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Methods for Medical Imaging– Prof. G. Baselli 2012 Diffusion weighted MRI and DTI tractography Maria Giulia Preti maria.preti@mail.polimi.it

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MRI contrasts Contrast between two tissues A and B C AB = abs (I A – I B ) / I REF NB: MRI offers several contrast types, they dipend on weighing (T1, T2, T2*, Proton Density, Diffusion, etc.) Definition: T1 T2 Diffusion weighted imaging, DWI Normally, acquisition sequences are designed to enhance a specific diffusion weight (e.g., T1, T2, DWI) Liquor White Matter, WM Gray Matter, GM

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The amount of motion of water molecules diffusing within tissues is observed Molecular Diffusion MOLECULAR DIFFUSION: caotic motion of molecules, due to their thermal agitation (Brownian motion) Definition (Einstein, 1905) free diffusion = equal displacement probability in all directions ISOTROPIC DIFFUSION D = DIFFUSION COEFFICIENT (mass, viscosity, temperature) Diffusion Weighted Imaging (DWI)

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Isotropic Diffusion Distribution of displacements Gaussian r = displacement of molecules from time t1 to time t2 Meand squard displacement in 1D In 3D: Δ = diffusion time (t2–t1)

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Diffusion in biological tissues In tissues, water diffusion finds barriers: it is hindered The apparent diffusion coefficient (ADC) is lower and depends on microscopic structure Higly hindered Less hindered ISOTROPIC NON ANISOTROPIC 3D description by the Diffusion Tensor (DT)

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Rephasing Dephasing Rephasing Dephasing Rephasing Dephasing Slice selection GzGz GyGy GxGx Phase Encoding Frequency Encoding Signal TE 90° 180° Diffusion weighted spin-echo EPI Addition of a bipolar gradient pulse Δ δ G

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y Diffusion weighing by bipolar gradient pulse G position dependent dephasing y -G Dephasing Rephasing

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The final phase shift of spins requires displacemnt Phase t=0 Phase t=Δ Position t=Δ Position t=0 x1=x2 (NO DIFFUSION)NO Dephase, NO signal attenuation G gradient pulse amplitude δ= duration of gradient pulse Δ = Δt between the two pulses = diffusion time γ = gyromagnetic ratio Dephasing Δ δ G Rephasing Diffusion weighing by bipolar gradient pulse

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Rephasing Dephasing 90° 180° B0B0 Diffusion weighing by bipolar gradient pulse

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Dephasing 90° 180° B0B0 Diffusion weighing: low diffusion

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Rephasing Dephasing 90° 180° B0B0 Diffusion weighing: high diffusion

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DWI Contrast DWI: MORE DIFFUSIONE LESS SIGNAL (DARKER) b-value DIFFUSION WEIGHING INDEX Liquor >diffusion

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Stejkal andTanner’s equation Diffusion weighing in the gradient direction b=0 imge weithed byT2 only b≠0 weighted by T2 and by diffusion DWI ADC estimate by log ratio of T2 and DWI: Signal attenuation: DWI G gradient pulse amplitude δ= duration of gradient pulse Δ = Δt between the two pulses = diffusion time γ = gyromagnetic ratio

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Apparent Diffusion Coefficient (ADC) ADC Map Image of diffusion voxel by voxel. A refernce (S0) and a DWI are necessary (or a low b and a high b DWI) b=0 S 0 b=1200 sec/mm² S Peri-tumoral edema area has the same intensity than other tissues ADC=-1/b ln(S/S 0 ) ADC map Edema area is enhanced

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Diffusion Tensor Imaging (DTI) Orderly oriented structures: Preferential diffusion parallel to fibers, hindered or even restricted in the orthogonal directions. NOTE: DTI model does not distinguish restricted diff. (not Gaussian) WHITE MATTER (WM) IN THE CNS Exploration in the 3D space Description in each voxel by a 3x3 symmetric matrix: DIFFUSION TENSOR DTI NON ISOTROPIC DIFFUSION in a preferred direction along fibers

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Calcolo del tensore di diffusione Diffusion Tensor (DT) symmetry 6 independent components each scan requires ad at least 6 DWI acquisitions along maximally distant directions + 1 reference image (b=0) Often, more directions are acquired: 12 and more Minimal set acquisition and gradient components Least squares solution of a system of Stejkal andTanner eq. Z X Y i,j = x,y,z B ij = ( ɣ δ) 2 (Δ - δ /3) G i G j

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1. PRINCIPAL DIFFUSION DIRECTION: eigenvector (e1) of the largest eignevalue The DT of each voxel provides the eigenvalues and eigenvectors 2. MEAN DIFFUSIVITY: diffusion averaged over all directons 3. FRACTIONAL ANISOTROPY: measure of ordered directionality Diffusion Tensor Imaging (DTI) e1e1 e2e2 e3e3 fiber Tensor eigen- vectors oriented parallel (e1) and orthogonally (e2, e3) to fibers scanner reference system Isotropic Non Isotropic

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Reconstruction of fibers following the principal direction voxel through voxel 2 STOPPING RULES: o Minimum AF o Maximum bending angle from voxel to voxel Start from: seed points [ ROI of seed points ] ASSUMPTION Principal direction = average fiber orientation AF < threshold X angle > threshold X Diffusion Tensor Tractography (DTT)

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ILF ARCUATE UNCINATE CINGULATE CORPUS CALLOSUM IFOF WHOLE BRAIN Tractography: reconstructed bundles or fascicles

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Positioning of ROI for seed points ROI of seed points - ideally: anatomical region crossed by all fascicle fibers and not crossed by other fascicles. Locate usual on the FA map good contrast of fbers. FA Example: 3 ROIs for identifying 3 portions of corpus callosum (CC) (genu- body-splenium) ROIs on the central sagittal plane CC extends from ROIs to the emispheres

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Afferent and efferent fibers not distinguish One single principal direction per voxel, no distinction of fibers with different directions (see below) Partial volume effects (e.g. GM); particularly severe the effect of free water (isotropic) in edema FA drop fiber reconstruction stops Low resolution for SNR and acquisition time DT Tractorgraphy limitations In case of mixed directions the principal directions is actually the average direction “kissing”, “crossing” and “diverging” fibers.

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