1. Pelvic MR scans for radiotherapy planning: Correction of system- and patient-induced distortions Simon J Doran 1, Liz Moore 2, Martin O Leach 2 1 Department of Physics, University of Surrey 2 CRC Clinical Magnetic Resonance Research Group, Institute of Cancer Research, Sutton S Dr. S. J. Doran Department of Physics, University of Surrey, Guildford, GU2 5XH, UK

2. Acknowledgements David Finnigan Steve Tanner Odysseas Benekos David Dearnaley Steve Breen Young Lee Geoff Charles-Edwards

3. Summary of Talk The problem of distortion Strategy for solving the problem  Chang and Fitzpatrick algorithm (B 0 -induced distortion)  Linear test object (gradient distortion) Current limitations of the method Patient trials and validations of system in progress

5. 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? Potential Applications Radiotherapy Thermotherapy Stereotactic surgery Correlation of MR with other modalities (image fusion)

6. Mathematical statement of the problem I (r)  I true (r  r) where  r   r (r)  r is a 3-D vector, whose magnitude and direction both depend on position.

7. Sources of distortion: (1) B 0 -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

8. 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 x / mm z / mm  error in B z Isocentre 0 +15 -10 250 0 z / cm x / mm  B z / arb. units Isocentre 0 250

9. 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 B 0 -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.

10. Chang and Fitzpatrick algorithm We have two data sets, F and R, which we treat row by row. For a given row,  F(x F ) dx F =  R(x R ) dx R. Calculate points x R corresponding to x F. Then x true = (x F + x R ) / 2. corr - fwd corr - rev fwd rev corr

11. 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.

12. The “linearity test phantom” (2) Coronal Sagittal Transverse

13. X-ray CT vs. MRI of linearity test phantom Slice offset 0 mm Slice offset -185 mm

14. 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   x,  y Reformat the data to give sagittal and coronal projections. (A different matrix of spots appears in each plane.) Repeat the matching process: Coronal   x,  z Sagittal   y,  z

15. System distortion mapping algorithm: Step 2 Interpolate and smooth data to provide complete 3-D matrices of gradient distortion values. -200 200 -100 100 x / mm y / mm x-distortion / mm -10 10 Example: x-distortion on transverse plane at slice offset 117.5 mm reconstructed from transverse images

16. System distortion mapping algorithm: Step 3 Taking the known distortion data, correct the images:  Sample the 3-D data I dist at appropriately interpolated points.  Correct for intensity distortions using the Jacobian. I( x, y, z ) = I dist ( x  x, y  y, z  z ). J( x, y, z ) ^ B 0 corrected B 0 &Grad B 0 &Grad - B 0 corrected

17. 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

18. 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 mm 3 (256 x 192 x 84 pixels) 5mm “slices”  FOV 480 x 360 x 160 mm 3 (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.

19. Once we have the corrected MR images... Validation via 3-D image registration of MRI with CT using champfer-matching Assess impact of MR- based radiotherapy plans Ultimate goal: to give us the ability to use MRI alone for radiotherapy planning CTMRI MRI dataset fed into treatment planning software

20. MR vs. CT Dose-volume histogram for planning treatment volume - patient data Data for 4 patients analysed so far Early indications show excellent agreement between treatments calculated with X-ray CT and those calculated on the basis of MR images.

21. System distortion mapping algorithm: Step 3 Problem: The slices are not themselves flat — slice warp! The slice we actually get ! E.g., for a transverse plane, we have  x and  y, but we don’t know exactly which z- position they correspond to The slice the scanner tells us we are selecting

22. System distortion mapping algorithm: Step 3 Solution: Use the complete set of data acquired Consider the x-distortion  We have two estimates of  x, acquired from matching spots on transverse and coronal reformats of the original dataset.  For  x tra (x, y, z), z is not known correctly because of slice warp.  For  x cor (x, y, z), y is not known correctly. But we can estimate unknowns from the data we have...   z can be estimated from the coronal or transverse reformats and so used to correct  x tra and similarly  y can be estimated to correct  x cor.