Guest editorial: Optimization of the three‐dinensional dose delivery and tomotherapy

Over the last decade a very fast and interesting development has taken place in the field of therapeutic radiology, with many similarities to the development started about 1 decade earlier in the diagnostic radiology field. The development of computed tomography, single photon and positron emission computed tomography and, more recently, magnetic resonance imaging, has revolutionized the diagnostic field and allowed a considerably improved three-dimensional delineation of the spread of tumors. The rapid development of new threedimensional radiation therapy techniques during the last decade has resulted in an equally important increase in our ability to accurately localize and treat tumors without causing adverse reactions in surrounding healthy tissues. Interesting enough, the therapeutic and diagnostic developments have several properties in common, as I hope will be clear from this special issue on the new developments that are taking place in the therapeutic radiology arena. The first therapeutic applications of X-rays started very soon after the initial discovery of their diagnostic potential almost 100 years ago. Since then, the therapeutic goal has been almost exclusively to deliver as uniform a dose as possible by each beam incident on the tumor to avoid “hot or cold regions’’ capable of producing burns or recurrences in surrounding tumor infiltrated normal tissues. It was not until the early 1980s that it was realized the strongly nonuniform beams were required to deliver a high uniform dose to a tumor located close to critical radiation-sensitive normal tissue requiring protection. At the same time it was also realized that the associated mathematical formulation had many similarities with the Abel integral equation and Radon’s and Birkhoff‘s problems. The relation to tomographic imaging was further illustrated by the fact that the required dose distribution in some cases was very similar to the filter function used in slice reconstruction by filtered back projection. Since then, it has become clear that the problem of delivering an arbitrary dose distribution in a patient does not have a simple solution in the real world, because negative energy deposition or dose delivery is impossible. From this point of view the inverse problem of therapeutic radiology is harder to solve than that of diagnostic radiology, where you always know that there is an exact solution to the reconstruction problem, at least with sufficient noise-free projection data. The problem of producing the best possible dose distribution in the tumor region of a patient therefore has to be reformulated as an optimization problem where stated clinical objectives determine the optimum solution. The associated increased difficulty of finding a solution to such optimization problems has similarities with the diagnostic reconstruction problem with incomplete or noisy data where, for example, maximum likelihood or maximum entropy methods are used. In such cases, as for the therapeutic problem, no exact selfconsistent solution exists unless the statistical uncertainty is taken into account. However, in the field of radiotherapy optimization the introduction of the clinical objectives such as the probability of curing the patient with minimal normal tissue damage adds a new dimension to the optimization. This is so because we no longer have to guess the shape of the most suitable dose distribution: it is one of the results of the optimization process. In this issue, after discussions on the problems of therapeutic and diagnostic radiology and the role of imaging in radiation therapy, a number of different approaches to the important problem of treatment optimization are described.