Formulating tumor models that predict growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simplified nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. The applied immunotherapy decreases the proliferative cell concentration. Here, we model the immunotherapeutic agent concentration in the entire lung over time by an ordinary differential equation (ODE). Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to calibrate our model. For the reduced 1D model, we show that our model can qualitatively describe observations during immunotherapy by fitting our model parameters to existing patient data. Our model covers cases in which the immunotherapy is successful and limits the tumor size, as well as cases predicting a sudden relapse, leading to exponential tumor growth. Finally, we move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we show the predictive benefits a more detailed patient-specific simulation including spatial information could yield in the future.

翻译：构建能够预测治疗过程中肿瘤生长的模型对于制定个体化治疗方案至关重要。在此背景下，我们展示了近期工作：在确定性简化框架下，模拟两位接受免疫治疗的非小细胞肺癌（NSCLC）患者。模型核心基于Cahn-Hilliard型相场方程，描述增殖性肿瘤细胞与坏死性肿瘤细胞的演化过程，并与驱动增殖细胞生长及其向坏死细胞转化的简化营养模型相耦合。所采用的免疫治疗会降低增殖性细胞浓度。本文通过常微分方程（ODE）对全肺内免疫治疗药物浓度随时间的变化进行建模，最终通过反应项实现所有方程间的耦合。通过假设肿瘤呈球对称生长且营养流入恒定，我们将完整的三维癌症模拟模型简化为降维一维模型。进而利用患者数年计算机断层扫描（CT）数据对模型进行参数校准。对于降维一维模型，我们证明通过拟合模型参数至现有患者数据，该模型能定性描述免疫治疗期间的观测现象。模型既涵盖免疫治疗成功抑制肿瘤生长的案例，也包含预测突发复发导致指数级肿瘤扩增的情形。最后，我们从降维模型回归至肺组织内完整三维癌症模拟，由此展示包含空间信息的精细化个体模拟在未来可能带来的预测优势。