title: Ultrafast convolution/superposition using tabulated and exponential kernels on GPU.
abstract: OBJECTIVE
  Collapsed-cone convolution/superposition (CCCS) dose calculation is the workhorse for IMRT dose calculation. The authors present a novel algorithm for computing CCCS dose on the modern graphic processing unit (GPU).
  
  
  METHODS
  The GPU algorithm includes a novel TERMA calculation that has no write-conflicts and has linear computation complexity. The CCCS algorithm uses either tabulated or exponential cumulative-cumulative kernels (CCKs) as reported in literature. The authors have demonstrated that the use of exponential kernels can reduce the computation complexity by order of a dimension and achieve excellent accuracy. Special attentions are paid to the unique architecture of GPU, especially the memory accessing pattern, which increases performance by more than tenfold.
  
  
  RESULTS
  As a result, the tabulated kernel implementation in GPU is two to three times faster than other GPU implementations reported in literature. The implementation of CCCS showed significant speedup on GPU over single core CPU. On tabulated CCK, speedups as high as 70 are observed; on exponential CCK, speedups as high as 90 are observed.
  
  
  CONCLUSIONS
  Overall, the GPU algorithm using exponential CCK is 1000-3000 times faster over a highly optimized single-threaded CPU implementation using tabulated CCK, while the dose differences are within 0.5% and 0.5 mm. This ultrafast CCCS algorithm will allow many time-sensitive applications to use accurate dose calculation.
authors.affiliation: TomoTherapy Inc., 1240 Deming Way, Madison, Wisconsin 53717, USA.
authors.forename: Quan
authors.initials: Q
authors.lastname: Chen
authors.forename: Mingli
authors.initials: M
authors.lastname: Chen
authors.forename: Weiguo
authors.initials: W
authors.lastname: Lu
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003201:Computers; D011829:Radiation Dosage; D011879:Radiotherapy Dosage; D050397:Radiotherapy, Intensity-Modulated; D013997:Time Factors