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Mathematical Models and High Performance Computing for Deposition and Absorption in Physiological Flows

Final Report Summary - MATCOMPHYS (Mathematical Models and High Performance Computing for Deposition and Absorption in Physiological Flows)

MatComPhys is an inter-disciplinary project, spanning several research fields to solve complex and coupled problems in human physiology. In specific two related problems are considered, both involving the transport of particles suspended in a fluid medium. The first problem focuses on the respiratory airways, investigating the fluid mechanics of inspiration, while the second problem concerns blood micro-circulation. These problems lie at different spatial scales three orders of magnitude apart, and exhibit transient fluid mechanics simulations in the highly complex geometries typical of biomedical applications.

Inspired air is conditioned in the upper respiratory tract before it reaches the lungs. Such conditioning involves the regulation of temperature and humidity, as well as filtering the air to exclude any suspended particles. Examples of suspended particles could be pollen or dust, but may include also antihistamine drug delivery by means of nebulisers. The deposition of such suspended particles in the upper airways may therefore be studied as a natural defence mechanism, as well as an effective modality for non-invasive drug delivery. The administration of drugs through the use of nebulisers is effective, firstly due to the highly vascularised linings of the nasal passages that allow for rapid uptake, and secondly by the high efficiency of the nasal passages in depositing inspired particles.

Blood is composed of cells suspended in plasma, and by circulating it delivers both solutes and cells throughout the body. The transport of nutrients, oxygen and the cells themselves ensures a healthy state of the tissues. Exchange processes between the blood and the tissues are a necessary step in the delivery process, and occur by an interaction at the vessel lining. At the smallest scales of the cardiovascular system, the arterioles and capillaries expose the blood to a large wetted surface area, hence facilitating exchange process between the blood and the surrounding tissues. At this micro-circulation scale, the blood cells individually play an important role in the interactions.

Possible applications and emerging technologies concerning these points may include development and calibration of devices to address drug delivery, in the airways by means of nebulisers, while for administration in the blood a range of methods exist for targeted and specialised delivery. Other equipment dedicated to artificial breathing devices or mask protection for hazardous industrial working environment may be considered. Cheap and disposable micro-labs for blood tests, are an ongoing and emerging technology that has seen intense research and development. The applications to medicine and healthcare are evident in both applications, and numerical simulations could greatly assist experimental and clinical studies, as well as the subsequent development of healthcare devices.

This project focuses on the development of integrated models to solve these multidisciplinary problems, and the work can be divided into two topics: i) developing mathematical models and numerical tools; ii) interfacing software code to execute efficiently on large supercomputing facilities and on small clusters. The impact scientifically and technologically lies in exploiting existing supercomputer resources and infrastructure. The project results have been published in scientific journals and conferences. Scientific data emerging from this project, and short multimedia presentations, are available on the web page of the hosting institution.

Regarding the respiratory airways, an extensive high resolution 3D model of a subject was reconstructed from medical scan data. Using this model, extreme large-scale simulations were undertaken on two of the largest European supercomputers: “Fermi” and “Marenostrum”, hosted respectively at CINECA and BSC. The Alya system software, developed in-house at BSC was used to perform these simulations. As a result, thanks to the fine spatial and temporal resolution achieved, and the extensive 3D model used, the intricate detail of flow in the human upper airways of this subject was unravelled. A simple sniff inspiration was investigated. It was found that the flow will assume slow recirculation regions and gentle flapping in some portions of the respiratory tract, while others are characterised by strong jets, vortices and turbulence. The nasal passage is a thin, scroll-like cavity, with undulating walls and protrusions into the breathing passage. Furthermore, the left and right passages exhibit asymmetry in form, that in due both to the nasal cycle (a temporal alteration in the degree of congestion of one side of the nose compared with that of the other) and the supporting bone structure. Due to the high surface area, the flow in the nasal passage remains constrained, and a high degree of temperature and humidity regulation is possible. As inspired air reaches the throat, higher velocity is attained and the flow becomes turbulent, with eddy structures in the order of 10 micrometres. Impressively disparate flow regimes are identified along the airway passages, influencing the local physiological functions at each stage.

The high concentration by volume of blood cells suspended in plasma, results in inter-cellular dynamic interactions as the blood circulates. Numerical methods have been specifically developed to study these complex flow problems. With interest in micro-circulation, as blood flows in arterioles and capillaries, the blood cells must be individually modelled in order to accurately capture these interactions. This results in a complex flow problem, in which blood cells collide, deform and the flow field is disturbed in the wake of the upstream suspended cells. Together, this gives rise to intricate cell motion and deformation, influencing the transport processes observed at these scales.