Modelling the invasion of solid tumours - the role of the extracellular matrix in invasion

该项目将重点关注两种类型的实体肿瘤，即肌肉骨骼肉瘤和胶质母细胞瘤。肉瘤是一种恶性肿瘤，可以在体内的许多部位发现，因为它们起源于支持组织或结缔组织。在英国，每天有15人被诊断出患有肉瘤。低度肉瘤可采用一种或多种手术、化疗或放疗治疗。然而，更高级别的肉瘤更具侵袭性，因此可以扩散到身体的其他部位，并且可能无法通过手术切除。胶质母细胞瘤是成人中最常见的恶性脑肿瘤，尽管与其他形式的癌症相比，它的发病率很低，但它的预后很差，平均只有15个月。胶质母细胞瘤的治疗需要多学科的方法，包括手术、化疗和放疗的结合。在手术过程中，并不是所有的胶质母细胞瘤肿瘤都可以从大脑中移除，因为有可能对健康的脑组织造成损害。因此，由于胶质母细胞瘤的高度侵袭性，复发是不可避免的。这凸显了研究侵袭过程的重要性，因为如果对它有了更好的了解，那么预防复发或癌症扩散的治疗方法就可能被开发出来。本项目的主要目的是建立数学模型，研究细胞外基质（ECM）在包括肌肉骨骼肉瘤和胶质母细胞瘤在内的实体肿瘤侵袭过程中的作用。异常的ECM是肿瘤微环境的一个组成部分，也是肿瘤侵袭的健康组织的一个组成部分。它具有控制转运机制和代谢以及肿瘤生长和扩散的作用。由于其复杂性，针对ECM的治疗尚未在患者身上实践。考虑到ECM在入侵过程中的关键作用，令人惊讶的是，在目前的数学模型中，关于它的信息相对较少。人们希望，如果ECM在侵袭过程中的作用得到更好的理解，那么年轻和老年患者基质成分的差异可以在肿瘤的侵袭中得到解释。本项目开发的模型将考虑到ECM的独特组成和建模能力。为了实现这一目标，肌肉骨骼肉瘤和胶质母细胞瘤的侵袭将使用包含生物学和临床数据的离散和连续数学模型进行建模。这些模型将进一步发展，以包括ECM与肌肉骨骼肉瘤或胶质母细胞瘤细胞之间的相互作用。这很重要，因为如果知道了ECM成分是如何影响侵袭的，那么就有可能根据患者的ECM成分来预测侵袭途径。该模型还将允许更深入地了解ECM的特定成分如何影响肿瘤侵袭，这可能导致未来的治疗靶点被确定。目的是开发一种肌肉骨骼肉瘤和胶质母细胞瘤肿瘤侵袭的混合离散-连续数学模型。连续模型将肿瘤表示为一个整体的连续介质，因此将肿瘤作为一个整体来关注其运动。偏微分方程（PDEs）通常用于表示模型的连续分量。离散模型考虑构成肿瘤的单个细胞的运动。使用混合模型可以将细胞表示为离散代理，同时也可以使用pde对其他组件（如ECM）进行建模。这使我们能够清楚地了解癌细胞与其环境之间的关系。这些模型将使用MATLAB（具有内置PDE求解器的优势）和Python（由于其广泛的库）开发。

This project will focus on two types of solid tumours namely, musculoskeletal sarcomas and glioblastoma. Sarcomas are a type of malignant tumour that can be found in many locations within the body as they originate in supportive or connective tissue. A total of 15 people per day in the UK are diagnosed with a sarcoma. Lower grade sarcomas can be treated using one or a combination of, surgery, chemotherapy or radiotherapy. However, higher grade sarcomas are much more aggressive so can spread to other parts of the body and may not be able to be removed using surgery. Glioblastoma is the most common type of malignant brain tumour in adults and although its occurrence is rare in comparison to other forms of cancer, it has a poor prognosis of an average of only 15 months. A multidisciplinary approach is required to treat glioblastoma which involves a combination of surgery, chemotherapy and radiotherapy. During surgery, not all the glioblastoma tumour can be removed from the brain due to the risk of causing damage to healthy brain tissue. Therefore, due to the highly invasive nature of glioblastoma reoccurrence is inevitable. This highlights the importance of investigating the invasion process because if it is better understood then treatments to prevent recurrence or the cancer from spreading might be able to be developed. The main aim of this project is to develop mathematical models which investigate the role of the extracellular matrix (ECM) in the invasion processes of solid tumours including musculoskeletal sarcomas and glioblastoma. Abnormal ECM is a component of the tumour microenvironment and the ECM is also a constituent of healthy tissue that the cancer invades. It has roles of controlling transport mechanisms and metabolism as well as the growth and spread of tumours. Due to its complexity, treatments targeting the ECM are not yet practised on patients. Given the key role of the ECM in the invasion process, it is surprising that relatively little information about it is included in current mathematical models. It is hoped that if the role of the ECM in the invasion process is better understood then the differences in the compositions of younger and older patients' matrix can be accounted for in the invasion of tumours. The models developed in this project will take into account the unique composition and remodelling capability of the ECM. To achieve this, the invasion of musculoskeletal sarcomas and glioblastoma will be modelled using discrete and continuous mathematical models which contain biological and clinical data. These models will be developed further to include the interactions between the ECM and either the musculoskeletal sarcomas or glioblastoma cells. This is important because if it is known how the ECM composition affects invasion then it may be possible to predict the invasion pathway based on a patient's ECM composition. The models will also allow for a deeper understanding into how specific components of the ECM affect tumour invasion and this could lead to future therapeutic targets being identified. The intention is to develop a hybrid discrete-continuous mathematical model of the invasion of musculoskeletal sarcomas and glioblastoma tumours. Continuous models represent the tumour as a whole continuous medium so focus on the movement of the tumour as one body. Partial differential equations (PDEs) are usually used to represent the continuous components of a model. Discrete models consider the movement of the individual cells which make up the tumour. Using a hybrid model will allow a combination of being able to represent cells as discrete agents whilst also being able to use PDEs to model other components such as the ECM. This allows a clear understanding of the relationship between the cancer cells and their environment. The models will be developed using MATLAB which has the advantage of an inbuilt PDE solver and Python due to its wide range of libraries.