# CTEX10stat

Models a capillary consisting of N compartments. Explores sensitivity analysis and optimization. Includes curve statistics.

Model number: 0332

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## Description

N compartments in series simulate a partial differential equation with convection and diffusion. The relative dispersion of N compartments in series is 1/sqrt(N). There is not an exact relationship between the diffusion coefficient and the relative dispersion in the partial differential equation for diffusion and convection in a bounded domain with inflow and outflow at the ends. This model explores sensitivity analysis and optimization in a guided exercise.

## Equations

#### Ordinary Differential Equations

, and for j=2..N: .#### Initial Conditions

for j=1..N.The equations for this model may also 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 project file

## References

W.C. Sangren and C.W. Sheppard. A mathematical derivation of the exchange of a labelled substance between a liquid flowing in a vessel and an external compartment. Bull Math BioPhys, 15, 387-394, 1953. C.A. Goresky, W.H. Ziegler, and G.G. Bach. Capillary exchange modeling: Barrier-limited and flow-limited distribution. Circ Res 27: 739-764, 1970. J.B. Bassingthwaighte. A concurrent flow model for extraction during transcapillary passage. Circ Res 35:483-503, 1974. B. Guller, T. Yipintsoi, A.L. Orvis, and J.B. Bassingthwaighte. Myocardial sodium extraction at varied coronary flows in the dog: Estimation of capillary permeability by residue and outflow detection. Circ Res 37: 359-378, 1975. C.P. Rose, C.A. Goresky, and G.G. Bach. The capillary and sarcolemmal barriers in the heart--an exploration of labelled water permeability. Circ Res 41: 515, 1977. J.B. Bassingthwaighte, C.Y. Wang, and I.S. Chan. Blood-tissue exchange via transport and transformation by endothelial cells. Circ. Res. 65:997-1020, 1989. Poulain CA, Finlayson BA, Bassingthwaighte JB.,Efficient numerical methods for nonlinear-facilitated transport and exchange in a blood-tissue exchange unit, Ann Biomed Eng. 1997 May-Jun;25(3):547-64.

## Related Models

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,

Osmotic Exchange:

- 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.

Pharmacology:

- 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.

## Key Terms

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## Model History

Get Model history in CVS.## 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 14Mar18, 3:17 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.