1117 - A New RBE Optimization Method with Iterative Jacobian-Based Linearization for Carbon Ion Radiation Therapy

C. Wang, Y. Zhu, W. Li, K. Reddy, Y. Lin, and H. Gao; Department of Radiation Oncology, University of Kansas Medical Center, Kansas City, KS

Purpose/Objective(s): Carbon ion radiotherapy (CIRT) capitalizes on the high relative biological effectiveness (RBE) of carbon ions to intensify DNA damage in tumor cells, presenting a promising treatment option for tumors resistant to conventional radiation therapy. However, RBE-based biological treatment planning for CIRT poses technical challenges due to the nonlinear mathematical formulation of RBE. This complexity may hinder the quality of achievable treatment plans and impose significant computational burden. This study aims to develop a novel biological optimization method for CIRT to enhance both treatment plan quality and computational efficiency. Materials/

Methods: The proposed method employs iterative Jacobian-based linearization (IJL) to enhance plan quality and computational efficiency. Biological treatment planning for CIRT is formulated as an optimization problem with least-square-based objectives, incorporating constraints such as dose-volume histogram and minimum-monitor-unit constraints. This optimization problem is solved using iterative convex relaxation (outer loop) and the alternating direction method of multipliers (inner loop), which iteratively solves simpler subproblems. The RBE subproblem, featuring a nonlinear biological dose model, is linearized using a Jacobian-based method and solved using the conjugate gradient method. For comparison, a standard Quasi-Newton (QN) method (limited-memory version) is implemented to directly solve the nonlinear biological optimization problem.
Results: The proposed IJL method demonstrates superior plan quality and computational efficiency compared to the standard method using a QN nonlinear optimizer. The dosimetric parameters of a head-and-neck case are shown in following table, including conformity index (CI) of CTV, the maximum dose of CTV D_max, the mean dose of CTV D_mean, and the mean dose of CVT1cm D_CTV1cm (a 1cm ring extension of CTV). It is shown that IJL achieves enhanced physical dose conformality within the treatment target per the prescribed target dose.
Conclusion: This study introduces a novel biological optimization method with iterative Jacobian-based linearization for CIRT, offering improvements in both plan quality and computational efficiency compared to the standard nonlinear optimization method employing a Quasi-Newton algorithm.

		CI	Dmax	Dmean	DCTV1cm	Time/Iteration
Clinical RBE dose	IJL	0.95	115.8	103.0	53.1	3.1s/100
	QN	0.86	129.8	111.6	61.7	67.6s/100
Biological RBE dose	IJL	0.52	187.1	161.2	97.9	3.1 s/100
	QN	0.46	194.1	172.0	109.6	67.6 s/100