Concise Matrix Analysis of Point-Based Prostate Targeting for Intensity Modulated Radiation Therapy

Intensity Modulated Radiation Therapy (IMRT) has recently emerged as an effective clinical treatment tool to treat various types of cancers by limiting the external beam dose to the surrounding normal tissue. However, the process of limiting external radiation dose to the tissue surrounding the tumor volume is not a trivial task. Several parameters including tumor volume and inhomogeneity, position and shape of the tumor volume, and the geometrical distribution of the radiation beams directly affect the determination of the external radiation dose. In addition, a major variable in effective delivery of the radiation dose is “set-up error” caused by the changes in patient position. Any changes in the position of the patient affect the geometrical location of the tumor volume and, therefore, need to be accommodated in the delivery of radiation beams during the treatment. This work presents a complete matrix representation required to calculate the three-dimensional rigid body homogeneous transformation matrices corresponding to external beam radiotherapy setup error and subsequent corrections in treatment beam parameters. A new concise orthogonal rotation solution is presented for use with clinical noisy data. Monte Carlo simulations prove the new matrix results are consistently better than the standard inverse solution. The required corrections in beam table, gantry, and collimator angles as function of the planned beam gantry angle are derived. For transformations that include a rotation on the sagittal plane, the required offsets to beam parameters are complex functions of the planned gantry angle but are clearly documented graphically for clinical use. A case study is presented with an error analysis that supports the use of the presented method in a clinical environment. Clinical implementation and evaluation of the presented method with patient data is also included in the paper.