Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

4

Share

Download to read offline

DTI lecture 100710

Download to read offline

Related Audiobooks

Free with a 30 day trial from Scribd

See all

DTI lecture 100710

  1. 1. Introduction to Diffusion Tensor Imaging  Why DTI?  Diffusion – what it is, how it affects MR signal  Tensor – how we represent diffusion  Imaging – how we measure it in MRI
  2. 2.  Stroke/ischemia  Alzheimer’s Disease  Multiple Sclerosis  Brain maturation studies  Ischemia and stroke  Neoplasm  Preoperative planning  Traumatic brain injury  Congenital anomalies and diseases of white matter  Encephalopathies  Neurodegenerative diseases  Spinal Cord Injury  Epilepsy  Dementia, schizophrenia, depression  Developmental disorders  Autism  Aging Why diffusion? http://www.vh.org/Providers/Textbooks/ BrainAnatomy/Ch5Text/Section18.html http://eclipse.nichd.nih.gov/nichd/DTMRI/mri/ Conceptually: in vivo histology
  3. 3. Why diffusion?  Diffusion is EXTREMELY SENSITIVE to differences and changes in tissue microstructure  Myelination/Demyelination  Axon damage/loss  Inflammation/Edema  Necrosis  It is NOT a biomarker of white matter integrity  It is NOT just about white matter  Gray matter  Cardiac tissue
  4. 4. Example DTI image  “Fractional Anisotropy” map  “map” is a computed parameter, unlike an “image” which is acquired signal  Also called a “tractogram” since it clearly shows major white matter fiber tracts
  5. 5. What is Diffusion?  stochastic movement of particles in a solvent, driven by the thermal molecular motion of the solvent…  … and also applies to motion of the solvent itself (Einstein, 1905) time τ∆ NOTE: In the limit N→∞, use the Central Limit Theorem to assume “step size” ∆ is fixed and equal to the average of individual displacements ∆i.
  6. 6. 1D Fick’s Law - what the flux? t = t0 + τ x t = t0 0 2x − ∆ 0x − ∆ 0x + ∆0x 0 2x + ∆ t = t0 + τ x t = t0 0 2x − ∆ 0x − ∆ 0x + ∆0x 0 2x + ∆ What is the flux (J) through x0 after one time interval τ ? C1(x)C2(x) dx dC J τ 2 2 1 ∆ −= Adolf Fick, 1855: Flux is proportional to the particle concentration gradient (conservation of mass)
  7. 7. The Diffusion Coefficient  3D Fick’s Law  Note the minus sign: flux goes from high to low concentration  del operator replaces partial derivative  factor of 6, not 2 (why?)  D is the diffusion coefficient  This is the expression for isotropic diffusion τ62 ∆=D CDJ ∇−=  CJ ∇ ∆ −= τ6 2
  8. 8. Isotropic Diffusion (water) water ink Dtr 6= r1 t1 r2 t2 τ62 ∆=D
  9. 9. Diffusion in Tissue (Anisotropic) t ink r2 r3 r1 diffusion ellipsoid tDr 11 2= tDr 22 2= tDr 33 2= x y z laboratory frame DON’T try this at lab!!!!!
  10. 10. The Diffusion Tensor           zzyzxz yzyyxy xzxyxx DDD DDD DDD x y z r2 r3 r1           3 2 1 00 00 00 D D D diagonalization Lab frame Intrinsic frame
  11. 11. Tensor Invariants  Eigenvalues: diagonalization (iterative QR factorization)  Eigenvectors xx xy xz xy yy yz xz yz zz D D D D D D D D D           { }1 2 3D D D { }321 eee 
  12. 12. Tensor Invariants  Shape invariants: analytical calculation directly from tensor coeffs xx xy xz xy yy yz xz yz zz D D D D D D D D D           ( )1 3 av xx yy zzD D D D= + + 1 2 2 2 2 1 3 xx yy xx zz yy zz surf xy xz yz D D D D D D D D D D + +  =    − − −  1 2 3 2 2 2 xx yy zz xx yz vol xy xz yz zz xy yy xz D D D D D D D D D D D D D  −  =  + − − 
  13. 13. Scalar Anisotropy Indices ( ) avND D DADC DDDADC = ++= 321 3 1 ( ) ( ) ( ) 2 2 2 3 2 2 2 1 2 3 2 2 2 1 1 2 3 mag surf ND D D D FA DDD DDDDDD FA −= ++ −+−+− =
  14. 14. FA vs. ADC FA (x 10 -4 ) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Probability 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 WM GM CSF MD (x 10 -3 mm2 /s) 0 500 1000 1500 2000 2500 3000 3500 4000 Probability 0.000 0.001 0.002 0.003 0.004 0.005 WM GM CSF FA and ADC are very useful clinically, but are very different. Tensor has a LOT of information! Q. Which metric would you use to detect brain cancer?
  15. 15. Vector anisotropy measures  We can use eigenvector information from the tensor as well  Represent direction of primary eigenvector as color on a scalar map  Or render the primary eigenvectors as “fibers” for astonishing* 3D visualizations Red = R/L Green = A/P Blue = S/I *but how “real” is it? Many PhD theses have asked….
  16. 16. Diffusion tensor coefficients Diffusion tensor invariants Scalar anisotropy indices Vector anisotropy indices
  17. 17. Effect of Diffusion on MRI signal Signal attenuation! Diffusion term
  18. 18. Diffusion weighted MRI ∆ δ G G echoπα ( ) ( )( )2 0 δexpδ 3 M G D M γ= − × ∆ − × ∆ δ ( ) ( )2 δδ 3 b Gγ= × ∆ − (boxcar gradients) “b-value” Consider simplified diffusion experiment…
  19. 19. MR Measurement of Diffusion Tensor j T j j j p G G q r     = ×      ur 0 xx xy xz j j j j xy yy yz j xz yz zz j D D D p p q r D D D q D D D r j b S S e          − × × ×             = ( ) 22 2 γ δ Δ δ 3b G= − ( ) 1 6 j N N = ≥ Kjth diffusion- weighted image Diffusion magnitude Diffusion direction Gz Gy Gx ... ... ...
  20. 20. Solving for D 20 0 xx xy xz j j j j xy yy yz j xz yz zz j D D D p p q r D D D q D D D r j b S S e          − × × ×             = 1. Acquire T2W image (b = 0 s/mm2 ) 3. Choose a diffusion gradient orientation2. Choose a b-value 4. Acquire image (Sj) 5. Repeat steps 1 – 3, j = 1 … N times 6. Solve for D…. How?
  21. 21. Let’s do some linear algebra… [ ]           ⋅           ⋅⋅−= zj yj xj zzzyzx yzyyyx xzxyxx zjyjxjj DDD DDD DDD bSS α α α αααexp0 ( ) ( ) ( ) ( ) ( ) ( )                     ⋅                     ⋅= yz xz xy xx yy xx T jxy jxy jxy jzz jyy jxx j D D D D D D b S S α α α α α α 2 2 2 ln 2 2 2 0 1661 xNxNx xAY ⋅=
  22. 22. B-matrix formalism 22 ( )yzyzxzxzxyxyzzzzyyyyxxxx DDDDDDb αααααα 222222 +++++⋅ ( )yzyzxzxzxyxyzzzzyyyyxxxx DbDbDbDbDbDb 222 +++++= ∑∑= = = 3 1 3 1i j ijij Db The “b-matrix” The b-matrix formalism summarizes total attenuating effect of all gradient waveforms in all directions (including imaging gradients)
  23. 23. T2W (b = 0 s/mm2 ) Y, -ZY, Z-X, Y X, Y-X, Z+X, Z
  24. 24. 24 SVD DIAG T2W (b = 0 s/mm2 ) … DWI (j = 1, 2, 3 … N) Dij
  25. 25. N=27 N=55 N=13N=6 N NEX # DWI 6 8 56 13 4 56 27 2 56 55 1 56 #DWI = (N + 1) x NEX If TR = 4 sec, then acq time = 56*4sec = 3.7 minutes Tradeoff: N vs NEX
  26. 26. Rotational invariance Hasan et al, JMRI 2001 Jones MRM 2004
  27. 27. 27 Empirical Image Quality increasing N, decreasing NEX increasingb-value
  28. 28. How low can you go?  High b-values mean more attenuation, lower SNR  Lower b-values mean higher SNR, room for more N  At very low b-values, imaging gradients’ diffusion effects are no longer negligible  Lower b-values also do not probe same diffusion scale, less clinically interesting b=100 s/mm2 b=500 s/mm2 (N = 6, 8 NEX)
  29. 29. Echo-Planar Imaging (EPI)  Advantages  Minimal motion artifacts  NEX  N  Disadvantages  Eddy current artifacts  T2* limits spatial resolution  Geometric distortion (susceptibility) 29
  30. 30. DT-MRI Alexander SLFSLF CRCR CCCC CINGCING Partial Volume Effects on Anisotropy
  31. 31. DT-MRI Alexander Mapping Complex Diffusion Based Upon Q-Space Theory – Model Independent  ODF – orientation density function (Tuch et al., Neuron 2003)  Diffusion Spectrum Imaging (DSI) (Tuch et al. Neuron 2003, Wedeen et al. 2005)  High Angular Diffusion Imaging (HARDI), Q-Ball (Frank 2002; Tuch et al. Neuron 2003)
  • AnuranjanaMinj

    Nov. 11, 2018
  • AbnaJ1

    Sep. 30, 2017
  • alfarttosi

    Feb. 22, 2016
  • mknaasan

    Oct. 31, 2015

Views

Total views

2,937

On Slideshare

0

From embeds

0

Number of embeds

10

Actions

Downloads

145

Shares

0

Comments

0

Likes

4

×