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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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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