VelocityProfiles

Model number
0152

Veloicty profiles in straight cylinders. Poiseuille Flow is parabolic (Model 2). Slip at wall is Roevros (Model 1) Two phase flow model (Wang Model 3) has lower viscosity at wall.

Description

```   Adjustable intravascular velocity profiles in straight tubes.
A model allowing flattening of the velocity profile,
parabolic at its maximum, and allowing slip at the
wall. Follows various equations:
1. Roevros 1974 (Roevros JMJG Analog processing of
CW-Doppler flowmeter signals... In "Cardiovascular
applications of ultrasound" Ed. by RS Reneman,
Amsterdam-London, North-Holland Publ Co. 1974 pp43-54
v(r) = vmax (1- [ar/R + b]^K), for a>0,
a allows for a non-zero interfcept at the wall
b gives shift away from vessel center
K=2 for parabolic flow, and K>2 for flattening
vmean = mean veloc = flow/(PI*R^2)
2. Poiseuille Flow v(r) = 2.0*vmean*(1-(r/R)^2)
3. 2-phase flow in straight tube. Derived from curved
tube model of Wang and JBB 2003, in the Appendix.
```

Equations

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.

References
``` Reneman, RS, T. Arts and APG Hoeks. Wall shear stress - an important determinant
of endothelial cell function and structure - in the arterila system in vivo.
Discrepancies with theory. J. Vasc Res. 43: 251-259, 2006.
```
``` Caro, CG, TJPedley, RC Schroter and WA Seed. The Mechanics of the Circulation.
Oxford Press, Oxford UK 1978.

Roevros JMJG pp 43-54 in 1. Reneman et al 2006

Milnor, WR. Hemodynamics. Williams and Wilkins, Baltimore 1982
```
Key terms
intravascular velocity
shear rate
viscosity
artery
Poiseuille Flow
blood flow
Acknowledgements

Please cite https://www.imagwiki.nibib.nih.gov/physiome 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.

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.