Diffusion tensor imaging (DTI):

Transcription

1 Diffusion tensor imaging (DTI): A basic introduction to data acquisition and analysis Matthew Cykowski, MD Postdoctoral fellow Research Imaging Center UTHSCSA Room cykowski@uthscsa.edu PART I: Acquiring DTI images 1

2 Diffusion as a probe into tissue architecture The diffusion of water molecules can be used as a probe into tissue architecture Not just for brain tissue, but also in skeletal muscle or cardiac tissue In tissues where diffusion is restricted to due some ordered structure (e.g., myelinated nerve fibers) diffusion is said to be anisotropic In MRI, diffusion is estimated by comparing the signal of images with and without (B o or S o image) dephasing gradients Restricted diffusion Due to (see figure): Closed spaces (A) e.g., within cells or axons Tortuous extracellular pathways (B) Exchange between intra- and extracellular compartments (C) At the voxel level, what is measured is apparent diffusion Le Bihan (2003) Nature Reviews Neuroscience 2

3 Diffusion-sensitizing gradients Mori and Zhang (2006) Neuron Diffusion-weighted images have signal intensities that reflect the random motion of water molecules in tissues This sensitivity is achieved by applying a pair of dephasing & rephasing gradient pulses Calculating an apparent diffusion coefficient In the most basic case, an apparent diffusion coefficient per voxel can be calculated if: a set of DWIs has been acquired One or more images without diffusion weighting have been acquired Features of the gradient pulse application (summarized in the b value ) are known 3

4 Fun stuff For a nice lecture: Diffusion-sensitizing gradients X Y Z (in magnet coordinate system) Diffusion gradients Above is a plot of a DTI experiment at the RIC: The first three rows are acquisitions without DW Rows 3-89 represent the application of DW along various non-collinear directions (this should appear relatively random!) 4

5 Sample gradients X Y Z Row 2, etc and the images formed D xx D yy D zz S o Row 1 of sample gradients D xy D yz D xz Back to the ADCs * S o Slope = D or ADC * Here are the definitions for the above: D xx 5

6 ADC mapping: limitations If you took three ADC measurements like this Gradient applications: zz xx Tissue A scanner orientation yy You could provide a fair estimate of the structure's anisotropy. However, if the three measurements were taken like this zz Gradient applications: yy xx You d have no measurements of the ADC that are either perpendicular or parallel to the long axis of the structure Tissue B scanner orientation Is there a more accurate way? Effective diffusion tensor follows from apparent diffusion coefficient ADC measurements alone can underestimate diffusion anisotropy 6

7 In a word: DT-MRI v. ADC mapping The diffusion tensor, D, removes the orientation bias in measures of tissue anisotropy Also, traditional ADC measurements imply a belief in the cylindrical symmetry of tissues According to this belief, only parallel and perpendicular measurements are needed Diffusion tensor MRI (DT-MRI) Peter Basser, NIH 7

8 DT-MRI The diffusion tensor, D, is simply a tool to account for diffusivity along the principal axes (x, y, z) of the magnet, as well as diffusivity along non-principal axes. It can be used to represent the size (e.g., mean diffusivity), the shape (e.g., fractional anisotropy), and the directional orientation (e.g., eigenvectors) of a diffusion ellipsoid. Whereas ADC was calculated with univariate linear regression, D, is estimated by multivariate regression** with the following known values: Signal intensity in DW images A b-matrix from: Vectors representing gradient application for each DWI b values used during each DW image acquisition Solve for: 6 non-redundant elements of D (in bold -->) S 0 (intercept) **there is a whole literature just on the various methods to do this.. ln(s) = ln(s 0 ) - D*b-matrix DT-MRI: the crux of the biscuit D xx D yy D zz S o (no DW) D xy/yx D xz/zx D yz/zy IMPORTANT: above are images of the tensor components AFTER these (previously) unknowns have been calculated. #1: These are NOT DW images! Therefore the intensity image corresponds to high diffusion coefficients - make sure this representation makes sense to you #2: Notice that the off-diagonal elements (e.g., Dxy or Dyz) have some seriously high intensities - this is expected and means that Peter Basser s original justification for DT-MRI (rather than ADC mapping) is pretty sound! 8

9 The tensor of diffusion coefficients.. D xx D yy D zz The tensor is manually reconstructed to test the calculation of scalar parameters.. D xy/yx D xz/zx D yz/zy An orientation-independent representation of anisotropy.. D (diff tensor) Diagonalization* *This procedure generates a representation of D in terms of its eigenvectors & eigenvalues - this representation of the data now has an intrinsic coordinate system. The eigenvalues furnish the effective diffusion distances in each of the three principal directions within the anisotropic medium - P Basser 9

10 Anisotropy With the tensor components (previous 2 slides), we can manually produce (in matlab) a rough estimate of FA FSL s FA image value = A rough estimate of diffusion ellipsoid PART II: DTI Parameters Commonly Used in Image Analysis 10

11 Quantities derived from D: What are they? Why use them? Utility: #1 : These are rotationally invariant representations: by calculating D you have removed the importance of their orientation in the patient (or monkey s) head! #2 : They are easily calculated by diagonalizing the diffusion tensor (in the simplest case a 3x3 matrix) and obtaining the eigenvalues (AKA, the principal diffusivities or L1, L2, and L3) These are the major diffusion coefficients of the intrinsic coordinate system of the voxel/ tissue #3 : Scalar parameters are more amenable to univariate statistical tests (a Student s t-test) than are matrices/ tensors to multivariate statistical tests. Tissue A scanner orientation Tissue B scanner orientation #4 : The principal diffusion directions (eigenvectors of the tensor) can be utilized to reconstruct white matter fiber tracts. DTI parameters or scalar invariants (FA, TrD, MD) Fractional anisotropy Relative anisotropy The trace of the tensor Mean diffusivity Their principal eigenvalues Axial diffusivity Some combination of non-principal eigenvalues Radial diffusivity Their principal eigenvectors 11

12 Synonyms Principal diffusion direction = 1st eigenvector = v1 L1 Highest diffusivity = l 1 = L1 = ADC II = axial diffusivity Intermediate and lowest diffusivity = l 2 & l 3 = L2 and L3 = ADC = transverse diffusivities An image formed from the L2 & L3 images is termed a radial diffusivity image V1 V1 (L2+L3)*0.5 Fractional anisotropy FA: A ratio of the squared difference between eigenvalues and their mean, to the sum of squared eigenvalues Fractional anisotropy Relative anisotropy 12

13 Anisotropy Some WM tissues exhibit very high L1 measurements relevant to L2/L3 Corpus callosum & pyramidal tracts Other WM regions exhibit lower anisotropy Centrum semiovale Trace of the tensor & mean diffusivity The trace is the sum of tensor eigenvalues and Tr(D) / 3 represents average or mean diffusivity (across all orientations) In healthy subjects, no statistically significant differences exist in the Trace measurement for gray/ white matter structures, except for the cerebral cortex 13

14 Principal eigenvectors (v1-v3) Though not discussed today, this data can be utilized in reconstructing & visualizing major fiber tracts Many of the algorithms that do this utilize some knowledge of human fiber characteristics, or will allow a probabilistic representation, or employ other restrictive features (e.g., not allowing a fiber tract to be created across the lateral ventricles) Axial & radial diffusivity: are they markers? "Although measures of anisotropy derived from DTI are commonly used as biomarkers of white matter pathology, an increase in radial diffusivity or a decrease in axial diffusivity will both cause a decrease in anisotropy. Therefore, although anisotropy is an exquisitely sensitive marker of pathology, it is not specific to either axonal damage or demyelination. The available evidence suggests that axial and radial diffusivities hold promise as specific biomarkers of white matter pathology. Specifically, demyelination is associated with an increase in radial diffusivity, presumably because the loss of myelin membrane integrity permits increased water movement perpendicular to the myelin layers. In contrast, axonal damage is associated with a decrease in axial diffusivity. Although the underlying mechanism is still unclear, the decreased axial diffusivity may result from the loss of coherent organization of the axon and many other structural and physiological mechanisms associated with axon damage and degeneration. Budde et al, (NMR Biomed., 2008) 14

15 PART III: Aligning DTI parameter images for analysis Issues The major concerns prior to carrying out voxelwise analysis are intersubject image registration & image smoothing Whole brain, VBM-style analyses Whole brain, VBM-style analyses using information about the location of WM ROI analyses (with or without alignment) Tract-Based Spatial Statistics (TBSS) 15

16 Tract-Based Spatial Statistics No n lin ear Linear N ea onlin r Target image MNI-152 FA > 0.3 Mean FA image (of study) FA > 0.2 Skeletonized FA images Tract-Based Spatial Statistics t jec b Su ) ile f d (4 Smith et al. (2006) Neuroimage Smith et al. (2006) Neuroimage 16

17 PART IV: Statistical inference on DTI parameters General linear model (GLM) X = dependent (DV) or response variable or regressand where i = scan, j = voxel g = explanatory ( EV ) or independent or predictor variable or regressor Can be a coding or dummy variable (young = 1 or not young = 0) Can be a continuous covariate (age) Could be a nuisance variable (regressor of no interest) β = parameter estimate or effect size coefficient This is the value that g must be multiplied by to fit the observed data (X) Some options for significance testing: Question 1: Is B1 significantly non-zero: t = B1 / error of B1 s estimation Question 2: Is B1 significantly > B2 : t = B1 - B2 / combined standard error If we had fmri data, Question 1 would ask where does something activate on average (where does the model fit the data really well) If we had DTI data, Question 2 would ask, where does the model fit the observed FA values for group 1 better than group 2 17

18 Sample design matrix: 2 groups, unpaired t-test (A) FSL Model (B) Manual model with real data (C) Raw fit Raw results 18

19 Assessing the significance of the raw result & then correcting for multiple comparisons We can generate a permutation distribution to assess the significance of the prior result P value = 1/N where N is the total number of labelings performed The data is still not corrected for the number of comparisons made across the TBSS skeleton so there are various approaches: Cluster size approach Cluster mass approach Maximum statistic approach False discovery rate (FDR) Theory underlying permutation testing If there is no experimental effect, then the labeling of observations by the corresponding experimental condition is arbitrary, because the same data would have arisen whatever the condition. These labels can be any relevant attribute: condition tags, such as rest or active ; a covariate, such as task difficulty or response time; or a label, indicating group membership. -Nichols & Holmes (2002) 19

20 Maximum statistic Basic principles: With a single corrected threshold, t, you can control the FWER for the entire image at 5 % An example of how to calculate: With the true condition, and for each permutation, record the maximum statistic to create the null distribution of T MAX Determine the threshold (t) as: alpha (e.g., 0.05) * permutations (e.g., 5000) and add 1 to this count (250+1 = 251). The 251st member of the T MAX distribution is the threshold to apply to the true condition SPI Report the corrected p-value as the proportion of the T MAX distribution more extreme than the observed t Cluster size corrections Basic principles: Define an arbitrary threshold (t = 2.3) and use this to threshold every SPI (resulting from the true and permutation labels). After applying the threshold, determine the volume of the largest continuous cluster of supra-threshold voxels (suprathreshold cluster size or STCS ). Using this procedure, form the null distribution of STCS MAX As with the maximal statistic approach (corrected threshold is the cluster size at = alpha * N labelings + 1). The corrected p-value is similarly reported as the area of cluster size null distribution more extreme than this threshold. 20

21 Cluster mass corrections Basic principles: Again, generate SPIs with the original and permutation labelings. As with cluster size correction, define an arbitrary threshold and find the suprathreshold cluster as before. This time though, subtract the arbitrary threshold from the observed voxel statistics (per voxel) in the STC - take the sum of the result as the cluster or exceedance mass (see excerpt from Bullmore et al., 1999, above left). With the permutation distribution formed, determine the threshold and correct p as with STCS and maximum statistic approaches. False discovery rate (FDR) In theory..& in practice.. Basic principles: A Bonferroni correction across an entire SPI might look like: Probability of rejecting null hypothesis when true (false positives) < α (e.g., 0.05) In contrast, an FDR correction would imply that: Proportion of false positives in all rejected null hypotheses < the rate specified as q (e.g., 0.05) 21

22 What does reduced FA represent? Caution must be taken when interpreting DTI studies in disorders such as PDS. This is especially important as the interpretation of anisotropy change may not be as straightforward as the measurements and the exact mechanisms governing anisotropy are not known (S. Mori in Brain Mapping: the Methods, p. 392). The contributions to diffusion from intra-axonal and extracellular spaces, and the myelin sheath and the exact mechanisms of anisotropy are unknown (D. Le Bihan in NRN). I encourage you to see out Le Bihan s publications for experimental studies on contribution of various compartments to the obtained signal! 22

23 References & further reading 1. Le Bihan D. Looking into the functional architecture of the brain with diffusion MRI. Nature reviews 2003;4(6): Genovese CR, Lazar NA, Nichols T. Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage 2002;15(4): Basser PJ, Jones DK. Diffusion-tensor MRI: theory, experimental design and data analysis - a technical review. NMR in biomedicine 2002;15(7-8): Basser PJ, Mattiello J, LeBihan D. Estimation of the effective self-diffusion tensor from the NMR spin echo. Journal of magnetic resonance 1994;103(3): Basser PJ, Pierpaoli C. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. Journal of magnetic resonance 1996;111(3): Pierpaoli C, Jezzard P, Basser PJ, Barnett A, Di Chiro G. Diffusion tensor MR imaging of the human brain. Radiology 1996;201(3): Le Bihan D, Poupon C, Amadon A, Lethimonnier F. Artifacts and pitfalls in diffusion MRI. Journal of Magnetic Resonance Imaging 2006;24(3): Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H. Diffusion tensor imaging: Concepts and applications. Journal of Magnetic Resonance Imaging 2001;13(4): Nichols TE, Holmes AP. Nonparametric permutation tests for functional neuroimaging: A primer with examples. Human brain mapping 2002;15(1): Smith SM, Jenkinson M, Johansen-Berg H, Rueckert D, Nichols TE, Mackay CE, Watkins KE, Ciccarelli O, Cader MZ, Matthews PM, Behrens TE. Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data. NeuroImage 2006;31(4): Smith SM, Johansen-Berg H, Jenkinson M, Rueckert D, Nichols TE, Miller KL, Robson MD, Jones DK, Klein JC, Bartsch AJ, Behrens TE. Acquisition and voxelwise analysis of multi-subject diffusion data with Tract-Based Spatial Statistics. Nature protocols 2007;2(3): Bullmore ET, Suckling J, Overmeyer S, Rabe-Hesketh S, Taylor E, Brammer MJ. Global, voxel, and cluster tests, by theory and permutation, for a difference between two groups of structural MR images of the brain. Ieee Transactions on Medical Imaging 1999;18(1):32-42.