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。开发一个准确的，定量的模型，适合于模拟软生物组织在不同的情况下的反应将是一个重要的里程碑，在应用生物科学。虽然传统的实验方法为生物科学的重大进步做出了贡献，但仍有显著改进的空间。需要新的方法来更深入地理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，在生物科学中，适当的数学/计算框架的应用领域是多方面的。这些范围从诸如脑积水（神经外科医生经常遇到的临床病症）的病症到临床肿瘤学中肿瘤的治疗和控制。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有助于转化研究，彻底改变了临床管理和治疗，从而降低了死亡率和医疗成本。我的长期研究计划专注于开发一个全面的定量模型，再加上实验信息的计算机模拟，以发展对生物组织在非常不同的加载情况下的反应的更基本的理解。数学建模和精心设计的实验的精心耦合将导致对引起许多长期存在的医学状况和疾病的潜在机制的更深入理解，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.