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TECHNICAL PAPERS: Fluids/Heat/Transport

A Mathematical Model of Alveolar Gas Exchange in Partial Liquid Ventilation

[+] Author and Article Information
Vinod Suresh, Joseph C. Anderson, James B. Grotberg

Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109

Ronald B. Hirschl

Department of Surgery, University of Michigan, Ann Arbor, MI 48109

J Biomech Eng 127(1), 46-59 (Mar 08, 2005) (14 pages) doi:10.1115/1.1835352 History: Received December 01, 2003; Revised September 08, 2004; Online March 08, 2005
Copyright © 2005 by ASME
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Figures

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Micrograph of mammalian lung parenchyma (200×) showing alveolar sac and associated alveoli (courtesy of Professor Rick Gillis, Department of Biology University of Wisconsin-La Crosse)
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Schematic of the alveolar sac model. An oscillating spherical shell of radius RS(t) encapsulated by a tissue layer of thickness h represents the sac. A well-mixed capillary blood compartment perfused at a constant blood flow rate Q̇ surrounds the sac. A well-mixed central core of radius Rg(t) inside the sac supplies fresh gas at a constant partial pressure Pin during inspiration and removes expired gas at partial pressure Pg(t) during expiration.
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Waveform of the duty cycle with I:E=1:2 over one breath. Time is normalized with the breathing period, 2π/ω, and the sac radius with the minimum radius, RFRC. The maximum radius is equal to RFRC(1+δ) and occurs at end inspiration.
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Partial pressure profiles during GV: (a) PO2 during inspiration, (b) PO2 during expiration, (c) PCO2 during inspiration, (d) PCO2 during expiration. Static diffusion profile is plotted for comparison. All profiles in the sac are flat because of the relatively high diffusivities of O2 and CO2 in air. Profiles are linear in the tissue layer; s is a normalized radial coordinate [see Eq. (21)]. The scale of the tissue layer is greatly exaggerated.
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Partial pressure profiles in the PFC and tissue layers during PLV: (a) PO2 during inspiration, (b) PO2 during expiration, (c) PCO2 during inspiration, (d) PCO2 during expiration. The static diffusion profile is plotted for comparison. Significant partial pressure gradients are seen in the PFC layer. Gradients are larger in the convective model during inspiration compared to static diffusion. Profiles are linear in the tissue. s is a normalized radial coordinate [see Eq. (21)]. The scale of the tissue layer is greatly exaggerated.
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Effect of varying RR at VT=7.5 ml/kg [(a) and (b)] and varying VT at RR=10 breaths/min [(c) and (d)] on PCO2 and PCCO2.Q̇N=3.57×10−4ml/min; circled points correspond to V̇A/Q̇≈1.
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Effect of varying RR at VT=7.5 ml/kg [(a) and (b)] and varying VT at RR=10 breaths/min [(c) and (d)] on (Pg-PC)O2 and (PC-Pg)CO2.Q̇N=3.57×10−4ml/min. Circled points correspond to V̇A/Q̇≈1.
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Effect of varying RR and VT at constant V̇A on (a) PCO2, (b) PCCO2, (c) (Pg-PC)O2, (d) (PC-Pg)CO2.Q̇N=3.57×10−4ml/min.
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Effect of varying RR at VT=0.5 ml/kg [(a) and (b)] and VT at RR=240 breaths/min [(c) and (d)] on PCO2 and PCCO2.Q̇N=3.57×10−4ml/min; circled points correspond to V̇A/Q̇≈1;Q̇N=3.57×10−4ml/min; circled points correspond to V̇A/Q̇≈1.
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Effect of varying RR at VT=0.5 ml/kg [(a) and (b)] and VT at RR=240 breaths/min [(c) and (d)] on (Pg-PC)O2 and (PC-Pg)CO2.Q̇N=3.57×10−4ml/min; circled points correspond to V̇A/Q̇≈1.
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Variation of (a) PCO2,PgO2 (left axis), (Pg-PC)O2 (right axis) and (b) dimensionless ventilation (V̇A) and mass transfer (V̇O2) rates over one breath for Pe=0.001.V̇A and V̇O2 are scaled with their peak values.
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Variation of (a) PCO2,PgO2 (left axis), (Pg-PC)O2 (right axis) and (b) dimensionless ventilation (V̇A) and mass transfer (V̇O2) rates over one breath for Pe=20.V̇A and V̇O2 are scaled with their peak values.

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