The Mathematical Modelling of Various Problems arising in the Biomedical Sciences

定量模型在生物科学中发挥着越来越重要的作用，并迅速成为这些领域未来发现的不可或缺的工具。开发一种准确的、定量的模型来模拟不同情况下软生物组织的反应将是应用生物科学的一个重要里程碑。虽然传统的实验方法对生物科学的重大进步做出了贡献，但仍有重大改进的余地。需要新的方法来更深入地了解生物系统的发展和功能的基本原理以及这些原理是如何出错的。显然，适当的数学/计算框架在生物科学中的应用领域是多方面的。这些范围从脑积水（神经外科医生经常遇到的一种临床病症）到临床肿瘤学肿瘤的治疗和控制。半个世纪的生物医学研究在治疗和管理这些病症和疾病方面取得了非常有限的进展。数学模型、计算机模拟和工程技术也促进了转化研究，使临床管理和治疗发生了革命性的变化，从而降低了死亡率和医疗保健成本。我的长期研究计划侧重于开发一个全面的定量模型，并结合实验信息计算机模拟，以对生物组织在不同负载情况下的反应有更基本的了解。数学建模和精心设计的实验的仔细结合将导致对产生许多长期医疗状况和疾病的潜在机制的更深入的理解，并为寻找适当的治疗方法提供合理的指导。

Quantitative models are playing an increasingly central role in the biological sciences and are rapidly becoming an indispensable tool for discoveries of the future in these fields. The development of an accurate, quantitative model suitable for simulating the response of soft biological tissues under different scenarios will be an important milestone in the applied biological sciences. Whilst conventional experimental approaches have contributed to major advances in the biological sciences, there is room for significant improvement. Fresh approaches are needed to gain a deeper understanding of the principles underlying the development and function of biological systems and how these may go awry.Clearly the application areas in the biosciences for appropriate mathematical/computational frameworks are manifold. These range from conditions such as hydrocephalus (a clinical condition frequently encountered by neurosurgeons) to the treatment and control of tumours in clinical oncology. Half a century of biomedical research has produced very modest improvements in the treatment and management of such conditions and diseases. Mathematical models, computer simulations and engineering technologies have also contributed to translational research that has revolutionized clinical management and treatment, resulting in decreased mortality and healthcare costs. My long term research program is focussed on the development of a comprehensive quantitative model, coupled with experimentally informed computer simulations to develop a more fundamental understanding of the response of biological tissues in vastly different loading situations. The careful coupling of mathematical modelling and well designed experiments will result in a deeper understanding of the underlying mechanisms that give rise to many long standing medical conditions and diseases and provide rational guidance in the search for appropriate therapies.