ArticleJournal of medical physics
4π Radiotherapy Using a Linear Accelerator: A Misnomer in Violation of the Solid Geometric Boundary Conditions in Three-Dimensional Euclidean Space.
Article in Journal of medical physics. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- CyberKnife in Pediatric Oncology: A Narrative Review of Treatment Approaches and Outcomes.Current oncology (Toronto, Ont.) · 2025Review
- A comparative dose-escalation analysis for reirradiated cancer patients with and without appropriate dose mapping.Radiation and environmental biophysics · 2024Article
- In regards to Pokhrel et al. Clinical validation of ring-mounted halcyon linac for lung SBRT: Comparison to SBRT-dedicated C-arm linac treatments. JACMP 2021 Jan;22(1):261-70.Journal of applied clinical medical physics · 2021Article
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Authors and funding
5 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
purposeThe concept of 4π MATERIALS AND
methodsA surface integral-based mathematical derivation for the maximum achievable solid angle for a linear accelerator was carried out respecting the rotational boundary conditions for gantry and couch in three-dimensional Euclidean space. The allowed movements include a gantry rotation of 0-2π
resultsTotal achievable solid angle by cantilever-type linear accelerator (or any teletherapy machine employing a cantilever design) is , which is applicable only for the foot and brain radiotherapy where the allowed table rotation is 90°-0°-270°. For other sites such as pelvis, thorax, or abdomen, achievable solid angle as the couch rotation comes down significantly. Practically, only suitable couch angle is 0° by avoiding gantry-couch-patient collision.
conclusionsPresent cantilever design of linear accelerator prevents achieving a 4π radian solid angle at any point in the patient. Even the most modern therapy machines like CyberKnife which has a robotic arm also cannot achieve 4π geometry. Maximum achievable solid angle under the highest allowable boundary condition(s) cannot exceed 2π
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