title: Integral dose investigation of non-coplanar treatment beam geometries in radiotherapy.
abstract: OBJECTIVE
  Automated planning and delivery of non-coplanar plans such as 4π radiotherapy involving a large number of fields have been developed to take advantage of the newly available automated couch and gantry on C-arm gantry linacs. However, there is an increasing concern regarding the potential changes in the integral dose that needs to be investigated.
  
  
  METHODS
  A digital torso phantom and 22 lung and liver stereotactic body radiation therapy (SBRT) patients were included in the study. The digital phantom was constructed as a water equivalent elliptical cylinder with a major axis length of 35.4 cm and minor axis of 23.6 cm. A 4.5 cm diameter target was positioned at varying depths along the major axis. Integral doses from intensity modulated, non-coplanar beams forming a conical pattern were compared against the equally spaced coplanar beam plans. Integral dose dependence on the phantom geometry and the beam number was also quantified. For the patient plans, the non-coplanar and coplanar beams and fluences were optimized using a column generation and pricing approach and compared against clinical VMAT plans using two full (lung) or partial coplanar arcs (liver) entering at the side proximal to the tumor. Both the average dose to the normal tissue volume and the total volumes receiving greater than 2 Gy (V2) and 5 Gy (V5) were evaluated and compared.
  
  
  RESULTS
  The ratio of integral dose from the non-coplanar and coplanar plans depended on the tumor depth for the phantom; for tumors shallower than 10 cm, the non-coplanar integral doses were lower than coplanar integral doses for non-coplanar angles less than 60°. Similar patterns were observed in the patient plans. The smallest non-coplanar integral doses were observed for tumor 6-8 cm deep. For the phantom, the integral dose was independent of the number of beams, consistent with the liver SBRT patients but the lung SBRT patients showed slight increase in the integral dose when more beams were used. Larger tumor size and larger patient body size did not change the overall relationship of integral doses between non-coplanar and coplanar cases. However, the thin disk-shaped tumor received at least 40% greater integral doses with the non-coplanar plans. Overall, patient non-coplanar integral doses and V5 were comparable to those of coplanar doses from the same optimization engine and 15%-20% lower than state of the art VMAT plans. However, non-coplanar beams significantly increased V2 in both the phantom and patients. On average, the lung and liver SBRT patient normal tissue volumes receiving dose greater than 2 Gy were increased by 749 and 532 cm(3), respectively.
  
  
  CONCLUSIONS
  The authors used a digital phantom simulating a patient torso and 22 SBRT patients to show that the integral doses from the plans employing optimized non-coplanar beams are comparable to those of the coplanar plans using an equal number of discrete beams and are significantly lower than those of VMAT plans. The non-coplanar beams expose a larger normal tissue volume to non-zero doses, whose impact will need to be evaluated individually to determine the risk/benefit ratio of the non-coplanar plans.
authors.affiliation: Department of Radiation Oncology, University of California, Los Angeles, California 90095.
authors.forename: Dan
authors.initials: D
authors.lastname: Nguyen
authors.affiliation: Department of Radiation Oncology, University of California, Los Angeles, California 90095.
authors.forename: Peng
authors.initials: P
authors.lastname: Dong
authors.affiliation: Department of Industrial and Operations, University of Michigan, Ann Arbor, Michigan 48109.
authors.forename: Troy
authors.initials: T
authors.lastname: Long
authors.affiliation: Department of Radiation Oncology, University of California, Los Angeles, California 90095.
authors.forename: Dan
authors.initials: D
authors.lastname: Ruan
authors.affiliation: Department of Radiation Oncology, University of California, Los Angeles, California 90095.
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Low
authors.affiliation: Department of Industrial and Operations, University of Michigan, Ann Arbor, Michigan 48109.
authors.forename: Edwin
authors.initials: E
authors.lastname: Romeijn
authors.affiliation: Department of Radiation Oncology, University of California, Los Angeles, California 90095.
authors.forename: Ke
authors.initials: K
authors.lastname: Sheng
mesh_terms: D006801:Humans; D008113:Liver Neoplasms / Q000601:surgery; D058958:Organs at Risk / Q000528:radiation effects; D019047:Phantoms, Imaging; D011829:Radiation Dosage; D016634:Radiosurgery / Q000009:adverse effects / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted