Modelling lung deposition of inhaled particles in cystic fibrosis

该项目将使用数学和计算模型来研究肺气道中流动和运输的基本物理机制，特别考虑与囊性纤维化和药物输送相关的方面。气道中大量高粘性粘液的存在是囊性纤维化的主要症状，这使得有效地实施深入肺部的吸入疗法具有挑战性。利用理论连续介质力学的机制，该项目将寻求提高我们对粘液如何在整个肺部分布和运输的理解，以及这如何影响不同药物输送方法的功效。最初将重点关注病变粘液的复杂流变特性（例如其屈服应力）对肺周围小气道内运输的影响，肺周围是难以通过实验研究和难以通过医学成像解决的肺区域。在项目的后期阶段，利用离散微积分工具的多尺度建模方法将用于评估小气道运输过程如何影响器官尺度上的药物输送，从而允许在整个气道树中纳入通气的影响。这将需要求解大规模离散网络上的传输方程，由于涉及到大量的航路，这将需要相对密集的计算。这种方法与降维技术相结合，将允许研究气道几何形状对肺部运输和疾病发展的影响。在整个项目中，模型的开发将受到生理和临床应用的推动，特别是吸入的雾化药物有效地输送到囊性纤维化患者受损或阻塞的肺区域。为了实现这一目标，学生将受到来自曼彻斯特大学数学系和感染、免疫和呼吸医学部门的多学科导师团队的指导。从该项目中产生的模型可能有更广泛的潜在应用，而不仅仅是囊性纤维化（例如，基本流体力学），但这种针对疾病的方法意味着该项目将提供新的能力，以实际测试和优化计算机上的药物输送方案，这将对患者的治疗产生真正的影响。

This project will use mathematical and computational modelling to investigate fundamental physical mechanisms of flow and transport in lung airways, considering in particular features relevant to cystic fibrosis and related aspects of drug delivery. The presence of large quantities of highly viscous mucus in airways is a primary symptom of cystic fibrosis, making it challenging to effectively administer inhaled therapies deep into the lungs. Using the machinery of theoretical continuum mechanics, this project will seek to improve our understanding of how mucus is distributed and transported throughout the lungs, and how this could affect the efficacy of different methods of drug delivery. There will be an initial focus on the impact of the complex rheological properties of diseased mucus (such as its yield stress) on transport within small airways in the lung periphery, regions of the lungs that are difficult to study experimentally and difficult to resolve using medical imaging. In the later stages of the project, multi-scale modelling approaches exploiting tools from discrete calculus will be used to assess how small-airway transport processes impact on drug-delivery at the organ scale, allowing incorporation of the effects of ventilation in the whole airway tree. This will require solution of transport equations on massive discrete networks, which will require relatively intensive computation due to the large number of airways involved. This approach, combined with dimensionality reduction techniques, will allow investigation into the effects of airway geometry on transport in the lungs and on development of disease. Throughout the project, model development will be motivated by the physiological and clinical applications, in particular the effective delivery of inhaled aerosolised pharmaceuticals to damaged or blocked lung regions in cystic fibrosis. To achieve this, the student will be guided by a multidisciplinary team of supervisors, drawn from the Department of Mathematics and the Division of Infection, Immunity & Respiratory Medicine at the University of Manchester. The models emerging from the project are likely to have broader potential application beyond cystic fibrosis (for example, to fundamental fluid mechanics), but this disease-specific approach means that the project will give new capabilities to realistically test and optimise drug-delivery protocols in silico that can make a real difference to patient treatment.