The optimal branching asymmetry of a bidirectional distribution tree

Florens, Magali; Sapoval, B.; Filoche, Marcel

doi:10.1016/j.cpc.2010.11.008

Cited by 11 publications

(4 citation statements)

References 20 publications

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“…Therefore, it is particularly adapted to analytical or numerical studies such as the computation of air flow or particle deposition. For instance, by adding airway compliance laws, this model allows computation of the dynamic behavior of the bronchial tree during the breathing cycle (3). Embedding this model in 3D would also permit reproduction and analyses of images of ventilation obtained by NMR of hyperpolarized gas.…”

Section: Discussionmentioning

confidence: 99%

An anatomical and functional model of the human tracheobronchial tree

Florens

Sapoval

Filoche

2011

Journal of Applied Physiology

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The human tracheobronchial tree is a complex branched distribution system in charge of renewing the air inside the acini, which are the gas exchange units. We present here a systematic geometrical model of this system described as a self-similar assembly of rigid pipes. It includes the specific geometry of the upper bronchial tree and a self-similar intermediary tree with a systematic branching asymmetry. It ends by the terminal bronchioles whose generations range from 8 to 22. Unlike classical models, it does not rely on a simple scaling law. With a limited number of parameters, this model reproduces the morphometric data from various sources (Horsfield K, Dart G, Olson DE, Filley GF, Cumming G. J Appl Physiol 31: 207-217, 1971; Weibel ER. Morphometry of the Human Lung. New York: Academic Press, 1963) and the main characteristics of the ventilation. Studying various types of random variations of the airway sizes, we show that strong correlations are needed to reproduce the measured distributions. Moreover, the ventilation performances are observed to be robust against anatomical variability. The same methodology applied to the rat also permits building a geometrical model that reproduces the anatomical and ventilation characteristics of this animal. This simple model can be directly used as a common description of the entire tree in analytical or numerical studies such as the computation of air flow distribution or aerosol transport.

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Section: Discussionmentioning

confidence: 99%

An anatomical and functional model of the human tracheobronchial tree

Florens

Sapoval

Filoche

2011

Journal of Applied Physiology

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“…Various models have been proposed to express the prefactor Z [14,3]. We choose to use the velocity profile proposed in [17].…”

Section: Fluid Dynamics In the Airwaysmentioning

confidence: 99%

Wall shear stress distribution in a compliant airway tree

Stéphano,

Mauroy

2020

Preprint

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In the lung, the walls of the bronchi are protected by a mucus layer that is constantly renewed and motioned toward the oesopharyngeal region. Its role is to capture the inhaled particles and to remove them from the lung. The mucus layer is submitted to a shear stress by the air flow in the bronchi. The conditions under which it induces a displacement of the mucus, such as during cough, are still not clearly established. Nevertheless, the air-mucus interaction justifies several common chest physiotherapy technics used to help the draining of the mucus in prevalent diseases such as asthma, bronchiolitis or cystic fibrosis. Hence, understanding how the wall shear stress distributes in the lung could bring interesting highlights on these therapies.Hence, we develop a mathematical model to study the distribution of the wall shear stress induced by an outgoing air flow in an airway tree. This model accounts for the main physical processes that determines the wall shear stresses, more particularly the compliance of the airways and the air inertia. We show that the wall shear stress exhibits a maximum within the tree whose amplitude and location depend on the amount of air flow and on the "tissue" pressure surrounding the airways. Our analysis suggests that a tuning of the air flow and tissue pressure might allow to control, at least partially, the air-mucus interaction in the lung.

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“…The respiratory system is extremely complex, both in terms of its anatomy and physiology, with the structure naturally designed for optimal gas transport and exchange 1–3 . This complexity is related in particular to the structure of the bronchial tree including millions of airways, dynamic and nonlinear mechanical properties of lung tissues, as well as to dynamic airflow through flexible airways 4–6 …”

Section: Introductionmentioning

confidence: 99%

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways

Polak

2022

Numer Methods Biomed Eng

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The complexity of the human respiratory system causes that one of the main methods of analyzing the dynamic pulmonary phenomena and interpreting experimental results are simulations of its computational models. Among the most compound elements of these models, apart from the bronchial tree structure, is the phenomenon of flow limitation in flexible bronchi, which causes them to collapse with increasing flow, thus their properties, such as resistance, compliance and inertance, are highly nonlinear and time‐varying. Commonly, this phenomenon is ignored, or a distributed model for the airway pressure drop is applied, simulated with a modified numerical solver of this differential equation (ODE). The disadvantages of this solution are the problems with taking into account the inherent singularity of the model and the long computation time due to iterative nature of the ODE procedure. The aim of the work was to derive an algebraic approximation of this distributed model, suitable for implementation in continuous dynamic models, to validate it by comparing the results of simulations with the respiratory system model including approximate and original (ODE solver) numerical procedures, as well as to evaluate possible acceleration of calculations. All simulations, including spontaneous breathing, mechanical ventilation with the optimal ventilatory waveform and forced expiration, proved that algebraic approximation yielded results negligibly differing from the ODE solution, and shortened the computation time by an order. The proposed approach is an attractive alternative in the case of computer implementations of pulmonary models, where simulations of flows and pressures in the complex respiratory system are of primary importance.

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The optimal branching asymmetry of a bidirectional distribution tree

Cited by 11 publications

References 20 publications

An anatomical and functional model of the human tracheobronchial tree

An anatomical and functional model of the human tracheobronchial tree

Wall shear stress distribution in a compliant airway tree

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways

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