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Various reduced-order surrogate models for fluid flow and mass transfer in human bronchial tree

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Abstract

The bronchial tree plays a main role in the human respiratory system because the air distribution throughout the lungs and gas exchange with blood occur in the airways whose dimensions vary from several centimeters to micrometers. Organization of about 60,000 conducting airways and 33 million respiratory airways in a limited space results in a complex structure. Due to this inherent complexity and a high number of airways, using target-oriented dimensional reduction is inevitable. In addition, there is no general reduced-order model for various types of problems. This necessitates coming up with an appropriate model from a variety of different reduced-order models to solve the desired problem. Lumped formulation, trumpet, or typical path model of whole or parts of bronchial tree are frequently used reduced-order models. On the other hand, using any of these models results in underestimation of flow heterogeneity leading to inaccurate prediction of the systems whose mechanisms depend on the fluid heterogeneity. In this study, a simple robust model combining mechanistic and non-mechanistic modeling approaches of the bronchial tree is proposed which overcomes the limitations of the previous reduced-order models and gives the same results of a detailed mechanistic model for the first time. This model starts from an accurate multi-branching model of conducting and respiratory airways (i.e., the base model) and suggests a proxy model of conducting airway and reduced-order model of respiratory airways based on the base model to significantly reduce computational cost while retaining the accuracy. The combination of these models suggests various reduced-order surrogate models of the human bronchial tree for different problems. The applications and limitations of each reduced-order model are also discussed. The accuracy of the proposed model in the prediction of fluid heterogeneity has been examined by the simulation of multi-breath inert gas washout because the alveolar slope is the reflection of fluid heterogeneity where the computational time decreases from 121 h (using the base model) to 4.8 s (using the reduced-order model). A parallel strategy for solving the equations is also proposed which decreases run time by 0.18 s making the model suitable for real-time applications. Furthermore, the ability of the model has been evaluated in the modeling of asthmatic lung as an instance of abnormal lungs, and in the modeling of O2–CO2 exchange as an instance of nonlinear reacting systems. The results indicate that the proposed model outperforms previous models based on accuracy, robustness, and run time.

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Abbreviations

AS:

Air sac

C f :

Estimated concentration at acinus entrance

C i :

Fractional concentration

C p :

Concentration at acinus entrance at end of pause

\(C_{TB}^{e}\) :

Concentration at acinus entrance during exhalation

d :

Diameter of airway

D :

Diffusion coefficient of species in gas phase

d eff :

Effective diameter of airway

D M :

Diffusion coefficient of species through plasma layer

FRC :

Functional residual capacity

g strength :

Strength of the gravitational gradient

gen:

Generation

h :

Height of respiratory airway at lung

h min :

Minimum height of respiratory airways at lung

h max :

Maximum height of respiratory airways at lung

k :

Overall mass transfer coefficient

LCI:

Lung clearance index

N typ :

Number of typical paths

P i :

Partial pressure of i'th species in gas phase

P i,b :

Partial pressure of i'th species in blood

P pl :

Pleural pressure

Q :

Flow rate

Q i :

Total inhalation flow rate

Q seg :

Flow rate at entrance of bronchopulmonary segment

Q TB, i :

Flow rate at i'th TB

R(Q):

Resistance of airway

RB:

Respiratory bronchiole

Re:

Reynolds number

R p :

Range of pleural pressure

S tb :

Ratio of total surface area to pulmonary blood volume

Std :

Ratio of total surface area to surface area of airways excluding alveoli.

t :

Time

t p :

Time at end of pause

TB :

Terminal bronchiole

u :

Mean axial velocity

V :

Volume

V acinus :

Volume of acinus

Vt:

Tidal volume

z :

Distance along the airways from trachea

ℂ:

Compliance

δ:

Thickness of respiratory membrane

ΔP :

Pressure drop along airway

σ:

Solubility of species in blood

τi :

Adjusted parameter of reduced-order model for i'th TB

τ mean :

Mean of τi’s

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Authors and Affiliations

  1. Department of Chemical and Petroleum Engineering, Sharif University of Technology, P. O. Box 11365-9465, Tehran, Iran

    Zeinab Abbasi & Ramin Bozorgmehry Boozarjomehry

Authors
  1. Zeinab Abbasi
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  2. Ramin Bozorgmehry Boozarjomehry
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Contributions

ZA and RB participated in ideas, development and design of the study, and evolution of the research goals. ZA implemented the computer codes using C++, validated the model results with experimental data, wrote the initial draft, and participated in the editing and revision of final version of the manuscript. RB supervised the research, edited, and revised the manuscript.

Corresponding author

Correspondence to Ramin Bozorgmehry Boozarjomehry.

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Abbasi, Z., Bozorgmehry Boozarjomehry, R. Various reduced-order surrogate models for fluid flow and mass transfer in human bronchial tree. Biomech Model Mechanobiol 20, 2203–2226 (2021). https://doi.org/10.1007/s10237-021-01502-z

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  • DOI: https://doi.org/10.1007/s10237-021-01502-z

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