Visualization of Diffusion Tensor Imaging DTI data and Image by MikeJenny

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									Visualization of Diffusion Tensor
Imaging (DTI) data and Image
Distortion Correction

  Yangming Ou and Christopher L. Wyatt, Ph.D.
    School of Biomedical Engineering and Sciences
                    Virginia Tech
Outline
   Principle of DTI
   Tensor, FA and IntraVoxel Coherence map
   Distortion Correction of DWI images
I. Working principle of DTI
   Water diffusion –Brownian motion
    - isotropic: equal in all directions
    - anisotropic: not isotropic

                                   Source:
                                   Shenton et al. Diffusion
                                   Tensor Imaging. Image
                                   Acquisition and
                                   Processing Tools.
                                   SPL Technical Report
                                   #354, Harvard Medical
                                   School
    Three indices of diffusion
    Apparent Diffusion Coefficient (ADC) – symmetric(!)
         Dxx    Dxy    Dxz                            1         
                            
    D   D yx   D yy   D yz   EE 1  (e1 e2   e3 ) 
                                                           2       (e e
                                                                     1 2    e3 ) 1
         Dzx    Dzy    Dzz                            
                                                                3 
                                                                    
                            

    Predominant orientation of diffusion
                                             3
          ei  eigenvector (i )  i  max(k )
                                            k 1
   Degree of anisotropy
    -typically, Fractional Anisotropy, FA
    - FA represents the deviation from isotropic diffusion
Source image data
   DTI images can not obtained directly from
    MRI scanning
   T2 images without gradient (b=0)
   At least 6 gradients applied to the diffusion
    weighted image (DWI) —— (b!=0)
   ‘b’ stands for diffusion weight, function of
    imaging parameters including strength,
    duration, gradient time
Outline
   Principle of DTI
   Tensor, FA and IntraVoxel Coherence map
   Distortion Correction of DWI images
II. Subsequent Image Processing
   1, How to build diffusion tensor- ADC?
   2, How to calculate Fractional Anisotropy (FA)
       - FA represents deviation from isotropic
       - isotropic FA=0; totally anisotropic FA=1
       - normally, FA belongs to [0 1]
   3, How to calculate coherence?
       - coherence means average angle of primary
         diffusion direction of one voxel to its adjacent 8
         voxels
    1, To build Diffusion Tensor - D
    Attenuation Equation
                              bk ( g k Dgk )
                                      T
         Sk (r )  S0 (r )e                     (k=1,2,3,4,5,6)

S k (r ) :attenuated signal intensity after gradients are applied
S 0 ( r ) : original signal intensity of voxel r on T2 image
g k  ( g k1 g k 2 g k 3 )T : gradient directions
1, To build Diffusion Tensor (2)
                                                Dxx          Dxy          Dxz   
  T                                                                             gk1 
g k Dg k  (   g k1        gk 2        g k 3 )  Dyx          Dyy          Dyz   g k 2 
                                                                                        
                                                Dzx          Dzy          Dzz  
                                                                                   gk 3 
                                                                              
      2           2             2
 g k 1 D xx  g k 2 D yy  g k 3 D zz  2 g k 1 g k 2 D xy  2 g k 2 g k 3 D yz  2 g k 1 g k 3 D xz

   1  Sk ( r ) 
  ln         
   b  S0 ( r ) 
               
                                    k=1,2,3,4,5,6


-6 equations are sufficient to solve 6 unknown parameter
- Dxx , D yy , Dzz , Dxy , D yz , Dxz  D33
Tensor: slide 30, voxel(155,155)
                        Diffusion tensor:
                        10^(-3)*
                          0.5764 -0.3668 0.1105
                         -0.3668 0.8836 -0.1152
                          0.1105 -0.1152 0.8373

                        Eigenvalue=
                          0.0003
                                  0.0008
                                             0.0012
                        Eigenvector:
                          0.8375 -0.1734 0.5182
                          0.5432 0.3669 -0.7552
                         -0.0592 0.9140 0.4015

                        Primary diffusion direction:
                        (0.5182 -0.7552 0.4015)
Tensor: slide 30, voxel(155,155)
2, calculate FA
    For each voxel, diagonalize the diffusion tensor D
     Dxx    Dxy    Dxz                                1         
                        
D   D yx   D yy   D yz   EE 1  (e1 e2       e3 ) 
                                                           2       (e e
                                                                     1 2    e3 ) 1
     Dzx    Dzy    Dzz                                
                                                                3 
                                                                    
                        

                1  2  3
    let :  
                     3
           (1   ) 2  (2   ) 2  (3   ) 2
                                                    0 1
         3
    FA 
         2              2  2  2
                               1      2        3
FA: slide 30, voxel(155,155)
                        Diffusion tensor:
                        10^(-3)*
                          0.5764 -0.3668 0.1105
                         -0.3668 0.8836 -0.1152
                          0.1105 -0.1152 0.8373

                        Eigenvalue=
                          0.0003
                                  0.0008
                                            0.0012

                        FA = 0.5133
FA: slide 30
3, Intervoxel Coherence (C)
   Step1:
    For each voxel, find the eigenvector that
    corresponds to the greatest eigenvalue, that
    represents the primary diffusion direction of this
    voxel

                                         3
     ei  eigenvector (i )  i  max(k )
                                        k 1
3, Intervoxel Coherence (C) - cont.
   Step2:
    - inner product of the primary diffusion direction of a
    given voxel to its surrounding 8 primary diffusions
    - arc cos() of each product value represents the angle
    of two primary diffusion directions
    - average and nomalize:
                       1       1 1                        
              i, j     arccos   ei , j , ei  m, j  n  
                                                            
                       8       m 1n 1                 
                        i, j
              Ci , j  2         [0,1]
                        
                              2
Possible Coherence image
   8 neighboring voxels
   6 neighboring voxels
   26 neighboring voxels
  In all: DTI Visualization - results
                T2, no gradient   DWI, diffusion gradient


Source
image set




                    FA map         Intervoxel coherence



Visualization
results
Outline
   Principle of DTI
   Tensor, FA and IntraVoxel Coherence map
   Distortion Correction of DWI images
III, Image Distortion Correction
   Displacement correction (a1 a2 a3)
   Rotation correction  (phi, theta, psi)
   Linear eddy current correction  (c1 c2 c3)
   Quadratic eddy current correction 
                           (c4 c5 c6 c7 c8)
III. Image Distortion Correction-cont.
 Image distortion induced by [4]
 - patient motion (translation & rotation)
 - magnetic field eddy current
                  (linear & quadratic)
 Correction method

 - mutual information (MI) based registration
      DWI image (with       registration   T2 image ( without
      diffusion gradient)                  diffusion gradient)
 1.Pre-analysis of displacement–a1, a2, a3
* assume independent (actually not)
* conclusions:
  1) one-to-one mapping:
    d  MI or MI=f(d)
  2) maximum MI appears
     all around -0.5
Displacement Optimization
   a1, a2, a3 are not independent
   Initial conditions: A=[0 0 0]’
   133 iterations  ~20s/iteration
   Optimal A =
    [-0.22132007643878  a1/1.0938 =-0.20 pxls
     -0.29780655561241  a2/1.0938 =-0.27 pxls
     -0.56072909526202]  a3/3.0=-0.1869 slices
      (155:160, 155:160, 25)                 (155:160 155:160 25)

141   145   136   109   111   149   142.2600 143.1331 135.8875 114.5674 107.1615 128.5527
123   133   139   126   126   144   131.5497 133.3051 134.0740 124.4849 122.8327 134.8237
106   119   133   133   131   131   116.6412 120.4705 127.5754 128.3776 130.6968 132.4184
                                    108.9253 116.2581 123.8874 123.0106 123.0444 122.6544
102   115   124   122   121   120
                                    109.3662 119.1860 122.9978 112.5411 107.7092 114.3735
107   119   116   102   105   119   112.8934 125.1752 124.0735 105.5998 98.9101 113.8279
113   129   116   91     97   125
2. Pre-analysis of rotation correction
•  assume
independent
(actually not)
  Pre-analysis of rotation correction(2)
* conclusions:
  1) one-to-one mapping:
   alfa MI , MI=f(alfa)

 2) maximum MI appears
  all around -0.5
Rotation Optimization
   phi: -0.00070012969894809
   theta: -0.00029465735870500
   psi: -0.00032238129890524
   Euler Rotation Matrix =
     1.0000 -0.0003 0.0003
     0.0003 1.0000 -0.0007
    -0.0003 0.0004 1.0000
  (155:160, 155:160,          25)           (155:160,     155:160,     25)
141   145   136   109   111   149
123   133   139   126   126   144   142.2402 143.1225 135.7745 114.3464 107.0665 128.7004
106   119   133   133   131   131   131.5992 133.4295 134.1196 124.3545 122.7060 134.8861
                                    116.6897 120.6027 127.6821 128.3711 130.6681 132.4655
102   115   124   122   121   120   108.9194 116.3323 123.9403 123.0585 123.1462 122.7436
107   119   116   102   105   119   109.3167 119.2383 122.9791 112.5313 107.8385 114.5086
113   129   116   91     97   125   112.8604 125.2335 123.9959 105.4793 98.9547 113.9674
3. Pre-analysis of Linear EC
Pre-analysis of linear eddy current corrections:
C1: 2*10^(-4)         c2: 2*10^(-4)       c3: 4.5*10^(-4)
Linear EC correction results
   C1:0.3841, C2:0.7474, C3:0.6102




Linear eddy current correction   Gradients for linear eddy current
converges to optimal values      correction converge to 0
 Linear EC Correction Result




       Original dwi data               After linear correction: (155:160,155:160,25)
141   145   136   109   111   149
123   133   139   126   126   144   142.3839    143.0430    136.4385    116.2896    107.7290    126.7246
                                     132.1519    133.2643    134.0571    125.2425    122.8565    133.7705
106   119   133   133   131   131    117.4032    120.2484    127.0387    128.3083    130.4578    132.3004
102   115   124   122   121   120    109.7081    115.6590    123.2469    123.1392    123.1381    122.7807
107   119   116   102   105   119    110.2054    118.3346    122.6372    113.4897    108.2705    113.8924
                                     113.4943    124.1033    124.1093    107.1827     99.5571   112.5766
113   129   116    91    97   125
4. Pre-analysis of Quadratic EC
Based on the assumption that c4-c8 are independent, correction
should be exactly 0 on scale of 10^(-8)
 Quadratic EC correction results




[0.4943 0.2785 0.4852 0.0558 -0.0291]*10^(-5)
 Quadratic EC corrected results




      Original dwi data                  After Quadratic EC correction
141   145   136   109   111   149
123   133   139   126   126   144   142.7446   142.8433   138.1097   121.1867   109.4007   121.7333
                                    133.5436   132.8475   133.8992   127.4873   123.2372   130.9439
106   119   133   133   131   131   119.2051   119.3523   125.4097   128.1490   129.9242   131.8808
102   115   124   122   121   120   111.7061   113.9515   121.4860   123.3443   123.1177   122.8752
107   119   116   102   105   119   112.4629   116.0361   121.7664   115.9334   109.3733   112.3175
                                    115.1092   121.2203   124.3991   111.5385   101.0992   109.0115
113   129   116    91    97   125
5. Distortion correction
             translation    rotation     Linear EC     Quadratic EC   Total time


gradient02     2505 s        2823 s        5305 s          9306 s      5 hours
             (133 times)   (150 times)   (287 times)     (34 times)    32 min

Gradient03     4149 s        8793 s        3190 s         15122 s      8 hours
             (221 times)   (471 times)   (172 times)     (57 times)    40 min

gradient04     13418 s       2690 s        9788 s         14,867 s    11 hours
             (715 times)   (143 times)   (529 times)     (52 times)    20 min

gradient05     4344 s        12,656 s      8049 s         20,008 s    12 hours
             (232 times)   (686 times)   (438 times)     (72 times)    31 min

gradient06     5935 s        5749 s        2960 s         15,579 s     8 hours
             (322 times)   (311 times)   (159 times)     (56 times)    24 min
  6. Distortion Correction - results
                                difference
            Before correction   After correction



DWI image




 FA map
    7. Conclusions
   Visualization of DTI helps explicit human
    brain white matter from DWI images
   Image distortion correction remarkably
    increases the image quality. It is effective
    especially for heavily distorted images, and
    corrects the patient motion and eddy current
    induced distortion simultaneously, but it
    costs calculation time in hours for each DWI
    image.
Reference
   [1] Adolf Pfeferbaum, et al, Age-Related Decline in Brain White Matter
    Anisotropy Measured With Spatially Corrected Echo-Planar Diffusion
    Tensor Imaging, Magnetic Resonance in Medicine 44:259-268 (2000)
   [2] Denis Le Bihan, et al, Diffusion Tensor Imaging: Concepts and
    Applications. Journal of Magnetic Resonance Imaging 13: 534-546 (2001)
   [3] Van J. Wedeen, et al, Demonstration of Primary and Secondary
    Muscle Fiber Architecture of the Bovine Tongue by Diffusion Tensor
    magnetic Resonance Imaging. Biophysical Journal, Volume 80, February
    2001: 1024-1028
   [4] G.K. Rohde, et al, Comprehensive Approach for Correction of Motion
    and Distortion in Diffusion-Weighted MRI, Magnetic Resonance in
    Medicine 51:103–114 (2004)
   [5] Shenton et al. Diffusion Tensor Imaging. Image Acquisition and
    Processing Tools. SPL Technical Report #354, Harvard Medical School

								
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