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rearing up

I appreciate all the dialog on this interesting subject.  These types of
discussions allow me to review my anatomy and physiology, and are quite
enjoyable.  I have a few more thoughts and then will return to lurking.
I also agree that mammals and birds may not be good models for sauropods
because of brain size differences.  Within a smooth rigid tube, flow (F)
varies with the pressure drop over a unit of length (P/L) , the radius
of the tube (r), and the viscosity of the fluid (n), giving us the
always dreaded Hagen-Poiseuille equation:  F=(P)(pi)(r4)/8(L)(n)--note
that flow varies with the fourth power of the radius.  I argue that flow
requirements for rearing sauropod brains to function are small, that
cerebral artery radiuses (radii?) are correspondingly small, and hence
even with a long neck length the pressure changes would not have to be
great.  This can be tested if someone could give a good estimate of the
size of the carotid arteries.  I haven't taken any physics classes for
some time (and I never really understood them) so someone please let me
know if this reasoning is flawed.  Lastly, are giraffes good model for
rearing sauropods? There is an article in Comp Biochem Physiol A Physiol
1997 Nov; 118 (3) 573-6 (I have only read the abstract) that suggests
that the gravitational effects on giraffe neck arteries are
counterbalanced by the gravitational effects on the neck veins and "that
the heart does not spend extra energy to raise the blood to the head."
As usual there are also studies disagreeing with this conclusion.--Ken
Clay, M.D.