# Presentation: 852612

## Neuronal Connectivity Imagingwith Diffusion MRI

- Wang Zhan, Ph.D.
- Tel: 415-221-4810x2454, Email: _[Wang.Zhan@ucsf.edu](mailto:Wang.Zhan@ucsf.edu)_
- Center for Imaging of Neurodegenerative Diseases
- UCSF / Radiology / VA Medical Center
- 02/05/2007

- Medical Imaging Informatics, 2/12/2008  --- W. Zhan

## Outline

- MRI measurement for diffusion
- Diffusion tensor imaging (DTI)
- High angular resolution diffusion imaging
- HARDI, DSI, QBI, SHD, CSI, etc.
- DTI-Tractography
- HARDI-tractography
- Novel methods of tractography
- DTD, FFM, PFT, DDI, etc.,

## Diffusion in 2-D

## Diffusion in 3-D: White Matter

**Diffusion in 3-D: White Matter**

**Water in an Oriented Tissue**

**Water Motion**

## Stejskal-Tanner Experiment

- Stejskal, EO. & Tanner, JE. 1965: J. Chem. Phys. 42, 288–292

## Apparent Diffusion Coefficients (ADC)

- T

*Journal of Cerebral Blood Flow & Metabolism* (1996) **16**, 892–905

## Diffusion Tensor : 3x3 Matrix

** ****Seven Images / Slice**

- I0

- Basser, PJ. et al., J Magn Reson 1994;103:247–54

## Eigen-system Analysis of Diffusion Tensor

## FA

- FA: Fractional Anisotropy; <D>: Mean Diffusivity

- Fractional Anisotropy (FA)

- Directionally-Encoded Color Map

- DEC

- W.Zhan et. al.

## Field of Diffusion Tensor Ellipsoids

- W.Zhan et. al.

## Fiber Assignment by Continuous Tracking

- FACT Algorithm

- Xue R., et.al.,*  Magn. Reson. Med.* 42 (1999), 1123–1127

## Fiber Tracking in Tensor Field

- Representation of a white matter fiber trajectory as a space curve, **r**(s). The local tangent vector, **t**(s1), is identified with the eigenvector, e1(**r**(s1)), associated with the largest eigenvalue of the diffusion tensor, _**D**_ at position **r**(s1).

- Frenet Equation
- Euler’s Method
- Runge-Kutta Method (2nd 4th Order)

_**D**_

- Basser, PJ. et al., Magn Reson Med.  44, 625-632

## DTI – Tractography 

**DTI – Tractography**

- S. Mori - JHU

- D. Jones – U Nottingham, UK

## DTI-Tractography:  Corpus Callosum

- W.Zhan et. al.

## DTI-Tractography:  Corticospinal Tract

- W.Zhan et. al.

## DTI Limitation: Crossing Fibers

- P.J. Basser et. al. MRM 2002

## High Angular Resolution Diffusion (HARDi)

- HARD Encoding

- Frank, MRM 2002

- Identify complex white matter structures
- Improve diffusion MRI based tractography

## Diffusion Circular Spectrum Imaging

- Case 1:    Single Fiber

- W.Zhan et. al. MRM 2003

- W.Zhan et. al. MRM 2003, 49:1077

## Diffusion Circular Spectrum Imaging

- Case 2:    Fiber-Crossing

- W.Zhan et. al. MRM 2003, 49:1077

## Brain Regions with Higher 4th Order Values

- W.Zhan et. al. MRM 2003, 49:1077

## Phase CSI  Fiber-crossing Orientation

**Phase CSI ******** Fiber-crossing Orientation**

- Regular DTI: major eigenvector map

- Phase CSI: intravoxel crossed fibers

- W.Zhan et. al. NeuroImag 2004, 23: 1358

## Phase CSI Fiber-crossing Orientation

**Phase CSI******** Fiber-crossing Orientation**

- Regular DTI: major eigenvector map

- Phase CSI: intravoxel crossed fibers

- W.Zhan et. al. NeuroImag 2004, 23: 1358

## Diffusion Circular Spectrum Imaging – Fiber Crossings 

**B**

**A**

**D**

**C**

- Diffusion Circular Spectrum Imaging – Fiber Crossings

- W.Zhan et. al. NeuroImag 2004, 23: 1358

## Diffusion Spectrum Imaging (DSI)

- Vedeen, MRM 2005, 54: 1377

## Q-Ball Imaging (QBI)

- Tuch,  MRM 2004, 52: 1358

## ODF Recon: Spherical Deconvolution

- Christopher P. Hess et al.,  MRM 2006, 56 (1): 104-117

## HARDI-based Tractography

- Schmahmann JD. et al.,  BRAIN 2007, 130 (3): 630-653

- Berman JI, et al., NeuroImage, 2008;39(1):215-22

## Tract-Selective Visualization

- Schmahmann JD. et al.,  BRAIN 2007, 130 (3): 630-653

## DSI Tractography: Associate Pathways 

- Schmahmann JD. et al.,  BRAIN 2007, 130 (3): 630-653

## Novel Method 1: Tensor Deflection

- Laza M., et al., Human Brain Mapping 18:306 –321(2003)

## Novel Method 2: Fast Marching

- Parker GJM, et al., IEEE TMI 25:505 –512 (2002)

## Advanced Fast Marching Method

- Staempfli P., et al., NeuroImage 30(1):110-120 (2005)

## Novel Method 3: Probabilistic Tractography 

- Parker, GJM. The British Journal of Radiology, 77 (2004), S176–S185

## Novel Method 3: Dynamic Diffusion Imaging

- W.Zhan et. al. MRI 2008, In Press

## Alexander AL, Hasan HM, Kindlmann G, Parker DL, Tsuruda JS(2000): A geometric analysis of diffusion anisotropy measures. Magn Reson Med 44:283–291.
Alexander AL, Hasan HM, Lazar M, Tsuruda JS, Parker DL (2001): Analysis of partial volume effects in diffusion-tensor MRI. Magn Res Med 45:770 –780.
Alexander D.C., Barker G.J., Arridge S.R., Detection and modeling of non-Gaussion apparent diffusion coefficient profiles in human brain data, Magn. Reson. Med. 48 (2002) 331-340.
Basser PJ, Pierpaoli C (1996): Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B 111:209 –219.
Basser PJ, Pierpaoli C (1998): A simplified method to measure thediffusion tensor from seven MR images. Magn Res Med 39:928–934.
Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A (2000): In vivo tractography using DT-MRI data. Magn Res Med 44:625– 632. 
Berman JI, Chung S, Mukherjee P, Hess CP, Han ET, Henry RG.  Probabilistic streamline q-ball tractography using the residual bootstrap. Neuroimage. 2008 Jan 1;39(1):215-22. 
Callaghan P.T., 1990. PGSE-MASSEY, a sequence for overcoming phase instability in very high-gradient spin-echo NMR. J. Magn Reson. 88, 493-500.
Conturo TE, Lori NF, Cull TS, Akbudak E, Snyder AZ, Shimony JS, McKinstry RC, Burton H, Raichle ME (1999): Tracking neuronal fiber pathways in the living human brain. Proc Natl Acad Sci 96:10422–10427.
Frank L.R., 2002. Characterization of anisotropy in high angular resolution diffusion weighted MRI. Magn Reson Med. 47, 1083-1099.
Hess CP, Mukherjee P. Visualizing white matter pathways in the living human brain: diffusion tensor imaging and beyond. Neuroimaging Clin N Am. 2007 Nov;17(4):407-26, 
Jones DK, Simmons A, Williams SCR, Horsfield MA (1999): Noninvasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magn Reson Med 42:37– 41.
Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H (2001): Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging 13:534 –546.

- Alexander AL, Hasan HM, Lazar M, Tsuruda JS, Parker DL (2001): Analysis of partial volume effects in diffusion-tensor MRI. Magn Res Med 45:770 –780.
- Alexander D.C., Barker G.J., Arridge S.R., Detection and modeling of non-Gaussion apparent diffusion coefficient profiles in human brain data, Magn. Reson. Med. 48 (2002) 331-340.
- Basser PJ, Pierpaoli C (1996): Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B 111:209 –219.
- Basser PJ, Pierpaoli C (1998): A simplified method to measure thediffusion tensor from seven MR images. Magn Res Med 39:928–934.
- Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A (2000): In vivo tractography using DT-MRI data. Magn Res Med 44:625– 632.
- Berman JI, Chung S, Mukherjee P, Hess CP, Han ET, Henry RG.  Probabilistic streamline q-ball tractography using the residual bootstrap. Neuroimage. 2008 Jan 1;39(1):215-22.
- Callaghan P.T., 1990. PGSE-MASSEY, a sequence for overcoming phase instability in very high-gradient spin-echo NMR. J. Magn Reson. 88, 493-500.
- Conturo TE, Lori NF, Cull TS, Akbudak E, Snyder AZ, Shimony JS, McKinstry RC, Burton H, Raichle ME (1999): Tracking neuronal fiber pathways in the living human brain. Proc Natl Acad Sci 96:10422–10427.
- Frank L.R., 2002. Characterization of anisotropy in high angular resolution diffusion weighted MRI. Magn Reson Med. 47, 1083-1099.
- Hess CP, Mukherjee P. Visualizing white matter pathways in the living human brain: diffusion tensor imaging and beyond. Neuroimaging Clin N Am. 2007 Nov;17(4):407-26,
- Jones DK, Simmons A, Williams SCR, Horsfield MA (1999): Noninvasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magn Reson Med 42:37– 41.
- Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H (2001): Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging 13:534 –546.

- Literatures (1)

## Mori S, Crain B, Chacko VP, van Zijl PCM (1999): Three dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann Neurol 45:265–269.
S. Mori, and P.C.van Zijl. Fiber tracking: principles and strategies–a technical review. NMR Biomed, 15(7-8):468-480, 2002. 
Mori S, Kaufmann WE, Davatzikos C, Stieljes, Amodei L, Fredericksen K, Pearlson GD, Melhem ER, Solaiyappan M, Raymond GV, Moser HW, van Zijl PC (2002): Imaging cortical association tracts in the human brain using diffusion-tensor-based axonal tracking. Magn Reson Med 47:215–223. 
Mukherjee P, Hess CP, Xu D, Han ET, Kelley DA, Vigneron DB. Development and initial evaluation of 7-T q-ball imaging of the human brain. Magn Reson Imaging. 2007 
Hess CP, Mukherjee P, Han ET, Xu D, Vigneron DB.
Ozarslan E., Spepherd T.M., Vemuri B.C., Blankband S.J., Mareci T.H., Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT), NeuroImage 31 (2006) 1086-1103.
Parker, G. J. M., Wheeler-Kingshott, C. A. M. & Barker, G. J. 2002c Estimating distributed anatomical brain connectivity using fast marching methods and diffusion tensor imaging. IEEE Trans. Med. Imaging 21, 505–512.
Parker, G. J. M., Haroon, H. A. & Wheeler-Kingshott, C. A. M. 2003 A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J. Magn. Reson. Imaging 18, 242–254.
Parker GJ, Alexander DC. Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue. Philos Trans R Soc Lond B Biol Sci. 2005 May 29;360(1457):893-902. 
Pajevic S, Pierpaoli C (1999): Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magn Reson Med 42:526 –540.
Poupon C, Clark CA, Frouin V, Regis J, Bloch I, Le Bihan D, Mangin J (2000): Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. Neuroimage 12:184 –195.

- S. Mori, and P.C.van Zijl. Fiber tracking: principles and strategies–a technical review. NMR Biomed, 15(7-8):468-480, 2002.
- Mori S, Kaufmann WE, Davatzikos C, Stieljes, Amodei L, Fredericksen K, Pearlson GD, Melhem ER, Solaiyappan M, Raymond GV, Moser HW, van Zijl PC (2002): Imaging cortical association tracts in the human brain using diffusion-tensor-based axonal tracking. Magn Reson Med 47:215–223.
- Mukherjee P, Hess CP, Xu D, Han ET, Kelley DA, Vigneron DB. Development and initial evaluation of 7-T q-ball imaging of the human brain. Magn Reson Imaging. 2007
- Hess CP, Mukherjee P, Han ET, Xu D, Vigneron DB.
- Ozarslan E., Spepherd T.M., Vemuri B.C., Blankband S.J., Mareci T.H., Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT), NeuroImage 31 (2006) 1086-1103.
- Parker, G. J. M., Wheeler-Kingshott, C. A. M. & Barker, G. J. 2002c Estimating distributed anatomical brain connectivity using fast marching methods and diffusion tensor imaging. IEEE Trans. Med. Imaging 21, 505–512.
- Parker, G. J. M., Haroon, H. A. & Wheeler-Kingshott, C. A. M. 2003 A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J. Magn. Reson. Imaging 18, 242–254.
- Parker GJ, Alexander DC. Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue. Philos Trans R Soc Lond B Biol Sci. 2005 May 29;360(1457):893-902.
- Pajevic S, Pierpaoli C (1999): Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magn Reson Med 42:526 –540.
- Poupon C, Clark CA, Frouin V, Regis J, Bloch I, Le Bihan D, Mangin J (2000): Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. Neuroimage 12:184 –195.

- Literatures (2)

## Schmahmann JD, Pandya DN, Wang R, Dai G, D'Arceuil HE, de Crespigny AJ, Wedeen VJ. Association fibre pathways of the brain: parallel observations from diffusion spectrum imaging and autoradiography. Brain. 2007 Mar;130(Pt 3):630-53. 
Stejskal, E. O. & Tanner, J. E. (1965) Spin diffusion measurements: spin echoes in the presence of a time dependent field gradient. J. Chem. Phys. 42, 288–292.
Tuch D.S., Reese T.G., Wiegell M.R., Wedeen V.J., Diffusion MRI of complex neural architecture, Neuron 40 (2003) 885-895.
Tuch D.S., Q-Ball Imaging, Magn. Reson. Med. 52 (2004) 1358-1372.
Wedeen VJ, Hagmann P, Tseng WY, Reese TG, Weisskoff RM. Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn Reson Med. 2005 Dec;54(6):1377-86. 
Wiegell MR, Larsson HB, Wedeen VJ (2000): Fiber crossing in human brain depicted with diffusion tensor MR imaging. Radiology 217:897–903.
Xue R, van Zijl PCM, Crain BJ, Solaiyappan M, Mori S (1999): In vivo three-dimensional reconstruction of rat brain axonal projections by diffusion tensor imaging. Magn Res Med 42:1123–1127.
Zhan W., Gu H., Xu S., Silbersweig D.A., Stern E., Yang Y., Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients, Magn. Reson. Med. 49 (2003) 1077-1088.
Zhan W., Stein E.A., Yang Y., Mapping the orientation of intravoxel crossing fibers based on the phase information of diffusion circular spectrum, NeuroImage 23 (2004) 1358-1369.
Zhan W., Stein E.A., Yang Y., A rotation-invariant spherical harmonic decomposition method for mapping intravoxel multiple fiber structures, NeuroImage 29 (2006) 1212-1223.
Zhan W, Yang Y. How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI. J Magn Reson. 2006 Dec;183(2):193-202. 
Zhan W, Jiang L, Loew M, Yang Y. Mapping Spatio-Temporal Diffusion inside the Human Brain Using a Numerical Solution of the Diffusion Equation, Magn. Reson. Imag. (2008)- In Press

- Stejskal, E. O. & Tanner, J. E. (1965) Spin diffusion measurements: spin echoes in the presence of a time dependent field gradient. J. Chem. Phys. 42, 288–292.
- Tuch D.S., Reese T.G., Wiegell M.R., Wedeen V.J., Diffusion MRI of complex neural architecture, Neuron 40 (2003) 885-895.
- Tuch D.S., Q-Ball Imaging, Magn. Reson. Med. 52 (2004) 1358-1372.
- Wedeen VJ, Hagmann P, Tseng WY, Reese TG, Weisskoff RM. Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn Reson Med. 2005 Dec;54(6):1377-86.
- Wiegell MR, Larsson HB, Wedeen VJ (2000): Fiber crossing in human brain depicted with diffusion tensor MR imaging. Radiology 217:897–903.
- Xue R, van Zijl PCM, Crain BJ, Solaiyappan M, Mori S (1999): In vivo three-dimensional reconstruction of rat brain axonal projections by diffusion tensor imaging. Magn Res Med 42:1123–1127.
- Zhan W., Gu H., Xu S., Silbersweig D.A., Stern E., Yang Y., Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients, Magn. Reson. Med. 49 (2003) 1077-1088.
- Zhan W., Stein E.A., Yang Y., Mapping the orientation of intravoxel crossing fibers based on the phase information of diffusion circular spectrum, NeuroImage 23 (2004) 1358-1369.
- Zhan W., Stein E.A., Yang Y., A rotation-invariant spherical harmonic decomposition method for mapping intravoxel multiple fiber structures, NeuroImage 29 (2006) 1212-1223.
- Zhan W, Yang Y. How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI. J Magn Reson. 2006 Dec;183(2):193-202.
- Zhan W, Jiang L, Loew M, Yang Y. Mapping Spatio-Temporal Diffusion inside the Human Brain Using a Numerical Solution of the Diffusion Equation, Magn. Reson. Imag. (2008)- In Press

- Literatures (3)