I2M UMR 7373 Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France.
SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
Cancer Res. 2014 Nov 15;74(22):6397-407. doi: 10.1158/0008-5472.CAN-14-0721. Epub 2014 Sep 12.
Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidγ mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were [Formula: see text] for primary tumor growth and [Formula: see text] for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading during the earliest stages of cancer.
在诊断时确定肿瘤分期是制定患者治疗策略的关键。在这方面，早期发现当前成像方法无法检测到的隐匿性转移将对最佳治疗和长期生存产生重大影响。描述转移扩散的数学模型可以在没有临床证据的情况下估计转移的风险。在这项研究中，我们改编了一个自上而下的模型来进行这种估计。该模型由一个描述转移生长的输运方程组成，并具有转移排放的边界条件。将模型预测与在 Nod/Scidγ 小鼠中进行的原位乳腺癌肿瘤异种移植实验的实验结果进行了比较。通过 3D 生物发光断层扫描监测原发肿瘤生长、转移扩散和生长。定制的计算方法允许使用 Monolix 软件对偏微分方程模型进行混合效应建模。Bertalanffy、West 和 Gompertz 模型最能描述原发肿瘤生长，涉及初始指数生长阶段。所有其他测试的模型都被拒绝。最佳的转移性模型涉及分别描述转移扩散和生长的两个参数。可视化预测检查、残差分析和引导研究验证了该模型。决定系数分别为[公式：见正文]用于描述原发肿瘤生长，[公式：见正文]用于描述转移生长。基于数据的模型开发揭示了一些具有生物学意义的发现。首先，可以从总转移负担的测量中获得关于生长和扩散的信息。其次，验证了原发肿瘤大小和发射率之间假定的联系。最后，快速生长的腹膜转移只能通过这种复杂的偏微分方程模型来描述，而不能通过常微分方程模型来描述。这项工作推进了在癌症的最早阶段预测转移扩散的努力。
