Fast iterative algorithms for three-dimensional inverse treatment planning

Three types of iterative algorithms, algebraic inverse treatment planning (AITP), simultaneous iterative inverse treatment planning (SIITP), and iterative least-square inverse treatment planning (ILSITP), differentiated according to their updating sequences, were generalized to three dimension with true beam geometry and dose model. A rapid ray-tracing approach was developed to optimize the primary beam components. Instead of recalculating the dose matrix at each iteration, the dose distribution was generated by scaling up or down the dose matrix elements of the previous iteration. This significantly increased the calculation speed. The iterative algorithms started with an initial intensity profile for each beam, specified by a two-dimensional pixel beam map of M elements. The calculation volume was divided into N voxels, and the calculation was done by repeatedly comparing the calculated and desired doses and adjusting the values of the beam map elements to minimize an objective function. In AITP, the iteration is performed voxel by voxel. For each voxel, the dose discrepancy was evaluated and the contributing pencil beams were updated. In ILSITP and SIITP, the iteration proceeded pencil beam by pencil beam instead of voxel by voxel. In all cases, the iteration procedure was repeated until the best possible dose distribution was achieved. The algorithms were applied to two examples and the results showed that the iterative techniques were able to produce superior isodose distributions.