MODEL NUMBER: 0002 MODEL NAME: OneAlvLung.Chest SHORT DESCRIPTION: A compliant 1 compartment lung with resistance to air flow, driven by intrapleural negative pressure (chest or diaphragmatic breathing) or by a positive pressure ventilator or both together, even competing, interfering.. END OF MML CODE FIGURE: (for ventilator) Pmouth R Plung Pintrapl || \\ o------------/\/\/\/\----o ---O-----||---|| for chest breathing __|__ || // ----- Com ComAir = Boyle's Law | Vlung Vintrapleural __|__ ___ . DETAILED 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 air flow is analogous to electrical resistance. Compliance, the relationship between pressure and volume, is analogous to capacitance, the relationship between charge and voltage. The response to a negative step input in Pintrapl is an exponentially decaying flow with time constant tau=R*Com. The main assumption is that the human lungs 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. GENERAL RESULTS: Normally breathing is simulated when the driving force is provided by expansion of the chest, creating a negative pressure in the intrapleural space, just the oppposite of a positive pressure ventilator. Using Pmusc = 2-second pulse of negative driving pressure of -10 mmHg pressure intrapleural gives an approximately normal tidal volume. Both sources of driving the system can be used at once, mimicking the patient struggling to breath on his own when still being ventilated by a purely periodic ventilatory cycle. (The ventilator should be replaced with a "ventilatory assist" device, i.e. one that is triggered to provide at assisting positive pressure ventilation to augment flow when the patient initiates inflow by chest or diaphragmatic breathing. Aplying the Ideal Gas Law to Vintrapl shows that the error in assuming air to be incompressible air is small: Boyle's Law for Ideal gas in intrapleural space *********************************************************************************** * Boyle's Law: P*V = n*R*T STP =standard temp pressure is 0 deg C, 1 atm * * with P mmHg, V ml, n moles of gas where 1 mole at STP occupies 22,414 ml * * R = Boltzmann const or Gas Const = 0.082 l * atm * mol^(-1) * K^(-1) * * T = deg K = 273.16 + deg C * * so that nRT at 37C and 760 mmHg (1 atmos) * * (volume of gas in ml)* 0.082 l * atm * mol^(-1) *K^(-1) * 310 K * * P*V = --------------------------------------------------------------- * * (volume of 1 mole of gas, 22.4 * 310/273 l) * * * * PV(for 100 ml)= (100/(22400*310/273))moles * 0.082 mole^(-1) * 760mmHg * 310 * * * * = 0.082 * 760 * 273 / 224 = 75.95 mmHg *100ml = 0.7595 mmHg * ml * * * * Using P*V= Const, then with a const amount of gas in intrapleural space there is* * a small volume change with each breath, the direction depending on the driver. * * V2 = V1 * P1/P2 See Eqn for Plung * *********************************************************************************** SHORTCOMINGS: 1. Air breathed is assumed incompressible. The maximum error with a 20 mmHg driving force is only 10/760 or 1.3%. 2. There is no deadspace volume, so if there were to be gas exchange, this model would assume that all of the volume is available for exchange. 3. The effects of chest compression or exhalation against a closed or partially closed glottis need accounting. 4. The effects of high Mouth pressure on effective intrapleural pressure need Rx. To do this, the chest compliance should be separated from lung compliance. 5. Setting Vintrapl has no effect on S.S.Volumes. 6. The shape of the volume/pressure plot is dependent on the time step length 7. The compliance of the chest and lung are lumped KEY WORDS: lung compliance, resistance, RC circuit, lung mechanics, airflow in trachea, tidal volume, positive pressure ventilation, chest or diaphragmatic breathing, tutorial REFERENCES: M.G. Levitsky, Pulmonary Physiology, Sixth Edition, McGraw Hill, 2003. REVISION HISTORY: Original Author: JBB Date: 13.12.17 (Yr.Mo.Day notation) Revised by: BEJ Date:14.6.23 : Update Comments Revised by: BEJ Date:15.6.01 : Separate compliance for lung and chest, Add param set, Notes COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE: Copyright (C) 1999-2015 University of Washington. From the National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061. Academic use is unrestricted. Software may be copied so long as this copyright notice is included. When citing JSim please use this reference: Butterworth E, Jardine BE, Raymond GM, Neal ML, Bassingthwaighte JB. JSim, an open-source modeling system for data analysis [v3; ref status: indexed, http://f1000r.es/3n0] F1000Research 2014, 2:288 (doi: 10.12688/f1000research.2-288.v3) This software was developed with support from NIH grants HL088516 and HL073598, NIBIB grant BE08417 and the Virtual Physiological Rat program GM094503 (PI: D.A.Beard). Please cite this grant in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.

Functional Residual Capacity = Lung Vol at rest (at 760 mmHg)

Volume of air in lung

Volume of air in intrapleural space (regarded as compressible)

Resistance of airway

Chest volume at FRC (incl heart,etc. of about 1000 ml)

Flow at mouth

Pressure in the lung

Reference Pressure external to body (for Boyle's Law calculation)

Pressure at the mouth

Test of FlowAir; FlowAir = TestF when ScalPvent * Pvent = 10 mmHg at t = 0

Chest volume at FRC = approx FRC (or TLC-heart and lung tissue)

Linear Compliance of the chest

Intrapleural press < 0: lung is stretched; chest wall pulled inward

Scalar of amplitude of Pvent (Ventilator) :: for convenience

Time constant of system, resistance* compliance, sec

Pressure in intrapleural space (Neg to inhale)

External ventilator at mouth creates positive inhalation pressure

Chest Expansion (positive to inhale by creating negative Pintrapl)

Linear Compliance of the lung

Scalar of amplitude of Pchest ( +ve to expand Chest) :: for convenience

Arbitrary amount air in pleura to allow Vintrapl changes

Chest expansion defined by fn generator Pmusc(t)

Ohm's Law, flux = driving force / resistance

= Ventil Pr at mouth. (Set PscalVentil = 0 for Chest breathing.)

Pintrapleural diminishes with chest expansion countered by lung compliane

Assumes constant compliance

Flow at mouth

Assumes compressible intrapleural air