title: Accelerated ray tracing for radiotherapy dose calculations on a GPU.
abstract: OBJECTIVE
  The graphical processing unit (GPU) on modern graphics cards offers the possibility of accelerating arithmetically intensive tasks. By splitting the work into a large number of independent jobs, order-of-magnitude speedups are reported. In this article, the possible speedup of PLATO's ray tracing algorithm for dose calculations using a GPU is investigated.
  
  
  METHODS
  A GPU version of the ray tracing algorithm was implemented using NVIDIA's CUDA, which extends the standard C language with functionality to program graphics cards. The developed algorithm was compared based on the accuracy and speed to a multithreaded version of the PLATO ray tracing algorithm. This comparison was performed for three test geometries, a phantom and two radiotherapy planning CT datasets (a pelvic and a head-and-neck case). For each geometry, four different source positions were evaluated. In addition to this, for the head-and-neck case also a vertex field was evaluated.
  
  
  RESULTS
  The GPU algorithm was proven to be more accurate than the PLATO algorithm by elimination of the look-up table for z indices that introduces discretization errors in the reference algorithm. Speedups for ray tracing were found to be in the range of 2.1-10.1, relative to the multithreaded PLATO algorithm running four threads. For dose calculations the speedup measured was in the range of 1.5-6.2. For the speedup of both the ray tracing and the dose calculation, a strong dependency on the tested geometry was found. This dependency is related to the fraction of air within the patient's bounding box resulting in idle threads.
  
  
  CONCLUSIONS
  With the use of a GPU, ray tracing for dose calculations can be performed accurately in considerably less time. Ray tracing was accelerated, on average, with a factor of 6 for the evaluated cases. Dose calculation for a single beam can typically be carried out in 0.6-0.9 s for clinically realistic datasets. These findings can be used in conventional planning to enable (nearly) real-time dose calculations. Also the importance for treatment optimization techniques is evident.
authors.affiliation: Department of Radiation Oncology, University of Amsterdam, Meibergdreef 9, 1105 AZ Amsterdam, The Netherlands. m.degreef@amc.uva.nl
authors.forename: M
authors.initials: M
authors.lastname: de Greef
authors.forename: J
authors.initials: J
authors.lastname: Crezee
authors.forename: J C
authors.initials: JC
authors.lastname: van Eijk
authors.forename: R
authors.initials: R
authors.lastname: Pool
authors.forename: A
authors.initials: A
authors.lastname: Bel
mesh_terms: D000465:Algorithms; D003201:Computers; D016208:Databases, Factual; D006258:Head and Neck Neoplasms / Q000532:radiotherapy; D006801:Humans; D010386:Pelvic Neoplasms / Q000532:radiotherapy; D019047:Phantoms, Imaging; D011829:Radiation Dosage; D011878:Radiotherapy / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D013997:Time Factors