Uncoupled, independent fluxes of water and of 2 solutes, across a membrane separating 2 stirred tanks of equal elasticity.
Model number: 0273
|Run Model: ||    Help running a JSim model.|
MacOS: Adjust "System Preferences" -> "Security & Privacy" to allow Java JSim jnlp app to execute.
More info here.
Uncoupled, independent fluxes of water and of 2 solutes, A and B, across a membrane separating 2 stirred tanks. Solute activities are assumed unity so concentrations = thermodynamic activity. The model describes a situation similar to that for the simplest expressions of Kedem and Katchalsky (1958) but omits all interactions between solutes and between water and any solute. One can think of the solutes passing though the membrane by passive permeation with permeability coefficients PermA and Perm B, and the water passing through aqueous pores with filtration coefficient or hydraulic conductivity, Lp. The aqueous pores do not permit solute passage. Lp is the same as the traditional filtration coefficient Kf. Lp translates to a conventional permeability for water filtration coefficienr, Pf cm/s, Pf = Lp* Vw / RT where RT = 19.347*10^6 mmHg*cm^3*mol^(-1) at 37C, Vw is the partial molar volume of water, 18 ml/mol or the concentration of water in water is 55.55 M The driving forces are the pressure difference for water flux and the concentration for the solute fluxes. The pressure difference across the membrane is the hydrostatic pressure difference minus the osmotic pressure difference. The osmotic pressure is given by Van't Hoff's Eq: p_osm = a.C.RT, where p_osm is the osmotic pressure, mmHg, "a" is the activity coefficient, assumed in this model to equal unity, C is concentration, M, and RT is the Gas Constant times Temperature Kelvin. In this model the solute doesn't permeate the aqueous pore so there is no consideration of a reflection coefficient, or rather it is assumed to be unity. Thus solute concentration in the pore water is zero, andthere is no solute advection.. The system is composed of two volumes of pressure-dependent size, yet stirred instantaneously continually. The pressure/volume relationship is expressed via the elasticity of the chambers, Elast, the slope of the pressure/volume relationship. An equivalent structure is to use rigid chambers from each of which there rises narrow columns of fluid to heights h1 and h2. The fluid in the columns is considered to be instantaneously mixed with that in the chamber from which it rises. Fluid or volume flux, Jv, from side 1 to side 2 raises difference in the column heighta between the two sides by Base*(h2-h1) = Jv, where Base = area of the base of the column, and the pressure difference rises to (h2-h1)*rho cm H2O, where rho is the fluid density. g/ml. The linear chamber elastance used in this model, Elast mmHg/ml, gives an equivalent measure for flexible chambers, assuming a linear relationship between the pressure change and the volume change. (1 mmHg = 13.59 cm H2O.) Notes: Situation 1:= Model parameter set: par1 PermA = 0, PermB > 0.1. See Notes. Situation 2 = Model parameter set: par2 PermB > 0. See Notes tab for more discussion.
Figure: Top shows concentration of solute A and solute B as a function of time (A1, B1: conc in volume 1, A2, B2 conc in volume 2). Note change in volume 1 (V1) from initial volume of 1 ml. Bottom figure shows hydrostatic pressure in V1 and volume 2 (V2) as a function of time. Permeability of A into V2 is zero and A2init and B1init are 0 mM for both figures.
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.
Download JSim model MML code (text):Information on JSim
Download translated SBML version of model (if available):Information on SBML conversion in JSim
Katchalsky A and Curran PF. Nonequilibrium Thermodynamics in Biophysics. Cambridge, MA: Harvard University Press, 1965. Kedem O and Katchalsky A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim Biophys Acta 27: 229-246, 1958. Stein WD. The Movement of Molecules across Cell Membranes. New York: Academic Press, 1967. Stein WD. Transport and Diffusion across Cell Membranes. Orlando, Florida: Academic Press Inc., 1986.
Single Compartment Models:
- Comp1Decay: Single Compartment with Decay,
- Comp1Flow: Single Compartment with Flow,
- Comp1FlowDecay: Single Compartment with Flow and Decay,
- Comp1Reaction: Single Compartment with One Reaction,
- Comp1FlowReaction: Single Compartment with Flow and One Reaction,
- Comp1FlowReactions2: Single Compartment with Flow and Two Reactions,
Two Compartment Models:
- Comp2Exchange: Two Compartments with Exchange,
- Comp2ExchangeReaction: Two Compartments with Exchange and One Reaction,
- Comp2FlowExchange: Two Compartments with Flow and Exchange Fit to a data set,
- Comp2FlowExchangeReaction: Two Compartments with Flow, Exchange, and One Reaction.
- Comp2FlowMMExchangeReaction: Two Compartments with Flow, Exchange using a Michaelis-Menten transporter, and One Reaction.
- Comp2FlowMRIContrast: Two Compartments with Flow, conversion of water to water spin for MRI contrast.
- Cortisol secretion: Two compartments with feedback control of precursor to cortisol and its adrenal secretion.
N>2 Compartment Models:
- Comp3FlowExch: Three compartmental model for plasma, interstitial fluid, and parenchymal cell,
- Comp6Propofol: Six compartmental model for propofol anaesthesia,
- CTEX10: N Compartments in series with Flow, emphasizes sensitivity analysis and optimization,
- CTEX10stat: CTEX10 model with statistics on inflow and outflow curves,
- CTEX20: N Compartments in series with Flow, each compartment exchanging with a compartment in parallel,
- CTEX20 5 path: Weighted sum of up to 5 paths of CTEX 20 modeled capillaries.
- CompNFlowDelay: N Compartments in series with Flow and Delay.
- Comp6_Recirc: Six compartmental recirculating model,
- Comp2x2Recirc: Dual two compartment models with recirculation and clearance,
- Uncoupled fluxes of water and solute across membrane.
- Uncoupled fluxes of water and solute across membrane w/ columns for measuring pressure.
- Transport of a hard spherical solute through a cylindrical pore.
- Washout curve simulation by sum of three decaying exponentials.
- Three reactions in series with no enzymes.
- Michaelis-Menton reactions in series.
- Enzymatic reactions in series.
- Four sequential enzymatic reactions.
We welcome comments and feedback for this model. Please use the button below to send comments:
Model HistoryGet Model history in CVS.
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 29Jan20, 1:02 pm.]
Model development and archiving support at physiome.org provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, 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.