The biophysics of cancer model systems: combined mathematical and experimental approaches for image analyses and interpretations

我们一直在以图像的形式获取数据，这些数据来自于在细胞培养中分离悬浮在3D中的癌细胞，以及对小鼠和大鼠癌症生长的现代成像，捕捉它们在有和没有辐射影响的情况下的时间演变。我们建议加强对这些序列图像的常规分析，从肿瘤体积或肿瘤血液供应的基本变化，到包括在成像时间点之间对肿瘤生长和治疗反应的数学生物物理模型。我们将建立一个解释实验的框架，这将增进我们的理解，促进假设的产生，并促进新实验的设计。 3D细胞培养系统显示，尽管细胞来自相同的细胞系，但细胞的行为更加异质性，这在培养皿中是看不到的。只有一小部分细胞会生长，一旦播种它们就不会立即开始分裂。通过数学建模，我们的目标是确定细胞进入细胞周期、生长速度的概率，并研究不同浓度的营养物质对这些概率的影响，以及辐射的影响。 对于动物肿瘤图像的分析，我们建议将可变形图像配准与肿瘤生长和对辐射的响应的数学模型相结合，包括通过血流成像测量的肿瘤血管模型。 上述模型将是我们的起点，将指导我们进行未来的实验。这项拟议的工作强调了数学建模和实验相结合的方法来回答特定科学问题的重要性，特别是在本质上复杂的肿瘤中。

We have been acquiring data in the form of images from dividing cancer cells suspended in 3D in cell cultures, as well as modern imaging of cancer growth in mice and rats, capturing their time evolution with and without radiation effects. We propose to augment the conventional analysis of these serial images, from basic change in tumour volume or tumour blood supply, to the inclusion of mathematical biophysical modeling of tumour growth and responses to treatment between the imaging time points. We will create a framework for the interpretation of experiments, which will enhance our understanding, for hypothesis generation, and facilitating design of new experiments. The 3D cell culture system revealed that cells behave much more heterogeneously, even though they are from the same cell line, not seen in Petri dishes. Only a fraction of cells will grow and they do not immediately begin dividing once seeded. With mathematical modeling, we aim to determine the probabilities of cell entering cell cycle, growth rates and investigate the impact of these probabilities with varying concentration of nutrients, as well as effect of radiation. For the animal tumour image analysis, we propose to combine deformable image registration with mathematical models of tumour growth and responses to radiation, including a model of tumour vasculatures as measured by blood flow imaging. The aforementioned models will be our starting points which will guide us to perform future experiments. The proposed work highlights the importance of a combined approach of mathematical modeling and experiments to answer specific scientific questions, especially in tumours that are inherently complex.