View Full Version : Circulatory system modelling

M Swanepoel
07-10-1998, 12:51 AM
Hello Everyone,

I have been asked to model pressure waves in the aorta, and have
found it necessary to develop a broader model than I had anticipated.
The references I have give widely differing values for the capillary
bed total cross-sectional area - for a dog I have what seems to be a
ludicrously small value of 100 square centimetres, whereas
for adult humans I have estimates of 2900 and 4500 square
centimetres, no body mass being stated. Does anyone know of a
reliable figure for an adult human having a stated mass?

It would also be nice to know the distributions of the diameter sizes of
undeformed capillaries - books give values for the average capillary diameter
anywhere from 6 to 9 micrometres, and numbers of capillaries from 5
to 7 billion. (This is important as the Hagen-Poiseuille eqn gives flow
resistance as being proportional to the fourth power of the vessel's diameter.)

There also appears to be no consensus as to whether there are more or
less postcapillary venules in the circulatory system than capillaries
themselves! I would have thought that each venule could serve
several capillaries, but one source I have gives this relationship
inversely - one capillary draining into several venules, another gives the
numbers as being equal, one venule per capillary, while a third seems to
imply that there is a very slight excess of venules over capillaries.
What is the truth? Is there some logic to this that I don't know?

Finally, I have been trying to reconcile division of the arterial
tree into several billion capillaries, with the stated number of
divisions, blood volume, and cross-sectional areas of arteries,
small arteries, and arterioles. The model I have estimates the
number of divisions occurring at each level such that the total number
of capillaries would only be a few tens of thousands at most, not the
several billion which actually exist! (My model assumes that
most branches occur at the aortic level, and the number of branches declines
uniformly with arterial tree level to just 3 branches for each
capillary. My inclination is that the number of branches per blood vessel
should increases to a maximum at the small arterial level, and then
drop dramatically to the capillary level. However this is contradicted
by the literature.) Somewhere along the line (artery?) I'm missing
a few hundred thousand arterial divisions! Where have they disappeared?

Mark W Swanepoel
School of Mechanical Engineering
University of the Witwatersrand

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