Mathematical modelling for nano- and microscale medical challenges

微流体是一个新兴的领域，指的是行为，精确控制和操纵流体的几何约束到一个小规模（通常是亚毫米）。这是一个多学科领域，涉及工程，物理，化学，生物化学，纳米技术和生物技术。Scott Tsai教授是瑞尔森大学场、流和界面实验室（LoFFI）的负责人，其工作重点是开发用于医疗应用的新型纳米和微流体技术。在这个博士项目中，我们将考虑LoFFI中生物医学微流体的两个最新发现，以开发生物医学微流体应用的数学模型：用于超声应用的纳米气泡生成和声学刺激生物细胞的营养吸收。研究方法将使用实验数据来指导适当的渐近制度，并验证我们的理论。相反，该方法的预测将用于指导未来的实验室实验。数学家和实验学家之间的这种密切合作将伴随着与临床医生的互动，这将是推进这一研究领域的关键。为描述这一问题而开发的数学模型将具有更广泛的范围，增强对复杂两相流的数学理解。这项工作的结果有可能在未来的靶向药物递送策略，基因沉默，DNA编辑技术，细胞内成像和基因治疗中发挥作用。为解决这一问题而开发的数学模型也将提供对弹性介质中声波传播的更全面的理解。这个博士项目属于以下三个EPSRC研究领域：连续介质力学，流体动力学和空气动力学，数学生物学福尔斯。

Microfluidics is a burgeoning field that refers to the behaviour, precise control, and manipulation of fluids that are geometrically constrained to a small scale (typically sub-millimetre). This is a multidisciplinary field that involves engineering, physics, chemistry, biochemistry, nanotechnology, and biotechnology. Professor Scott Tsai is the head of the Laboratory of Fields, Flows, and Interfaces (LoFFI) at Ryerson University whose efforts are focused on the development of novel nano and microfluidic technologies for medical applications. In this DPhil project, we will consider two recent discoveries in biomedical microfluidics in the LoFFI to develop mathematical models for biomedical microfluidic applications: nanobubble generation for ultrasound application and acoustic stimulation for nutrient uptake of biological cells. The research methodology will use experimental data to guide the appropriate asymptotic regimes and validate our theories. Conversely, predictions from the methodology will be used to guide future laboratory experiments. This close collaboration between mathematicians and experimentalists will be accompanied by interactions with clinicians, which will be key in advancing this research area. The mathematical models developed to describe this problem will have broader reach, enhancing mathematical understanding in complex two-phase flows. The results of this work have the potential to play a role in future targeted drug-delivery strategies, gene silencing, DNA editing technologies, intracellular imaging and gene therapies. The mathematical modelling developed to tackle this problem will also provide a more general understanding of the propagation of acoustic waves in elastic media. This DPhil project falls within the following three EPSRC research areas: Continuum Mechanics, Fluid dynamics and Aerodynamics, and Mathematical Biology.