216
Dynamics
of
the
Vascular
System
1
-
-
1
Compliance
=
dp
I
dV
stiffness
(8.1.4)
Thus, a more compliant the pressure transducer means that volume
displacement (dV) of its diaphragm is greater when subjecting to the
same amount of applied pressure (dp). The consequence of this in the
accuracy of blood
pressure
recording
is
explained below.
The
compliance of the needle (typically made of stainless steel with high
Young's modulus of elasticity and therefore, very stiff) is negligible.
Equation (8.1.1) can be re-written as:
11
fn
=Gk
(8.1.5)
When the needle is narrow, the Poiseuille resistance,
R,
becomes
important in the determination of the frequency response.
A
second-order
RLC
system representation is necessary.
As
we have seen in earlier chapters that blood pressure waveform is
periodic and can be represented by a Fourier series as the sum of a mean
pressure and a number of sine waves of fundamental frequencyf(heart
ratehec) and harmonics,
nf(n
=
1,2,
.
. .
,
N):
N
p(t>
=
j
+
Cp, sin(nwt
+
w=2?lf
(8.1.6)
n=l
which, when substituted into the second order differential equation
describing the fluid motion, results in the amplitude ratio for the nth
harmonic:
(8.1.7)
1
-
LC
+
(~CDRC)'
its corresponding phase angle:
nwRC
1
-
nwLC
(bn
=
tan-'
(8.1.8)