Journal of Medical Physics
 Home | Search | Ahead of print | Current Issue | Archives | Instructions | Subscription | Login  The official journal of Association of Medical Physicists of India      
 Users online: 480  Home  EMail this page Print this page Decrease font size Default font size Increase font size 
TECHNICAL NOTE
Year : 2019  |  Volume : 44  |  Issue : 4  |  Page : 283-286

4π radiotherapy using a linear accelerator: A misnomer in violation of the solid geometric boundary conditions in three-dimensional Euclidean space


1 Department of Radiation Oncology, Manipal Hospitals, Dwarka, New Delhi, India
2 Department of Medical Physics, Apollo Proton Cancer Center, Chennai, Tamil Nadu, India

Correspondence Address:
Biplab Sarkar
Manipal Hospitals, Dwarka, New Delhi - 110 075
India
Login to access the Email id

Source of Support: None, Conflict of Interest: None


DOI: 10.4103/jmp.JMP_2_19

Rights and Permissions

Purpose: The concept of 4πc radiotherapy is a radiotherapy planning technique receiving much attention in recent times. The aim of this article is to disprove the feasibility of the 4π radiotherapy using a cantilever-type linear accelerator or any other external-beam delivery machines. Materials and Methods: A 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 0–2πc and a table rotation of πc/2 - 0 - 3πc/2) . Results: Total achievable solid angle by cantilever-type linear accelerator (or any teletherapy machine employing a cantilever design) is 1/r2 π ∫ - θ=0 π ∫ φ=0 (rSinθdφ). (rdθ) = 2πc, 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. Conclusions: Present 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 2πc, which is restricted for only extremities such as foot and brain radiotherapy. For other parts of the body such as pelvis, thorax, and abdomen, the solid angle is reduced to 1/5th (maximum value) of the 4πc. To obtain a 4πc solid angle in a three-dimensional Euclidean space, the patient has to be a zero-dimensional point and X-ray head of the linear accelerator has a freedom to rotate in every point of a hypothetical sphere of radius 1 m. This article establishes geometrically why it is not possible to achieve a 4πc solid angle.


[FULL TEXT] [PDF]*
Print this article     Email this article
 Next article
 Previous article
 Table of Contents

 Similar in PUBMED
   Search Pubmed for
   Search in Google Scholar for
 Related articles
 Citation Manager
 Access Statistics
 Reader Comments
 Email Alert *
 Add to My List *
 * Requires registration (Free)
 

 Article Access Statistics
    Viewed161    
    Printed0    
    Emailed0    
    PDF Downloaded30    
    Comments [Add]    

Recommend this journal