JAMES D. MEINDL 
1169 
To achieve a practical transit time flowmeter, 
differences in acoustic transit times on the order 
of 10-^° sec must be measured.^ This time in- 
terval is extremely small and the instrumenta- 
tion required to measure it tends to be complex, 
bulky, drift-prone and expensive. Consequently, 
techniques have been developed for measuring 
the phase difference a0 between the upstream 
and downstream sound pulses.^'^'^^ In this case, 
it appears that the baseline or zero flow output 
of the instrument depends on accurately setting 
the phase relationships of the two transmitter 
and receiver channels. This is done initially 
by adjusting a tank circuit but cannot be 
checked during implantation when, for exam- 
ple, changes in transducer impedances and 
hence channel phase shifts cause zero drift. 
Continuous Wave (CW) Doppler Ultrasonic 
Flowmeters 
A second type of ultrasonic blood flovmieter 
is based upon the Doppler effect. In this instru- 
ment a beam of ultrasonic energy is transmitted 
through the wall of a blood vessel where it is 
scattered by the red cells of the bloodstream. 
The scattered energy, which is shifted in fre- 
quency according to the Doppler principle, is 
detected by a second transducer on the opposite 
side of the vessel. ^^-^^ The Doppler frequency 
shift (fd) in the scattered ultrasound is given by 
f<3 = fi — f , = 2 — fi cos a 
c 
(4) 
where fj is the incident frequency, fg the fre- 
quency of the scattered sound, v the blood veloc- 
ity, c the velocity of sound in blood, and a the 
angle between the blood velocity and incident 
sound vectors. Because blood velocity is a func- 
tion of radial position within the lumen, (4) 
represents only a description of the physical 
principle of operation of the CW Doppler flow- 
meter and not necessarily its quantitative be- 
havior. The design details of the transducers 
and the demodulator determine whether this in- 
strument provides an estimate of flow velocity 
at a particular position or average velocity over 
the lumen (i.e., volume flow) or neither.i*'^^ 
To measure blood velocity at the center of the 
lumen the CW Doppler flowmeter transducers 
should be designed such that the diameter (aD) 
of the volume of intersection of the two trans- 
ducers beam patterns is small compared with 
the lumen diameter (D) as illustrated in Figure 
2. In this case v is effectively a constant and (4) 
accurately describes fd as essentially a single 
line spectrum. Consequently, a simple zero 
crossing demodulator (which in effect computes 
the second moment of the scattered signal power 
density spectrum) provides an accurate esti- 
mate of velocity at the center of the lumen.^^-^^ 
The benefits to the user of measuring central 
lumen blood velocity are significant. It is an 
unambiguous measurement; the measuring in- 
strument can be electronically precalibrated 
with a high degree of absolute accuracy; and, 
the measurement is virtually immune to zero 
drift and changes in scale factor. In addition, 
estimates of volume flow for a particular vessel 
can be made by assuming a flow profile and a 
lumen diameter or by empirical calibration of 
the instrument. 
In contrast, to measure volume flow with a 
CW Doppler flowmeter specifically designed for 
the purpose, three distinctly different require- 
ments must be met r^*-^^ 
(1) the entire lumen cross-section must be 
uniformly illuminated by the trans- 
mitting and receiving transducers ; 
(2) the demodulator must compute the 
first moment of the power spectral 
density function of the Doppler shifts 
S(f) such that 
fS(f)df 
_S(f)df - 2 If. cos ^ (5) 
where fd is the average frequency in 
S(f) and V is the average blood veloc- 
ity; and 
(3) lumen diameter must be measured by 
some independent technique to com- 
pute volume flow in accordance with 
(3). 
Pulsed Doppler Ultrasonic Flowmeter 
In principle, the pulsed Doppler ultrasonic 
flovmaeter is an elegant extension of the CW 
Doppler velocity flowmeter. In this instrument 
a short burst of ultrasonic waves is transmitted 
through the wall of a blood vessel where it is 
scattered by the red cells of the bloodstream. 
