BTEX40
Models a tissue cylinder consisting of four regions: interstitial fluid, endothelial cells, and parenchymal cells.
Model number: 0082
Further reading: Distributed Blood Tissue Exchange Models Explained Download PDF file.
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Description
These partial differential equations model a "tissue cylinder" consisting of four regions. The four regions are capillary plasma, p; endothelial cell, ec; interstitial fluid, isf; and parenchymal cell, pc; and are separated by three barriers--the luminal or plasma surface and endothelial cell layer; the albuminal surface of the endothelial cell facing the interstitium; andthe membrane between the interstitial fluid and parenchymal cell. In addition, there is a diffusional path from plasma to ISF bypassing endothelial cells via intercellular clefts.
Equations
Differential Equations
-\frac{PS_{ecl}}{V_p}\cdot (C_{p}-C_{ec})
+D_p \cdot \frac{\partial^2 C_p}{\partial x^2}
)
-\frac{PS_{eca}}{V'_{ec}} \cdot (C_{ec}-C_{isf})
+D_{ec} \cdot \frac{\partial^2 C_{ec}}{\partial x^2}
)
- \frac{PS_{pc}}{V'_{isf}} \cdot (C_{isf}-C_{pc})
-\frac{PS_{eca}}{V'_{isf}} \cdot (C_{isf}-C_{ec})
+D_{isf} \cdot \frac{\partial^2 C_{isf}}{\partial x^2}
)
+D_{pc} \cdot \frac{\partial^2 C_{pc}}{\partial x^2}
)
Left Boundary Conditions
 }{{\it V_p}}}+{
\it D_p}\cdot {\frac {\partial}{\partial x}}C_p=0
)
,
,
,
.
Right Boundary Conditions
,
,
,
,
.
Initial Conditions
,
,
,
or
)
,
)
,
)
,
)
.
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
Blood Tissue Exchange (BTEX) models
- BTEX10 : Single region (Capillary) model,
- BTEX10 model with Terminology plots,
- BTEX10stat : BTEX10 with inflow and
outflow concentration statistics,
- BTEX10x2CircularFlow :
Two BTEX10s used as a pipes for circular flow illustrating right and left
flows,
- BTEX10_OscillatingFlow :
BTEX10 used as a pipe for oscillating flow,
- BTEX20 : Two region (Capillary and ISF) model,
- BTEX20_Augmented : BTEX20 with visual
interface and additional calculations,
- DiffusionLimitedProfiles : BTEX20 with
radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) ,
- BTEX20radialDiffusion : BTEX20 with
radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) with Java
interface to Matlab(TM) ,
- How the Modular Program Constructor (MPC) tool
generated the BTEX20radialDiffusion model (contains documentation and code for
MPC)
- BTEX30 : Three region (Capillary, ISF, and parenchymal cell) model,
- BTEX40 : Four region (Capillary, endothelial cell, ISF, and parenchymal cell) model,
- BTEX40_Augmented : BTEX40 with visual
interface,
- BTEX50 : Five region (Capillary, endothelial cell, ISF, parenchymal cell, and mitochondria)) model,
- MID4pde : Multiple indicator dilution model for vascular (BTEX10), extravascular (BTEX20) and permeant (BTEX40) tracers,
Key Terms
BTEX40,PDE,convection,diffusion,permeation,reaction,distributed,capillary,plasma,isf,interstitial fluid,endothelial,parenchymal,cell
Model Feedback
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Model History
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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
10Sep10, 9:30 am.]
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.
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
Blood Tissue Exchange (BTEX) models
- BTEX10 : Single region (Capillary) model,
- BTEX10 model with Terminology plots,
- BTEX10stat : BTEX10 with inflow and outflow concentration statistics,
- BTEX10x2CircularFlow : Two BTEX10s used as a pipes for circular flow illustrating right and left flows,
- BTEX10_OscillatingFlow : BTEX10 used as a pipe for oscillating flow,
- BTEX20 : Two region (Capillary and ISF) model,
- BTEX20_Augmented : BTEX20 with visual interface and additional calculations,
- DiffusionLimitedProfiles : BTEX20 with radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) ,
- BTEX20radialDiffusion : BTEX20 with radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) with Java interface to Matlab(TM) ,
- How the Modular Program Constructor (MPC) tool generated the BTEX20radialDiffusion model (contains documentation and code for MPC)
- BTEX30 : Three region (Capillary, ISF, and parenchymal cell) model,
- BTEX40 : Four region (Capillary, endothelial cell, ISF, and parenchymal cell) model,
- BTEX40_Augmented : BTEX40 with visual interface,
- BTEX50 : Five region (Capillary, endothelial cell, ISF, parenchymal cell, and mitochondria)) model,
- MID4pde : Multiple indicator dilution model for vascular (BTEX10), extravascular (BTEX20) and permeant (BTEX40) tracers,
Key Terms
BTEX40,PDE,convection,diffusion,permeation,reaction,distributed,capillary,plasma,isf,interstitial fluid,endothelial,parenchymal,cell
Model Feedback
We welcome comments and feedback for this model. Please use the button below to send comments:
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
10Sep10, 9:30 am.]
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.
Model Feedback
We welcome comments and feedback for this model. Please use the button below to send comments:
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 10Sep10, 9:30 am.]
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.
