Physical Concepts and Basic
Fluid
Mechanics
51
clearly seen. It is also clear that the pulmonary aorta is stiffer (less
diameter distention with increasing pressure) along the major axis than
the minor axis. In small peripheral vessels the viscous modulus is larger
and the phase shift becomes more pronounced.
This
can be seen in the
simultaneously measured pressure-diameter relation obtained for the
femoral artery, for instance.
The static modulus
of
elasticity differs from the dynamic elastic
value.
Measurement of dynamic elasticity has gained considerable
attention, mainly because of its applicability to pulsatile conditions. The
approach employs the measurement
of
pressure-diameter relations, and
the subsequent calculations of the incremental elastic modulus
(EinC)
which is complex
(Ec):
Einc
=
Edyn
+
To
(3.1.21)
When
an elastic modulus is complex, it implies
frequency-
dependence. The in-phase component defines the dynamic elastic
modulus,
and the viscous modulus is defined by
qo
=
1
E,
I
sin$
(3.1.23)
where
$
is the phase lag, generally between pressure (p) and diameter
(d).
In the case that pressure leads diameter, or that the diameter
distention delays after the arrival of the pressure pulse,
+
is positive.
When considering the artery as purely elastic, i.e. no viscosity damping is
present, then the arterial lumen diameter change instantaneous with the
distending pressure pulse. In this case,
$
is zero and the viscous term
qo
disappears.
A
similar form of complex elastic modulus was given by Cox (1
975),
accounting for arterial wall thickness:
