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There is ongoing and rapid advancement in approaches to modelling the fate of exhaled particles in different environments relevant to disease transmission. It is important that models are verified by comparison with each other using a common set of input parameters to ensure that model differences can be interpreted in terms of model physics rather than unspecified differences in model input parameters. In this paper, we define parameters necessary for such benchmarking of models of airborne particles exhaled by humans and transported in the environment during breathing and speaking.

Additional material on breathing rates, exhaled particle size distributions and relative viral loads

The potential for acute shortages of ventilators at the peak of the COVID-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs, we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard set-up where we simulate the introduction of T-splitters to supply air to two patients and a modified set-up where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard set-up, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified set-up, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate that, with appropriate modifications, two patients could be supported from a single ventilator with independent control of tidal volumes.

The potential for acute shortages of ventilators at the peak of the Covid-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard setup where we simulate the introduction of T-splitters to supply air to two patients and a modified setup where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard setup, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically-significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified setup, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate that, with appropriate modifications, two patients could be supported from a single ventilator with independent control of tidal volumes.Data, code and materials:The Simulink models used in this research have been uploaded to a Git repository at the following address: https://github.com/splitvent/splitvent.

Although medical imaging can provide relatively accurate geometric data of in vivo bypass grafts, as will be discussed in Section 12.1.2, to obtain an understanding of the general flow features it is instructive to consider an idealisation of a distal bypass graft. In this example we therefore consider the problem shown in Fig. 12.1, which consists of three vessels, all of the same diameter D, where the bypass (connecting) vessel has a centreline length of 3D and the host vessel is represented by two co-aligned vessels of lengths 5D (distal) and 10D (proximal) from the junction.

This review outlines some of the different scales involved in computationally modelling arterial networks. Starting at the largest O(1m) scale we highlight current activities in reduced modelling of the pulse waves. We then focus on the O(10-1m) scale and provide an example of how CFD can be applied to understand the role of mixing in small amplitude helical pipes at physiologically relevant flow conditions. Finally we motivate the interaction at O(10-3m) scale by considering how localised flow features are suggestive of different types of arterial disease patterns.