Mathematical Model of Patient Support System in Medical Linear Accelerators for External Beam Radiation Therapy

Abstract

In this study, a mathematical model of the patient support system (PSS) in medical linear accelerators was presented. The PSS consists of a treatment table capable of performing vertical, horizontal and rotational movements to position patients to the required location. The mathematical model includes the set of differential equations of motion. The model was developed for two basic designs of the lifting mechanisms: (a) a PSS mounted above the floor, and (b) a PSS mounted in a deep pit. In addition, this model includes dynamic equations of motions for the linear accelerator gantry and treatment head. The proposed model can be utilized for various tasks, such as adaptive or robust control design, tracking and motion compensation or collision avoidance assessments. The use of the proposed mathematical model can potentially improve real-time tracking of target-volumes when delivering a highly conformal radiation dose at full duty cycle while minimizing irradiation to healthy tissues and sparing critical organs during radiation treatments with linear accelerators. Furthermore, the equation of motion can be used to confirm the position of the mechanical isocenter of the linear accelerator. Such results can be compared against the radiation isocenter; thus, possible deviations can be tested more frequently without additional resources.