End‐to‐end differentiable volumetric modulated arc therapy optimization via computation graph–driven automatic differentiation
Hongkai Wang, Wenzheng Sun, Wenlong Xia, Bin LiangAbstract
Background
Conventional volumetric modulated arc therapy (VMAT) optimization relies on gradient‐based methods in which analytical gradients must be explicitly derived for each objective function and machine constraint. This dedicated mathematical derivation imposes substantial barriers to extending the optimization framework with new clinical objectives or delivery constraints, and the resulting CPU‐based implementations do not natively exploit modern GPU hardware.
Purpose
To develop an end‐to‐end differentiable VMAT optimization framework using computation graphs that enable automatic differentiation–based gradient computation for both fluence map optimization (FMO) and direct aperture optimization (DAO), while incorporating VMAT machine delivery constraints within a unified, GPU‐accelerated pipeline.
Methods
A two‐stage pipeline—fluence map optimization (FMO) followed by DAO—was developed. FMO reformulates dose calculation as a differentiable computation graph, enabling gradient computation for arbitrary objective functions including non‐smooth Heaviside step terms. For DAO, a novel analytically derived computation graph maps MLC leaf positions to delivered fluence through closed‐form time‐averaged bixel exposure integration with finite‐width boundary corrections, ensuring exact differentiability. Machine delivery constraints—including leaf collision, speed limits, and dose rate bounds—are incorporated as differentiable penalty terms for joint end‐to‐end optimization. Twenty lung cancer cases from the GDP‐HMM AAPM Challenge dataset (60 Gy/30 fractions) were optimized using objectives derived from clinical Eclipse reference plans and compared against MatRad and Eclipse.
Results
The proposed method achieved PTV D98 of 58.88 ± 0.33 Gy, comparable to Eclipse (59.07 ± 0.55 Gy, p = 0.26) and significantly higher than MatRad (57.27 ± 0.48 Gy, p < 0.001). The Paddick conformity index was 0.81 ± 0.06, comparable to Eclipse (0.84 ± 0.22, p = 0.48) and superior to MatRad (0.64 ± 0.11, p < 0.001). OAR sparing closely matched Eclipse: heart mean dose 10.74 ± 4.89 Gy vs. 11.55 ± 4.76 Gy; lung mean dose 15.33 ± 3.50 Gy vs. 16.70 ± 3.29 Gy; LAD mean dose 9.55 ± 4.97 Gy vs. 9.05 ± 3.94 Gy ( p = 0.18). MatRad achieved lower heart doses at the cost of degraded PTV coverage and conformity. Optimization time was significantly shorter (59.28 ± 43.95 s vs. 390.30 ± 184.90 s, p < 0.001), while delivery times were equivalent ( p = 0.92).
Conclusions
The proposed differentiable VMAT framework demonstrated superior goal‐directed optimization fidelity compared with MatRad—more reliably translating objectives into intended dosimetric outcomes—achieving plan quality approaching clinical Eclipse plans with faster optimization.