# A Conjugate Fluid–Porous Approach for Simulating Airflow in Realistic Geometric Representations of the Human Respiratory System

TL;DR: Results are presented for a realistic lung geometry obtained from computed tomography (CT) images, which show the method's potential as being more efficient and practical than attempting to directly simulate flow in the full lung.

Abstract: Simulation of flow in the human lung is of great practical interest as a means to study the detailed flow patterns within the airways for many physiological applications. While computational simulation techniques are quite mature, lung simulations are particularly complicated due to the vast separation of length scales between upper airways and alveoli. Many past studies have presented numerical results for truncated airway trees, however, there are significant difficulties in connecting such results with respiratory airway models. This article presents a new modeling paradigm for flow in the full lung, based on a conjugate fluid-porous formulation where the upper airway is considered as a fluid region with the remainder of the lung being considered as a coupled porous region. Results are presented for a realistic lung geometry obtained from computed tomography (CT) images, which show the method's potential as being more efficient and practical than attempting to directly simulate flow in the full lung.

## Summary (1 min read)

### 1 Introduction

- The ability to numerically simulate flow in the human lung is of great interest to the medical community because of the potential advancements in respiratory drug delivery, particle deposition, etc., that can be attained with detailed knowledge of the flow patterns within the lung [1].
- As computational power has increased over the years, the total number of airway segments considered in upper airway simulations has increased from seven [3] to over 1400 [11] (although the computational mesh was not sufficiently refined in this case to have grid-independent results).
- The authors hypothesize that the large upper airways can be treated as a fluid region and the remaining airways and alveoli can be treated as a connected, coupled porous region where the flow is driven by the moving boundary of the lung.
- Finally, results are presented using the coupled fluid–porous model of the lung solved using the proposed numerical method.

### 3 Results and Discussion

- The model for air flow in the human lung described in Sec. 2 was run for five full breath cycles to ensure that any initial transient behavior was dissipated and results were extracted from the final full breath cycle that was computed.
- In Figs. 4(e)–4(g), it is shown that the pressure is lower near the base of the lung as the air is drawn into the lung.
- These figures show the velocity magnitude dropping significantly after the main bronchi bifurcate, such that the velocity vectors are hardly visible.
- With the results presented, it is important to put into perspective the advantages of the proposed approach to simulating processes in the lung.
- To estimate the number of control volumes actually required, consider the work of Yin et al. [17] who were able to obtain grid-independent results in a realistic 4–5 generation airway geometry using 4.6 106 control volumes.

### 4 Conclusions

- In summary, the development of a numerical method for computing flows in conjugate fluid–porous domains with moving boundaries has been presented and applied to the simulation of flow in a complex, physiologically realistic geometry of the human lung.
- This approach provides a convenient method of simulating processes in the full lung that may be considerably more efficient than simulating flow in large airway trees, since as the airways become smaller and more numerous, the computational costs increase dramatically.

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##### Citations

385 citations

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### Cites methods from "A Conjugate Fluid–Porous Approach f..."

...…modeling air flow in the lung by considering the development and closure of the associated governing equations using the method of volume-averaging (Gray, 1975; Whitaker, 1967), which is then relatively straightforward to couple with models for the upper airways, as in DeGroot and Straatman (2016)....

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...The permeability model described in this work has been previously implemented in conjugate simulations of airflow in the human lung by DeGroot and Straatman (2016)....

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...DeGroot and Straatman (2016) used this modeling concept and the method of volume averaging to develop a conjugate fluid-porous CFD model for the whole lung, where the upper airways were considered as a pure fluid region and the remainder of the lung volume was considered to be porous....

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...It should be taken into consideration that the simulations of DeGroot and Straatman (2016) were conducted for about 80% of the normal tidal volume for breathing, so the pressure drop would be expected to be somewhat smaller....

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2 citations

##### References

5,189 citations

### "A Conjugate Fluid–Porous Approach f..." refers methods in this paper

...The segmentation obtained in OSIRIX was then exported as a new image series and segmented using ITK-SNAP [42], which produced significantly smoother surfaces than OSIRIX....

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...The truncated airway tree was extracted using the segmentation software ITK-SNAP [42], however, only a limited number of bifurcations were captured to prevent the segmented volume from leaking into regions of the lung outside of the airways....

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1,646 citations

### "A Conjugate Fluid–Porous Approach f..." refers methods in this paper

...The resulting segmentation was exported as a stereolithography (STL) file and was smoothed and decimated, to reduce the total number of facets, using MESHLAB.3 The remaining lung volume was segmented by first using the automatic threshold segmentation feature in OSIRIX [43], however, due to limitations in the segmentation algorithm, it was not possible to exclude the airway tree from the segmented volume....

[...]

...The segmentation obtained in OSIRIX was then exported as a new image series and segmented using ITK-SNAP [42], which produced significantly smoother surfaces than OSIRIX....

[...]

...The remaining lung volume was segmented by first using the automatic threshold segmentation feature in OSIRIX [43], however, due to limitations in the segmentation algorithm, it was not possible to exclude the airway tree from the segmented volume....

[...]

1,362 citations

1,116 citations

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##### Frequently Asked Questions (2)

###### Q2. What future works have the authors mentioned in the paper "A conjugate fluid-porous approach for simulating airflow in realistic geometric representations of the human respiratory system" ?

At this stage, the conjugate fluid–porous approach shows promise as an efficient method of simulating air flows in the lung, given that the predicted pressure drop across all airways is reasonable, however, detailed comparisons to experimental measurements should be considered in the future for validation or calibration purposes.