An IMRT Optimization Approach That Minimizes the Total MLC Segments

An IMRT optimization problem is formulated as searching for the set of intensities for the selected beam segments or beamlets so that various objectives are reached or approximated. The resulting intensity pattern can be delivered by MLCs (multi-leaf collimator) through dynamic movements of the leaves or by adding up multiple static MLC fields. Extensive research has found that the delivery efficiency is closely related to the smoothness of the intensity pattern for the delivery through multiple static fields. Cimmino’s iterative projection method has been used to solve systems of linear inequalities. We found that such an algorithm not only yields a feasible solution when one exists, the solution is also close to contain the least intensity, therefore driving at a smoother intensity pattern. When compared with feasible solutions obtained through linear programming (LP) approach, the reduction in average segments of static MLC fields can be as much as 50%. Mathematically, the fact that Cimmino’s algorithm repeatedly gets close to a least intensity solution can be explained. Cimmino’s algorithm is actually a close approximation of the least-squares solution in product space used for signal feasibility problems: x k+1 = (1- k)x0 k[ (1- [k j=1n wjPj(xk )] where x is the intensity vector; k, iteration number; α, number series, lim αk = 1 when k → Inf.; λ, a constant between 0 and 2; j, voxel number; w, importance weight; P, projection of vector x. With vector x0 =0 and αk=1, the above formulation becomes the Cimmino iteration.