Collaborative Research: A New Multiscale Methodology and Application to Tumor Growth Modeling

肿瘤生长的复杂性涉及细胞内、细胞间以及细胞与其环境之间的相互作用，需要开发数学和计算模型，这些模型可以将细胞和亚细胞尺度的过程连接到组织水平尺度。需要这些方法来帮助肿瘤生物学家进一步了解这些过程的潜在机制（例如，增殖、分化和迁移）在影响其行为的尺度上参与肿瘤发展。由于这种复杂性，在功能上连接细胞和组织尺度过程一直是具有挑战性的，其知识是开发预测性多尺度肿瘤模型的关键。然而，目前的模型通常使用ad-hoc规则来桥接尺度，这限制了它们的预测能力。该项目将通过开发一种新的多尺度方法来应对这一挑战，在该方法中，通过严格的数学放大技术，在细胞尺度上直接测量的量可以在连续组织尺度上告知模型参数。将通过比较模拟结果与实验获得的关于不同细胞和肿瘤的总体生长速率和时空行为的信息来测试和验证多尺度模型。新的多尺度方法将用于研究胰腺肿瘤，以阐明胰腺病变向浸润性胰腺导管腺癌（PDAC）的转变。通过将患者数据分析与定量肿瘤建模相结合，该项目将开发可靠的方法，可以使用相对非侵入性的方法预测胰腺囊肿进展为PDAC的可能性。该项目团队将开发一类新的多尺度模型，通过应用严格的放大技术以非现象学的方式桥接这些尺度，以便在组织尺度上关闭连续方程，并提供跨细胞和组织尺度的过程的准确描述。具体而言，随机代理为基础的模型在细胞尺度和连续偏微分方程模型在组织尺度将被开发。通过使用和扩展动态密度泛函理论（DDFT）的框架来放大离散模型，以获得多细胞尺度连续方程，该方程解释细胞之间的相关性以及生物过程（例如细胞出生和死亡），从而发现在组织尺度的变量与在细胞尺度的测量之间的一致的函数关系。将通过识别和推导缓慢变化变量的方程来进一步放大到组织规模。将测试和验证尺度重叠领域中不同模型的一致性。新的多尺度方法将用于模拟胰腺肿瘤进展为浸润性癌，以估计这种进展的概率。我们的顾问通过一个单独资助的项目提供的胰腺病变的大规模人类患者数据集将用于验证和完善模型。该项目将加强学生的跨学科培训。

The complexity of tumor growth, which involves interactions within cells, among cells, and between cells and their environment, calls for development of mathematical and computational models that can connect processes from the cell, and sub-cell scales, to tissue level scales. These methods are needed to help tumor biologists gain further insight into the underlying mechanisms of the processes (e.g., proliferation, differentiation, and migration) involved in tumor development, at the scales which influence their behavior. Because of this complexity, it has been challenging to functionally link cell and tissue scale processes, the knowledge of which is key to development of predictive multiscale tumor models. However, current models typically use ad-hoc rules to bridge between scales, which limits their predictive capability. This project will address this challenge by developing a new multiscale method where directly measurable quantities at the cell-scale inform the model parameters at the continuum tissue scale through rigorous, mathematical upscaling techniques. The multiscale model will be tested and validated by comparing simulation results against experimentally obtained information about the overall growth rates and spatiotemporal behaviors of the different cells and tumors. The new multiscale method will be used to study pancreatic tumors to elucidate the transition of pancreatic lesions into invasive pancreatic ductal adenocarcinoma (PDAC). By integrating patient data analysis with quantitative tumor modeling, the project will develop reliable methods that can predict the likelihood of pancreatic cyst progression to PDAC using relatively non-invasive approaches. The project team will develop a new class of multiscale models that bridge these scales non-phenomenologically through application of rigorous upscaling techniques in order to close the continuum equations at the tissue scale and provide an accurate description of the processes across both cell and tissue scales. Specifically, stochastic agent-based models at the cell-scale and continuum partial differential equation models at the tissue-scale will be developed. Consistent functional relationships between the variables at the tissue-scale and measurements at the cell-scale will be found by upscaling the discrete models by using and extending the framework of dynamic density functional theory (DDFT) to obtain multi-cell scale continuum equations that account for correlations among cells as well as biological processes such cell birth and death. Further upscaling to the tissue scale will be done by identifying and deriving equations for slowly varying variables. The consistency of the different models in domains where the scales overlap will be tested and validated. The new multiscale method will be applied to model the progression of pancreatic neoplasms into invasive carcinomas in order to estimate the probability of this progression. Large-scale human patient datasets of pancreatic lesions, provided by our consultants through a separately funded project, will be used to validate and refine the models. The project will enhance the cross disciplinary training of students.