On the role of modeling parameters in IMRT plan optimization

The formulation of optimization problems in intensity-modulated radiotherapy (IMRT) planning comprises the choice of various values such as function-specific parameters or constraint bounds. In current inverse planning programs that yield a single treatment plan for each optimization, it is often unclear how strongly these modeling parameters affect the resulting plan. This work investigates the mathematical concepts of elasticity and sensitivity to deal with this problem. An artificial planning case with a horse-shoe formed target with different opening angles surrounding a circular risk structure is studied. As evaluation functions the generalized equivalent uniform dose (EUD) and the average underdosage below and average overdosage beyond certain dose thresholds are used. A single IMRT plan is calculated for an exemplary parameter configuration. The elasticity and sensitivity of each parameter are then calculated without re-optimization, and the results are numerically verified. The results show the following. ( 1) elasticity can quantify the influence of a modeling parameter on the optimization result in terms of how strongly the objective function value varies under modifications of the parameter value. It also can describe how strongly the geometry of the involved planning structures affects the optimization result. ( 2) Based on the current parameter settings and corresponding treatment plan, sensitivity analysis can predict the optimization result for modified parameter values without re-optimization, and it can estimate the value intervals in which such predictions are valid. In conclusion, elasticity and sensitivity can provide helpful tools in inverse IMRT planning to identify the most critical parameters of an individual planning problem and to modify their values in an appropriate way.