Rapid Re-optimization of Prostate Intensity-Modulated Radiation Therapy Using Regularized Linear Programming

Abstract

<p>This thesis presents a new linear programming approach for re-optimizing a intensity modulated radiation therapy (IMRT) treatment plan, in order to compensate for inter-fraction tissue deformations. Different formulations of the problem involve different constraints, but a common constraint that is difficult to handle mathematically is the constraint that the dose be deliverable using a small number of multi-leaf collimator positions. MLC leaves are tungsten alloy attenuators which can be moved in and out to shape of the radiation aperture. Since leaves are solid, photon fluence profiles will follow a staircase function and this constraint is not convex, and difficult to formulate. In this thesis, we propose a relaxation of this constraint to the `1-norm of the differences between adjacent radiation fluxes. With the appropriate bound, this constraint encourages the dose to be deliverable with a series of shrinking or growing openings between the leaves. Such a solution can be made realizable by rounding, which is beyond the scope of this thesis. This approach has been tested on an anonymized prostate cancer treatment plan with simulated deformations. Without rounding, solutions were obtained in five of nine cases, in less than 4 to 5 seconds of computation on a NEOS server. Solved cases demonstrated excellent target coverage (minimum dose in the target was 95% of the prescribed dose) and organ sparing (mean dose in normal tissues was below 25% of the prescribed dose).</p>