AbstractID: 6709 Title: Optimization Algorithm for IMRT Using Vector Space Methods
We develop a new inverse treatment-planning algorithm for intensity-modulated
radiation therapy (IMRT), based on optimization in a complex vector space. The method
uses the complex vectors generated by the discrete Fourier Transform of dose distribution
produced by pencil beams. Since the DVH-based dose prescription can also be
represented by a complex vector, the optimization problem reduces to finding the beam
weight for each pencil beam so that the sum vector of those pencil beams closely matches
the desired vector. This becomes an approximation problem in Hilbert space. The l2
norm of the vector space chosen for our minimization problem leads to a least-square
type objective function, with the penalty coefficients specified for each structure of
interest. Because of the non-negative constraints for the beam weights, the resulting
equation that gives the solution for usual least-square problems cannot be applied directly
in our case. We modify the resulting equations under the non-negative constraints so that
the problem can be solved by the nonlinear (quadratic) programming techniques. A 2-D
model is used to demonstrate the feasibility of this new algorithm. In general, this
algorithm offers the following advantages: 1) guaranteed global minimum; 2) nonnegativity of beam weight included a priori; and 3) vast improvement of efficiency over
conventional techniques such as simulated annealing and conjugate gradient methods.
The algorithm has been applied to several problems and the results show that it has the
potential for IMRT applications.