AI 中文总结
研究提出量子广义等效均匀剂量（QgEUD），通过引入相位变量扩展传统gEUD。利用伊辛哈密顿量建模，经 metropolis 蒙特卡罗模拟，结果表明QgEUD能整合多种效应，为放射生物学建模和量子兼容优化提供基础。
AI 中文摘要
广义等效均匀剂量（gEUD）可衡量非均匀剂量分布，但仅依赖剂量大小，未明确考虑细胞集体相互作用或相位相关生物反应。本文提出量子广义等效均匀剂量（QgEUD），通过引入相位变量将传统gEUD核扩展到复域，保留原始剂量加权形式。其产生二维响应面，在实轴上恢复传统gEUD，并通过相位调制纳入相互作用相关的放射生物学效应。通过伊辛哈密顿量建模局部剂量元素，用 metropolis 蒙特卡罗模拟获得平衡响应图。虚拟放疗模型模拟结果表明QgEUD能保留整体剂量分布，产生受集体相互作用支配的空间调制生物效应图，相应的凯勒响应识别出仅剂量大小之外具有增强敏感性的区域，参数敏感性分析证实了实际模拟条件下的稳定收敛。这些结果将QgEUD确立为gEUD的量子启发扩展，为相互作用感知放射生物学建模和未来量子兼容优化提供了基础。
英文摘要
The generalized equivalent uniform dose (gEUD) provides a biologically interpretable measure of heterogeneous dose distributions and is widely used in radiobiological modeling. However, because gEUD depends solely on dose magnitude, it does not explicitly account for collective cellular interactions or phase-dependent biological responses. Here, we propose a quantum generalized equivalent uniform dose (QgEUD), which extends the conventional gEUD kernel into the complex domain by introducing a phase variable while preserving the original dose-weighting formalism. This formulation yields a two-dimensional response surface that recovers conventional gEUD on the real axis and incorporates interaction-dependent radiobiological effects through phase modulation. The local response of the surface is characterized by a Kähler metric, providing an intrinsic measure of sensitivity to dose weighting and phase perturbations. To demonstrate the framework, local dose elements are modeled by an Ising Hamiltonian with dose- and phase-dependent interactions, and equilibrium response maps are obtained using Metropolis Monte Carlo simulations. Simulations in a virtual radiotherapy phantom preserve the overall dose distribution while producing spatially modulated biological-effect maps governed by collective interactions. The corresponding Kähler response identifies regions exhibiting enhanced sensitivity beyond dose magnitude alone, and parameter sensitivity analysis confirms stable convergence under practical simulation conditions. These results establish QgEUD as a quantum-inspired extension of gEUD that integrates heterogeneous dose aggregation, phase-dependent interactions, and geometric response within a unified mathematical framework, providing a basis for interaction-aware radiobiological modeling and future quantum-compatible optimization.
