Ready availability has prompted the use of computed tomography (CT) data in various applications in radiation therapy. For example, some radiation treatment planning systems now utilize CT data in heterogeneous dose calculations algorithms. In radiotherapy imaging applications, CT data are projected onto specified planes, thus producing "radiographs," which are compared with simulator radiographs to assist in proper patient positioning and delineation of target volumes. All these applications share the common geometric problem of evaluating the radiological path through the CT array. Due to the complexity of the three-dimensional geometry and the enormous amount of CT data, the exact evaluation of the radiological path has proven to be a time consuming and difficult problem. This paper identifies the inefficient aspect of the traditional exact evaluation of the radiological path as that of treating the CT data as individual voxels. Rather than individual voxels, a new exact algorithm is presented that considers the CT data as consisting of the intersection volumes of three orthogonal sets of equally spaced, parallel planes. For a three-dimensional CT array of N3 voxels, the new exact algorithm scales with 3N, the number of planes, rather than N3, the number of voxels. Coded in FORTRAN-77 on a VAX 11/780 with a floating point option, the algorithm requires approximately 5 ms to calculate an average radiological path in a 100(3) voxel array.

Dose distributions produced by small circular beams of 6 MV x-rays have been measured using ionisation chambers of small active volume. Specific quantities measured include tissue maximum ratios (TMR), total scatter correction factors (St), collimator scatter correction factors (Sc) and off-axis ratios (OAR). Field sizes ranged from 12.5 to 30 mm diameter, and were defined by machined auxiliary collimators with the movable jaws set for a 4 cm x 4 cm field size. Due to the lack of complete lateral electronic equilibrium for these small fields, the accuracy of the measurements was also investigated. This was accomplished by studying dose response as a function of detector size. Uncertainties of 2.5% were observed for the central axis dose in the 12.5 mm field when measuring with an ionisation chamber with a diameter of 3.5 mm. The total scatter correction factor exhibits a strong field size dependence for fields below 20 mm diameter, while the collimator scatter correction factor is constant and is defined by the setting of the movable jaws. Off-axis ratio measurements show larger dose gradients at the beam edges than those achieved with conventional collimator systems. Corrected profiles measured with an ionisation chamber are compared with measurements made with photographic film and LiF thermoluminescent dosemeters.

We have developed a new isocentric two-film reconstruction algorithm for brachytherapy seed and needle implants. The algorithm has no requirements that the two films be orthogonal, symmetric, or even be taken in a transverse plane. In addition, there is no requirement that the two films even have the same number of images. We have found removal of these usual constraints useful for head and neck implants where images are often obscured by patient anatomy. The inherent image matching ambiguities associated with traditional two-film techniques are minimized by considering the image end points, rather than just the image centroids. For two films, the new algorithm, which considers all image combinations at one time, matches all the end-point images on one film with those on the other, and then reconstructs the end-point positions of the seeds. The algorithm minimizes the difference between the actual images and the projected images from the reconstructed seeds. The new two-film image matching problem is shown to be equivalent to the well-known assignment problem. For an implant of N seeds, this equivalence allows the two-film problem to be solved by an algorithm (ACM algorithm 548) that scales with a polynomial power of N, rather than N! as is usually assumed. An implant of N seeds can be matched and reconstructed in approximately (N/20)2s on a VAX 11/780.

No abstract

The majority of radiation treatment planning problems are relatively straightforward, involving only specified gantry angles in a treatment plane which is perpendicular to the patient longitudinal axis. In addition, there are a number of more complex three-dimensional problems which require combined rotation of the gantry, collimator, and turntable for their solutions. These include, for example, the use of non-coplanar fields and oblique treatment planes, the matching of field edges in three dimensions, the treatment of the breast with opposing tangential fields, and the treatment of inclined elongated lesions. Unfortunately, there is no general systematic approach to the solution of these more complex problems. One may attempt an analytic solution, but this approach is often too cumbersome and tedious. On the other hand, one may resort to a "trial and error" session with the simulator. This paper, therefore, presents a mathematical method which is easily applied and applicable to a wide variety of complex three-dimensional treatment planning problems. The method considers the gantry, collimator, and turntable as coordinate systems. These coordinate systems are derivable from each other by specified coordinate transformations, which contain the rotation angles of the gantry, collimator, and turntable. Within this mathematical framework, the treatment planning problems are found to reduce to two general types, of which various clinical examples are then given.