218
Dynamics
of the
Vascular
System
is
then rapidly “popped” (thus, pop-test) with
a
sharp needle.
The
pressure in the chamber thus falls to atmospheric pressure, completing
the step decrease in pressure. If the catheter system had a perfect
dynamic response, then its response would follow exactly the step
decline in pressure.
However, clinically and experimentally used
catheter-transducer combinations are usually underdamped, resulting in
oscillations in amplitudes.
The damped natural resonance frequency,fd is obtained as the inverse
of
the period of oscillation:
1
fd
=r
(8.1.9)
where T is the period of oscillation. This can be obtained from the
interval
of
the peak-to-peak or trough-to-trough oscillations. The
exponential damping,
a,
is determined from the peak amplitudes
A,
and
A29
or in terms of amplitude ratio,
A,
,
4
4
Ap
=
ln-
(8.1.10)
(8.1.1
1)
The relative damping factor,
ad,
is obtained
from the following
expression:
(8.1
.12)
AP
Most catheter-manometer systems exhibit underdamped responses,
where the damping factors are typically of 0.1-0.3. The useful frequency
range can be estimated by multiplying the resonant frequency by the
damping factor. For instance, if the resonant frequency is 45
Hz
and the
damping factor is
0.2,
then the “useful flat frequency range” is
35x0.2
or
9
Hz.
The flat frequency response refers to an amplitude ratio (equation
