Inverse radiation therapy planning - a multiple objective optimization approach

For some decades radiation therapy has been proved successful in cancer treatment. It is the major task of clinical radiation treatment planning to realise on the one hand a high level dose of radiation in the cancer tissue in order to obtain maximum tumour control. On the other hand it is obvious that it is absolutely necessary to keep in the tissue outside the tumour, particularly in organs at risk, the unavoidable radiation as low as possible. No doubt, these two objectives of treatment planning – high level dose in the tumour, low radiation outside the tumour – have a basically contradictory nature. Therefore, it is no surprise that inverse mathematical models with dose distribution bounds tend to be infeasible in most cases. Thus, there is need for approximations compromising between overdosing the organs at risk and underdosing the target volume. Differing from the currently used time consuming iterative approach, which measures deviation from an ideal (non-achievable) treatment plan using recursively trial-and-error weights for the organs of interest, we go a new way trying to avoid a priori weight choices and consider the treatment planning problem as a multiple objective linear programming problem: with each organ of interest, target tissue as well as organs at risk, we associate an objective function measuring the maximal deviation from the prescribed doses. We build up a data base of relatively few efficient solutions representing and approximating the variety of Pareto solutions of the multiple objective linear programming problem. This data base can be easily scanned by physicians looking for an adequate treatment plan with the aid of an appropriate online tool. 1 The inverse radiation treatment problem – an introduction Every year, in Germany about 450.000 individuals are diagnosed with life-threatening forms of cancer. About 60% of these patients are treated with radiation; half of them are considered curable because their tumours are localised and susceptible to radiation. Nevertheless, despite the use of the best radiation therapy methods available, one third of these “curable” patients – nearly 40.000 people each year – die with primary tumours still active at the original site. Why does this occur ? Experts in the field have looked at the reasons for these failures and have concluded that radiation therapy planning – in particular in complicated anatomical situations – is often inadequate, providing either too little radiation to the tumour or too much radiation to nearby healthy tissue. Effective radiation therapy planning for treating malignent tumours is always a tightrope walk between ineffective underdose of tumour tissue – the target volume – and dangerous overdose of organs at risk being relevant for maintaining life quality of the cured patient. Therefore, it is the challenging task of a radiation therapy planner to realise a certain high dose level conform to the shape of the target volume in order to have a good prognosis for tumour control and to avoid overdose in relevant healthy tissue nearby. Part of this challenge is the computer aided representation of the relevant parts of the body. Modern scanning methods like computer tomography (CT), magnetic resonance tomography 1 on sabbatical leave at the Department of Engineering Science, University of Auckland,