Section 1 Schematic of surface tension-bubble surface aire loop.
Parameter set "Default" + Plot page "Tens_Area_P_V"
Figure 1. Surface tension (gamma) - bubble surface area loop demonstration surfactant transfer mechanisms for each loop segment: kinetic adsorption or desorption for gamma > gammaStar (gammaStar is gamma when G=Gstar, here gammaStar is 22.2 dyn/cm);insoluble monolayer for gammaMin < gamma< gammaStar (gammaMin is gamma when G at Gmax, gammaMin is 10 dyn/cm), and squeeze-out as area is lowered beyond point where gammaMin is reached.
Figure 2. Pressure-volume loops.
The varible of pressure is plotted as function of volume. The bubble is consindered as a spherical balloon.
Section 2 Isotherm relating gamma to surface concentration.
Parameter set"Tens_Conc" + Plot page "Para_Tens_Conc"
Figure 3. Isotherm relating gamma to surface concentration. The surface tension gamma is showed as a function of G/Gstart. It mathces slopes at low G (G<Gstar) and high G (G>Gstar) and these two
lines to meet at G=Gstar at minimum equilibrium surface tension.
Section 3 Predictions of model.
Parameter set "Fig4E""Fig4F""Fig4G""Fig4H" + Plot page"gamma_A"
Parameter set "Fig4E" and Run loops with:
"parameter" "start" "other values"
f 10 100
G__init 0.99712742 0.91032786
Figure 4E. gamma-A loops at frequencies of 10 cycles/min and 100 cycles/min with adsorption coefficient k1=10E5 cm^3/g/min and desorption coefficient k2=1/min and C=7.3 mg/ml.
Parameter set "Fig4F" and Run loops with:
"parameter" "start" "other values"
f 1 10
G__init .98503595 .89710683
Figure 4F. gamma-A loops at frequencies of 1 cycles/min and 10 cycles/min with adsorption coefficient k1=10E5 cm^3/g/min and desorption coefficient k2=1/min and C=0.73 mg/ml.
Parameter set "Fig4G" and Run loops with:
"parameter" "start" "other values"
f 1 10, 100
G__init .81356186 .64750589, .61285566
Figure 4G. gamma-A loops at frequencies of 1 cycles/min, 10 cycles/min, and 100 cycles/min with adsorption coefficient k1=10E5 cm^3/g/min and desorption coefficient k2=1/min and C=0.073 mg/ml.
Parameter set "Fig4H" and Run loops with:
"parameter" "start" "other values"
f 1 10, 100
G__init .33342904 .32781165, .33233267
Figure 4H. gamma-A loops at frequencies of 1 cycles/min, 10 cycles/min, and 100 cycles/min with adsorption coefficient k1=10E5 cm^3/g/min and desorption coefficient k2=1/min and C=0.0073 mg/ml.
// MODEL NUMBER: 0197
// MODEL NAME: Surfactant
// SHORT DESCRIPTION:
//Surfactant effect on single bubble dynamics: This models the
//dynamic adsorption, desorption, and squeeze-out phenomena of surfactant
import nsrunit; unit conversion on;
math Surfactant { realDomain t sec;
// PARAMETERS:
real
k1 = 1e5 ml/g/min, // ADSORPTION COEFFICIENT
k2 = 1 1/min, // DESORPTION COEFFICIENT
C = 0.73 mg/ml, // BULK SURFACTANT CONCENTRATION
Gstar = 1 scalar, // MAXIMUM PASSIVE CONCENTRATION
Gmax = 1.15 scalar, // MAXIMUM PACKING CONCENTRATION
Vmean = 0.482 mm^3, // MEAN BUBBLE VOLUME
DelV = 0.214 mm^3, // CHANGE IN BUBBLE VOLUME
f = 10 1/min, // OSCILLATION FREQUENCY
numCycles =1 scalar; // NUMBER OF CYCLES YOU WANT TO RUN
t.min = 0; t.max = numCycles / f;
t.delta = 0.2/(f * 60); // 60 POINTS PER CYCLE
// VARIABLES
real
R(t) mm, // Radius
A(t) mm^2, // BUBBLE AREA
V(t) mm^3, // BUBBLE VOLUME
G(t) scalar, // SURFACE SURFACTANT CONCENTRATION
P(t) dyn/cm^2, // PRESSURE
gamma(t) dyn/cm; // SURFACE TENSION
// INITIAL CONDITION
when (t=t.min) {G = 0.89710682; }
// ALGEBRAIC AND ODE EQUATIONS
V = Vmean + DelV *sin(2*PI*f*t + PI/2); // Volume
R = (3*V/(4*PI))^(1/3); // Radius
A = 4 * PI * R^2; // Surface area
// surfactant adsorption/desorption kinetics
// describes what happens to the surfactant between
// the bulk and the interface
G:t= if (G<Gstar)
-G/A*A:t + k1*C*(Gstar-G)-k2*G
else
if (G>=Gmax and V:t<0)
0
else
-G/A*A:t;
// Equation of state = surface tension as a fn of surface conc g
gamma = if (G<=Gstar)
72.0 - (49.8 dyn/cm) * G // UPPER PORTION
else
103.5 - (81.3 dyn/cm) * G; // LOWER PORTION
// pressure as a fn of surface tension and radius
P = 2*gamma/R; // LAPLACE'S LAW for tension in sphere
}// END OF MML CODE
/*
DETAILED DESCRIPTION:
This models the dynamic adsorption, desorption, and squeeze-out
phenomena of an exogenous pulmonary surfactant (surfactant TA)
solution surrounding an oscillating bubble.
The influence of the alveolar surface tension on the concentration
of the surfactant lining the alveolus can be simulated by this
model describing the adsorption/desorption kinetics of a surfactant
on a bubble and the change in surface tension generated. The volume
of the bubble is driven in a sinusoidal manner.
KEY WORDS:
lung alveolus, surface tension, bubble dynamics, surfactant
TA concentration, lung compliance, functional residual volume,
pulmonary mechanics, intrapleural pressure, lung elasticity,
Respiratory mechanics, Airway mecahnics
REFERENCES:
Otis et al.; Dynamic surface tension of surfactant TA:
experiments and theory. J Appl Physiol 77:2681-2688, 1994.
Y.C. Fung; Biomechanics: Mechanical Properties of Living Tissues,
Second Edition, Springer-Verlag, New York, 1993, pp16-17
REVISION HISTORY:
Original Author: Melissa Kreuger Date: 2004
Revised by: Feng Gao Date: 10/08/2008
Revision: Added figures and pramater sets
Revised by: BEJ Date:28sep11 : Update comments
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2011 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.
This software was developed with support from NIH grant HL073598.
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.
*/