146
Dynamics
of
the
Vascular
System
5.1.3 Space-Filling Properties and Modeling
It has been shown that the greater the body surface area, the greater the
need for an expansion of vascular networks to perfuse the tissues. Many
cardiac indices have therefore, been normalized to body surface area.
With a given organ vascular bed, space-filling is then a property, whether
in terms of area-expansion or volume-filling.
One approach takes into consideration of the space-filling problem is
the structured tree model shown in Fig.
5.1.4.
Here small arteries and
arterioles exercise minimization principles to perfuse tissues with blood.
Olufsen (2000) modeled branching small arteries and large arterioles
with the termination reached when the arterioles reach a prescribed
minimal radius. The determinants of the structured tree model are the
scaling parameters
a
(4)
and
p
(<l),
the order of the tree and the
geometric and elastic properties of the vessels. Results show the pressure
and flow waveforms manifested in large arteries have similar forms to
the measured data.
1
Fig.
5.1.4:
A
structured tree model in which at each bifurcation the radii of the daughter
vessels are scaled linearly by factors
a
and
p,
respectively. From Olufsen
(2000).
