Sequential annealing–gradient Gamma-Knife radiosurgery optimization

Abstract

Simulated annealing and gradient methods are commonly employed for inverse planning of radiotherapy delivery schemes. Annealing is effective in finding an approximation of the global solution, suffering from slow late convergence and in some cases poor dose homogeneity. Gradient methods converge well but not necessarily to the global minimum. We explored simulated annealing followed by gradient optimization to improve on either method alone, using radiosurgery as the model system. Simulated annealing and gradient inverse planning programs using the same objective function were adapted for radiosurgical optimization. The objective function chosen is a least-squares dose-matching function, with differential weighting of tissues. A simple test target allowing local minima in the objective function was evaluated. Two hundred trials using the gradient method were done. The gradient method approximated the global solution only 12% of the time, commonly finding a local minimum. The annealing–gradient technique converged to the global minimum in 78 out of 80 trials, more efficiently than annealing alone. Dose homogeneity was improved. In conclusion, sequential annealing–gradient optimization can improve on either method alone. The technique may be extensible to radiotherapy inverse planning in general, with benefit expected for problems characterized by slow gradient method convergence and local minima.