Applications of mathematics in medicine

医疗保健显然已成为许多政府议程上的优先事项。医学界面临的巨大挑战之一是如何从基础科学实验和临床试验收集的大量信息中组织和提取有用的知识。数学模型在这一努力中发挥着越来越重要的作用，因此将成为未来生物医学发现的一个组成部分。生理事件建模的新研究范式和计算机模拟的发展使理论概念成为实用的医疗工具。其中一些基于数学的工具，如外科训练模拟器，已经彻底改变了临床管理和治疗，并降低了死亡率和医疗成本。脑损伤是一系列疾病过程中常见的结果，并导致残疾，从社会角度来看，这是情感上的破坏性和代价高昂的。开发一种适合模拟大脑机械行为的精确数学模型，将是临床神经科学的一个重要里程碑，因为它将有助于预测大脑在各种情况下遭受的损伤，并有助于做出治疗决定。确定影响脑肿瘤和其他癌性肿瘤治疗反应的主要因素一直是临床肿瘤学长期关注和相关的问题。虽然放疗和化疗等传统治疗方法在癌症的管理和控制方面取得了重大进展，但仍有进一步改善的空间。因此，数学建模和新型计算方法的结合，通过实验和临床数据验证，为生物医学研究提供了一个强大的新工具。我的研究项目是使用数学/计算模型来研究医学中出现的问题，以开发与临床相关和使用的模型。我试图理解和模拟临床条件，如脑积水，以及肿瘤的生长和控制在一个更基本的水平上使用连续介质力学。

Medical healthcare is clearly becoming a priority on many government agendas. One of the enormous challenges facing the medical community is how to organise and extract useful knowledge from the enormous amount of information gathered from basic science experiments and clinical trials. Mathematical models are playing an increasingly central role in this endeavour and will therefore be an integral part of biomedical discoveries of the future. New research paradigms for the modelling of physiological events and the development of computer simulations have enabled theoretical concepts to become practical medical tools. Some of these mathematically-based tools, such as surgical training simulators, have revolutionised clinical management and treatment, and have led to decreased mortality and healthcare costs. Brain injury, is a frequent outcome in a range of disease processes and leads to disabilities that are emotionally devastating and costly from a societal viewpoint. The development of an accurate mathematical model suitable for the simulation of the mechanical behaviour of the brain, will be an important milestone in the clinical neurosciences because it will help to predict the damage sustained by the brain in a variety of circumstances and aid in treatment decisions. The identification of major factors that influence treatment response in brain and other cancerous tumours has been a problem of longstanding interest and relevance to clinical oncology. Whilst conventional treatments like radiotherapy and chemotherapy have contributed to major advances in the management and control of cancer, there is still room for significant further improvement. Thus the combination of mathematical modelling and novel computational methods, validated using experimental and clinical data, provides a powerful new tool in biomedical research. My research program is directed at using mathematical/computational modelling to study problems arising in medicine with a view to developing models of clinical relevance and use. I attempt to understand and model clinical conditions such as hydrocephalus, as well as tumour growth and control at a more fundamental level using continuum mechanics.