Diffusion MR Imaging Analysis (Prac6cal Aspects)

Transcription

1 Diffusion MR Imaging Analysis (Prac6cal Aspects) Jeffry R. Alger Department of Neurology Department of Radiological Sciences Ahmanson- Lovelace Brain Mapping Center UCLA

2 Acknowledgement Some slides/images were provided by Sumumu Mori (Johns Hopkins University) Derek Jones (Cardiff University)

3 General References

4 General References Alger JR. The Diffusion Tensor Imaging Toolbox. The Journal of Neuroscience 2012; 32(22): Jones DK, Cercignani M. Twenty- five piualls in the analysis of diffusion MRI data. NMR in Biomedicine 2010; 23(7):

5 Volume Image Sensitized direction 1 Fractional Anisotopy Volume Image Volume Image Sensitized direction 2 Volume Image Sensitized direction 3. Volume Image Sensitized direction N Software Color-coded Volume Image Fiber tract Volume Image Other derived Volume Images

6 Outline Preliminary issues to be aware of Diffusion image processing sowware Diffusion image processing strategy Tractography

7 General Issues to Be Aware of Noise EPI B0 spa6al distor6ons Spa6al Eddy current problems Spa6al & temporal distor6ons DICOM reading Mo6on

8 Does anyone know this man?

9 Noise

10 Noise MRI signal is oscillatory Amplitude and phase Real and Imaginary MRI reconstruc6on on most scanners throws away phase (imaginary) component The end user works with Signal Magnitude The noise is characterized by a Rician Distribu6on

11 Noise At high signal to noise levels the signal distribu6on is very Gaussian Rician distribu6on ~ Gaussian distribu6on At low signal to noise levels the signal distribu6on is very skewed Signal can not be nega6ve- valued In diffusion MRI analysis high SNR and low SNR images are used The effects of the Rician distribu6on in the low SNR can have an impact.

12 EPI Spa6al Distor6ons Diffusion MRI almost universally uses Spin Echo EPI as an image acquisi6on technique Sta6c varia6on in B 0 causes spa6al distor6on along the phase encode direc6on Diffusion MRI uses strong/fast gradient switching to achieve diffusion sensi6za6on B 0 is temporally and spa6ally unstable producing Eddy current distor6ons

13 Eddy Currents

14 Eddy Currents

15 Spa6al Distor6ons Stanford UCLA b = 0 MP- RAGE

16 Eddy current distor6ons

17 Spa6al Distor6ons Remedia6on Find a nonlinear remapping that makes the intensity under the red and blue lines equivalent Repeat for each line in the volume

18 Spa6al Distor6ons Remedia6on Non- determinis6c methods Computa6onally intensive Determinis6c approaches Use B 0 map obtained just before or awer DTI Trades off addi6onal acquisi6on 6me for faster postprocessing

19 SoWware

20 Volume Image Sensitized direction 1 Fractional Anisotopy Volume Image Volume Image Sensitized direction 2 Volume Image Sensitized direction 3. Volume Image Sensitized direction N Software Color-coded Volume Image Fiber tract Volume Image Other derived Volume Images

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23 Reading b- vectors (or b- matrices) from DICOM headers

24 ? Volume Image Sensitized direction 1? Volume Image Sensitized direction 2 2D DICOM Images? Volume Image Sensitized direction 3. Software? Volume Image Sensitized direction N

25 Jack van Horn (paraphrased): It s the craziest thing I have ever seen. In every DTI study I have worked on somebody gives me a liele post- it on which they have scribbled the gradient table. Isn t there a way to read it from the DICOM header? FW: dcm2nii questionfrom: Theo van Erp [vanerp@lifesci.ucla.edu] Sent: Monday, March 09, :34 AM To: Jeffry R. Alger Subject: FW: dcm2nii question FYI: From Chris Rorden, he just replied. See dicomcompat.pas For GE, I look at group $0019, specifically $10BB or $a0bb $10BC or $A0BC $10BD or $A0BD For the x, y, z vectors... and $0043:$1039 or $A039 for the bval I also read b-values from $2010:$1003 I think Philips vectors are in group $2005, elements $10b0,$10b1,$10b2. Siemens is trickier, as you need to read the CSA shadow header... you need to look at convert.pas and dicomtypes.pas for the details...

26 Digital Imaging and Communica6ons in Medicine (DICOM) All MRI scanners marketed awer ca 2000 use the DICOM standard for digital image representa6on Diffusion imaging did not exist when the standard was developed There are no standard iden6fiers for diffusion imaging acquisi6on informa6on in the DICOM standard Anything that is standard is obsolete The DICOM standard permits manufacturers to encode private informa6on within a DICOM- compliant image Manufacturers encode diffusion acquisi6on informa6on as private informa6on

27 DICOM and diffusion imaging acquisi6on informa6on DICOM does not use human readable filenames DICOM usually uses 2D images DICOM image volume informa6on some6mes does not count the different DWI volumes Image acquisi6on 6me is some6mes not stored accurately Order of image acquisi6on is some6mes not stored accurately There is no DICOM tag for slices per volume

28 DICOM and diffusion imaging acquisi6on informa6on There are three methods of encoding private informa6on Use of code words in the standard tags As parameters but in odd- numbered group tags (the Private ) tags Embedded within long strings of informa6on that are usually represented as an OB value representa6on DICOM mavens refer to OB as Old Blob Siemens uses all three methods to encode diffusion imaging acquisi6on informa6on Depends on scanner vintage GE & Philips use odd- numbered group tags Custom- wrieen pulse sequence sowware may not store the relevant informa6on in the DICOM header PACS, anonymizer and DICOM services sowware may delete encode diffusion imaging acquisi6on informa6on

29 Co- ordinate System Confound DICOM expresses gradient vectors in the absolute X, Y, Z reference frame of the magnet (pa6ent centered space) Z is perfectly aligned with the magnet bore X is horizontal Y is ver6cal Most inves6gators assume X and Y are parallel to the image slice plane Z is normal to the image slice plane The inves6gator assumed vectors may be rotated by as much as 30 in the YZ plane rela6ve to the true reference frame Depends on slice prescrip6on Co- ordinate system confusion can be avoided by use of pure axial un6lted slice prescrip6on Co- ordinate system confusion can be fixed by recalcula6on of the diffusion data awer rota6ng the vector table There is enough informa6on in the DICOM header to do this

30 Reliable SoWware SortDICOM (Alger) Runs under Interac6ve Data Language Virtual Machine No cost to user Runs on Windows, Mac Sorts files into folders named according to Subject ID, Image Acquisi6on Date, Image Acquisi6on Time, Series Name ProcessDTI (Alger) Runs under Interac6ve Data Language Virtual Machine No cost to user Runs on Windows, Mac Stable as of 12/26/2009 Uses a new ground up DICOM reader Reads all DICOM elements including privates Reads OB of private header informa6on for GE, Siemens, Philips Input Folder full of dicom files produced by the DTI study Siemens, GE or Philips Output Folder full of ANALYZE- formaeed 3D parametric images (color maps, FA, tensor images etc) Images useful for QC/QA

31 Diffusion Image Processing Strategy

32 Diffusion Tensor Imaging Basser & Jones. NMR in Biomedicine 2002;15: The goal of DTI is determining the values of the elements of the diffusion tensor for each voxel in the image space It is assumed that the diffusion is random and therefore that the diffusion tensor is symmetric At least 6 unique diffusion- weighted measurement and one non- diffusion weighted measurement are required to determine the symmetric tensor More than 6 diffusion weighted measurements improves the accuracy D =" D xx D xy D xz" D xy D yy D yz" D xz D yz D zz"

33 The Diffusion Tensor Voxels that are anisotropic are oriented in specific direc6ons rela6ve to the scanner x, y and z co- ordinates This is expressed quan6ta6vely as a matrix or tensor D =" D xx D xy D xz" D yx D yy D yz" D zx D zy D zz"

34 The Diffusion Tensor If the white maeer fiber tract is oriented perfectly along the scanner s x, y, or z gradient co- ordinate system, then only the tensor s diagonal terms are non- zero If the white maeer fiber is rotated with respect to the scanner s x, y, z gradient co- ordinate system, then the tensor s off- diagonal terms are non- zero D =" D xx D xy D xz" D yx D yy D yz" D zx D zy D zz"

35 The diffusion signal equa6on (for each voxel) ln(s b ) = ln(s 0 ) Σ Σ b ij D ij S 0 : MRI signal strength in the absence of diffusion- weigh6ng S b : MRI signal strength in the presence of diffusion- weigh6ng D: the diffusion tensor b: the b- matrix describing the extent of diffusion sensi6za6on in all spa6al direc6ons

36 b- matrix Mauello. J Magn Reson A 1994; 108, Basser & Jones. NMR in Biomedicine 2002;15: The imaging gradient pulses can produce significant diffusion- weigh6ng When this is the case, the en6re b- matrix is needed The b- matrix is mostly diagonal Due to the use of very strong diffusion encoding gradients OWen it is sufficient to use only b xx, b yy, b zz Some authors use the term b- vector b =" b xx b xy b xz" b xy b yy b yz" b xz b yz b zz"

37 Linear Systems Analysis Determining the diffusion tensor requires solving the linear system of equa6ons DWI # 1: ln(s b ) = ln(s 0 ) Σ Σ b ij1 D ij DWI # 2: ln(s b ) = ln(s 0 ) Σ Σ b ij2 D ij DWI # 3: ln(s b ) = ln(s 0 ) Σ Σ b ij3 D ij DWI # 4: ln(s b ) = ln(s 0 ) Σ Σ b ij4 D ij DWI # 5: ln(s b ) = ln(s 0 ) Σ Σ b ij5 D ij DWI # 6: ln(s b ) = ln(s 0 ) Σ Σ b ij6 D ij b = 0: ln(s b ) = ln(s 0 )

38 System of signal equa6ons for one voxel 12 gradient direc6ons DWI # 1: ln(s b ) = ln(s 0 ) Σ Σ b1 ij D ij DWI # 2: ln(s b ) = ln(s 0 ) Σ Σ b2 ij D ij DWI # 3: ln(s b ) = ln(s 0 ) Σ Σ b3 ij D ij DWI # 4: ln(s b ) = ln(s 0 ) Σ Σ b4 ij D ij DWI # 5: ln(s b ) = ln(s 0 ) Σ Σ b5 ij D ij DWI # 6: ln(s b ) = ln(s 0 ) Σ Σ b6 ij D ij DWI # 7: ln(s b ) = ln(s 0 ) Σ Σ b7 ij D ij DWI # 8: ln(s b ) = ln(s 0 ) Σ Σ b8 ij D ij DWI # 9: ln(s b ) = ln(s 0 ) Σ Σ b9 ij D ij DWI # 10: ln(s b ) = ln(s 0 ) Σ Σ b10 ij D ij DWI # 11: ln(s b ) = ln(s 0 ) Σ Σ b11 ij D ij DWI # 12: ln(s b ) = ln(s 0 ) Σ Σ b12 ij D ij b = 0: ln(s b ) = ln(s 0 )

39 Solving the signal equa6on Linear systems approaches are the most commonly used methods Easy to code Fast Well understood sta6s6cal characteris6cs Non- linear fiung More complex Slower

40 Rician noise and one dimensional D calcula6on slope = - D! ln(s)! 0! 500! 1000! b-value!

41 Rician noise and one dimensional D calcula6on slope = - D! ln(s)! 0! 500! 1000! b-value!

42 Rician Noise Influences the high b measurement Causes the diffusion coefficient to appear larger than it actually is Causes the signal equa6on to appear to have more than one exponen6al term

43 Diagonaliza6on The diffusion matrix is usually diagonalized using eigenvector- eigenvalue methodology A standard method in linear algebra Leads to the use of the terms eigenvector and eigenvalue to describe the diffusion Principal Eigenvector preferred direc6on of diffusion Eigenvalue Rate of diffusion in this direc6on

44 Diffusion Tensor Imaging Eigenvector/eigenvalue decomposi6on D =" V 1" V 2" λ " 0 λ 2 0 " V 1 V 2 V 3" V 3" 0 0 λ 3"

45 Results Presenta6on

46 Characterizing Diffusion V 1 = The direction in space (a vector) in which the diffusion speed (diffusivity) is the greatest" λ 1 = Diffusivity in the V 1 direction" " " V 2 = A direction perpendicular to V 1 having the second highest diffusion speed" λ 2 = Diffusivity in the V 2 direction" " " V 3 = The direction perpendicular to V 1 and V 2" λ 3 = Diffusivity in the V 3 direction"

47 Diffusion Tensor Imaging An image voxel is likely in white maeer fiber if there is a great difference in the diffusivity between direc6ons (i.e. a large anisotropy) λ 1 >> λ 2, λ 3 If this is true, V 1 is parallel to the white maeer fiber orienta6on An inference!

48 Parametric DTI Images! Trace: " Trace(D) = λ 1 + λ 2 + λ 3" " Mean Diffusivity:" MD = 1/3(Trace(D))" " MD ~ ADC" " Radial Diffusivity:" RD = (λ 2 + λ 3 )/2 " " Fractional Anisotropy: " FA = ((λ 1 - λ 2 ) 2 + (λ 1 λ 3 ) 2 + (λ 2 λ 3 ) 2 ) 1/2 /(2(λ λ λ 32 )) 1/2"

49 Parametric DTI Images!

50 A/P fiber bundles L/R fiber bundles S/I fiber bundles

51 Rota6onally invariant parametric images Basic goal of most analyses is to reduce the diffusion informa6on to a rota6onally invariant parametric image MD, FA, RD, AD are examples Rota6onal invariance means image intensity does not depend on How the head was posi6oned Which gradient vectors were used

52 Ellipsoids and Diffusion isotropic" anisotropic" anisotropic" Place a drop of dye somewhere in space Take a snapshot of the dye some6me later

53 White Maeer Diffusion anisotropic" The ellipsoid will not necessarily be oriented with it s principle axes aligned with the gradient x, y, z co- ordinate system Need a method to determine alignment

54 Blobograms!

55 Vector field plots!

56 Tractography

57 Can axonal projec6ons be reconstructed? At each voxel, average fiber orientation can be estimated Axonal projection reconstruction may be possible

58 What is needed? 3D data acquisi6on High resolu6on data

59 Fiber reconstruc6on

60 Two thresholds for termina6on Low anisotropy (Gray maeer) (Larger noise effect) Sharp turn (Par6al voluming) (Error accumula6on)

61 UNCERTAINTY IN EIGENVECTOR Mean eigenvector, Ψ 1 95% cone of uncertainty 1

62 Examples of the tracking ROI- ini6a6on Brute- Force Search Mul6ple- ROI edi6ng

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