DIM-Free Monte-Carlo–Integrated Planning Optimization Using Randomized-Gradient-Free-Method (RGFM) for MCF Mkm Rbe Dose In Carbon Ion Therapy
Abstract
Purpose
The Mayo Clinic Florida microdosimetric kinetic model (MCF MKM) provides highly accurate relative biological effectiveness (RBE) calculations for carbon ion radiation therapy (CIRT), but its clinical use is limited by extreme memory and computational demands arising from large dose influence matrices (DIMs). We present a DIM-free optimization framework that performs RBE dose optimization directly during Monte Carlo (MC) simulation using a stochastic zeroth-order method.
Methods
The proposed approach tightly couples MC simulation with optimization, eliminating DIM precomputation. Optimization is initiated using low particle statistics (≈100 particles per spot), with particle histories incrementally increased during iterations. A zeroth-order stochastic optimization algorithm estimates descent directions using only two-sample evaluations per iteration, avoiding explicit gradient calculations of the highly nonlinear MCF MKM RBE model using DIM. Monte Carlo dose, α, and β parameters are computed using TOPAS, while optimization is implemented in MATLAB through an asynchronous simulation–optimization workflow. Iterations terminate when cumulative particle histories reach 10⁶ per beam.
Results
A prostate plus lymph-node clinical case was evaluated. The objective function initially showed large fluctuations due to high Monte Carlo (MC) noise, followed by rapid descent and convergence as particle histories increased and MC uncertainty decreased. Compared with physical-dose–optimized plans, the proposed method achieved improved RBE-weighted DVHs with enhanced target coverage and acceptable organ-at-risk trade-offs. The total MC simulation time was approximately 10 minutes, with the optimization requiring an additional 2 minutes for 25,000 scanning spots, compared with several hours for conventional DIM-based workflows.
Conclusion
This DIM-free, Monte Carlo–integrated optimization framework enables clinically feasible MCF MKM–based RBE dose planning and provides a practical pathway toward biologically optimized CIRT.