1168 
MONITORING 
ploitation of an implantable instrument, it 
should be immediately adaptable to automated 
data collection. 
Electromagnetic Flowmeters 
For many years the most widely used instru- 
ment for measurement of pulsatile blood flow 
has been the electromagnetic flowmeter.^'^ Re- 
cently a battery operated version of this instru- 
ment was announced.^ The most attractive fea- 
ture of the electromagnetic flowmeter is that 
the "flow induced" voltage (e) between its elec- 
trodes is proportional to the average velocity of 
blood (v) flowing in a circular vessel of lumen 
diameter (D). Assuming axial flow symmetry 
and a uniform magnetic field intensity (B), 
solving Maxwell's equations for electromagnetic 
field yields 
e=[SBD]V (1) 
where the sensitivity (S) depends on vessel wall 
thickness, the tensor conductivity of the wall 
and the blood conductivity.* If the factor (SBD) 
is known, (1) clearly indicates that the electro- 
magnetic flowmeter provides a measurement of 
average blood velocity (v) only; to convert this 
information unambiguously to instantaneous 
volume of flow (Q) an entirely independent 
measurement of lumen diameter (D) is essential 
since 
Q = 7r (D/2)2 V (2) 
Considering the factors which influence S, the 
product (SBD) can be determined accurately 
only by the user through in vivo calibration of 
a given flow transducer via a process such as 
excisting the vessel and collecting a known 
amount of blood in a given interval of time. 
Electronic calibration of the instrument is not 
feasible. 
Baseline or zero drift is one of the most diffi- 
cult problems encountered in electromagnetic 
flowmeters. The principal cause of zero drift 
in most instances is unwanted voltages induced 
within the blood and the vessel wall by the sine 
wave or square wave excitation of the field coils 
of the flowmeter. To appreciate this problem, 
one might think of a field coil as an inductor im- 
bedded in a lossy conductive medium consisting 
of the blood and the vessel wall. Eddy currents 
induced in this medium by the alternating ex- 
citation of the field coil persist for indefinite 
periods; the potentials they generate between 
the electrodes of the cuff constitute an unpre- 
dictable source of baseline shift which is partic- 
ularly obscure in chronicallj^ implanted trans- 
ducers. Leakage currents between the field coils 
and the input electrodes as well as other fac- 
tors^ also give rise to baseline shift. Conse- 
quently, to establish the approximate baseline 
it is necessary to clamp the vessel at both ends 
of the flow cuff in order to insure that there is 
no movement of blood within the cuff. In addi- 
tion to baseline shifts, scale factor changes may 
occur during chronic implantation of a flow cuff 
due to variations in sensitivity (S) resulting 
from changes in vessel dimensions and tensor 
conductivity as well as blood conductivity as 
previously discussed. 
Ultrasonic Transit Time Flowmeters 
The difference in effective velocity of sound 
pulses propagated alternately upstream and 
downstream through moving blood is a measure 
of blood velocity that has been used as the basis 
of an ultrasonic blood flowmeter.'^ The difference 
in transit times upstream and downstream is 
where L is the distance between transducers, Vp 
is the average flow velocity along the path of 
sound, c is velocity of sound in blood and a the 
angle between the blood velocity and sonic vec- 
tors. ''^ An approximation implicit in (3) if it 
is to be used to describe an actual blood vessel 
is that the length of the sound path in the ves- 
sel wall and surrounding tissue is very small 
compared to the path length in blood. However, 
the key factor to recognize is that Vp in (3) is 
not the velocity averaged over the entire lumen 
area (i.e., v) but rather the velocity averaged 
along the linear path of sound between the two 
transducers. Since various velocity profiles or 
average velocities v may give rise to the same 
Vp there is clearly an ambiguity present in at- 
tempting to measure volume flow.^ Conse- 
quently, empirical calibration by the user is 
necessary if one attempts to use this device to 
estimate volume of flow. 
