Diffusion MRI
• Diffusion MRI: a marker of tissue microstructure • Sensitizing the MRI signal to diffusion • Measuring diffusion rates with MRI • Diffusion tensor imaging • Tractography • Acquisition Considerations. • Bonus Material: Less conventional diffusion MRI methods.
1 J.McNab - RAD 229 Diffusion MRI in the Brain
Clinical Applications Neuroscience Stroke White Matter Pathways
Diffusion
Perfusion Structural Connectivity Zaharachuk G, et. al. 2012.
Intracranial Infections Brain Tumours Trauma Edema
2 J.McNab - RAD 229 Diffusion MRI in the Body Breast Prostate
Park M-J et. al. 2007 Bonekamp S, et. al. 2012 Liver Musculoskeletal
Bonekamp S, et. al. 2012 Staroswiecki E, et. al. 2012
3 J.McNab - RAD 229 What is diffusion?
• The result of random collisions between molecules in liquids and gases.
• A form of passive transport that causes mixing but no bulk motion.
• A spontaneous, random process.
J.McNab - RAD 229 Water Diffusion in Tissue
Types of Obstacles: • membranes • macromolecules
Effect on Water Diffusion: • decreased diffusion rates • limited displacement Darwin, M. et. al. 1995. distances (restrictions) • distinct geometric patterns of water displacements
5 J.McNab - RAD 229 Hindered Diffusion
• molecules bump into obstacles (e.g. cell membranes) • decreased diffusion rate More Obstacles Fewer Obstacles
Slower diffusion. Faster diffusion. Shorter displacements. Longer displacements.
J.McNab - RAD 229 Restricted Diffusion
Impermeable boundaries limit the displacement distance.
Time
J.McNab - RAD 229 Diffusion Anisotropy
Isotropic Diffusion Anisotropic Diffusion
Glass of Water White Matter Tissue
x100
health.utas.edu.au
J.McNab - RAD 229 Diffusion MRI: a marker of tissue microstructure
Patterns of water diffusion in tissue reflect the tissue microstructure.
• membranes • permeability of membranes • macromolecules • packing density • compartment sizes
Darwin, M. et. al. 1995.
Sensitizing the MRI signal to water diffusion is a way to indirectly get information about tissue microstructure.
9 J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Hahn 1950. Carr and Purcell 1954.
Case #1: Without DiffusionDiffusion-Weighted Spin Echo
Echo Gx encode Gx decode
90° 180° Δ
x Stejskal-Tanner, 1965. J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Case #1: Without Diffusion
Echo Gx encode Gx decode
90° 180°
x Stejskal-Tanner, 1965. Low Gx High Gx J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Case #1: Without Diffusion
Echo Gx encode Gx decode
90° 180°
x Stejskal-Tanner, 1965. Low Gx High Gx J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Case #1: Without Diffusion
Echo Gx encode Gx decode
90° 180°
x Stejskal-Tanner, 1965.
J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Case #1: Without Diffusion
Echo Gx encode Gx decode
90° 180°
x Stejskal-Tanner, 1965.
J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Case #1: Without Diffusion
Echo Gx encode Gx decode
90° 180°
x Low Gx High Gx J.McNab - RAD 229 Sensitizing the MRI Signal to Diffusion
Case #1: With Diffusion
Echo Gx encode Gx decode
90° 180°
spins change position
x Low Gx High Gx J.McNab - RAD 229 The Bloch Equation
torque due to B0
relaxation
J.McNab - RAD 229 The Bloch-Torrey Equation
Torrey H.C. Physical Review 1956.
Diffusion equation/Heat Equation:
J.McNab - RAD 229 The Bloch-Torrey Equation
Torrey H.C. Physical Review 1956.
with
J.McNab - RAD 229 b-value
Echo G G
90° 180°
J.McNab - RAD 229 Measuring the Diffusion Coefficient
b-value:
Non-Diffusion-Weighted Signal: Diffusion-Weighted Signal:
Diffusion Coefficient:
J.McNab - RAD 229 Apparent Diffusion Coefficient
• For Diffusion MRI, the diffusion coefficient is referred to as the “Apparent” Diffusion Coefficient (ADC). Why?
J.McNab - RAD 229 Diffusion in Tissue
slower faster diffusion diffusion
• In tissue the self-diffusion of water molecules is hindered and restricted by membranes and macromolecules.
• In brain tissue, water can diffusion more freely along white matter fibers than across them.
J.McNab - RAD 229 Diffusion Anisotropy
Isotropic Diffusion Anisotropic Diffusion
Glass of Water White Matter Tissue
x100
health.utas.edu.au
J.McNab - RAD 229 Diffusion Contrast in the Brain
Gx Gy Gz
J.McNab - RAD 229 Measuring Anisotropy: Diffusion Tensor Imaging
diffusion tensor
• Eigenvectors = axes of ellipsoid (e1 orientation of fibers)
• Eigenvalues = length of axes (rate of diffusion)
Basser et. al. 1994. Pierpaoli and Basser 1996.
J.McNab - RAD 229 Measuring Anisotropy: Diffusion Tensor Imaging
diffusion tensor
• Eigenvectors = axes of ellipsoid (e1 orientation of fibers)
• Eigenvalues = length of axes (rate of diffusion)
Basser et. al. 1994. Pierpaoli and Basser 1996.
J.McNab - RAD 229 Measuring Anisotropy: Diffusion Tensor Imaging
Directionally Encoded Line Representation of Colour Map Principal Eigenvector
Basser et. al. 1994. Pierpaoli and Basser 1996.
J.McNab - RAD 229 Measuring Anisotropy: Diffusion Tensor Imaging
Fractional Anisotropy:
Mean Diffusivity:
J.McNab - RAD 229 Diffusion Tractography
• Principal diffusion direction relates to direction of fiber orientations and can be used for fiber tracking (tractography).
J.McNab - RAD 229 Diffusion Tractography • Piece together discrete (voxel-wise) estimates of the underlying continuous fibre orientation field to infer on the 3-D trajectories of anisotropic tissue structures. • Starting (“seed”) voxel is selected in an anatomical region of interest and voxel-wise estimates of the principal diffusion orientation are followed from one voxel to the next.
J.McNab - RAD 229 Two Classes of Tractography Algorithms
Deterministic Probabilistic
uncertainty
(θ0, ϕ0 ) θ pdf ϕ pdf
θ 0 ϕ 0 Behrens et al., MRM 2003; 50:1077–1088
J.McNab - RAD 229 Two Classes of Tractography Algorithms
Deterministic Probabilistic
Iterative Monte Carlo approach
J.McNab - RAD 229 Two Classes of Tractography Algorithms
Deterministic Probabilistic
Streamlines Multiple “sample” streamlines
J.McNab - RAD 229 Tractography Stopping Criteria
When to stop? Heuristics to avoid error propagation. + Knowledge of the anatomy.
Curvature Threshold: To avoid crossing boundaries and very bended trajectories, impose a smoothness criterion.
Anisotropy Threshold: To avoid propagating in regions where the vector field is meaningless.
Anatomical Criteria: e.g. reach grey matter.
J.McNab - RAD 229 Interpretation of Tractography
What does Quantitative Measures probabilistic of Connectivity? tractography measure? • Number of axons connecting 2 areas? • The probability that the dominant path through the • Proportion of axons from a seed that diffusion field passes reach a target? through this region.
• “Integrity” of the connecting white matter… • degree of myelination • packing density • fiber size or shape
J.McNab - RAD 229 Probabilistic Tractography Measures
• They may reflect anatomical connectivity strength • But they also reflect ….
• Connection Length: Longer connections have smaller probability than shorter ones.
• Geometric complexity: Probabilities of connections that go through regions of complex structure will be smaller than connections that go through more coherent regions.
• Resolution of the spatial grid: Probabilities change if we change the size of “bins” for displaying the spatial histogram.
J.McNab - RAD 229 Diffusion Tractography
Robust mapping of large white matter fiber bundles.
In Vivo Diffusion MRI Resolution: ~2 mm
WM Bundles: 2-6 mm (106-107 axons)
Axon Diameter ~ 2-10 µm
Schuz A and Miller R. Cortical Lebel C. et. al. ISMRM 2007. Areas: Unity and Diversity, 2002.
J.McNab - RAD 229 Intra-Voxel Crossing Fibers
Diffusion tensor fails to model crossing fibers.
J.McNab - NeuroRad Fellows Diffusion Spectrum Imaging
•Diffusion spectrum imaging (DSI) maps crossing fibers by estimating orientation distribution functions (ODFs). Wedeen et al. 2005. J.McNab - RAD 229 q-space Imaging Diffusion-weighted Spin Echo gradient gradient duration strength
diffusion time interval
• Spin displacement probability density function: • Gradient wave vector: Callaghan 1991. J.McNab - RAD 229 q-space Imaging sample q-space
DWIs
3D radial qz FFT projection y y
qx x x qy spin displacement orientation distribution q space probability density function (ODF) function (PDF) Wedeen et al. 2005. J.McNab - RAD 229 q-ball Imaging Funk-Radon Transform
•Approximates the dODF using! the Funk-Radon Transform on a spherical acquisition scheme (i.e. one q-value). Tuch, 2004. Tuch et. al. 2003. J.McNab - RAD 229 Spherical Deconvolution
Anderson and Ding, 2002. Tournier et. al. 2004.
⊗-1 =
Response DWI Signal fiber ODF Function
Deconvolve DWI signal with a response function to recover the fiber ODF.
J.McNab - RAD 229 Several Model-Based Approaches
•Multi-Tensor Model
+
•Ball and two stick model, Behrens, 2003.
+ +
J.McNab - RAD 229 Intra-Voxel Crossing Fibers
parallel fanning crossing kissing bending
tensor
Jbabdi S, et. al. Brain Connect, 1:169-183, 2011.
J.McNab - RAD 229 False Positives in Diffusion Tractography
O’Donnell LJ and Westin C-F, Neurosurg Clin N Am, 22:185-188, 2011.
J.McNab - RAD 229 False Negatives in Diffusion Tractography
O’Donnell LJ and Westin C-F, Neurosurg Clin N Am, 22:185-188, 2011.
J.McNab - RAD 229 We Need More Validation Tools
Very few methods exist (in vivo or ex vivo) to map 3D white matter pathways and they all have limitations.
Polarized Classical Electron Tracers Light 2D Histology Dissection Microscopy Imaging Myelin Stains
Saleem (2008) J. Comp. Neur. Larsen (2007) Seung S. eyewire.org Microsc Res Tech Lawes (2008) NeuroImage Optical Coherence CLARITY 3D Histology Tomography
Magnain (2015) Neurophotonics Tomer (2014) Nature Protocols
J.McNab - RAD 229 Post-mortem Diffusion Imaging
Benefits • Diffusion orientation preserved. • No motion. • Long scan times possible. • Can be compared with histology.
McNab,..Miller, 2009. McNab, Edlow et. al. 2013. Acquisition Considerations
J.McNab - RAD 229 The effect of b-value Multi-Shell Diffusion Acquisitions Why bother? One Orientation Two Orientations Three Orientations
Signal at different b values (s/mm2) b=1000 b=2000 b=3000 b=4000 b=5000
Higher b value gives us more angular contrast!!!
http://fsl.fmrib.ox.ac.uk/fslcourse/lectures/fdt2.pdf
J.McNab - RAD 229 Multi-Shell Diffusion Acquisitions The effectWhy bother? of b-value One Orientation Two Orientations Three Orientations Multi-Shell Diffusion Acquisitions Why bother? Signal at different One Orientation Two Orientations Three Orientations b values 2 (s/mm ) Signal at b=1000 different b=2000 b values b=3000 (s/mm2) b=4000 b=1000 b=2000 b=5000 b=3000 b=4000 b=5000
b=300 b=1000 b=2000 b=3000
But SNR goes down Higher b value gives us more angular contrast!!! very quickly with b…
http://fsl.fmrib.ox.ac.uk/fslcourse/lectures/fdt2.pdf
J.McNab - RAD 229 b-value: q-value vs. diffusion time
c c
q diffusion time
Time
J.McNab - RAD 229 Different Types of Resolution for Diffusion MRI
spatial resolution spin displacement angular resolution resolution 30°
40°
50°
60°
90° 1/k 1/q max max no. of diffusion how far out area of diffusion encoding directions in k-space encoding gradient J.McNab - RAD 229 Benefits of Strong Gradients for Diffusion MRI
90° 180° 90° 180°
G G G G
TE TE
1) Improved SNR at high q-values. 2) Ability to obtain short diffusion times and high q- values simultaneously. 3) Closer to the short pulse approximation.
J.McNab - RAD 229 Bonus Material
Lots of different flavors of diffusion imaging.
Variations in the acquisition and/or modeling that help to gain sensitivity to different microstructure features.
J.McNab - RAD 229 Gaussian vs. Non-Gaussian Diffusion
Gaussian Diffusion: •large displacement and small q Diffusion Tensor •for isotropic or a single fiber population
Non-Gaussian Diffusion: •small displacement and large q •intra-voxel crossing fibers •bi-exponential diffusion ➡ restriction, multiple compartments, exchange
J.McNab - RAD 229 Diffusion Kurtosis Imaging
Cumulative Expansion of Diffusion MRI Signal
Gaussian kurtosis DTI • quantify the non-Gaussianity of the diffusion signal.
Jensen J et. al. 2005.
J.McNab - RAD 229 What about fiber patterns in grey matter?
Deep Grey Matter Lizard Brain Cerebral Cortical Grey Matter Cognitive Processing
White Matter Information Pathways
Atlas of the Human Brain in Section, 2nd ed., Roberts et. al. 1987.
J.McNab - RAD 229 Cortical Diffusion Orientations In Vivo 2 mm Ex Vivo 0.7 mm In Vivo 1 mm No coherent pattern of Radial diffusion Radial diffusion diffusion orientations orientations orientations
McNab JA et. al. NI McNab JA et. al. NI 46:775-785, 2009. 69:87-100, 2013.
J.McNab - RAD 229 Cortical Diffusion Orientations
Qiyuan Tian, Christoph Leuze
J.McNab - RAD 229 b-value: q-value vs. diffusion time
c c
q diffusion time
Time
J.McNab - RAD 229 Oscillating Gradient DWI
Diffusion-Encoding Frequency Time Integral Waveforms Spectrum f(t) |F(w)|2 g(t) PGSE
OGSE sine
OGSE cosine π π/2 RF 0 TE Does et. al. 2003. Parsons EC et. al. 2006. Gore et. al. 2010. J.McNab - RAD 229 Oscillating Gradient DWI Study time dependence of ADC over a series of short diffusion times rather than looking at the mean displacement after a single long diffusion time. T2 Can be used to distinguish:
• disperse flow vs. restriction PGSE • pore sizes
• surface-to-volume ratio OGSE • diffusion path tortuosities tumour microstructure
Does et. al. 2003. Parsons EC et. al. 2006. Gore et. al. 2010.
J.McNab - RAD 229 Diffusion-Diffraction Minima NMR in Porous Media z Signal,E(q, Δ ) • minima occur at q=1/Lr, where Lr is the restriction length. Callaghan 1991. Shemesh et. al. 2010. J.McNab - RAD 229 Mapping Compartment Sizes in Brain Tissue
Axon Diameter Mapping: Acquire a range of q-values and diffusion times and fit the data to a model for intra and extra-axonal diffusion.
AxCaliber Model Stanisz GJ et. al. MRM (1997). Assaf Y. et. al. MRM (2008). Barazany D.et. al. Brain (2009). Ong HH et. al. NI (2010). Alexander DC et. al. NI (2010). Zhang H et. al. NI (2011). hindered restricted
J.McNab - RAD 229 Initial Work in Fixed Tissue
Assaf Y. et .al. MRM 59:1347-1354 (2008).
Optic Nerve SignalDecay SignalDecay
q-value (µm-1) q-value (µm-1)
Sciatic Nerve Probability Probability
Axon Diameter (µm) Axon Diameter (µm) Spectroscopy: 7T, Gmax=1200mT/m,51min.
J.McNab - RAD 229 Initial Work in In Vivo Humans Using 300 mT/m Gradients
0.4 µm
0.35
0.3
Genu 0.25
0.2
Probability Splenium
0.15
0.1
0.05
0 0 2 4 6 8 10 12 a (um)
McNab, Edlow,....Wald. NeuroImage, 2013. Huang, ....McNab. ISMRM 2014.
J.McNab - RAD 229 Angular-Double Pulsed Field Gradient Imaging
Cory 1990, Mitra 1995, Koch 2008.Shemesh and Cohen 2011.
Ψ = angle between dir1 and dir2 NormalizedSignal NormalizedSignal
Ψ [deg] Ψ [deg]
J.McNab - RAD 229 Angular-Double Pulsed Field Gradient Imaging
Free Diffusion NormalizedSignal NormalizedSignal
Ψ [deg] Ψ [deg] Cory 1990, Mitra 1995, Koch 2008.Shemesh and Cohen 2011. J.McNab - RAD 229 Diffusion MRI
• Diffusion MRI: a marker of tissue microstructure • Sensitizing the MRI signal to diffusion • Measuring diffusion rates with MRI • Diffusion tensor imaging • Tractography • Acquisition Considerations. • Bonus Material: Less conventional diffusion MRI methods.
72 J.McNab - RAD 229