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S
Dr. S. J. Doran
Department of Physics,
University of Surrey,
Guildford, GU2 5XH, UK
Pelvic MR scans for radiotherapy planning:
Correction of system- and patient-induced
distortions
Simon J Doran1, Liz Moore2, Martin O Leach2
1Department
2CRC
of Physics, University of Surrey
Clinical Magnetic Resonance Research Group,
Institute of Cancer Research, Sutton
Acknowledgements
•
David Finnigan
•
Steve Tanner
•
Odysseas Benekos
•
David Dearnaley
•
Steve Breen
•
Young Lee
•
Geoff Charles-Edwards
Summary of Talk
•
The problem of distortion
•
Strategy for solving the problem
 Chang and Fitzpatrick algorithm (B0-induced distortion)
 Linear test object (gradient distortion)
•
Current limitations of the method
•
Patient trials and validations of system in progress
The Problem
• For many applications, MR provides better diagnostic
information than other imaging modalities.
• However, MR images are not geometrically accurate
 they cannot be used as a basis for planning procedures
• Can we correct all the sources of distortion in an MR image?
Radiotherapy
Potential Applications
Thermotherapy
Stereotactic surgery
Correlation of MR with other
modalities (image fusion)
Mathematical statement of the problem
I(r) = Itrue (r-Dr)
where Dr =
Dr(r)
Dr is a 3-D vector, whose
magnitude and direction
both depend on position.
Sources of distortion: (1) B0-induced
• Source of the problem is incorrect precession
frequency in the absence of gradients due to
poor shim or susceptibility
variations in sample
chemical shift variations
in sample
Data source: C.D. Gregory, BMRL
Sources of distortion: (2) gradient-induced
• Source of the problem is incorrect change in precession
frequency when gradients are applied.
Data courtesy R Bowtell, University of Nottingham
% error in Bz
DBz / arb. units
+15
0
-10
250
250
Isocentre
0
Isocentre
250
250
0
Strategy for solving problem
• FLASH 3-D sequence – susceptibility and CS lead to
distortion only in read direction (unlike EPI)
• Acquire data twice – forward and reverse read gradients.
• Correct for B0-induced distortions with Chang and
Fitzpatrick algorithm. IEEE Trans. Med. Imag. 11(3), 319-329 (1992).
• Use linearity test phantom to establish gradient distortions.
• Remove gradient distortions using interpolation to correct
position and Jacobian to correct intensity.
Chang and Fitzpatrick algorithm
• We have two data sets, F and R, which we treat row by row.
• For a given row, F(xF) dxF = R(xR) dxR .
• Calculate points xR corresponding to xF.
corr - fwd
Then xtrue = (xF + xR) / 2 .
fwd
corr
corr - rev
rev
The “linearity test phantom” (1)
• Why do we need it? Can’t we get theoretical results?



Manufacturers very protective of this sort of data
Need to guarantee “chain of evidence” for e.g., radiotherapy
Is the gradient system subtly malfunctioning?
•
robust, light, fixed geometry
•
mechanical interlocks give
reproducible position in magnet
•
3 orthogonal arrays of water-filled
tubes
•
square lattice of spots in each
orthogonal imaging plane.
The “linearity test phantom” (2)
Coronal
Transverse
Sagittal
X-ray CT vs. MRI of linearity test phantom
Slice offset
0 mm
Slice offset
-185 mm
System distortion mapping algorithm: Step 1
• Acquire 3-D datasets with forward and reverse read
gradients.
• Match spots between the CT and MRI datasets for
transverse plane and correct for distortion in read
direction to give single MRI dataset.
• Calculate displacement of each point  Dx, Dy
• Reformat the data to give sagittal and coronal projections.
(A different matrix of spots appears in each plane.)
• Repeat the matching process: Coronal  Dx, Dz
Sagittal  Dy, Dz
System distortion mapping algorithm: Step 2
• Interpolate and smooth data to provide complete 3-D
Example:
x-distortion on
transverse plane at slice
offset 117.5 mm
reconstructed from
transverse images
x-distortion / mm
matrices of gradient distortion values.
10
-10
100
200
y / mm
-100 -200
x / mm
System distortion mapping algorithm: Step 3
• Taking the known distortion data, correct the images:
 Sample the 3-D data Idist
at appropriately interpolated points.
 Correct for intensity distortions using the Jacobian.
^
I(x, y, z) = Idist(x-Dx, y-Dy, z-Dz) . J(x, y, z)
B0 corrected
B0&Grad
B0&Grad - B0 corrected
Problems remaining with the technique
• We currently have incomplete mapping data from the
current phantom.
Modifications to
design of linearity
test phantom
• Problem of slice warp:
Further data
processing using
full 3-D dataset
Patient study and validation
• Protocol is being tested on patients diagnosed with
prostate cancer and undergoing CT planning for conformal,
external beam radiotherapy.
• 4 patients have undergone both CT and MRI to date.
• Protocol (total time ~20 mins.)
 3-D FLASH, TR / TE 18.8 ms / 5 ms
 FOV 480 x 360 x 420 mm3 (256 x 192 x 84 pixels) 5mm “slices”
 FOV 480 x 360 x 160 mm3 (256 x 192 x 80 pixels) 2mm “slices”
 Each sequence repeated twice (forward and reverse read gradient)
• Image registration and comparison with CT now underway.
Once we have the corrected MR images ...
CT
• Validation via 3-D image
MRI
registration of MRI with CT
using champfer-matching
• Assess impact of MRbased radiotherapy plans
• Ultimate goal: to give us
the ability to use MRI alone
for radiotherapy planning
MRI dataset fed into treatment planning software
MR vs. CT
Dose-volume histogram for planning
treatment volume - patient data
• Data for 4 patients
analysed so far
excellent agreement
between treatments
calculated with X-ray
CT and those
calculated on the basis
of MR images.
80
% volume
• Early indications show
100
60
full C T numbers
40
segmented bone
bone density variations
20
water
0
95
100
% d o se
105
System distortion mapping algorithm: Step 3
• Problem: The slices are not themselves flat — slice warp!
The slice the scanner tells us
we are selecting
E.g., for a transverse plane,
we have Dx and Dy, but we
don’t know exactly which zposition they correspond to
The slice we actually get !
System distortion mapping algorithm: Step 3
• Solution: Use the complete set of data acquired
• Consider the x-distortion
 We have two estimates of Dx, acquired from matching spots on
transverse and coronal reformats of the original dataset.
 For Dxtra(x, y, z), z is not known correctly because of slice warp.
 For Dxcor(x, y, z), y is not known correctly.
•
But we can estimate unknowns from the data we have ...
 Dz can be estimated from the coronal or transverse reformats and so
used to correct Dxtra and similarly Dy can be estimated to correct
Dxcor.