tomography: from medicine to accelerator physics, and back again Ander Biguri, Manjit Dosanjh, Steven Hancock, Manuchehr Soleimani a.biguri@bath.ac.uk

Index Lung Cancer and Image guided radiation therapy X-ray tomography: FDK, iterative algorithms TIGRE toolbox Algorithms Examples Motion in Tomography Tomography at CERN: phase space tomography Motion problem “solved” Conclusions

Cancer – a growing challenge More than 3 million new cancer cases in Europe each year and 1.75 million associated deaths Increase by 2030: 75% in developed countries and 90% in developing countries

Radiotherapy in the 21st century Cure (~ 50% cancer cases are cured) Conservative (non-invasive, few side effects) Cheap ( 5-10% of total cost of cancer on RT) There is no substitute for RT in the near future The rate of patients treated with RT is increasing More than 50% patients treated with RT

X-ray tomography X-ray images from different angles Generally solved using the “Radon transform” (FDK) In medicine, FDK is king Iterative algorithms!

Iterative algorithms express A: For 5123 image, 5122 detector, ~320Gb of memory [A·x , AT·b] ,1 of each per iteration by operator GPU: [A·x , AT·b] → [A(x) , AT(b)] > 99% of time Multiple processors (> 60K in a TESLA k40) Optimized memory Hardware accelerated interpolation

Why do we like iterative algorithms Better performance against noise Better performance with low projections “Tuneable” e.g. Total variation But….. 1 iteration is slower than FBP/FDK Memory expensive

TIGRE toolbox BSD Licensed, more info at github.com/CERN/TIGRE

Algorithms in TIGRE 5122 detector 2563 image FDK “SART type” algorithms (gradient descend) SART OS-SART SIRT Krylov Subspace CGLS Statistical inversion MLEM Total Variation ASD-POCS OSC-TV B-ASD-POCS- β SART-TV 5122 detector 2563 image

Examples – Gradient descend SART “Real” SIRT OS-SART

Example- few projections FDK Normally 300~500 in medical scenario Potential reduction of dose for the same quality of image ASD-POCS OSC-TV SART-TV B-ADS-POCS- β

Motion in X-rays: the problem Image reconstruction

Tomography at CERN Phase Space tomography: Particles “move” between projections. “Motion” information is measured and encoded system matrix (A) Images are reconstructed at arbitrary time using SART cern.ch/tomography , 1999!

Motion: solution

Motion: solution

Conclusions and future work Fast, complete MATLAB-CUDA CBCT toolbox Choice of algorithm matters! Iterative algorithms are superior than FDK (but slower) CERN to medical applications: on the fly computation of operators A(x) , AT(b) allows to introduce motion knowledge. Full 4D imaging is the next step

Thanks CERN and EPSRC The Christie Hospital Manjit Dosanjh Steven Hancock Imanol Luengo Manucherh Soleimani NVIDIA

Questions