Research Papers

The Role of Airway Shunt Elastance on the Compartmentalization of Respiratory System Impedance

[+] Author and Article Information
Jason H. T. Bates

Department of Medicine,
Larner College of Medicine,
University of Vermont,
Burlington, VT 05405
e-mail: jason.h.bates@uvm.edu

Manuscript received September 12, 2018; final manuscript received October 24, 2018; published online January 18, 2019. Assoc. Editor: Chun Seow.

ASME J of Medical Diagnostics 2(1), 011001 (Jan 18, 2019) (8 pages) Paper No: JESMDT-18-1052; doi: 10.1115/1.4042308 History: Received September 12, 2018; Revised October 24, 2018

An inverse model consisting of two elastic compartments connected in series and served by two airway conduits has recently been fit to measurements of respiratory impedance in obese subjects. Increases in the resistance of the distal conduit of the model with increasing body mass index have been linked to peripheral airway compression by mass loading of the chest wall. Nevertheless, how the two compartments and conduits of this simple model map onto the vastly more complicated structure of an actual lung remain unclear. To investigate this issue, we developed a multiscale branching airway tree model of the respiratory system that predicts realistic input impedance spectra between 5 and 20 Hz with only four free parameters. We use this model to study how the finite elastances of the conducting airway tree and the proximal upper airways affect impedance between 5 and 20 Hz. We show that progressive constriction of the peripheral airways causes impedance to appear to arise from two compartments connected in series, with the proximal compartment being a reflection of the elastance of upper airway structures proximal to the tracheal entrance and the lower compartment reflecting the pulmonary airways and tissues. We thus conclude that while this simple inverse model allows evaluation of overall respiratory system impedance between 5 and 20 Hz in the presence of upper airway shunting, it does not allow the separate contributions of central versus peripheral pulmonary airways to be resolved.

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Grahic Jump Location
Fig. 1

Example of a Horsfield airway branching structure with Δ=2. The airways become progressively wider and longer with increasing order number, while every terminal airway (order 1) terminates in an identical tissue unit (circles).

Grahic Jump Location
Fig. 2

Electrical analog of the impedance,Zk, subtended by an airway of order k. The airway flow resistance (Rk) and gas inertance (Ik) are connected in series, and their sum is itself in series with the parallel combination of the two downstream daughter impedances Zk−1 and Zk−1−Δ. The result is then connected in parallel with the elastance (Ek) of the parent airway.

Grahic Jump Location
Fig. 3

Electrical analog of the complete model showing how a shunt elastance (Eshunt) due to the compliance upper airways operates in parallel with the impedance of the respiratory system (Zrs)

Grahic Jump Location
Fig. 5

Impedance of human respiratory system between 5 and 20 Hz representing (a) normal healthy conditions (rN=0.75 cm, γ=0.86, HL=30 cmH2O L−1, and Etis=30 cmH2O), (b) uniform relative constriction of all airways (rN=0.5 cmH2O, γ=0.86, HL=30 cmH2O L−1, and Etis=30 cmH2O), (c) peripheral airway constriction (rN=0.75 cm, γ=0.84, HL=30 cmH2O L−1, and Etis=30 cmH2O), and (d) alveolar consolidation (rN=0.75 cm, γ=0.84, HL=30 cmH2O L−1, and Etis=100 cmH2O). Thick solid line—airway elastance and shunt elastance not included; thin solid line—compressibility of airways gas included; dashed line—airway gas compressibility and wall distensibility included; and short-dashed line—gas compressibility, wall distensibility, and shunt elastance included.

Grahic Jump Location
Fig. 6

Fit of the two-compartment inverse model (solid lines) to the real part (solid symbols) and imaginary part (open symbols) of Z in the presence of severe airway constriction: (a) constriction concentrated peripherally by setting γ=0.82 and (b) constriction uniform at all levels in the airway tree by setting RN=0.35 cm. In each case, the remaining model parameters were set at their baseline values, with airway tree and upper airway elastances included.

Grahic Jump Location
Fig. 7

Parameters of the two-compartment inverse model (Fig.4) versus degree of peripheral airway constriction determined by the value of γ in the simulation model. (a) Solid line—peripheral resistance (Rp) and dashed line—total airway tree resistance in the simulation model. (b) Solid line—peripheral compartment elastance (Ep) and dashed line—value of total tissue elastance in the simulation model. (c) solid line—central compartment elastance (Ec) and dashed line—value of upper airway shunt elastance in the simulation model.



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