This model illustrates the variation in blood hematocrit seen in narrow tubes from the blood hematocrit at the tube outlet.
Description
This model shows the variation of tube hematocrit as a function of discharge hematocrit and inside diameter of the tube based on the observations of Fahraeus and the empirical formulation by Pries et al. It has been noted and confirmed that in small tubes the ratio of red blood cell velocity and the plasma velocity differ resulting in a difference in the hematocrit inside the tube from that of the discharge or supply.
To illustrate this point take an extreme case where the cells go twice as fast as the plasma through the tube. The supply and the discharge hemtocrit must be equal so in order to have the same hematocrit leaving the tube outlet we must have half the hematocrit in the tube at any given time as is in the supply or discharge.
The following expression was developed by Pries et al in 1990 (see reference below) to represent tube hematocrit as a function of discharge hematocrit and tube diameter the for the compilation of data from literature at the time documenting the Fahraeus effect.
Ht
---- = Hd + (1 + Hd) * (1 + 1.7*exp(-0.415D) - 0.6*exp(-0.011D)
Hd
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.
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1. Pries AR, Secomb TW, Gaehtgens P and Gross JF.
Blood flow in microvascular networks: Experiments and simulation.
Circulation Research 67:826-834, 1990
2. Fahraeus R.
The suspension stability of the blood.
Physiological Review 9:241-274, 1929.
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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.