Stepwise multi-criteria optimization for robotic radiosurgery

Achieving good conformality and a steep dose gradient around the target volume remains a key aspect of radiosurgery. Clearly, this involves a trade-off between target coverage, conformality of the dose distribution, and sparing of critical structures. Yet, image guidance and robotic beam placement have extended highly conformal dose delivery to extracranial and moving targets. Therefore, the multi-criteria nature of the optimization problem becomes even more apparent, as multiple conflicting clinical goals need to be considered coordinate to obtain an optimal treatment plan. Typically, planning for robotic radiosurgery is based on constrained optimization, namely linear programming. An extension of that approach is presented, such that each of the clinical goals can be addressed separately and in any sequential order. For a set of common clinical goals the mapping to a mathematical objective and a corresponding constraint is defined. The trade-off among the clinical goals is explored by modifying the constraints and optimizing a simple objective, while retaining feasibility of the solution. Moreover, it becomes immediately obvious whether a desired goal can be achieved and where a trade-off is possible. No importance factors or predefined prioritizations of clinical goals are necessary. The presented framework forms the basis for interactive and automated planning procedures. It is demonstrated for a sample case that the linear programming formulation is suitable to search for a clinically optimal treatment, and that the optimization steps can be performed quickly to establish that a Pareto-efficient solution has been found. Furthermore, it is demonstrated how the stepwise approach is preferable compared to modifying importance factors.