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Computational analysis of human upper airway aerodynamics

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Abstract

There is a considerable interest in understanding transient human upper airway aerodynamics, especially in view of assessing the effects of various ventilation therapies. Experimental analyses in a patient-specific manner pose challenges as the upper airway consists of a narrow confined region with complex anatomy. Pressure measurements are feasible, but, for example, PIV experiments require special measures to accommodate for the light refraction by the model. Computational fluid dynamics can bridge the gap between limited experimental data and detailed flow features. This work aims to validate the use of combined lattice Boltzmann method and a large eddy scale model for simulating respiration, and to identify clinical features of the flow and show the clinical potential of the method. Airflow was computationally analyzed during a realistic, transient, breathing profile in an upper airway geometry ranging from nose to trachea, and the resulting pressure calculations were compared against in vitro experiments. Simulations were conducted on meshes containing about 1 billion cells to ensure accuracy and to capture intrinsic flow features. Airway pressures obtained from simulations and in vitro experiments are in good agreement both during inhalation and exhalation. High velocity pharyngeal and laryngeal jets and recirculation in the region of the olfactory cleft are observed.

The Lattice-Boltzmann Method combined with Large Eddy Simulations was used to compute the aerodynamics in a human upper airway geometry. The left side of this graphical abstract shows the velocity and vorticity (middle figure in bottom row, and right figure of the right bottom figure) profiles at peak exhalation. The simulations were validated against experiments on a 3D-print of the geometry (shown in the top figures on the right hand side). The pressure drop (right bottom corner) shows a good agreement between experiments and simulations.

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Funding

Compute resources on the Dutch national supercomputer Cartesius were provided by SURFSara through NWO grant 2019/ENW/00768083.

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  1. Engineering Fluid Dynamics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Rutger H.J. Hebbink, Bas J. Wessels, Rob Hagmeijer & Kartik Jain

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Correspondence to Kartik Jain.

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Appendix: : Mesh convergence study

Appendix: : Mesh convergence study

To ensure that the computed solution did not depend on the spatial and temporal resolutions, a mesh convergence study was performed in the case of nasal airflow. Previous findings on suitable mesh sizes for oscillatory [26] and transitional flows [25] were used to get an initial estimate. The convergence study was conducted because nasal airflows were being simulated for the first time using the LBM solver Musubi, and LES turbulence model was being employed. In the mesh convergence study, the breathing velocity profile was scaled to \(\frac {1}{8}\)th of its value to save computing resources.

The spatial and temporal resolutions chosen are listed in Table 1.

Table 1 Spatial (δx) and temporal (δt) resolutions as well as the lattice sites for various mesh densities studied in the mesh convergence study
Full size table

The L1 norm is calculated for the velocity magnitude, where the L1 is defined as the mean of the sum of the absolute differences between the velocity magnitudes on the grids and the velocity magnitude on the finest grid (δx = 0.075 mm) on each time step:

$$ L_{1} = \frac{1}{N} {\sum}_{t=1}^{N}\left( |U_{t} - U_{t, 0.075} |\right) $$
(5)

The results are shown in Fig. 10. It can be seen that the velocity norm decreases linearly for most of the resolutions. Due to the transient nature of the flow, there is a slight fluctuation at resolution h4, which settles down at finer resolutions. Thus, it is inferred that this resolution is sufficient for the simulation of nasal airflow reported in this article. Based on these findings and the scaling of the breathing profile, the resolution of 0.048 mm was employed that resulted in 925 M cells. Further details about lattice parameters and their scaling can be referred in [25].

Fig. 10
figure 10

L1 norm (mm/s) of the velocity magnitude

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Hebbink, R.H., Wessels, B.J., Hagmeijer, R. et al. Computational analysis of human upper airway aerodynamics. Med Biol Eng Comput 61, 541–553 (2023). https://doi.org/10.1007/s11517-022-02716-8

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