Cancer Therapy Optimisation: A Mathematical Approach

癌症对全球健康构成了深刻的挑战，需要创新的方法来改善治疗结果。这项为期3.5年的博士研究计划深入数学建模领域，主要关注微分方程式，以深入了解癌症进展的动力学和对治疗的反应。该项目的第一阶段包括对数学建模领域的全面文献进行审查。具体地说，在癌症生物学领域，目标是为癌症治疗的优化奠定坚实的基础。研究的核心包括开发和验证癌症治疗优化的数学模型。研究人员将制定一个或多个详细的数学模型，以捕捉癌症生长的动态及其对治疗的反应。这些模型将被描述为微分方程组，并将纳入生物学上相关的参数和变量。随着模型的建立，研究将进入模拟和分析阶段。这些数学模型将使用计算软件实现，从而能够探索各种治疗方案及其对癌症动力学的影响。将对模拟结果进行严格分析，并对模型进行改进，使其与观察到的生物现象保持一致。第三年是研究的优化阶段。重点将放在探索适合于优化癌症治疗计划的优化算法上，基于微分方程组模型。这些算法将被定制，以解决癌症治疗背景下治疗优化的独特挑战。一旦开发了优化框架，它将被实施并通过模拟场景进行测试。与临床合作伙伴的合作将发挥关键作用，因为优化的治疗计划使用真实的患者数据进行验证。这一阶段有望弥合理论与实际应用之间的鸿沟。博士研究计划的最后一年包括延长0.5年，侧重于研究成果的实际应用和传播。

Cancer poses a profound challenge to global health, necessitating innovative approaches to improve therapeutic outcomes. This 3.5-year PhD research plan dives into the world of mathematical modelling, with a primary focus on differential equations, to gain insights into the dynamics of cancer progression and response to treatment. The first phase of the project consists of a thorough literature review in the field of mathematical modelling. Within cancer biology specifically, the aim is to build a strong foundation in the optimisation of cancer therapy.The core of the research consists of the development and validation of a mathematical model for cancer therapy optimisation. The researcher will formulate one or more detailed mathematical models that capture the dynamics of cancer growth and its response to therapy. These models will be described as systems of differential equations and will incorporate biologically relevant parameters and variables. With the models in place, the research will progress to simulation and analysis. The mathematical models will be implemented using computational software, enabling the exploration of various therapy scenarios and their impact on cancer dynamics. Simulation results will be rigorously analysed, and the model will be refined to align with observed biological phenomena. The third year introduces the optimisation phase of the research. The focus will be on exploring optimisation algorithms suitable for optimising cancer therapy plans, based on the differential equations model. These algorithms will be customised to address the unique challenges of therapy optimisation within the context of cancer treatment. Once the optimisation framework is developed, it will be implemented and tested with simulated scenarios. Collaboration with clinical partners will play a crucial role as the optimised therapy plans are validated using real patient data. This phase is expected to bridge the gap between theory and real-world application. The final year of the PhD research plan then includes a 0.5-year extension to focus on practical application and dissemination of research findings.