Inverse treatment planning by physically constrained minimization of a biological objective function

Abstract

In the current state-of-the art of clinical inverse planning, the design of clinically acceptable IMRT plans is predominantly based on the optimization of physical rather than biological objective functions. A major impetus for this trend is the unproven predictive power of radiobiological models, which is largely due to the scarcity of data sets for an accurate evaluation of the model parameters. On the other hand, these models do capture the currently known dose-volume effects in tissue dose-response, which should be accounted for in the process of optimization. In order to incorporate radiobiological information in clinical treatment planning optimization, we propose a hybrid physico-biological approach to inverse treatment planning based on the application of a continuous penalty function method to the constrained minimization of a biological objective. The objective is defined as the weighted sum of normal tissue complication probabilities evaluated with the Lyman normal-tissue complication probability model. Physical constraints specify the admissible minimum and maximum target dose. The continuous penalty function method is then used to find an approximate solution of the resulting large-scale constrained minimization problem. Plans generated by our approach are compared to ones produced by a commercial planning system incorporating physical optimization. The comparisons show clinically negligible differences, with the advantage that the hybrid technique does not require specifications of any dose-volume constraints to the normal tissues. This indicates that the proposed hybrid physico-biological method can be used for the generation of clinically acceptable plans.

Mathematical optimization in intensity modulated radiation therapy

“…Choi and Deasy (2002) show that this Poisson-based TCP objective function (if one neglects inter-patient heterogeneity) is strictly concave. NTCP models have also been developed by many researchers, see, e.g., Kutcher et al (1991), Niemierko and Goitein (1991), Jackson and Kutcher (1993), Lyman and Wolbrast (1989), Stavrev et al (2003), Alber and Nüsslin (2001). Out of those models, the relative seriality model which is based on the Poisson dose-response model and categorizes volumes into serial, parallel, or both functional subunits has attracted more attention.…”

Mathematical optimization in intensity modulated radiation therapy

“…Choi and Deasy (2002) show that this Poissonbased TCP objective function (if one neglects inter-patient heterogeneity) is strictly concave. NTCP models have also been developed by many researchers, see, e.g., Kutcher et al (1991), Niemierko and Goitein (1991), Jackson and Kutcher (1993), Lyman and Wolbrast (1989), Stavrev et al (2003), Alber and Nüsslin (2001). Out of those models, the relative seriality model which is based on the Poisson dose-response model and categorizes volumes into serial, parallel, or both functional subunits has attracted more attention.…”

On the Robustness of Global Optima and Stationary Solutions to Stochastic Mathematical Programs with Equilibrium Constraints, Part 2: Applications

“…The gEUD function is attractive from several points of view, not the least from the fact that it is convex if a ≥ 1, which is the case for organs. There are also other biologically based functions that have been used in IMRT, for example tumor control probability (TCP) (e.g., [10]), normal tissue complication probability (NTCP) (e.g., [57]), and P + ( [9]). Physically based objective functions are used in the clinic, whereas recent research focuses on biologically based functions.…”