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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.

Dose-surface histograms are studied and compared with dose-volume histograms, as an evaluation tool for prostate treatment planning. For thin walled hollow organs, such as the rectum and bladder, the surface area irradiated is a more appropriate measure of the biological effect than the full volume. It is also more accurate and efficient to define the surface for a hollow structure and compute the surface area histograms. Application of the dose-surface histograms provide new insights into prostate treatment planning. A simple idealized geometry model demonstrates that the percentage surface area intersected by the geometric beam edge differs from the percentage volume intersected. For a group of prostate patients, it is shown that the dose-surface histograms yield substantially different results from the dose-volume histograms in ranking four-, six-, and, eight-field treatment plans and in calculating the fraction of the rectum irradiated to high dose. The difference in terms of surface area between these plans in the high-dose region is usually less than that in terms of the volume, and a reverse of plan ranking order can consequently occur. The percentage of organ surface irradiated to high dose is typically greater than the percentage volume by 5% to 10%. The use of the dose-surface histograms in analysis of organ motion and/or patient setup uncertainty, and analysis of rectal complications, is also discussed.

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