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Research Papers

Dynamics of Voluntary Cough Maneuvers: A Theoretical Model

[+] Author and Article Information
Shailesh Naire

School of Computing and Mathematics, Keele University, Keele ST4 5BG, UKs.naire@maths.keele.ac.uk

J Biomech Eng 131(1), 011010 (Nov 24, 2008) (9 pages) doi:10.1115/1.3005168 History: Received October 18, 2007; Revised August 28, 2008; Published November 24, 2008

Voluntary cough maneuvers are characterized by transient peak expiratory flows (PEFs) exceeding the maximum expiratory flow-volume (MEFV) curve. In some cases, these flows can be well in excess of the MEFV, generally referred to as supramaximal flows. Understanding the flow-structure interaction involved in these maneuvers is the main goal of this study. We present a simple theoretical model for investigating the dynamics of voluntary cough and forced expiratory maneuvers. The core modeling idea is based on a 1D model of high Reynolds number flow through flexible-walled tubes. The model incorporates key ingredients involved in these maneuvers: the expiratory effort generated by the abdominal and expiratory muscles, the glottis, and the flexibility and compliance of the lung airways. Variations in these allow investigation of the expiratory flows generated by a variety of single cough maneuvers. The model successfully reproduces the transient PEFs, reported in cough studies. The amplitude of the PEFs is shown to depend on the cough generation protocol, the glottis reopening time, and the compliance of the airways. The particular highlight is in simulating supramaximal PEFs for very compliant tubes. The flow-structure interaction mechanisms behind these are discussed. The wave-speed theory of flow limitation is used to characterize the PEFs. Existing hypotheses of the origin of PEFs, from cough and forced expiration experiments, are also tested using this model. This modeling framework could be a first step toward more sophisticated cough models as well as in developing ideas for new bench-top experiments.

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Figures

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Figure 1

Sketch of the model lung geometry

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Figure 2

An illustration of the prescribed time evolution of the external pressure Pe (solid line) and the glottis resistance η (dashed line)

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Figure 3

Qa(1,t) versus V for varying Pe,max during a forced expiration

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Figure 4

Qa(1,t) versus (a) V and (b) t. Curve 1: forced expiration with Pe,max=10, curve 2: almost instantaneous glottis reopening; curves 3 and 4: glottis reopening times 5 and 10, respectively.

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Figure 5

Qa(1,t) versus V for varying Pe,max during a forced expiration

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Figure 6

Evolution of A, Ua, and pa for a forced expiration with Pe,max=7 ((a), (b), and (c)) and cough with almost instantaneous reopening of glottis ((d), (e), and (f))

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Figure 8

Steady-state solutions of Eq. 6 (solid lines) characterized by the exit flux Qa(1) versus the pressure drop pa(0)−pa(1), for varying Pe,max. The solid circles are the corresponding steady-state solutions of the initial value problem Eq. 3. The dashed line is an oscillatory instability, which develops from the steady-state solution corresponding to Pe,max=9.

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Figure 7

Qa(1,t) versus (a) V and (b) t. Curve 1: forced expiration with Pe,max=7; curve 2: almost instantaneous glottis reopening; curves 3 and 4: glottis reopening times 5 and 10, respectively.

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