随机药代动力学逃逸：一种基于场论的波动诱导肿瘤复发研究方法
Stochastic Pharmacokinetic Escape: A Field-Theoretic Approach to Fluctuation-Induced Tumor Relapse
AI总结：
该研究针对经典数学肿瘤学忽略种群波动的缺陷，构建随机PK-PD场论揭示高剂量化疗下肿瘤微簇因种群噪声产生的随机药代动力学逃逸机制，推导节拍式给药等抑制条件并经临床数据验证。
AI中文摘要：
经典数学肿瘤学采用确定性平均场模型，预测足够高的化疗剂量可使肿瘤密度降至零。我们发现这种看似治愈的结果是忽略种群波动的人为产物。我们构建了非平衡随机药代动力学-药效动力学（PK-PD）场论，将双室药代动力学模型与Doi-Peliti形式主义中的随机肿瘤-免疫部分相结合，随后通过Martin-Siggia-Rose/Janssen-De Dominicis方法将其映射为耦合的乘性朗之万方程。在免疫耗竭的庇护位点中，动力学简化为随时间变化的费勒扩散，其福克-普朗克方程可得到解析生存泛函：种群噪声意味着高剂量化疗下肿瘤微簇存在严格非零的复发概率。标准推注给药作为非选择性湮灭过程，驱动免疫场进入吸收态，形成空间免疫耗竭真空，从而引发波动诱导的复发——即随机药代动力学逃逸。我们推导了节拍式给药和佐剂免疫疗法抑制该随机脆弱窗口的定量条件。对1461份纵向患者记录的模型无关分析显示，大部分可评估病灶在达到最低点后出现可测量的再生，而非单调消除；将模型的漂移泛函拟合至这些轨迹可定量再现该模式，对预测的种群噪声标度律的直接测试表明，最小观测肿瘤体积处的尺寸依赖性噪声最大，与所提出的机制一致。
英文摘要：
Classical mathematical oncology employs deterministic mean-field models predicting that sufficiently high chemotherapy doses drive tumor density to zero. We show that this apparent cure is an artifact of neglecting demographic fluctuations. We construct a nonequilibrium stochastic PK-PD field theory combining a two-compartment pharmacokinetic model with a stochastic tumor-immune sector in the Doi-Peliti formalism, then map it to coupled multiplicative Langevin equations via the Martin-Siggia-Rose/Janssen-De Dominicis approach. In immune-depleted sanctuary sites, the dynamics reduce to a time-dependent Feller diffusion whose Fokker-Planck equation yields an analytical survival functional: demographic noise implies a strictly nonzero relapse probability for tumor micro-clusters under high-dose chemotherapy. Standard bolus administration acts as a nonselective annihilation process, driving immune fields into an absorbing state and creating a spatially immune-depleted vacuum that enables fluctuation-induced relapse -- Stochastic Pharmacokinetic Escape. We derive quantitative conditions under which metronomic dosing and adjuvant immunotherapy suppress this stochastic window of vulnerability. A model-agnostic analysis of 1461 longitudinal patient records shows that the majority of evaluable lesions exhibit a nadir followed by measurable regrowth rather than monotonic elimination; fitting the model's drift functional to these trajectories reproduces this pattern quantitatively, and a direct test of the predicted demographic-noise scaling law reveals size-dependent noise largest at the smallest observed tumor volumes, consistent with the proposed mechanism.
