hotspots` of significantly altered FA).

Individual longitudinal comparison of FA-maps is performed by detecting differences in FA-maps of measurements at different timepoints after affine stereotaxic alignment (Figure 2).

1. Quality check (QC) including correction for corrupted gradient directions
   In case of motion disturbances during the acquisition, i.e. in case of corrupted volumes, an SNR increase is obtained by omitting single gradient directions (GD) for tensor calculation. For that purpose, a quality check (QC) algorithm ³² was developed. In brief, for scans that contained corrupted volumes, an SNR increase is achieved by omitting single gradient directions one at a time before tensor estimation: for each GD, the weighted variance is computed from all remaining directions in the sequence by weighting with the angle in which they differed from the index GD.
   1. Perform an artifact correction by detecting GD with at least one slice showing decreased intensity, i.e. motion artifacts caused by spontaneous subject movement (Figure 3, upper panel). For any diffusion weighted volume, compute the mean intensity for each slice and compare its intensity with the same slice in all other volumes by using a weighted average approach - the weighting factor is the dot product of vectors of two GD :
      
      
      denotes the arithmetic average intensity of the slice under observation and a slice for comparison. The relative average intensity deviation is weighted by the dot product of the GD. Thus, in order to define a global parameter:
      
      reflects the minimum of slicewise comparisons of all slices.
   2. If Q is under a certain threshold (in the example, a threshold of 0.8 is used for this purpose), eliminate that whole volume, or GD. A threshold of 0.8 is considered a stable solution ³². Figure 3 illustrates motion artifacts visible in sagittal reconstructions and detected by the QC algorithm. In this example, out of the total number of GD (blue dots in Figure 3c), 17 were below the red line which corresponds to Q = 0.8 and should be eliminated. An example of a volume elimination statistics for a whole study is presented in Figure 3d. In this exemplary study, DTI data of 29 presymptomatic HD subjects were compared to DTI data of 30 controls. Further details of this algorithm are presented in ^{32, 33}.
2. Preprocessing and spatial normalization
   1. Perform the correction of eddy current-induced geometric distortions of the echo-planar imaging data sets by the method proposed by ³⁴.
   2. For the stereotaxic normalization, create a study-specific (b = 0) - template and an FA-template as previously described ^17,28,31. Basically, a complete non-linear stereotaxic normalization consists of three deformation components. Consequently, the resulting diffusion tensor of each voxel i has to be rotated according to all the rotations listed above (Figure 4):
      1. Figure 4a shows a rigid brain transformation to align the basic coordinate frames. The rotation resulting from the aligning to the basic coordinate frame has to be applied
         
      2. Figure 4b shows a linear deformation according to landmarks. The components of the Eigenvectors have to be adapted according to the six normalization parameters of S (dependent on the brain region s_a,, a=1...6) of the linear deformation.
         v_w,j'''=s_av_w,j'''
         w=1,2,3 and j=x,y,z.
      3. Figure 4c shows a non-linear normalization equalizing non-linear brain shape differences. The 3-D vector shifts are different for each voxel leading to a separate transformation for each voxel of the 3-D voxel array ). Standard trigonometry gives a rotation matrix independently for each voxel, resulting from the 3-D vector shifts following the concepts of ¹⁶ in order to preserve the directional relations between Eigenvectors of neighbored voxels. Thus, different shifts of two neighbored voxels result in rotations of the corresponding Eigenvectors. Use the dilation matrices for the alignment of the tensor of each voxel to the surrounding voxels.
         
         are the components of
      The whole normalization process is iterative, i.e. create a scanner- and sequence-specific (b = 0) - template for this study in the first step by arithmetically averaging the (b = 0) - volumes of all subjects after linear transformation according to manually set landmarks. After this first normalization, create improved templates in order to optimize the normalization matrices. The following steps 1.2.3 up to 1.2.5 are schematically visualized in Figure 5a.
   3. After this individual normalization procedure (step (i) - DTI-data I₀), use all individual DTI data sets for creating a study-specific (b = 0) - template and an FA-template (step (ii) - templates T₁). As the non-affine registration to an FA-template has the advantage that it provides more contrast in comparison to (b = 0) images ¹⁰, define an FA-template by averaging all individually derived FA-maps of the patients and the controls.
   4. In a second step, following the basic ideas of Ashburner and Friston ³⁵, perform a non-linear MNI normalization (step (iii)) of the DTI data sets by minimizing the mismatch between regional intensities of the FA-map to be fitted and of the FA-template according to the squared differences (X²) - that way, you obtain DTI data I₁.
   5. Based on these data, new templates T₂ are derived (step (iv)). Repeat this iterative process until the correlation between individual FA-maps and the FA-template is > 0.7. Usually this is reached after two iterations.
3. Whole brain-based spatial statistics
   The following steps 1.3.1 up to 1.3.5 are visualized schematically in Figure 5b.
   1. Calculate FA-maps from normalized DTI data with respect to normalization procedure of 1.2. in order to preserve directional information (step (i)).
   2. As a preprocessing step before voxelwise statistical comparison, apply a smoothing filter (step (ii)) to the individual normalized FA-maps. For smoothing, the fact that the filter size influences the results of DTI data analysis ³⁶ requires application of the matched filter theorem which states that the width of the filter used to process the data should be tailored to the size of the expected difference, as detailed in previous applications to DTI data of patients with neurodegenerative disorders (e.g. ²⁸).
   3. Perform statistical comparison between the patient groups and the corresponding control group voxelwise by Student´s t-test, i.e. compare FA values of the patients' FA-maps with the FA values of the controls' FA-maps, for each voxel separately (step (iii)). FA values below 0.2 are not considered for calculation since cortical grey matter shows FA values up to 0.2 ³⁷.
   4. Statistical results have to be corrected for multiple comparisons using the false-discovery-rate (FDR) algorithm at p < 0.05 ³⁸ (step (iv)). Further reduction of the alpha error has to be performed by a spatial correlation algorithm (clustering - step (v)) that eliminated isolated voxels or small isolated groups of voxels in the size range of the smoothing kernel, leading to a threshold cluster size of 512 voxels.
   5. To display the results on a morphological background (step (v)), normalize the 3-D T1 weighted data sets to MNI space and average arithmetically. Perform this normalization procedure by use of a study-specific template in analogy to the normalization applied to the DTI data sets ¹⁷.

Figure 6 shows results of the whole brain-based spatial statistics (WBSS) of ALS patients vs. controls. Figure 6a shows the local maximum of decreased FA values in a sagittal, coronar and axial view (thresholded at p < 0.01, corrected for multiple comparisons). Figure 6b shows projectional FT with starting points in the corticospinal tract used as basis for TFAS. Figure 6c shows group differences in FA-maps detected by whole brain based spatial statistics (WBSS) between a sample of ALS patients and matched controls in a slicewise visualization.

4. Tractography and tractwise fractional anisotropy statistics (TFAS)
   Figure 7 illustrates the process of group-based FT including TFAS as described in 1.4.1 up to 1.4.4.
   1. In order to apply group-based FT algorithms, generate averaged DTI data sets from the patients' data and from the controls' data together according to the methods previously described ¹⁷. This averaging requires careful treatment of the orientational information which is preserved during the normalization process according to techniques described by ¹⁶ - for details see ³⁰.
   2. Perform tractography in averaged DTI data sets of subject groups by application of a streamline tracking technique ³¹. Identify manually defined seed points adjacent to the local maxima by the whole brain-based FA analyses which are the basis for the consecutive FT analysis. After identification of the seeds, perform tractography and define the voxels of the delineated fibers as a group-specific mask for the following TFAS ³⁰.
   3. In order to quantify the tractography results, apply the technique of TFAS by using the fiber tracts that were created on the averaged DTI data sets of all subjects of each group (patient data and control data together) for the selection of the voxels that contribute to a comparison between the patients' and the controls' FA-maps.
   4. Consider all resulting voxels with an FA value above 0.2 for statistical analysis by Student's t-test.
   5. If desired, the TFAS technique could be applied to any derived DTI metrics, such as mean diffusivity (MD), radial anisotropy, axial anisotropy, etc. (for an example, see ²⁸).
   6. The results are displayed on a morphological background consisting of the MNI-normalized 3-D T1-weighted data sets.

Wyniki

1. QC and correction for corrupted gradient directions in application to data of patients with hyperkinetic disorders

As an example for the effect of the application of QC and subsequent volume exclusion (as a consequence from the correction for corrupted GD), Figure 8 shows differences in whole brain based spatial statistics with and without volume exclusion for group comparison of 29 premanifest Huntington's disease subjects vs. 30 age and gender matched controls. The scanning ...

Dyskusje

Inter-subject averaging of DTI data can be achieved with respect to diffusion amplitude (by use of FA information) and diffusion direction (based upon FT), respectively. Averaging of FA maps allows for the statistical comparison of subject groups by WBSS and TFAS. This methodological framework gives an introduction to DTI techniques with inter-subject averaging and group comparison. Stereotaxic normalization and comparison of FA maps at the group level allows for several possibilities to quantify differences between subj...

Materiały

Name	Company	Catalog Number	Comments
MR scanner			Siemens 1.5 T Magnetom Symphony
analysis software			TIFT - Tensor Imaging and Fiber Tracking