Probabilistic constraint satisfaction: application to radiosurgery

Although quite successful in a variety of settings, standard optimization approaches can have drawbacks within medical applications. For example, they often provide a single solution which is difficult to explain, or which can not be incrementally modified using secondary "soft" constrains that are difficult to encode within the optimization. In order to address these issues, we have developed a probabilistic optimization technique that allows the user to enter prior probability distributions (Gaussian) for the parameters to be optimized as well as for the constraints on the parameters. Our technique combines the prior distributions with the constraints using Bayes' rule. The algorithm produces not only a set of parameter values, but variances on these values and covariances showing the correlations between parameters. We have applied this method to the problem of planning a radiosurgical ablation of brain tumors. The radiation plan should maximize dose to tumor, minimize dose to surrounding areas, and provide an even distribution of dosage across the tumor. It also should be explainable to and modifiable by the expert physicians based on external considerations. We have compared the results of our method with the standard linear programming approach.