H1 spectroscopy

1
Imaging Translational Water Diffusion with
Magnetic Resonance for Fiber Mapping in the
Central Nervous System

• Basics of diffusion-weighted MRI
• Fiber Mapping from Rank-2 Tensor Model
• High-Angular-Resolution Diffusion Imaging
• Matrix Acquisition
• Model fitting
• Diffusion parameter images
• 3D fiber tract mapping
• Example structures in brain and spinal cord
• Challenges and limitations
• Acknowledgements

2
Magnets, Magnetic Resonance, and Imaging
Black Horizontal-solenoid magnet field Gray
Spatial gradients in magnetic field White
Perpendicular rf magnetic field Subject
stationary
Timing determines contrast
3
Image Acquisition
4
Magnetic Resonance Imaging of 1H in Human Head
(THM) at 3 Tesla (128 MHz)
Gray Matter (cortex)
White Matter (sub-cortex)
Cerebral-Spinal Fluid
Proton density and T1 weighted Spin echo image
acquisition TR 3700 ms, TE 15 ms
T2 weighted Spin echo image acquisition TR 3700
ms, TE 90 ms
5
White Matter and Tissue Structure
Axon, 0.2 - 20 mm Microtubules, 0.024
mm Neurofilaments, 0.010 mm
x 160,000 EM Waxman, et al., The Axon, Oxford UP,
1995
aS, glial cell aT, axonal cell
EM, Bovine optic nerve a) parallel, b) transverse
G. Stanisz, A. Szafer, G. Wright, R. M.
Hendelman, 1997
6
Tissue Microstructure andMR Measures of Water
Diffusion

Inglis, et al., Magn. Reson. Med. 2001 45
580-587Chin, et a, Magn. Reson. Med. 2002 47
455-460

• Microstructure properties that affect diffusion
• Cell size and density
• Cell orientation (anisotropy)
• Membrane permeability
• Intracellular viscosity
• Extracellular viscosity

7
Spin Echo Method for Diffusion Weighted MRI
Gradient, G has strength and direction
Stejskal-Tanner Equation
8
Diffusion-weighting GradientStrength and
Orientation Dependence
x-gradient diffusion weighting
z-gradient diffusion weighting
3
9
15
21
27 G/cm
Increasing diffusion weighting
9
Diffusion Tensor Imaging and Displacement Profiles
Basser et al. J. Magn. Reson. B 1994103 247-254
Diffusion tensor imaging assumes a rank-2,
symmetric, positive-definite tensor model for
diffusivities. In this case, the Bloch-Torrey
equation for magnetization can be written as,
Using a spin-echo measurement method, the
diffusion-dependent part of the measured signal,
that results from solving this equation, can be
written as
Diffusivity in the direction defined by the unit
vector , along which the gradient
is applied, is given by,
Diffusivity in each voxel can be described by an
ellipsoidal displacement profile, such as the
following, with major and minor axes
(eigenvectors).
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Anisotropic Diffusion Tensor

• Diffusion is highly anisotropic in fibrous
  structures.
• MR is sensitive to the molecular diffusion in the
  direction of the gradient applied.

D, Cartesian tensor for rank 2

• Each voxel is described by a cartesian tensor of
  rank 2 (32 9 elements), but only 6 are unique
  (real, symmetric matrix), i.e. Diffusion has
  antipodal symmetry.
• Allows measurement of anisotropy
• Allows determination of fiber directions.

Rank-2 Diffusion tensor image of an excised rat
brain at 17.6T (off-diagonal x 10)
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Scalar Measures of Diffusion (orientation
independent)
Basser, NMR Biomed. 19958333-344
Eigenvalues of
Mean diffusivity
Fractional anisotropy, FA
FA 0 0.5 1.0
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MR Microscopy of Injured Rat Spinal Cord at 600
MHz (14.1 T, 5.2 cm)
SE DWI HARDI acquisition, multiple
slice TR3000ms, TE27.7ms ?17.8ms, d2.4ms b
0, NA 24 b 1250 s/mm2 in 21 directions, NA
8 FOV 4.8 x 4.8 x 12 mm3 (0.2 mm slices) Matrix
96 x 96 x 60 Resolution 50 x 50 x 200
micron3 Total time, 12 hours
So
FA ltDgt
Tr(D)color EVcolor
Injured excised fixed SD rat spinal cord
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Fiber Tract Mapping Algorithm
Basser, et al., MRM 200044625-632
Using the principle eigenvector, e1, at all
locations in the image to suggest the direction
of tracts, a fiber trajectory, , along an
arc length, s, may be calculated by solving a
Frenet equation,
where the tangent vector, , is assumed to
the equal to the principle eigenvector along the
path,
Therefore the Frenet equation can be solved with
the initial condition,
The trajectory is terminated when the principle
eigenvector can no longer be assumed to
represents the tract direction (low anisotropy).
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Fiber Tract Mapping Implementation
a) Specific regions of interest are defined
within the three dimensional MR
image. b) Starting from these user supplied
initial conditions (ROIs), fiber tracing is
initiated in both directions (antipodal symmetry)
along the direction defined by the principle
eigenvector. c) Then the tract is continued
until the anisotropy falls below a pre-specified
threshold value (e.g. fractional anisotropy)
since it is assumed that fibers do not exist
below this level of anisotropy.
a)
b)
c)
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Fiber Tracking Results
MR Microscopy at 750 MHz (17.6 T, 89 cm) Normal
fixed rat brain
MR Microscopy at 750 MHz (17.6 T, 89 cm) Normal
(L) and injured (R) excised fixed rat spinal cord
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A Problem with rank-2 Diffusion-Tensor MRI
Rank-2 DT-MRI assumes that there is single fiber
orientation within the voxel.
Typically voxel size, 100 x 100 x 100 micron3,
which in white matter might contain 25 to
125,000,000 axons

• What happens when there is directional
  heterogeneity?
• Fiber direction is uncertain
• Anisotropy is reduced

Idealize Voxel
Possible Improvement High Angular Resolution
Diffusion Imaging (HARDI) and modeling with a
higher rank Cartesian tensor (gtrank 2). Then
diffusion measurement can be performed with
gradients along many directions making it
possible to directly measure distribution of
diffusivities. (Tuch et.al., Proc. ISMRM, 1999.)
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Extention to Generalized Diffusion Tensor Imaging
Ozarslan and Mareci, Magn. Reson. Med
200350955-965 Ozarslan, Vemuri and Mareci,
Magn. Reson. Med. 200553866-876
Reformulate DTI by incorporating Cartesian
tensors of higher rank
Rewrite Bloch-Torrey equation in terms of a
rank-l Cartesian tensor
Derive a new expression for signal attenuation
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Diffusion Displacement Probabilities
The generalized diffusion tensor defines the rate
of diffusion along each direction.
Assuming mono-exponential attenuation, the
normalized signal can be written as,
Therefore, the water displacement probability
function is given by the Fourier integral,
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Generalized Diffusion Tensor Imaging
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Effect of Noise on Calculated Voxel Structure
Ozarslan, et al., NeuroImage 2006, in press

• Simulated system of two crossing fiber bundles.
• Probability surfaces calculated using the
  expansion of the probability on the surface of a
  sphere.
• (c-f) Surfaces in the framed area of panel b
  recalculated under increasing levels of noise
  added to the signal values. These panels
  represent images with signal-to-noise ratios
  (SNRs) between 501 and 12.51.

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Generalized Diffusion Tensor Imagingof Excised
Rat Spinal Cord at 14.1 Tesla (600 MHz)
Multiple-slice spin echo acquisition 46 gradient
directions, 1 non-weighted image Matrix 72 x 72 x
40, resolution 60 x 60 x 300 mm3 Total
acquisition time, 9 hrs, 47 mins
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Structures in Optic Chiasm of the Excised Rat
Brain
Ozarslan, et al., NeuroImage 2006, in press
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Calculated Voxel Structures in Excised Rat Brain
Ozarslan, et al., NeuroImage 2006, in press
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Challenges and Limitations

• Limitation
• MR image measurement
• Signal strength
• Time for measurement
• Motion

• Challenges
• Fiber mapping and probabilistic mapping
• Modeling
• Optimize data acquisition with modeling
• Smoothing
• Segmentation
• Calculate most probable paths
• Relate structure to function
• Fiber structure to pathology
• Fiber structure to neuronal processing

Mark Griswold, Univ. Wurzburg in collaboration
with Siemens Medical
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Acknowledgements

• Research Group
• Sara Berens Neuroscience
• Min Sig Hwang Biomed Engineering
• Tom Mareci Biochemistry
• Evren Ozarslan (now at NIH)
• Hector Sepulveda Biomed Engineering
• Nelly Volland Biomed Engineering

• Collaborators
• Doug Anderson Neuroscience
• Steve Blackband Neuroscience
• Paul Carney Pediatrics
• Tim Shepherd Neuroscience
• Baba Vemuri Comp. Info. Sci. Eng.
• Bob Yezierski Orthodontics/Neuroscience

• AMRIS Facility Staff
• Barbara Beck Kelly Jenkins
• Jim Rocca Dan Plant
• Xeve Silver Raquel Torres

• Grant Support
• NIH R01 NS042075
• R01 NS004752
• P41 RR16105
• Dept. of Defense