Numerical study of the effects of bronchial structural abnormalities on respiratory flow distribution
© The Author(s) 2016
Published: 28 December 2016
The anatomical configurations of respiratory tract would be directly associated with their ventilatory function. It is necessary to fully understand the association between airway configurations and their functions as well as the interactions between different airway segments. In this study, we developed a respiratory airway model to investigate the effects of bronchial structural abnormalities on flow distribution in the bronchi and upper airway.
Derived from computed tomography (CT) scanner data, three-dimensional (3D) finite element (FE) models of healthy human respiratory tracts were developed with anatomically realistic configurations, including the nasal cavity, oral cavity, pharynx, larynx, trachea, and partial bronchi. Abnormal bronchial configurations were built to correspond to four common bronchial diseases. Through numerical simulation, airway configurations of normal and abnormal bronchi were obtained, and flow patterns were compared between normal and abnormal respiratory tracts, as well as the effects of lower airway changes on flow distribution in the upper airway.
The simulation results showed that during inspiration, abnormal bronchial structures can cause flow redistribution in each generation of bronchi and have significant effects on flow distribution in the daughter bronchi of abnormal segments, but no effect on flow distribution of the upper airway. During expiration, abnormal bronchus structures had a remarkable influence on flow distribution in the trachea, while there was no significant difference in flow distribution when airflow passed from the vocal cords and entered the laryngeal cavity.
Therefore, abnormal bronchial structures can affect the downstream flow distribution and cause flow redistribution throughout the entire bronchial branches. During expiration, the configurations of the trachea and glottis can diminish the effects of abnormal bronchial structures on flow distribution.
KeywordsRespiratory tract Trachea Bronchi Biomechanical modelling Numerical simulation
The respiratory tract is the channel of the human body connected to the external environment for air exchange, and consists of structures including the mouth, nose, pharynx, larynx, trachea, and bronchi. The anatomical configurations of each segment are directly associated with their ventilatory function. The structural abnormalities of certain segments can affect flow distribution of other segments in the airway and even lead to pathological changes [1–3]. It is necessary to fully understand the association between airway configurations and their functions as well as the interactions between different airway segments, and to develop numerical platforms for investigating the structural respiratory lesions and help clinicians understand the lesions from the biomechanical point of view.
In recent years, domestic and international researchers have investigated flow patterns and related functions of respiratory airways, including the upper airway, trachea, and bronchi, using numerical simulations and experimental methods [4–7]. However, most of this research has only considered the effects of mouth-open breathing or adopted Weibel’s Type A symmetrical airway model [8, 9]. Developing a realistic configuration of the upper airway, trachea, and partial bronchi and using it as a whole system for investigating airway flow patterns has seldom been reported. Starting from normal airway structures, this study developed realistic airway models from computed tomography (CT) scanner data, consisting of the nasal cavity, oral cavity, pharynx, larynx, trachea, and bronchi extending to the fifth generation. On the basis of normal respiratory structures, the configurations of the bronchial tree were modified to build two common bronchial disease models: cancer and bronchostenosis. Flow distribution in abnormal airways was simulated and compared to that of normal airways, and the effects of bronchial abnormalities on flow distribution of the entire airway were analysed.
The governing equations were Navie-stocks equations. The k-epsilon solver models is used in the simulation. The scheme of SIMPLE is adopted for the pressure–velocity coupling. Boundary conditions were chosen as follows: the nostrils were set as a velocity inlet boundary and a sinusoidal velocity boundary condition was imposed with a 3-s cycle. The tidal volume of respiration was set at 600 ml. After computing the resistances of both nasal cavities, they were essentially equal; therefore, both nostrils were considered as having the same flow rate. A relative pressure condition was placed at the bronchus end (P = 0) that was elongated appropriately to limit the assumption of equivalent pressure and the effects on the downstream airway . Complete respiratory tract walls were treated as rigid with no-slip; i.e., V = 0 m/s.
Velocity profiles of airflow in the normal respiratory track
Velocity profiles of airflow in the abnormal respiratory track
Velocity profiles of airflow in the bronchus
Flow distributions in the left and right primary bronchi under five conditions
Cases 2, 3, and 4 all had unilateral structural abnormalities of the bronchi. Compared to normal airways (Fig. 2), during inspiration, the total airflow entering the right side decreased in the airway of case 2 due to narrowing of the right bronchus, leading to a decrease in maximum flow rate on the right side of Plane 2. In Plane 3, due to the reduced cross-sectional area, the flow rate increased, indirectly increasing the maximum flow rate in Plane 6. Planes 4, 7, and 8 were from the left bronchus. The maximum flow rate in these planes was slightly increased due to increased airflow; however, there were no significant changes in overall velocity profiles. A remarkable vortex structure formed in Plane 5. During expiration, the increased airflows in Planes 4, 7, and 8 led to a higher flow rate, but there were no significant changes in velocity profiles. In Plane 3, the flow rate increased because of the airway narrowing. Plane 2 is located nearby the downstream component of Plane 3, and therefore the flow rate of the right braches in Plane 2 was significantly higher. Plane 1 is downstream of Plane 2, and therefore its velocity profile was different from that of normal airways. In the bronchi of cases 3 and 4, the changing patterns in flow distribution caused by structural changes were similar to that of case 2, and all these changes can result in alterations in flow distribution near or downstream of the structurally altered region. In case 4, the bronchial structural abnormalities were located in the fifth generation bronchus. As seen in Fig. 6, its influence on the overall bronchial flow distribution was smaller than that caused by structural changes of primary bronchi.
Pressure distribution of airflow in the respiratory track
Analysis of the effect of respiratory tract structure on its function
From the flow distributions of normal airways and the airways of four cases with structural abnormalities, it can be concluded that during inspiration, abnormal bronchi configurations didn’t affect the velocity profiles in the trachea or the upstream segments of the upper airway. As the flow-restricted segment of the nasal cavity, the lumen nasi has a narrow air duct and thus the maximum flow rate and a large pressure gradient occurred in this region. The glottis is a regional narrow segment of the airway, where flow accelerates down to the trachea, which is consistent with Lin et al’s findings . The orientation of the glottis on airflow directly affected the flow distribution of the trachea. Therefore, although the cross section of the trachea showed a tubal shape with a narrow opening and a wide end, the high flow rate zone in the upper segment of the trachea remained close to the anterior wall of the bronchi. When flow entered two bronchial branches from the trachea, the high flow rate zone was also divided into two and occurred near the inner bronchial wall. This phenomenon was also reported in studies by Adler  and GroBe . The maximum flow rate was slightly higher in the left bronchus than in the right bronchus. According to Sebastian et al., this was due to the different angles formed between the two bronchi and trachea, and in fact it was also associated with the resistance of both lungs as well as the flow distributions of both branches. Based on the flow distribution of bronchi on both sides, the airway resistance in both branches were similar and slightly greater in the right airway than in the left airway, which is consistent with Katrin et al’s study results . In secondary bronchi, the lower lobe of the bronchus was the extension of the primary bronchus while the upper lobe of the bronchus formed a 90° angle with the primary bronchus. Therefore, the main flow entered the lower bronchus lobe, which was also observed in a study by Soodt . When the configurations of the trachea and bronchus changed due to disease processes, the resistances of both bronchi were altered correspondingly, and therefore airflow was redistributed in both bronchi. In case 1, the tumour at the bifurcation of the trachea and the primary bronchi reduced the cross-sectional area of both primary bronchi (Plane 2) by 50%. Because the cross-sectional areas of both branches were decreased to the same extent, there were no significant changes in flow distribution in both branches. However, due to the decreased cross-sectional area, the flow rate of the cross section increased. The transverse planes of the primary bronchus (Plane 3 and 4) were close to Plane 2. Therefore, although the cross-sectional area remained the same, the maximum flow rate in this cross section increased. This local change had less effect on the distal regions (such as Plane 8). In case 2, the decreased cross-sectional area of the right primary bronchus led to an increase in airway resistance in the right branches. While the entire respiratory flow remained the same, the flow entering the right airway was reduced when more flow entered the left airway. Due to the decreased cross-sectional area of the right airway, the flow rate increased in both the left and right bronchi (Plane 3 and 4). In case 3, the pattern changes of flow distribution in the bronchus were similar to case 2. In a study by Kim , it was shown that narrowing of the right bronchus led to flow redistribution as well as an increase in the maximum flow rate in both bronchi. Case 4 had a bronchostenosis of the fifth generation of the right bronchus (90% of original size). The narrowing of this bronchus caused an increase in total resistance in the right bronchus; thus, airflow decreased in the right branches and the airflow increased in the left branches. Because the narrowing only occurred in one branch of the fifth generation bronchi, there was no significant influence on total airway resistance of the right branches, and therefore fewer changes appeared in both the left and right flow distributions, as well as in the flow rate of both airways. During expiration, flow moved down from the primary bronchus to the trachea and entered the upper airway. The bronchial flow was upstream of the entire airway: the flow distribution of the bronchi can directly affect that of the trachea and further affect the upper airway. The flow from two primary bronchi converge into the trachea and form an M-shaped flow pattern with double peaks in the trachea, which was also observed in the study by Sebastian et al. . After the flow moved a certain distance in the trachea and nearly reached a steady state, the flow pattern changed into a single peak . In the four abnormal cases, structural changes in the local bronchus led to changes in the velocity profile at the bifurcation of the trachea and primary bronchus (Plane 2). The positions of the changes in cases 1–3 were located near Plane 2, and therefore had greater influence on the velocity profile of Plane 2. On the other hand, in case 4, the structural change occurred in the fifth generation bronchus, and therefore the velocity profile of Plane 2 was less affected and was similar to that of the normal case. When flow entered the trachea through the bronchus, the flow velocity profile in the trachea was affected by the flow upstream of Plane 2. Hence, there were significant differences in the velocity profile of the trachea between case 1–3 and the normal case, while the flow velocity profile of the trachea of case 4 was similar to the normal case. The trachea has a length of 10–12 cm, and when flow was moving through the trachea, the velocity profile of the transverse planes will gradually reach a steady state. When flow was passing from Plane 2 to Plane 1, the difference in the flow velocity profile of Plane 1 between cases 1–3 and the normal case decreased. When the flow arrived at the region inferior to the glottis, the difference in the flow velocity profiles of transverse planes was further reduced. The air duct at the glottis is relatively narrow, which can accelerate the flow that passes by. From the glottis to the larynx, the patterns of the flow velocity profiles were very similar and the influence on downstream flow distribution of the nasal cavity was also very small. Therefore, it can be concluded that one of the functions of the trachea and glottis structures is to eliminate the influence from the changes of the altered flow distribution caused by structural abnormalities of the bronchus, on the flow distribution in the upper airway. Ma  found that in each generation of bronchial branches, the flow distribution tended to reach a stabilised distribution within a short distance, which might explain the above phenomenon.
From the pressure distributions in the normal airway and the abnormal airways of the four cases, it was apparent that the pressure difference in the nasal cavity was approximately 50% of the entire respiratory tract during expiration and the largest pressure gradient was found in the lumen nasi. A relatively remarkable pressure gradient also occurred in the glottis. The overall pressure distributions in all cases were essentially similar, and the larger pressure gradients were only found in cases 2–4 at the region of the narrowed bronchi. There were no significant differences in the pressure difference between normal airways and the abnormal airways of the four cases. In case 1, the tumour occupied 50% of the cross-section of the airway at the bifurcation of the trachea and primary bronchus. However, there were no significant pressure gradients, indicating that the air duct was relatively wide at the bifurcation. Even though the cross-sectional area had changed to certain degree, the ventilatory function remained relatively unaffected. For cases 2 and 3 with unilateral narrowing of a local primary bronchus, because the left and right primary bronchi are parallel airways, when the narrowing occurred in the unilateral local region to a limited extent (70% in left, 80% in right), the total resistance was not greatly affected and the total pressure drop was only slightly higher than that of the normal case. Case 4 had a bronchostenosis of the fifth generation bronchus. The fifth generation bronchus has a limited influence on the overall airway resistance, and therefore pressure differences in case 4 were only slightly higher than that of the normal case, while it was lower than that of cases 2 and 3. During expiration, the pressure distribution was similar to the pressure gradient pattern during inspiration, and the pressure gradient was more significant at the local stenosis in the airway, such as the lumen nasi, glottis, and the bronchial stenosis of the abnormal airway.
It can be concluded from the above that there were some common patterns in airway flow distribution. The narrowness of unilateral bronchi led to an increase in airway resistance in the same branches and decreased airflow. Meanwhile, due to the decreased area of the narrowed transverse planes, the flow rate in the planes was increased, as did the pressure gradients in the adjacent area. Meanwhile, the airflow increased in the airway of the other side, and therefore the total flow velocity increased. The influence of the narrowed unilateral airway on the flow distribution of both airways was related to the location of the stenosis. The bronchostenosis of a higher bronchial generation would have greater effects on the flow distribution ratio for both sides. During expiration, local bronchostenosis can affect the flow velocity profile in the trachea, and the effects can be largely diminished by the narrow and long configurations of the trachea and glottis. After airflow entered the laryngeal cavity, the velocity profiles of abnormal cases were almost the same as in the normal case.
Some limitations of this study have to be discussed. First, in this paper, only one numerical model was made. Due to the difference in the structure of human body, additional cases will be investigated in the future, which will make the conclusions more general. Second, the model contains only a small portion of the bronchus, due to the limitation in the resolution of the CT used in current study. Developing bronchial models from higher resolution CT images will better reflect the mutual influence between the various parts of the respiratory tract. Finally, in the numerical simulation of airflow in the respiratory tract, the turbulence model was selected. In the nasal and pharyngeal cavity, the airflow is transitional flow or turbulence flow, and in the bronchi the airflow should be laminar flow, which is determined by the function of different parts of the respiratory tract. We are continuing our efforts to solve the above problems to get more reliable results.
SY and YL were responsible for computational modeling and data analysis part. JW and XS were responsible for the CT acquisition part. All authors (1) have made substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; (2) have been involved in drafting the manuscript or revising it critically for important intellectual content; and (3) have given final approval of the version to be published. Each author has participated sufficiently in the work to take public responsibility for appropriate portions of the content. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
About this supplement
This article has been published as part of BioMedical Engineering OnLine Volume 15 Supplement 2, 2016. Computational and experimental methods for biological research: cardiovascular diseases and beyond. The full contents of the supplement are available online http://biomedical-engineering-online.biomedcentral.com/articles/supplements/volume-15-supplement-2.
Availability of data and materials
All data are fully available without restriction.
Ethics approval and consent to participate
This study was approved by the ethics committee of the second affiliated hospital of Dalian medical university. Written consent was obtained from all participates.
Publication of this article was funded by the National Nature Science Foundation of China (11572079, 11372069, 11472074, 31500765).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
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