Thick_Wall_Cylinder_Variable_E | Interagency Modeling and Analysis Group

Model number

0221

This model simulates the pressure and geometry resulting from changes in the internal radius of a thick-walled,

Description

 This model simulates the pressure and geometry resulting from changes in 
 the internal radius of a thick-walled, distensible, isotropic, cylindrical
 vessel.  Stresses in the radial and axial directions are neglected and vessel 
 wall material is assumed to be incompresible.  An external function "ri" sets 
 the inner radius values within the time domain.  In the available parameter 
 sets, time in seconds equals the internal radius in centimeters.

 The model is used to fit six pressure-radius curves from Drzewiecki et al. 1997 - three 
 from blood vessels and three from surgical tubes

fig1

Equations

$e8$

$e9$

$e10$

$e12$

$e13$

$e14$

$e15$

$e16$

$e17$

$e18$

$e19$

$e20$

$e21$

$e22$

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.

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References

Drzewiecki G, Field S, Moubarak I, and John K.-J. Li: Vessel growth and collapsible 
pressure-area relationship. Am J Physiol Heart Circ Physiol 273:H2030-H2043, 1997.

Popov EP.  Mechincs of Materials, SI version.  Prentice Hall.  Englewood Cliffs, NJ. 1978.

Related Models

Key terms

Thick

Variable

Young's modulus

vessel wall

material properties

thick wall

pressure-radius curve

pressure-volume curve

pressure-area curve

Data

Publication

Acknowledgements

Please cite https://www.imagwiki.nibib.nih.gov/physiome 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:
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome 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.