OneAlvLung

A compliant 1 compartment lung with resistance to air flow driven by a positive pressure ventilator is modeled as an electrical RC circuit.

Model number: 0001

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Description

The equations governing airflow in and out of a one compartment lung are given by the following analogy to electrical circuits:

Airway pressure is analogous to voltage.
Air flow is analogous to current flow.
Volume is analogous to charge.
Resistance to flow is analogous to electrical resistance.
Compliance, the relationship between pressure and volume, is analogous to capacitance, the relationship between charge and voltage.

The model shows that various quantities are governed by exponential decay with time constant τ = R Com.

The main assumption is that the human lung can be approximated as a single compartment modeled by an RC circuit where the quantities of interest, air flow, volume of air, pressure, compliance, and resistance are analogous to current, charge, voltage, capacitance, and resistance respectively.

Equations

${\it P}_{\text{\small{mouth}}}={\it P}_{\text{\small{scalar}}}\,{\it P}_{\text{\small{drive}}}$

${\it Flow}=\left({\it P}_{\text{\small{mouth}}}-{\it P}_{\text{\small{lung}}}\right)/{{\it R}}$

${\frac {d}{dt}}{\it V}_{\text{\small{lung}}}={\it Flow}$

${\it P}_{\text{\small{lung}}}={\it P}_{\text{\small{ref}}}+\left({\it V}_{\text{\small{lung}}}-{\it V}_{\text{\small{FRC}}}\right)/{{\it Com}}$

where P_mouth is the pressure at the mouth; P _scalar scales the amplitude of P_drive, the driving pressure from a ventilator; P_lung is the pressure in the lung; P_ref is the reference pressure external to the lung; Flow is the air flow at the mouth; R is the resistance of the airway; Com is the compliance of the lung; V_FRC is the functional residual capacity of the lung; and V_lung is the volume of air in the lung.

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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References

M.G. Levitzky: Lange Physiology Series: Pulmonary Physiology, 6th edition. McGraw Hill, 2003

Related Models

Lung RC circuit

Key Terms

lung, compliance, resistance, RC circuit, mechanics, airflow, trachea, tidal volume, positive pressure, ventilation

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Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 10Aug11, 3:13 pm.]

Model development and archiving support at physiome.org provided by the following grants: NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.