# Multiscale CT-Based Computational Modeling of Alveolar Gas Exchange during Artificial Lung Ventilation, Cluster (Biot) and Periodic (Cheyne-Stokes) Breathings and Bronchial Asthma Attack

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model of the Respiratory Gas Flow in the Lung

#### 2.2. Boundary Conditions

#### 2.3. Mathematical Model of the Oxygen and Carbon Dioxide Transport in the Lung

#### 2.4. Numerical Implementation

#### 2.5. Computed Tomography (CT) Data Processing

## 3. Results

#### 3.1. The Model Validation

#### 3.2. Carbon Dioxide Elimination Efficiency during Artificial Ventilation

#### 3.3. The Study of Pathological Breathing Patterns

#### 3.4. Asthma Model

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CT | Computed tomography |

FSI | Fluid-structure interaction |

ARR | Artificial respiratory rate |

## Appendix A

Symbol | Value | Unit |
---|---|---|

$\rho $ | 1.23 × 10^{−6} | $\mathrm{kg}/{\mathrm{cm}}^{3}$ |

$\eta $ | 1.8 × 10^{−3} | $\mathrm{kg}/\left(\mathrm{cm}\text{\hspace{0.17em}}\mathrm{s}\right)$ |

${\theta}_{{\mathrm{O}}_{2}}$ | 0.17 | ${\mathrm{cm}}^{2}/\mathrm{s}$ |

${\theta}_{{\mathrm{CO}}_{2}}$ | 0.16 | ${\mathrm{cm}}^{2}/\mathrm{s}$ |

${D}_{{\mathrm{O}}_{2}}$ | 1.2 × 10^{−3} | $\mathrm{l}/\mathrm{s}$ |

${D}_{{\mathrm{CO}}_{2}}$ | 6.7 × 10^{−2} | $\mathrm{l}/\mathrm{s}$ |

${E}_{a}$ | 0.5 | $\mathrm{kPa}/\mathrm{l}$ |

$\nu $ | 0.16 | $\mathrm{Hz}$ |

${V}_{0}^{tot}$ | 5 | $\mathrm{l}$ |

${p}_{g}$ | 1.3 | $\mathrm{kPa}$ |

${p}_{atm}$ | 101.3 | $\mathrm{kPa}$ |

${V}_{blood}$ | 4 | $\mathrm{l}$ |

${V}_{minute}$ | 5 | $\mathrm{l}$ |

${Q}_{{\mathrm{O}}_{2}}^{b}$ | 0.25 | $\mathrm{l}/\mathrm{min}$ |

${Q}_{{\mathrm{CO}}_{2}}^{b}$ | 0.2 | $\mathrm{l}/\mathrm{min}$ |

${C}_{{\mathrm{O}}_{2}}^{atm}$ | 0.209 | |

${C}_{{\mathrm{CO}}_{2}}^{atm}$ | 2.8 × 10^{−4} | |

${T}_{pt}$ | 1 | $\mathrm{min}$ |

**Table A2.**Parameters of the 1D structure of the tracheobronchial tree (Figure 1b).

Index | Length, $\mathbf{cm}$ | Diameter, $\mathbf{cm}$ | ${\mathit{c}}_{0},\text{\hspace{0.17em}}\mathbf{cm}/\mathbf{s}$ |
---|---|---|---|

1 | 12.49 | 1.38 | 7700 |

2 | 5.41 | 0.87 | 7382 |

3 | 2.86 | 1.11 | 7382 |

4 | 1.25 | 0.68 | 7064 |

5 | 1.63 | 0.66 | 7064 |

6 | 2.45 | 0.84 | 7064 |

7 | 1.82 | 0.53 | 7064 |

8 | 2.32 | 0.25 | 6747 |

9 | 1.5 | 0.47 | 6747 |

10 | 3.86 | 0.26 | 6747 |

11 | 1.02 | 0.43 | 6747 |

12 | 2.1 | 0.44 | 6747 |

13 | 0.6 | 0.64 | 6747 |

14 | 0.54 | 0.4 | 6747 |

15 | 1,29 | 0.27 | 6747 |

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**Figure 1.**(

**a**) 3D segmentation of the individual computed tomography (CT) data of the tracheobronchial tree; (

**b**) 1D structure based on the 3D segmentation.

**Figure 2.**Comparison of the calculated and measured alveolar air flow (L/sec): curve—the data from [29], dots—simulations.

**Figure 3.**Comparison of the calculated and measured alveolar pressure (kPa): curve—the data from [29], dots—simulations.

**Figure 5.**Alveolar concentration of ${\mathrm{CO}}_{2}$: (1) Periodic breathing; (2) Cluster breathing; (3) normal breathing.

**Figure 6.**Alveolar concentration of ${\mathrm{O}}_{2}$: (1) Periodic breathing; (2) Cluster breathing; (3) normal breathing.

**Figure 7.**(1) Tidal volume; (2) Alveolar ${\mathrm{O}}_{2}$ concentration; (3) Alveolar ${\mathrm{CO}}_{2}$ concentration.

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**MDPI and ACS Style**

Golov, A.; Simakov, S.; Soe, Y.N.; Pryamonosov, R.; Mynbaev, O.; Kholodov, A.
Multiscale CT-Based Computational Modeling of Alveolar Gas Exchange during Artificial Lung Ventilation, Cluster (Biot) and Periodic (Cheyne-Stokes) Breathings and Bronchial Asthma Attack. *Computation* **2017**, *5*, 11.
https://doi.org/10.3390/computation5010011

**AMA Style**

Golov A, Simakov S, Soe YN, Pryamonosov R, Mynbaev O, Kholodov A.
Multiscale CT-Based Computational Modeling of Alveolar Gas Exchange during Artificial Lung Ventilation, Cluster (Biot) and Periodic (Cheyne-Stokes) Breathings and Bronchial Asthma Attack. *Computation*. 2017; 5(1):11.
https://doi.org/10.3390/computation5010011

**Chicago/Turabian Style**

Golov, Andrey, Sergey Simakov, Yan Naing Soe, Roman Pryamonosov, Ospan Mynbaev, and Alexander Kholodov.
2017. "Multiscale CT-Based Computational Modeling of Alveolar Gas Exchange during Artificial Lung Ventilation, Cluster (Biot) and Periodic (Cheyne-Stokes) Breathings and Bronchial Asthma Attack" *Computation* 5, no. 1: 11.
https://doi.org/10.3390/computation5010011