measurement of flow and volume of blood_ch08 jg webster.pdf

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8

MEASUREMENT OF FLOW ANDVOLUME OF BLOODJohn G. Webster

One of the primary measurements the physician would like to acquire from apatient is that of the concentration of O2 and other nutrients in the cells. Suchquantities are normally so difficult to measure that the doctor is forced toaccept the second-class measurements of blood flow and changes in bloodvolume, which usually correlate with concentration of nutrients. If blood flowis difficult to measure, the physician may settle for the third-class measurementof blood pressure, which usually correlates adequately with blood flow. If bloodpressure cannot be measured, the physician may fall back on the fourth-classmeasurement of the ECG, which usually correlates adequately with bloodpressure.

Note that the measurement of blood flow—the main subject of thischapter—is the one that most closely reflects the primary measurement ofconcentration of O2 in the cells. However, measurement of blood flow isusually more difficult to make and more invasive than measurement of bloodpressure or of the ECG.

Commonly used flowmeters, such as the orifice or turbine flowmeters, areunsuitable for measuring blood flow because they require cutting the vesseland can cause formation of clots. The specialized techniques described in thischapter have therefore been developed.

8.1 INDICATOR-DILUTION METHOD THAT USESCONTINUOUS INFUSION

The indicator-dilution methods described in this chapter do not measureinstantaneous pulsatile flow but, rather, flow averaged over a number ofheartbeats.

CONCENTRATION

When a given quantity m0 of an indicator is added to a volume V, the resultingconcentration C of the indicator is given by C ¼ m0=V. When an additional

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quantity m of indicator is then added, the incremental increase in concentra-tion is DC ¼ m=V. When the fluid volume in the measured space is continu-ously removed and replaced, as in a flowing stream, then in order to maintain afixed change in concentration, the clinician must continuously add a fixedquantity of indicator per unit time. That is, DC ¼ ðdm=dtÞ=ðdV=dtÞ. From thisequation, we can calculate flow (Donovan and Taylor, 2006).

F ¼ dV

dt¼ dm=dt

DC(8.1)

EXAMPLE 8.1 Derive (8.1) using principles of mass transport.

ANSWER The rate at which indicator enters the vessel is equal to the indi-cator’s input concentration Ci, times the flow F. The rate at which indicator isinjected into the vessel is equal to the quantity per unit time, dm=dt. The rate atwhich indicator leaves the vessel is equal to the indicator’s output concen-tration Co times F. For steady state, CiF þ dm=dt ¼ CoF or F ¼ ðdm=dtÞ=ðCo � CiÞ.

FICK TECHNIQUE

We can use (8.1) to measure cardiac output (blood flow from the heart) asfollows (Capek and Roy, 1988):

F ¼ dm=dt

Ca � Cv(8.2)

where

F¼ blood flow, liters/min

dm=dt¼ consumption of O2, liters/min

Ca¼ arterial concentration of O2, liters/liter

Cv ¼ venous concentration of O2, liters/liter

Figure 8.1 shows the measurements required. The blood returning to theheart from the upper half of the body has a different concentration of O2 fromthe blood returning from the lower half, because the amount of O2 extracted bythe brain is different from that extracted by the kidneys, muscles, and so forth.Therefore, we cannot accurately measure Cv in the right atrium. We mustmeasure it in the pulmonary artery after it has been mixed by the pumpingaction of the right ventricle. The physician may float the catheter into place bytemporarily inflating a small balloon surrounding the tip. This is done througha second lumen in the catheter.

As the blood flows through the lung capillaries, the subject adds theindicator (the O2) by breathing in pure O2 from a spirometer (see Figure 9.6).

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The exhaled CO2 is absorbed in a soda-lime canister, so the consumption of O2

is indicated directly by the net gas-flow rate.The clinician can measure the concentration of the oxygenated blood Ca in

any artery, because blood from the lung capillaries is well mixed by the leftventricle and there is no consumption of O2 in the arteries. An arm or leg arteryis generally used.

EXAMPLE 8.2 Calculate the cardiac output, given the following data:spirometer O2 consumption 250 ml/min; arterial O2 content, 0.20 ml/ml;venous O2 content, 0.15 ml/ml.

ANSWER From (8.2),

F ¼ dm=dt

Ca � Cv

¼ 0:25 liter/min

ð0:20 liter/literÞ � ð0:15 liter/literÞ¼ 5 liters/min (8.3)

The units for the concentrations of O2 represent the volume of O2 that canbe extracted from a volume of blood. This concentration is very high for blood,because large quantities of oxygen can be bound to hemoglobin. It would be

Figure 8.1 Several methods of measuring cardiac output In the Fick method,the indicator is O2; consumption is measured by a spirometer. The arterial-venous concentration difference is measured by drawing samples throughcatheters placed in an artery and in the pulmonary artery. In the dye-dilutionmethod, dye is injected into the pulmonary artery and samples are taken froman artery. In the thermodilution method, cold saline is injected into the rightatrium and temperature is measured in the pulmonary artery.

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very low if water were flowing through the vessels, even if the PO2 wereidentical in both cases.

The Fick technique is nontoxic, because the indicator (O2) is a normalmetabolite that is partially removed as blood passes through the systemiccapillaries. The cardiac output must be constant over several minutes so thatthe investigator can obtain the slope of the curve for O2 consumption. Thepresence of the catheter causes a negligible change in cardiac output.

8.2 INDICATOR-DILUTION METHOD THAT USES RAPID INJECTION

EQUATION

The continuous-infusion method has been largely replaced by the rapid-injection method, which is more convenient. A bolus of indicator is rapidlyinjected into the vessel, and the variation in downstream concentration of theindicator versus time is measured until the bolus has passed. The solid line inFigure 8.2 shows the fluctuations in concentration of the indicator that occurafter the injection. The dotted-line extension of the exponential decay showsthe curve that would result if there were no recirculation. For this case we cancalculate the flow as outlined in the following paragraphs.

An increment of blood of volume dV passes the sampling site in time dt.The quantity of indicator dm contained in dV is the concentration C(t) timesthe incremental volume. Hence dm ¼ CðtÞdV. Dividing by dt, we obtaindm=dt ¼ CðtÞdV=dt. But dV=dt ¼ Fi, the instantaneous flow; therefore

Figure 8.2 Rapid-injection indicator-dilution curve After the bolus is injectedat time A, there is a transportation delay before the concentration begins risingat time B. After the peak is passed, the curve enters an exponential decayregion between C and D, which would continue decaying along the dottedcurve to t1 if there were no recirculation. However, recirculation causes asecond peak at E before the indicator becomes thoroughly mixed in the bloodat F. The dashed curve indicates the rapid recirculation that occurs when thereis a hole between the left and right sides of the heart.

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dm ¼ FiCðtÞdt. Integrating over time through tl, when the bolus has passed thedownstream sampling point, we obtain

m ¼Z t1

0

FiCðtÞdt (8.4)

where t1 is the time at which all effects of the first pass of the bolus have diedout (point E in Figure 8.2). The mixing of the bolus and the blood within theheart chambers and the lungs smooths out minor variations in the instanta-neous flow Fi produced by the heartbeat. Thus we can obtain the average flowF from

F ¼ mR t10

CðtÞdt(8.5)

The integrated quantity in (8.5) is equal to the shaded area in Figure 8.2,and we can obtain it by counting squares or using a planimeter. A computer canextrapolate the dotted line in real time and compute the flow.

If the initial concentration of indicator is not zero—as may be the casewhen there is residual indicator left over from previous injections—then (8.5)becomes

F ¼ mR t10½DCðtÞ� dt

(8.6)

DYE DILUTION

A common method of clinically measuring cardiac output is to use acolored dye, indocyanine green (cardiogreen). It meets the necessaryrequirements for an indicator in that it is (1) inert, (2) harmless, (3) mea-surable, (4) economical, and (5) always intravascular. In addition, itsoptical absorption peak is 805 nm, the wavelength at which the opticalabsorption coefficient of blood is independent of oxygenation. The dye isavailable as a liquid that is diluted in isotonic saline and injected directlythrough a catheter, usually into the pulmonary artery. About 50% of thedye is excreted by the kidneys in the first 10 min, so repeat determinationsare possible.

The plot of the curve for concentration versus time is obtained from aconstant-flow pump, which draws blood from a catheter placed in the femoralor brachial artery. Blood is drawn through a colorimeter cuvette (Figure 2.17),which continuously measures the concentration of dye, using the principle ofabsorption photometry (Section 11.1). The 805 nm channel of a two-channelblood oximeter can be used for measuring dye-dilution curves. The clinician


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calibrates the colorimeter by mixing known amounts of dye and blood anddrawing them through the cuvette.

The shape of the curve can provide additional diagnostic information. Thedashed curve in Figure 8.2 shows the result when a left-right shunt (a holebetween the left and right sides of the heart) is present. Blood recirculatesfaster than normal, resulting in an earlier recirculation peak. When a right-leftshunt is present, the delay in transport is abnormally short, because some dyereaches the sampling site without passing through the lung vessels.

THERMODILUTION

The most common method of measuring cardiac output is that of injecting abolus of cold saline as an indicator. A special four-lumen catheter (Trautmanand D’ambra, 2006) is floated through the brachial vein into place in thepulmonary artery. A syringe forces a gas through one lumen; the gas inflates asmall, doughnut-shaped balloon at the tip. The force of the flowing bloodcarries the tip into the pulmonary artery. The cooled saline indicator is injectedthrough the second lumen into the right atrium. The indicator is mixed withblood in the right ventricle. The resulting drop in temperature of the blood isdetected by a thermistor located near the catheter tip in the pulmonary artery.The third lumen carries the thermistor wires. The fourth lumen, which is notused for the measurement of thermodilution, can be used for withdrawingblood samples. The catheter can be left in place for about 24 h, during whichtime many determinations of cardiac output can be made, something thatwould not be possible if dye were being used as the indicator. Also, it is notnecessary to puncture an artery.

We can derive the following equation, which is analogous to (8.6).

F ¼ Q

rbCb

Z t1

0

DTbðtÞ dt

ðm3/sÞ (8.7)

where

Q¼ heat content of injectate, Jð¼ ViDTiriciÞrb ¼ density of blood, kg/m3

cb ¼ specific heat of blood, J/(kg�K)

When an investigator uses the thermodilution method, there are a numberof problems that cause errors. (1) There may be inadequate mixing betweenthe injection site and the sampling site. (2) There may be an exchange of heatbetween the blood and the walls of the heart chamber. (3) There is heatexchange through the catheter walls before, during, and after injection.However, the instrument can be calibrated by simultaneously performingdye-dilution determinations and applying a correction factor that correctsfor several of the errors.

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8.3 ELECTROMAGNETIC FLOWMETERS

The electromagnetic flowmeter measures instantaneous pulsatile flow of bloodand thus has a greater capability than indicator-dilution methods, which measureonly average flow. It operates with any conductive liquid, such as saline or blood.

PRINCIPLE

The electric generator in a car generates electricity by induction. Copper wiresmove through a magnetic field, cutting the lines of magnetic flux and inducingan emf in the wire. This same principle is exploited in a commonly used bloodflowmeter, shown in Figure 8.3. Instead of copper wires, the flowmeter dependson the movement of blood, which has a conductance similar to that of saline.Faraday’s law of induction gives the formula for the induced emf.

e ¼Z L1

0

u � B�dL

where

B¼magnetic flux density, T

L¼ length between electrodes, m

u¼ instaneous velocity of blood, m/s

Figure 8.3 Electromagnetic flowmeter When blood flows in the vessel withvelocity u and passes through the magnetic field B, the induced emf e ismeasured at the electrodes shown. When an ac magnetic field is used, any fluxlines cutting the shaded loop induce an undesired transformer voltage.


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For a uniform magnetic field B and a uniform velocity profile u, the inducedemf is

e ¼ BLu (8.8)

where these three components are orthogonal.Let us now consider real flowmeters, several of which exhibit a number of

divergences from this ideal case. If the vessel’s cross section were square andthe electrodes extended the full length of two opposite sides, the flowmeterwould measure the correct average flow for any flow profile. The electrodes aresmall, however, so velocities near them contribute more to the signal than dovelocities farther away.

Figure 8.4 shows the weighting function that characterizes this effect forcircular geometry. It shows that the problem is less when the electrodes arelocated outside the vessel wall. The instrument measures correctly for auniform flow profile. For axisymmetric nonuniform flow profiles, such asthe parabolic flow profile resulting from laminar flow, the instrument mea-surement is correct if u is replaced by u, the average flow velocity. Because weusually know the cross-sectional area A of the lumen of the vessel, we canmultiply A by u to obtain F, the volumetric flow. However, in many locations of

Figure 8.4 Solid lines show the weighting function that represents relativevelocity contributions (indicated by numbers) to the total induced voltage forelectrodes at the top and bottom of the circular cross section. If the vessel wallextends from the outside circle to the dashed line, the range of the weightingfunction is reduced. (Adapted from J. A. Shercliff, The Theory of Electro-magnetic Flow Measurement, # 1962, Cambridge University Press.)

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blood vessels in the body, such as around the curve of the aorta and near itsbranches, the velocity profile is asymmetric, so errors result.

Other factors can also cause error.

1. Regions of high velocity generate higher incremental emfs than regions oflow velocity, so circulating currents flow in the transverse plane. Thesecurrents cause varying drops in resistance within the conductive blood andsurrounding tissues.

2. The ratio of the conductivity of the wall of the blood vessel to that of theblood varies with the hematocrit (percentage of cell volume to bloodvolume), so the shunting effects of the wall cause a variable error.

3. Fluid outside the wall of the vessel has a greater conductivity than thewall, so it shunts the flow signal.

4. The magnetic-flux density is not uniform in the transverse plane; thisaccentuates the problem of circulating current.

5. The magnetic-flux density is not uniform along the axis, which causescirculating currents to flow in the axial direction.

To minimize these errors, most workers recommend calibration for animalwork by using blood from the animal—and, where possible, the animal’s ownvessels also. Blood or saline is usually collected in a graduated cylinder andtimed with a stopwatch.

DIRECT-CURRENT FLOWMETER

The flowmeter shown in Figure 8.3 can use a dc magnetic field, so the outputvoltage continuously indicates the flow. Although a few early dc flowmeterswere built, none were satisfactory, for the following three reasons. (1) Thevoltage across the electrode’s metal-to-solution interface is in series withthe flow signal. Even when the flowmeter has nonpolarizable electrodes,the random drift of this voltage is of the same order as the flow signal, andthere is no way to separate the two. (2) The ECG has a waveform andfrequency content similar to that of the flow signal; near the heart, theECG’s waveform is much larger than that of the flow signal and thereforecauses interference. (3) In the frequency range of interest, 0 to 30 Hz, 1=f noisein the amplifier is large, which results in a poor SNR.

ALTERNATING-CURRENT FLOWMETER

The clinician can eliminate the problems of the dc flowmeter by operating thesystem with an ac magnet current of about 400 Hz. Lower frequencies requirebulky sensors, whereas higher frequencies cause problems due to stray capaci-tance. The operation of this carrier system results in the ac flow voltage shownin Figure 8.5. When the flow reverses direction, the voltage changes phase by1808, so the phase-sensitive demodulator (described in Section 3.15) is requiredto yield directional output.


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Although ac operation is superior to dc operation, the new problem oftransformer voltage arises. If the shaded loop shown in Figure 8.3 is not exactlyparallel to the B field, some ac magnetic flux intersects the loop and induces atransformer voltage proportional to dB=dt in the output voltage. Even whenthe electrodes and wires are carefully positioned, the transformer voltage isusually many times larger than the flow voltage, as indicated in Figure 8.5. Theamplifier voltage is the sum of the transformer voltage and the flow voltage.

There are several solutions to this problem. (1) It may be eliminated at thesource by use of a phantom electrode. One of the electrodes is separated into

Figure 8.5 Electromagnetic flowmeter waveforms The transformer voltageis 908 out of phase with the magnet current. Other waveforms are shown solidfor forward flow and dashed for reverse flow. The gated signal from the gated-sine-wave flowmeter includes less area than the in-phase signal from thequadrature-suppression flowmeter.


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two electrodes in the axial direction. Two wires are led some distance from theelectrodes, and a potentiometer is placed between them. The signal from thepotentiometer wiper yields a signal corresponding to a ‘‘phantom’’ electrode,which can be moved in the axial direction. The shaded loop in Figure 8.3 canthus be tilted forward or backward or placed exactly parallel to the B field.(2) Note in Figure 8.5 that we can sample the composite signal when thetransformer voltage is zero. At this time the flow voltage is at its maximum,and the resulting gated signal measures only the flow voltage. However, ifundesired phase shifts cause the gating to be done even a few degrees awayfrom the proper time, large errors and drifts result. (3) The best method forreducing the effects of transformer voltage is to use the quadrature-suppressioncircuit shown in Figure 8.6.

The magnitude of the voltage in the transformer at the amplifier outputis detected by the quadrature demodulator, which has a full-wave-rectifiedoutput. This is low-pass-filtered to yield a dc voltage, which is then modu-lated by the quadrature generator to produce a signal proportional to thetransformer voltage. The signal is fed to a balancing coil on the inputtransformer, thus balancing out the transformer voltage at the input. Withenough gain in this negative-feedback loop, the transformer voltage at theamplifier output is reduced by a factor of 50. This low transformer voltageprevents overloading of the in-phase demodulator, which extracts thedesired in-phase flow signal shown in Figure 8.5. By choosing low-noiseFETs for the amplifier input stage, the proper turns ratio on the step-uptransformer (Section 3.13), and full-wave demodulators, we can obtain anexcellent SNR.

Some flowmeters, unlike the sine-wave flowmeters described previously,use square-wave excitation. In this case the transformer voltage appears as avery large spike, which overloads the amplifier for a short time. After theamplifier recovers, the circuit samples the square-wave flow voltage and

Ves-sel

AmplifierIn-phasedemodulator

Low-passfilter

Low-passfilter

Output

Quadraturedemodulator

Quadraturegenerator

Magnetcurrentdriver

Oscillator

90° phase

Figure 8.6 The quadrature-suppression flowmeter detects the amplifierquadrature voltage. The quadrature generator feeds back a voltage to balanceout the probe-generated transformer voltage.


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processes it to obtain the flow signal. To prevent overload of the amplifier,trapezoidal excitation has also been used.

EXAMPLE 8.3 On a common time scale, sketch the waveforms for themagnet current, flow signal, and transformer voltage for the following electro-magnetic flowmeters: (1) gated sine wave, (2) square wave, and (3) trapezoi-dal. Indicate the best time for sampling each flow signal.

ANSWER For gated sine wave, waveforms are exactly like those in Figure8.5. Sample the composite signal when the transformer voltage is zero.Transformer voltage is proportional to dB=dt. Taking the derivative of squarewave B yields spikes at transitions. Because the amplifier is not perfect, thesetake time to decay. Best time to sample is near the end of transformer voltage¼ 0. Trapezoidal B yields reasonable dB=dt, so sample during time trans-former voltage ¼ 0.

PROBE DESIGN

A variety of probes to measure blood flow have been used (Cobbold, 1974).The electrodes for these probes are usually made of platinum. Best results areobtained when the electrodes are platinized (electrolytically coated withplatinum) to provide low impedance and are recessed in a cavity to minimizethe flow of circulating currents through the metal. When the electrodes must beexposed, bright platinum is used, because the platinized coating wears offanyway. Bright platinum electrodes have a higher impedance and a highernoise level than platinized ones.

Some probes do not use a magnetic core, but they have lower sensitivity. Acommon perivascular probe is shown in Figure 8.7, in which a toroidallaminated Permalloy core is wound with two oppositely wound coils. The


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resulting magnetic field has low leakage flux. To prevent capacitive couplingbetween the coils of the magnet and the electrodes, an electrostatic shield isplaced between them. The probe is insulated with a potting material that has avery high resistivity and impermeability to salt water (blood is similar tosaline).

The open slot on one side of the probe makes it possible to slip it over ablood vessel without cutting the vessel. A plastic key may be inserted into theslot so that the probe encircles the vessel. The probe must fit snugly duringdiastole so that the electrodes make good contact. This requires some con-striction of an artery during systole, when the diameter of the artery is about7% greater. Probes are made in 1 mm increments in the range of 1 to 24 mm toensure a snug fit on a variety of sizes of arteries. To be able to measure any sizeof artery requires a considerable expenditure for probes: Individual probestypically cost $500 each. The probes do not operate satisfactorily on veins,because the electrodes do not make good contact when the vein collapses.Special flow-through probes are used outside the body for measuring theoutput of cardiac-bypass pumps.

8.4 ULTRASONIC FLOWMETERS

The ultrasonic flowmeter, like the electromagnetic flowmeter, can measureinstantaneous flow of blood. The ultrasound can be beamed through the skin,thus making transcutaneous flowmeters practical. Advanced types of ultra-sonic flowmeters can also measure flow profiles. These advantages are making

Figure 8.7 The toroidal-type cuff probe has two oppositely wound windingson each half of the core. The magnetic flux thus leaves the top of both sides,flows down in the center of the cuff, enters the base of the toroid, and flows upthrough both sides.


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the ultrasonic flowmeter the subject of intensive development. Let us examinesome aspects of this development.

TRANSDUCERS

For the transducer to be used in an ultrasonic flowmeter, we select a piezo-electric material (Section 2.6) that converts power from electric to acousticform (Christensen, 1988). Lead zirconate titanate is a crystal that has thehighest conversion efficiency. It can be molded into any shape by melting. As itis cooled through the Curie temperature, it is placed in a strong electric field topolarize the material. It is usually formed into disks that are coated on oppositefaces with metal electrodes and driven by an electronic oscillator. The resultingelectric field in the crystal causes mechanical constriction. The pistonlikemovements generate longitudinal plane waves, which propagate into thetissue. For maximal efficiency, the crystal is one-half wavelength thick. Anycavities between the crystal and the tissue must be filled with a fluid or waterygel in order to prevent the high reflective losses associated with liquid–gasinterfaces.

Because the transducer has a finite diameter, it will produce diffractionpatterns, just as an aperture does in optics. Figure 8.8 shows the outline of thebeam patterns for several transducer diameters and frequencies. In the nearfield, the beam is largely contained within a cylindrical outline and there is littlespreading. The intensity is not uniform, however: There are multiple maxi-mums and minimums within this region, caused by interference. The near fieldextends a distance dnf given by

dnf ¼D2

4l(8.9)

where D ¼ transducer diameter and l ¼ wavelength.

Figure 8.8 Near and far fields for various transducer diameters and frequen-cies. Beams are drawn to scale, passing through a 10 mm-diameter vessel.Transducer diameters are 5, 2, and 1 mm. Solid lines are for 1.5 MHz, dashedlines for 7.5 MHz.

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In the far field the beam diverges, and the intensity is inversely propor-tional to the square of the distance from the transducer. The angle of beamdivergence f, shown in Figure 8.8, is given by

sin f ¼ 1:2l

D(8.10)

Figure 8.8 indicates that we should avoid the far field because of its lowerspatial resolution. To achieve near-field operation, we must use higher fre-quencies and larger transducers.

To select the operating frequency, we must consider several factors. For abeam of constant cross section, the power decays exponentially because ofabsorption of heat in the tissue. The absorption coefficient is approximatelyproportional to frequency, so this suggests a low operating frequency. How-ever, most ultrasonic flowmeters depend on the power scattered back frommoving red blood cells. The backscattered power is proportional to f 4, whichsuggests a high operating frequency. The usual compromise dictates a fre-quency between 2 and 10 MHz.

TRANSIT-TIME FLOWMETER

Figure 8.9(a) shows the transducer arrangement used in the transit-timeultrasonic flowmeter (Christensen, 1988). The effective velocity of sound inthe vessel is equal to the velocity of sound, c, plus a component due to u, the

Figure 8.9 Ultrasonic transducer configurations (a) A transit-time proberequires two transducers facing each other along a path of length D inclinedfrom the vessel axis at an angle f. The hatched region represents a singleacoustic pulse traveling between the two transducers. (b) In a transcutaneousprobe, both transducers are placed on the same side of the vessel, so the probecan be placed on the skin. Beam intersection is shown hatched. (c) Anytransducer may contain a plastic lens that focuses and narrows the beam.(d) For pulsed operation, the transducer is loaded by backing it with a mixtureof tungsten powder in epoxy. This increases losses and lowers Q. Shadedregion is shown for a single time of range gating. (e) A shaped piece of Luciteon the front loads the transducer and also refracts the beam. (f) A transducerplaced on the end of a catheter beams ultrasound down the vessel. (g) Forpulsed operation, the transducer is placed at an angle.


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velocity of flow of blood averaged along the path of the ultrasound. Forlaminar flow, u ¼ 1:33 u, and for turbulent flow, u ¼ 1:07 u, where u is thevelocity of the flow of blood averaged over the cross-sectional area. Becausethe ultrasonic path is along a single line rather than averaged over the cross-sectional area, u differs from u. The transit time in the downstream (þ) andupstream (�) directions is

t ¼ distance

conduction velocity¼ D

c� u cos u(8.11)

The difference between upstream and downstream transit times is

Dt ¼ 2 Du cos u

ðc2 � u2 cos2 uÞffi 2 Du cos u

c2(8.12)

and thus the average velocity u is proportional to Dt. A short acoustic pulse istransmitted alternately in the upstream and downstream directions. Un-fortunately, the resulting Dt is in the nanosecond range, and complex elec-tronics are required to achieve adequate stability. Like the electromagneticflowmeter, the transit-time flowmeter and similar flowmeters using a phase-shift principle can operate with either saline or blood as a fluid, because they donot require particulate matter for scattering. However, they do require inva-sive surgery to expose the vessel.

CONTINUOUS-WAVE DOPPLER FLOWMETER

When a target recedes from a fixed source that transmits sound, the frequencyof the received sound is lowered because of the Doppler effect. For smallchanges, the fractional change in frequency equals the fractional change invelocity.

fd

f0

¼ u

c(8.13)

where

fd¼Doppler frequency shift

f0¼ source frequency

u¼ target velocity

c¼ velocity of sound

The flowmeter shown in Figure 8.10 requires particulate matter such asblood cells to form reflecting targets. The frequency is lowered twice. One shiftoccurs between the transmitting source and the moving cell that receives the


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signal. The other shift occurs between the transmitting cell and the receivingtransducer.

fd

f0

¼ 2u

cþ uffi 2u

c(8.14)

The approximation is valid, because cffi 1500 m/s and uffi 1:5 m/s. The veloc-ities do not all act along the same straight line, so we add an angle factor

fd ¼2 f0u cos u

c(8.15)

where u is the angle between the beam of sound and the axis of the bloodvessel, as shown in Figure 8.10. If the flow is not axial, or the transducers do notlie at the same angle, such as in Figure 8.9(b), we must include additionaltrigonometric factors.

Figure 8.10 shows the block diagram of a simple continuous-waveflowmeter. The oscillator must have a low output impedance to drive thelow-impedance crystal. Although at most frequencies the crystal transducerhas a high impedance, it is operated at mechanical resonance, where theimpedance drops to about 100 V. The ultrasonic waves are transmitted to themoving cells, which reflect the Doppler-shifted waves to the receivingtransducer. The receiving transducer is identical to the transmitting trans-ducer. The amplified radio-frequency (RF) signal plus carrier signal isdetected to produce an audio-frequency (AF) signal at a frequency givenby (8.15).

Listening to the audio output using a speaker, we get much usefulqualitative information. A simple frequency-to-voltage converter provides a

Figure 8.10 Doppler ultrasonic blood flowmeter In the simplest instrument,ultrasound is beamed through the vessel walls, backscattered by the red bloodcells, and received by a piezoelectric crystal.


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quantitative output to a recorder. The zero-crossing detector emits a fixed-areapulse each time the audio signal crosses the zero axis. These pulses are low-pass-filtered to produce an output proportional to the velocity of the bloodcells.

Although the electromagnetic blood flowmeter is capable of measuringboth forward and reverse flow, the simple ultrasonic-type flowmeter full-wave rectifies the output, and the sense of direction of flow is lost. Thisresults because—for either an increase or a decrease in the Doppler-shiftedfrequency—the beat frequency is the same. Examination of the field inter-sections shown in Figure 8.10 suggests that the only received frequency is theDoppler-shifted one. However, the received carrier signal is very muchlarger than the desired Doppler-shifted signal. Some of the RF carrier iscoupled to the receiver by the electric field from the transmitter. Because ofside lobes in the transducer apertures, some of the carrier signal travels adirect acoustic path to the receiver. Other power at the carrier frequencyreaches the receiver after one or more reflections from fixed interfaces.The resulting received signal is composed of a large-amplitude signal at thecarrier frequency plus the very low (approximately 0.1%) amplitudeDoppler-shifted signal.

The Doppler-shifted signal is not at a single frequency, as implied by(8.15), for several reasons.

1. Velocity profiles are rarely blunt, with all cells moving at the samevelocity. Rather, cells move at different velocities, producing differentshifts of the Doppler frequency.

2. A given cell remains within the beam-intersection volume for a short time.Thus the signal received from one cell is a pure frequency multiplied bysome time-gate function, yielding a band of frequencies.

3. Acoustic energy traveling within the main beam, but at angles to the beamaxis, plus energy in the side lobes, causes different Doppler-frequencyshifts due to an effective change in u.

4. Tumbling of cells and local velocities resulting from turbulence causedifferent Doppler-frequency shifts.

All these factors combine to produce a band of frequencies. The resultingspectrum is similar to band-limited random noise, and from this we mustextract flow information.

We would like to have high gain in the RF amplifier in order to boost thelow-amplitude Doppler-frequency components. But the carrier is large, so thegain cannot be too high or saturation will occur. The RF bandwidth need not bewide, because the frequency deviation is only about 0.001 of the carrierfrequency. However, RF-amplifier bandwidths are sometimes much widerthan required, to permit tuning to different transducers.

The detector can be a simple square-law device such as a diode. The outputspectrum contains the desired difference (beat) frequencies, which lie in theaudio range, plus other undesired frequencies.


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EXAMPLE 8.4 Calculate the maximal audio frequency of a Doppler ultra-sonic blood flowmeter that has a carrier frequency of 7 MHz, a transducerangle of 458, a blood velocity of 150 cm/s, and an acoustic velocity of 1500 m/s.

ANSWER Substitute these data into (8.15).

fd ¼2ð7� 106 HzÞð1:5 m/sÞ cos 45�

1500 m/sffi 10 kHz (8.16)

The dc component must be removed with a high-pass filter in the AFamplifier. We require a corner frequency of about 100 Hz in order to rejectlarge Doppler signals due to motion of vessel walls. Unfortunately, this high-pass filter also keeps us from measuring slow cell velocities (less than 1.5 cm/s),such as occur near the vessel wall. A low-pass filter removes high frequenciesand also noise. The corner frequency is at about 15 kHz, which includes allfrequencies that could result from cell motion, plus an allowance for spectralspreading.

In the simplest instruments, the AF output drives a power amplifier andspeaker or earphones. The output is a band of frequencies, so it has awhooshing sound that for steady flows sounds like random noise. Venousflow sounds like a low-frequency rumble and may be modulated when thesubject breathes. Arterial flow, being pulsatile, rises to a high pitch once eachbeat and may be followed by one or more smaller, easily heard waves caused bythe under-damped flow characteristics of arteries. Thus this simple instrumentcan be used to trace and qualitatively evaluate blood vessels within 1 cm of theskin in locations in the legs, arms, and neck. We can also plot the spectrum ofthe AF signal versus time to obtain a more quantitative indication of velocitiesin the vessel.

The function of the zero-crossing detector is to convert the AF inputfrequency to a proportional analog output signal. It does this by emitting aconstant-area pulse for each crossing of the zero axis. The detector contains acomparator (a Schmitt trigger), so we must determine the amount of hysteresisfor the comparator. If the input were a single sine wave, the signal-to-hysteresisratio (SHR) could be varied over wide limits, and the output would indicate thecorrect value. But the input is band-limited random noise. If the SHR is low,many zero crossings are missed. As the SHR increases, the indicated frequencyof the output increases. A SHR of 7 is a good choice because the output doesnot vary significantly with changes in SHR. Automatic gain control can be usedto maintain this ratio. Very high SHRs are not desirable; noise may trigger thecomparator. The signal increases and decreases with time because of thebeating of the signal components at the various frequencies. Thus the short-term SHR fluctuates, and for a small portion of the time the signal is too low toexceed the hysteresis band.

EXAMPLE 8.5 Design a comparator with a SHR of 7, as required for theDoppler zero-crossing detector.


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ANSWER Assume that the signal has been amplified so that its input p–pvalue equals the�10 V linear range for an op amp. Then our thresholds shouldbe �10=7 ¼ �1:4 V. Use the circuit shown in Figure 3.6(a). Because the inputis symmetric about zero, vref ¼ 0 V. Assume the op amp output saturates at�12 V. The p�p width of the hysteresis loop is four times the voltage across R3,or 2:8=4 ¼ 0:7. Assume R3 ¼ 1 kV. Then

R2 þ R3

R3

¼ R2 þ 1 kV

1 kV¼ 12

0:7

R2 ¼ 16:1 kV:Choose R1 ¼ 10 kV:

The output of the zero-crossing detector is a series of pulses. These pulsesare passed through a low-pass filter to remove as many of the high-frequencycomponents as possible. The filter must pass frequencies from 0 to 25 Hz inorder to reproduce the frequencies of interest in the flow pulse. However, thesignal is similar to band-limited random noise. Thus the pulses are not atuniform intervals, even for a fixed flow velocity, but are more like a Poissonprocess. Hence the output contains objectionable noise. The low-pass filtermust therefore be chosen as a compromise between the high corner frequencydesired to reproduce the flow pulse and the low corner frequency desired forgood filtering of noise.

A major defect of the detector used in simple flowmeters is that it cannotdetect the direction of flow. The recorded output looks as it would if the truevelocity had been full-wave rectified. Compared with the electromagneticflowmeter, this is a real disadvantage, because reverse flow occurs frequently inthe body. A first thought might be to translate the Doppler-shifted frequenciesnot to the region about dc, but to the region about 20 kHz. Forward flow mightthus be 30 kHz, and reverse flow 10 kHz. The difficulty with this approach isthat the high-amplitude carrier signal is translated to 20 kHz. The Dopplersignals are so small that considerable effort is required to build any reasonablefrequency-to-voltage converter that is not dominated by the 20 kHz signal.

A better approach is to borrow a technique from radar technology, whichis used to determine not only the speed at which an aircraft is flying but also itsdirection. This is the quadrature-phase detector.

Figure 8.11(a) shows the analog portion of the quadrature-phase detector(McLeon, 1967). A phase-shift network splits the carrier into two componentsthat are in quadrature, which means that they are 908 apart. These referencecosine and sine waves must be several times larger than the RF-amplifieroutput, as shown in Figure 8.12(a). The reference waves and the RF-amplifieroutput are linearly summed to produce the RF envelope shown in Figure8.12(b). We assume temporarily that the RF-amplifier output contains nocarrier.

If the flow of blood is in the same direction as the ultrasonic beam, weconsider the blood to be flowing away from the transducer, as shown in Figure8.11(a). For this direction, the Doppler-shift frequency is lower than that ofthe carrier. The phase of the Doppler wave lags behind that of the reference


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carrier, and the Doppler vector [see Figure 8.12(a)] rotates clockwise. InFigure 8.12(b), for time 1, the carrier and the Doppler add, producing a largersum in the cosine channel. The sine channel is unchanged. For time 2, thecarrier and the Doppler add, producing a larger sum in the sine channel.Similar reasoning produces the rest of the wave for times 3 and 4. Note that thesine channel lags behind the cosine channel.

If the flow of blood is toward the transducer, the Doppler frequency ishigher than the carrier frequency, and the Doppler vector rotates counter-clockwise. This produces the dashed waves shown in Figure 8.12(b), and thephase relation between the cosine and sine channels is reversed. Thus, byexamining the sign of the phase, we measure direction of flow. The detectorproduces AF waves that have the same shape as the RF envelope.

Figure 8.11(b) shows the logic that detects the sign of the phase. The cosinechannel drives a comparator, the digital output of which, shown in Figure8.12(b), is used for gating and does not change with direction of flow of blood.The sine channel triggers a one-shot the width of which must be short.Depending on the direction of flow, this one-shot is triggered either at thebeginning of or halfway through the period, as shown in Figure 8.12(b). The

Figure 8.11 Directional Doppler block diagram (a) Quadrature-phase detec-tor: Sine and cosine signals at the carrier frequency are summed with the RFoutput before detection. The output C from the cosine channel then leads (orlags) the output S from the sine channel if the flow is away from (or toward) thetransducer. (b) Logic circuits route one-shot pulses through the top (orbottom) AND gate when the flow is away from (or toward) the transducer.The differential amplifier provides bidirectional output pulses that are thenfiltered.


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AND gates then gate it into the top or bottom input of the differentialamplifier, thus producing a bidirectional output.

The preceding discussion is correct for a sinusoidal RF signal. Our RFsignal is like band-limited random noise, however, so there is some timeshifting of the relations shown in Figure 8.12(b). Also, a large fixed componentat the carrier frequency is present, which displaces the Doppler vectors awayfrom the position shown. As long as the reference cosine and sine waves aremore than twice the amplitude of the total RF output, time shifting of thegating relations is not excessive. These time shifts are not problems in practice;a short one-shot pulse can shift almost �908 before passing out of the correctcomparator gate.

It is possible to add another one-shot and several logic blocks to obtainpulse outputs on both positive and negative zero crossings. This doubles thefrequency of the pulse train and reduces the fluctuations in the output to 0.707of their former value.

Figure 8.12 Directional Doppler signal waveforms (a) Vector diagram: Thesine wave at the carrier frequency lags the cosine wave by 908. If flow is awayfrom the transducer, the Doppler frequency is lower than the carrier. The shortvector represents the Doppler signal and rotates clockwise, as shown by thenumbers 1, 2, 3, and 4. (b) Timing diagram: The top two waves represent thesingle-peak envelope of the carrier plus the Doppler before detection. Com-parator outputs respond to the cosine channel audio signal after detection.One-shot pulses are derived from the sine channel and are gated through thecorrect AND gate by comparator outputs. The dashed lines indicate flowtoward the transducer.


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PULSED DOPPLER

Continuous-wave flowmeters provide little information about flow profile.Therefore, several instruments have been built (Christensen, 1988) that oper-ate in a radarlike mode. The transmitter is excited with a brief burst of signal.The transmitted wave travels in a single packet, and the transmitter can also beused as a receiver, because reflections are received at a later time. The delaybetween transmission and reception is a direct indication of distance, so we canobtain a complete plot of reflections across the blood vessel. By examining theDoppler shift at various delays, we can obtain a velocity profile across thevessel.

To achieve good range resolution, the transmitted-pulse duration shouldideally be very short. To achieve a good SNR and good velocity discrimination,it should be long. The usual compromise is an 8 MHz pulse of 1 ms duration,which produces a traveling packet 1.5 mm long, as shown in Figure 8.9(d). Theintensity of this packet is convolved with the local velocity profile to producethe received signal. Thus, the velocity profile of the blood vessel is smeared to alarger-than-actual value. Because of this problem, and also because the wavepacket arrives at an angle to normal, the location of the vessel walls isindistinct. It is possible, however, to mathematically ‘‘deconvolve’’ the instru-ment output to obtain a less smeared representation of the velocity profile.

There are two constraints on pulse repetition rate fr. First, to avoid rangeambiguities, we must analyze the return from one pulse before sending out thenext. Thus

fr <c

2Rm

(8.17)

where Rm is the maximal useful range. Second, we must satisfy the samplingtheorem, which requires that

fr > 2fd (8.18)

Combining (8.17) and (8.18) with (8.15) yields

umðcos uÞRmax <c2

8f0

(8.19)

which shows that the product of the range and the maximal velocity along thetransducer axis is limited. In practice, measurements are constrained evenmore than indicated by (8.19) because of (1) spectral spreading, whichproduces some frequencies higher than those expected, and (2) imperfectcutoff characteristics of the low-pass filters used to prevent aliasing (generationof fictitious frequencies by the sampling process).

Because we cannot easily start and stop an oscillator in 1 ms, the first stageof the oscillator operates continuously. The transmitter and the receiver both


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use a common piezoelectric transducer, so a gate is required to turn off thesignal from the transmitter during reception. A one-stage gate is not sufficientto isolate the large transmitter signals from the very small received signals.Therefore, two gates in series are used to turn off the transmitter.

The optimal transmitted signal is a pulse-modulated sine-wave carrier.Although it is easy to generate this burst electrically, it is difficult to transducethis electric burst to a similar acoustic burst. The crystal transducer has a high Q(narrow bandwidth) and therefore rings at its resonant frequency long after theelectric signal stops. Therefore, the transducer is modified to achieve a lower Q(wider bandwidth) by adding mass to the back [Figure 8.9(d)] or to the front[Figure 8.9(e)]. The Q is not lowered to a desirable value of about 2 to 5, becausethis would greatly decrease both the efficiency of the transmission and thesensitivity of the reception. The Q is generally 5 to 15, so some ringing still exists.

When we generate a short sine-wave burst, we no longer have a singlefrequency. Rather, the pulse train of the repetition rate is multiplied by thecarrier in time, producing carrier sidebands in the frequency domain. Thisspectrum excites the transducer, producing a field that is more complex thanthat for continuous-wave excitation. This causes spectral spreading of thereceived signal.

LASER DOPPLER BLOOD FLOWMETER

In a laser Doppler blood flowmeter, a 5 mW He–Ne laser beams 632.8 nm lightthrough fiber optics into the skin (Khaodhiar and Veves, 2006). Moving redblood cells in the skin frequency shift the light and cause spectral broadening.Reflected light is carried by fiber optics to a photodiode. Filtering, weighting,squaring, and dividing are necessary for signal processing. Capillary blood flowhas been studied in the skin and many other organs.

8.5 THERMAL-CONVECTION VELOCITY SENSORS

PRINCIPLE

The thermodilution methods described in Sections 8.1 and 8.2 depend on themixing of the heat indicator into the entire flow stream. In contrast, thermalvelocity sensors depend on convective cooling of a heated sensor and aretherefore sensitive only to local velocity.

Figure 8.13(a) shows a simple probe. The thermistor Ru is heated to atemperature difference DT above blood temperature by the power W dissi-pated by current passing through Ru. Experimental observations (Grahn et al.,1969) show that these quantities are related to the blood velocity u by

W

DT¼ aþ b log u (8.20)

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where a and b are constants. Thus the method is nonlinear, with a largesensitivity at low velocities and a small sensitivity at high velocities.

PROBES

Catheter-tip probes are designed with two types of sensors (Cobbold, 1974). Thefirst type uses the thermistors shown in Figure 8.13 and provides a high sensitivityand reasonable resistance values. Because the thermistor shown in Figure 8.13(a)is cooled equally for both directions of velocity, the output of the instrument is afull-wave-rectified replica of the true velocity. To overcome this limitation, theprobe shown in Figure 8.13(b) has two additional thermistors located a fewtenths of a millimeter downstream and upstream from Ru. Depending on thedirection of velocity, one or the other is heated by the heat carried through theblood from the thermistor Ru. These two additional thermistors are placed in abridge that is balanced for zero velocity. A comparator detects the bridgeunbalance and switches the output from positive to negative. The probe shownin Figure 8.13(c) uses two velocity sensors arranged so that one is exposed to thefluid velocity while the other is shielded from the fluid velocity.

The second type of sensor uses a glass bead with a thin strip of platinumdeposited on its surface. The platinum may be painted on and then fired in afurnace, or it may be sputtered (deposited by electric discharge in a vacuum). Adisadvantage of platinum-film sensors is their low resistance (a few ohms) andlow sensitivity.

A real question arises about what is actually being measured. When acatheter is inserted into a blood vessel, the sensor may be centered and thusmeasure maximal velocity, or it may be against the wall of the vessel and thusmeasure a low velocity. One way of ensuring that the sensor is not against thewall is to rotate the catheter, searching for the maximal output. Catheters arealso sensitive to radial velocity of blood, as well as to radial vibrations of thecatheter (catheter whip). Thus, in addition to any errors due to measuringvelocity, errors in trying to estimate flow can arise from lack of knowledgeabout location of the sensor. Either type of probe (if it is made sufficientlysmall) can be placed at the end of a hypodermic needle and inserted perpen-dicular to the vessel for measuring velocity profiles.

Figure 8.13 Thermal velocity probes (a) Velocity-sensitive thermistor Ru isexposed to the velocity stream. Temperature-compensating thermistor Rt isplaced within the probe. (b) Thermistors placed down- and upstream from Ru

are heated or not heated by Ru, thus indicating velocity direction. (c) Therm-istors exposed to and shielded from flow can also indicate velocity direction.


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CIRCUIT

A constant-current sensor circuit cannot be used for two reasons. First, the timeconstant of the sensor embedded in the probe is a few tenths of a second—

much too long to achieve the desired frequency response of 0 to 25 Hz. Second,to achieve a reasonable sensitivity at high velocities, the sensor current must beso high that when the flow stops, lack of convection cooling increases thesensor temperature more than 5 8C above the blood temperature and fibrincoats the sensor.

The constant-temperature sensor circuit shown in Figure 8.14 overcomesboth of these problems. The circuit is initially unbalanced by adjusting R1. Theunbalance is amplified by the high-gain op amp, and its output is fed back topower the resistance bridge. Operation of the circuit is as follows: Assume thatthermistor Ru is 5 8C higher than blood temperature because of self-heating. Ifthe velocity increases, Ru cools and its resistance increases. A more positivevoltage enters the noninverting op-amp terminal, so vb increases. This increasesbridge power and Ru heats up, thus counteracting the original cooling. Thesystem uses high-gain negative feedback to keep the bridge always in balance.Thus Ru remains nearly constant, and therefore its temperature remains nearlyconstant. The high-gain negative feedback divides the sensor time constant by afactor equal to the loop gain, so frequency response is greatly improved. Ineffect, if the sensor becomes slightly cooled, the op amp can provide a largequantity of power to rapidly heat it back to the desired temperature.

The circuit operates satisfactorily with only one sensor, Ru, provided thatthe blood temperature is constant. Should the blood temperature vary, atemperature–compensating thermistor Rt is added to keep the bridge inbalance. So that its rise in temperature is very small, Rt must have a muchlower resistance–temperature coefficient than Ru, to ensure that Rt is a sensorof temperature and not of velocity. The thermal resistance of Rt can be loweredby making it large in size, by using a heat sink, or by placing it within the probeso that the effective cooling area is much larger. Another solution is to increase

Figure 8.14 Thermal velocity meter circuit A velocity increase cools Ru, thevelocity-measuring thermistor. This increases voltage to the noninverting op-amp input, which increases bridge voltage vb and heats Ru. Rt providestemperature compensation.

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the resistance values for R2 and Rt so that their power dissipation is muchlower.

A linearizer is required to solve (8.20). We may square vb to obtain W andthen use an antilog converter to obtain vo. For the directional probe shown inFigure 8.17(b), a unity-gain inverting amplifier and switch may be used to yieldthe direction of flow.

Calibration can be accomplished by using a sinusoidal-flow pump or acylindrical pan of liquid rotating on a turntable.

The main use of thermal-velocity sensors is to measure the velocity of bloodand to compile velocity profiles in studies of animals, although such sensorshave also been regularly used to measure velocity and acceleration of blood atthe aortic root in human patients undergoing diagnostic catheterization. Thesame principle has also been applied to the measurement of the flow of air inlungs and ventilators by installing a heated platinum wire in a breathing tube.

8.6 CHAMBER PLETHYSMOGRAPHY

Plethysmographs measure changes in volume. The only accurate way tomeasure changes in volume of blood in the extremities noninvasively is touse a chamber plethysmograph. By timing these volume changes, we canmeasure flow by computing F ¼ dV=dt. A cuff is used to prevent venous bloodfrom leaving the limb—hence the name venous-occlusion plethysmography(Seagar et al., 1984).

EQUIPMENT

Figure 8.15 shows the equipment used in a venous-occlusion plethysmograph.The chamber has a rigid cylindrical outer container and is placed around the leg.

Figure 8.15 In chamber plethysmography, the venous-occlusion cuff is inflatedto 50 mm Hg (6.7 kPa), stopping venous return. Arterial flow causes an increasein volume of the leg segment, which the chamber measures. The text explains thepurpose of the arterial-occlusion cuff.


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As the volume of the leg increases, the leg squeezes some type of bladder anddecreases its volume. If the bladder is filled with water, the change in volume maybe measured by observing the water rising in a calibrated tube. For recordingpurposes, some air may be introduced above the water and the change in airpressure measured. Water-filled plethysmographs are temperature controlled toprevent thermal drifts. Because of their hydrostatic pressure, they may constrictthe vessels in the limb and cause undesirable physiological changes.

Air may be used in the bladder and the resulting changes in pressuremeasured directly. Some systems do not use a bladder. They attempt to sealthe ends of a rigid chamber to the limb, but then leaks may be a problem. Onedevice uses a pneumotachometer to measure the flow of air into and out of thechamber. This flow is then integrated to yield changes in volume. This equipmentis designed to accommodate a variety of limb sizes, so the chambers and bladdersare made in a family of sizes. Alternatively, a single chamber may be used forseveral sizes of limb. Devices that are capable of doing this are made with irisdiaphragms that form the ends of the chamber and close down on the limb.

METHOD

Figure 8.16 shows the sequence of operations that yields a measurement of flow(Raines and Darling, 1976). A calibration may be marked on the record byinjecting into the chamber a known volume of fluid, using the volume-calibration syringe. The venous-occlusion cuff is then applied to a limb andpressurized to 50 mm Hg (6.7 kPa), which prevents venous blood from leavingthe limb. Arterial flow is not hindered by this cuff pressure, and the increase involume of blood in the limb per unit time is equal to the arterial inflow. If thechamber completely encloses the limb distal to the cuff, the arterial flow intothe limb is measured. If the chamber encloses only a segment of a limb, asshown in Figure 8.15, an arterial-occlusion cuff distal to the chamber must beinflated to 180 mm Hg (24 kPa) to ensure that the changes in chamber volumemeasure only arterial flow entering the segment of the limb.

A few seconds after the cuffs are occluded, the venous pressure exceeds50 mm Hg (6.7 kPa), venous return commences, and the volume of blood in the

Figure 8.16 After venous-occlusion cuff pressure is turned on, the initialvolume-versus-time slope is caused by arterial inflow. After the cuff is released,segment volume rapidly returns to normal (A). If a venous thrombosis blocksthe vein, return to normal is slower (B).

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limb segment plateaus. When the clinician releases the pressure of the venous-occlusion cuff, the volume of blood in the limb segment rapidly returns tonormal (Figure 8.16, curve A). If a venous thrombosis (vein clot) partiallyblocks the return of venous blood, the volume of blood in the veins returns tonormal more slowly (Figure 8.16, curve B). This technique is a useful non-invasive test for venous thrombosis.

Brunswig Newring et al. (2006) note that the measurement of erection, orpenile tumescence, is the only physiological response that reliably differenti-ates male sexual arousal from other emotional states. Early water- or air-filledchamber plethysmographs for measuring tumescence have been replaced byless bulky circular metal bands and elastic strain gages.

8.7 ELECTRICAL-IMPEDANCE PLETHYSMOGRAPHY

It is simple to attach electrodes to a segment of tissue and measure the resultingimpedance of the tissue. As the volume of the tissue changes in response topulsations of blood (as happens in a limb) or the resistivity changes in responseto increased air in the tissue (as happens in the lung), the impedance of thetissue changes (Hutten, 2006).

Electrical-impedance plethysmography has been used to measure a widevariety of variables, but in many cases the accuracy of the method is poor orunknown.

PRINCIPLE

In the early 1950s, Nyboer (1970) developed the equations used in imped-ance plethysmography. However, we shall follow Swanson’s (1976) deri-vation, which is conceptually and mathematically simpler. Figure 8.17shows Swanson’s model of a cylindrical limb. The derivation requiresthree assumptions: (1) The expansion of the arteries is uniform. This assump-tion is probably valid in healthy vessels, but it may not be valid in diseasedones. (2) The resistivity of blood, rb, does not change. In fact, rb, decreaseswith velocity because of alignment of the cells with flow streamlines andmovement of cells toward the axis. Also, rb, is real for dc but has a smallreactive component at higher frequencies. (3) Lines of current are parallel tothe arteries. This assumption is probably valid for most limb segments, but notfor the knee.

The shunting impedance of the blood, Zb, is due to the additional bloodvolume DV that causes the increase in cross-sectional area DA.

Zb ¼rbL

DA(8.21)

DV ¼ L DA ¼ rbL2

Zb

(8.22)


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But we must replace the Zb of Figure 8.17(b) in terms of the normallymeasured DZ ¼ ½ðZb jjZÞ � Z� of Figure 8.17(c). Now

DZ ¼ ZZb

Z þ Zb

� Z ¼ �Z2

Z þ Zb

(8.23)

and because Z�Zb,

1

Zb

ffi �DZ

Z2(8.24)

Substituting (8.24) in (8.22) yields

DV ¼ �rbL2DZ

Z2(8.25)

If the assumptions are valid, (8.25) shows that we can calculate DV from rb

(Geddes and Baker, 1989) and from other quantities that are easily measured.Although (8.25) is valid at any frequency, there are several considerations

that suggest the use of a frequency of about 100 kHz.

1. It is desirable to use a current greater than 1 mA in order to achieveadequate SNR. At low frequencies this current causes an unpleasantshock. However, the current required for perception increases withfrequency (Section 14.2). Therefore, frequencies above 20 kHz areused to avoid perception of the current.

Figure 8.17 (a) A model for impedance plethysmography. A cylindrical limbhas length L and cross-sectional area A. With each pressure pulse, A increasesby the shaded area DA. (b) This causes impedance of the blood, Zb, to be addedin parallel to Z. (c) Usually DZ is measured instead of Zb.

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2. The skin–electrode impedance decreases by a factor of about 100 as thefrequency is increased from low values up to 100 kHz. High frequenciesare therefore used to decrease both the skin–electrode impedance and theundesirable changes in this impedance that result from motion of thepatient.

3. If a frequency much higher than 100 kHz is used, the low impedances ofthe stray capacitances make design of the instrument difficult.

TWO OR FOUR ELECTRODES

For reasons of economy and ease in application, some impedance plethysmo-graphs use two electrodes, as shown in Figure 8.18. The current i flows throughthe same electrodes used to measure the voltage v. This causes severalproblems.

1. The current density is higher near the electrodes than elsewhere in thetissue. This causes the measured impedance, Z ¼ v=i, to weight imped-ance of the tissue more heavily near the electrodes than elsewhere in thetissue.

2. Pulsations of blood in the tissue cause artifactual changes in the skin–electrode impedance, as well as changes in the desired tissue impedance.Because the skin–electrode impedance is in series with the desired tissue

Figure 8.18 In two-electrode impedance plethysmography, switches are inthe position shown, resulting in a high current density (solid lines) undervoltage-sensing electrodes. In four-electrode impedance plethysmography,switches are thrown to the other position, resulting in a more uniform currentdensity (dashed lines) under voltage-sensing electrodes.


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impedance, it is impossible to separate the two and determine the actualchange in impedance of the tissue.

3. The current density is not uniform in the region of interest, so (8.25)cannot be used.

To solve these problems, clinicians use the four-electrode impedanceplethysmograph shown in Figure 8.18. The current flows through the twoouter electrodes, so the current density is more uniform in the region sensed bythe two inner voltage electrodes. Variations in skin–electrode impedancecause only a second-order error.

CONSTANT-CURRENT SOURCE

Figure 8.19 shows the circuit of a four-electrode impedance plethysmograph.Ideally, the current source i causes a constant current to flow through Z,regardless of changes in DZ or other impedances. In practice, however, ashunting impedance Zi results from stray and cable capacitance. At 100 kHz,15 pF of stray capacitance causes an impedance of about 100 kV. Thus changesin Z1, DZ, and Z4 cause the constant current to divide between Z and Zi in achanging manner. In practice this is not a problem, because changes in Z1, DZ,and Z4 are small, and careful design can keep Zi large enough. Also, Z and Zi;are close to 908 out of phase, which reduces the effects of the problem.

Figure 8.19 In four-electrode impedance plethysmography, current is in-jected through two outer electrodes, and voltage is sensed between two innerelectrodes. Amplification and demodulation yield Z þ DZ. Normally, a bal-ancing voltage vb is applied to produce the desired DZ. In the automatic-resetsystem, when saturation of vo occurs, the comparator commands the sampleand hold to sample Z þ DZ and hold it as vb. This resets the input to the finalamplifier and vo to zero. Further changes in DZ cause changes in vo withoutsaturation.


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Frequently the constant current is supplied through a low-capacity transformerto prevent ground-loop problems.

VOLTAGE-SENSING AMPLIFIER

Figure 8.19 shows that electrodes Z2 and Z3 are used to sense the voltage.Ideally, the voltage amplifier has an input impedance sufficiently high that nocurrent flows through Z2 and Z3. In practice, however, a shunting impedanceZv results from stray, cable, and amplifier capacitance. Thus changes in Z2 andZ3 cause the desired voltage to be attenuated in a changing manner. In practicethis is not a problem, because changes in Z2 and Z3 are small, and carefuldesign can keep Zv large enough. Also, Z2 and Z3 are 908 out of phase with Zv,which reduces the effects of the problem. Not shown in Figure 8.19 arecommon-mode impedances from each amplifier input to ground. These im-pedances can convert common-mode voltages to erroneous differential volt-ages unless the instrument is carefully designed. Frequently, the voltage issensed through a low-capacity transformer, which greatly reduces common-mode and ground-loop problems. The amplifier requires only modest gain,because a typical voltage sensed is v ¼ iZ ¼ ð0:004Þð40Þ ¼ 0:16 V.

DEMODULATION

The output of the amplifier is a large 100 kHz signal, amplitude-modulated asmall amount by iDZ. This iDZ may be demodulated by any AM detector, suchas a diode followed by a low-pass filter. The phase-sensitive detector describedin Section 3.15 is a superior demodulator because it is insensitive to the noiseand 60 Hz interference that simpler demodulators detect.

METHODS OF BALANCE

The demodulator produces an output Z þ DZ. Frequently DZ contains theuseful information, but it may be only 1/1000th of Z. One approach is to use ahigh-pass filter to pass frequencies above 0.05 Hz and extract DZ. This issatisfactory for measuring pulsatile arterial changes, but not venous or respi-ratory changes. To build a dc-responding instrument, we subtract a balancingvoltage vb from the demodulated signal to yield DZ, as shown in Figure 8.19.We may derive vb from an adjustable dc source, but then slight changes in iproduce artifactual changes in DZ. A better technique is to derive vb from arectified signal from the master oscillator that generates i. Then the systembehaves like a Wheatstone bridge: A change in excitation voltage does notunbalance the bridge.

But still there is a problem. When the electrodes are first applied or whenthe patient moves, Z changes by an amount much larger than DZ. Theoperator must manually adjust vb to keep DZ small, which is necessary ifthe operator is to be able to amplify and display DZ adequately. An automatic-reset system has been developed to eliminate the bother of manual adjustment.


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Whenever DZ saturates its amplifier, a sample-and-hold circuit makesvb ¼ Z þ DZ, which momentarily resets DZ to zero. The sudden vertical-reset trace is easily distinguished from the slower-changing physiological data.Shankar and Webster (1984) detail design of an automatically balancingelectrical-impedance plethysmograph.

APPLICATIONS

Electrical-impedance plethysmography is used to measure a wide variety ofchanges in the volume of tissue (Geddes and Baker, 1989). Electrodes placedon both legs provide an indication of whether pulsations of volume are normal(Shankar and Webster, 1991). If the pulsatile waveform in one leg is muchsmaller than that in the other, this indicates an obstruction in the first leg. Ifpulsatile waveforms are reduced in both legs, this indicates an obstruction intheir common supply. A clinically useful noninvasive method for detectingvenous thrombosis in the leg is venous-occlusion plethysmography. Whenimpedance plethysmography measures the changes in volume shown in Figure8.16, this approach replaces the cumbersome chamber shown in Figure 8.15.

Electrodes on each side of the thorax provide an excellent indication ofrate of ventilation, but they give a less accurate indication of volume ofventilation. Such transthoracic electrical impedance monitoring is widelyused for infant apnea monitoring to prevent sudden infant death syndrome(SIDS). Computer algorithms use pattern recognition techniques such asthreshold crossing, adaptive threshold, and peak detection to reject cardio-genic and movement artifacts (Neuman, 2006).

Electrodes around the neck and around the waist cause current to flowthrough the major vessels connected to the heart. The resulting changes inimpedance provide a rough estimate of beat-by-beat changes in cardiac output(Kubicek et al., 1970). Mohapatra (1988) provides an extensive review of thisimpedance cardiography. The impedance-cardiographic outputs from theneck, upper thorax, and lower thorax during supine, sitting, and bicycleexercise have been measured (Patterson et al., 1991). Arrangements of spotelectrodes do not duplicate band electrodes and do not yield good estimates ofcardiac output but estimate only regional flow. Band electrodes yield goodestimates of cardiac output for normals, but they may fail to give reasonablepredictions on very sick patients.

Although Nyboer (1970) and others claim that flow of blood in the limbscan be measured, Swanson (1976) shows their techniques to be poor predictorsof flow.

An eight-electrode catheter in the left ventricle injects current throughband electrodes 1 and 8 and measures voltages from all the electrodes inbetween (Valentinuzzi and Spinelli, 1989). The change in impedance yieldschange in ventricular volume and, from this, cardiac output. Plots of pressure-volume diagrams and their area yield stroke work.

Some systems claim to measure body water and body fat by measuringthe electric impedance between the limbs. However, a wrist-to-ankle


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measurement is influenced mostly by the impedance of the arm and leg andless than 5% of the total impedance is contributed by the trunk, which hashalf the body mass. Separate measurements of the arms, legs, and trunkmight improve the prediction (Patterson, 1989).

The number of independent measurements from N electrodes is equalto N(N � 1)=2. If we place 16 electrodes around the thorax, we can obtain120 independent measurements and can use these data to compute a two-dimensional image of resistivity distribution within the thorax. A reviewdescribes methods of injecting current patterns, measuring electrode voltages,and optimizing reconstruction algorithms to create these images (Webster,1990). The spatial resolution is only about 10%, but this electrical-impedancetomography may be useful for monitoring the development of pneumonia,measuring stomach emptying, or monitoring ventilation.

The advantages of electrical-impedance plethysmography are that it isnoninvasive and that it is relatively simple to use. The disadvantages are that itis not sufficiently accurate for many of the attempted applications and thateven the cause of the changes in impedance is not clear in some cases.

8.8 PHOTOPLETHYSMOGRAPHY

Light can be transmitted through a capillary bed. As arterial pulsations fill thecapillary bed, the changes in volume of the vessels modify the absorption,reflection, and scattering of the light. Although photoplethysmography issimple and indicates the timing of events such as heart rate, it provides apoor measure of changes in volume, and it is very sensitive to motion artifact.

LIGHT SOURCES

Figure 8.20 shows two photoplethysmographic methods, in which sourcesgenerate light that is transmitted through the tissue (Geddes and Baker,1989). A miniature tungsten lamp may be used as the light source, but the

Figure 8.20 (a) Light transmitted into the finger pad is reflected off bone anddetected by a photosensor. (b) Light transmitted through the aural pinna isdetected by a photosensor.


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heat generated causes vasodilation, which alters the system being measured.This may be considered desirable, however, because a larger pulse is produced.A less bulky unit may be formed using a GaAs LED (Lee et al., 1975), whichproduces a narrow-band source with a peak spectral emission at a wavelengthof 940 nm [Figure 2.18(a)].

PHOTOSENSORS

Photoconductive cells have been used as sensors, but they are bulky andpresent a problem in that prior exposure to light changes the sensitivity of thecell. In addition, a filter is required to restrict the sensitivity of the sensor to thenear-infrared region so that changes in blood O2 content that are prominent inthe visible-light region will not cause changes in sensitivity. A less bulky unitcan be formed using an Si phototransistor. A filter that passes only infraredlight is helpful for all types of sensors to prevent 120 Hz signals fromfluorescent lights from being detected. This does not prevent dc light fromtungsten lights or daylight from causing baseline shifts, so lightproof enclosuresare usually provided for these devices.

CIRCUITS

The output from the sensor represents a large value of transmittance, modu-lated by very small changes due to pulsations of blood. To eliminate the largebaseline value, frequencies above 0.05 Hz are passed through a high-pass filter.The resulting signal is greatly amplified to yield a sufficiently large waveform.Any movement of the photoplethysmograph relative to the tissue causes achange in the baseline transmittance that is many times larger than thepulsation signal. These large artifacts due to motion saturate the amplifier;thus it is a good thing to have a means of quickly restoring the output trace.

EXAMPLE 8.6 Design the complete circuit for a solid-state photople-thysmograph.

ANSWER A typical LED requires a forward current of 15 mA. Using a 15 Vsupply would require a series resistor of RL ¼ v=i ¼ 15=0:015 ¼ 1 kV. Atypical phototransistor passes a maximum of 150 mA. To avoid saturation,choose a series resistor Rp ¼ v=i ¼ 15=0:00015 ¼ 100 kV. The largest con-venient paper capacitor is 2 mF. The output resistor Ro ¼ 1=ð2pf0CÞ ¼1=½2pð0:05Þð2� 10�6Þ� ¼ 1:6 MV. Figure 8.21 shows the circuit.

APPLICATIONS

For a patient who remains quiet, the photoplethysmograph can measure heartrate. It offers an advantage in that it responds to the pumping action of the heartand not to the ECG. When properly shielded, it is unaffected by the use ofelectrosurgery, which usually disables the ECG. However, when the patient is in a

8 . 8 P H O T O P L E T H Y S M O G R A P H Y 373

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state of shock, vasoconstriction causes peripheral flow to be greatly reduced, andthe resulting small output may make the device unusable. To prevent thisproblem, the device has been used to transmit light through the nasal septum(Groveman et al., 1966). This technique monitors terminal branches of the internalcarotid artery and yields an output that correlates with cerebral blood flow.

PROBLEMS

8.1 Clearance is defined as the minimal volume of blood entering an organper unit time required to supply the amount of indicator removed from theblood per unit time during the blood’s passage through the organ. Derive aformula for renal clearance, given the arterial concentration of the indicatorpara amino hippuric acid (PAH), all of which is excreted by the kidneys intothe urine. Give units.8.2 In Figure 8.2, the final concentration at time F is higher than the initialconcentration at time A. Write a formula that yields the circulating blood volumefrom the information obtained during an indicator dilution test. Give units.8.3 In the decaying exponential portion of Figure 8.2, the concentrations attimes C and D are given. Calculate the shaded area under the dotted curvebetween times C and E. Give units.8.4 A physician is using the rapid-injection thermodilution method of findinga patient’s cardiac output. Calculate the cardiac output (in milliliters persecond and in liters per minute) from the following data:

Vi ¼ 10 ml; DT i ¼ �30 K

ri ¼ 1005 kg/m3; ci ¼ 4170 J/ðkg�KÞrb ¼ 1060 kg/m3; cb ¼ 3640 J/ðkg�KÞZ t1

0

DTbdt ¼ �5:0 s�K

Figure 8.21 In this photoplethysmograph, the output of a light-emittingdiode is altered by tissue absorption to modulate the phototransistor. Thedc level is blocked by the capacitor, and switch S restores the trace. A


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8.5 Name the indicator-dilution technique for measuring cardiac output thatdoes not require arterial puncture. Give the equation for calculating cardiacoutput, and define all terms.8.6 For cardiac catheterization, describe the characteristics of the dye used toimprove visualization. Describe the characteristics of the dye used for meas-uring cardiac output.8.7 The maximal average velocity of blood in a dog, 1 m/s, occurs in the dog’saorta, which is 0.015 m in diameter. The magnetic flux density in an electro-magnetic blood flowmeter is 0.03 T. Calculate the voltage at the electrodes.8.8 In order to determine the frequency response of an electromagneticflowmeter, the clinician can transiently short-circuit the magnet current byusing a microswitch. For steady flow, sketch the resulting output of theflowmeter. Describe the mathematical steps you could implement on acomputer in order to convert the resulting transient wave to the flowmeter’sfrequency response.8.9 For Figure 8.6, design a simpler electromagnetic flowmeter withoutquadrature suppression. Show the block diagram and show all connectionsfor a ring demodulator.8.10 For the Doppler ultrasonic flowmeter shown in Figure 8.9(b), supposethat the two transducers are inclined at angles u and f to the axis. Derive aformula for fd, the Doppler frequency shift.8.11 For Figure 8.11, show how to add another one-shot block and severallogic blocks to obtain pulse outputs on both positive and negative zerocrossings.8.12 A pulsed Doppler flowmeter has fr ¼ 15 kHz; f0 ¼ 8 MHz; and u = 458.Calculate Rm and um.8.13 Expand Figures 8.14 and 8.13(b) to show a complete block diagram of adirectionally sensitive thermal velocity meter and probe.8.14 The chamber plethysmograph shown in Figure 8.15 has a volume of200 ml. Calculate the rapid change in tissue volume that produces a 120 Pachange in chamber pressure. Assume an adiabatic process: P(V)1.4¼ constant.8.15 Calculate the arterial inflow for the test shown in Figure 8.16.8.16 For Figure 8.19, assume Z þ DZ ¼ Z2 ¼ Z3 ¼ 100 V and ZV ¼� j2000 V (capacitive). How large is the error caused by a 5 V change in Z2?Is an error of this magnitude important?8.17 Design a circuit that uses the same two electrodes (plus one groundelectrode) to monitor ventilation by impedance and the conventional ECG,with no cross interference.

REFERENCES

Brunswig Newring, K. A., C. Draper, and W. O’Donohue, ‘‘Sexual instrumentation.’’ In J. G.Webster (ed.), Encyclopedia of Medical Devices and Instrumentation, 2nd ed., New York:Wiley, 2006, Vol. 6, pp. 149–163.

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Capek, J. M., and R. J. Roy, ‘‘Fick techniques.’’ In J. G. Webster (ed.), Encyclopedia of Medical

Devices and Instrumentation. New York: Wiley, 1988, pp. 1302–1314.Christensen, D. A., Ultrasonic Bioinstrumentation. New York: Wiley, 1988.Cobbold, R. S. C., Transducers for Biomedical Measurements: Principles and Applications. New

York: Wiley, 1974.Donovan, F. M, and B. C. Taylor, ‘‘Cardiac output, indicator dilution measurement of.’’ In J. G.

Webster (ed.), Encyclopedia of Medical Devices and Instrumentation, 2nd ed., New York:Wiley, 2006, Vol. 2, pp. 21–25.

Geddes, L. A., and L. E. Baker, Principles of Applied Biomedical Instrumentation, 3rd ed., NewYork: Wiley, 1989.

Grahn, A. R., M. H. Paul, and H. U. Wessel, ‘‘A new direction-sensitive probe for catheter-tipthermal velocity measurements.’’ J. Appl. Physiol., 1969, 27, 407–412.

Groveman, J., D. D. Cohen, and J. B. Dillon, ‘‘Rhinoplethysmography: Pulse monitoring at thenasal septum.’’ Anesth. Analg., 1966, 45, 63.

Hutten, H., ‘‘Impedance plethysmography.’’ In J. G. Webster (ed.), Encyclopedia of Medical

Devices and Instrumentation, 2nd ed., New York: Wiley, 2006, Vol. 4, pp. 120–132.Khaodhiar, L., and A. Veves, ‘‘Cutaneous blood flow, Doppler measurement of.’’ In J. G. Webster

(ed.), Encyclopedia of Medical Devices and Instrumentation, 2nd ed., New York: Wiley, 2006,Vol. 2, pp. 378–384.

Kubicek, W. G., A. H. L. From, R. P. Patterson, D. A. Witsoe, A. Castenda, R. G. Lilleki, andR. Ersek, ‘‘Impedance cardiography as a noninvasive means to monitor cardiac function.’’ J.

Assoc. Adv. Med. Instrum., 1970, 4, 79–84.Lee, A. L., A. J. Tahmoush, and J. R. Jennings, ‘‘An LED-transistor photoplethysmograph.’’

IEEE Trans. Biomed. Eng., 1975, BME-22, 243–250.McLeod, F. D., ‘‘A directional Doppler flowmeter.’’ Dig. Int. Conf. Med. Biol. Eng., Stockholm,

1967, 213.Mohapatra, S. N., ‘‘Impedance cardiography,’’ In J. G. Webster (ed.), Encyclopedia of Medical

Devices and Instrumentation. New York: Wiley, 1988, pp. 1622–1632.Neuman, M. R., ‘‘Neonatal monitoring,’’ In J. G. Webster (ed.), Encyclopedia of Medical Devices

and Instrumentation, 2nd ed., New York: Wiley, 2006, Vol. 5, pp. 11–32.Nyboer, J., Electrical Impedance Plethysmography, 2nd ed. Springfield, IL: C. C. Thomas, 1970.Patterson, R. P., L. Wang, and B. Raza, ‘‘Impedance cardiography using band and regional

electrodes in supine, sitting, and during exercise.’’ IEEE Trans. Biomed. Eng., 1991, 38,393–400.

Patterson, R., ‘‘Body fluid determinations using multiple impedance measurements.’’ IEEE Eng.Med. Biol. Magazine, 1989, 8 (1), 16–18.

Raines, J., and R. C. Darling, ‘‘Clinical vascular laboratory: Criteria, procedures, instrumentation.’’Med. Electronics Data, 1976, 7 (1), 33–52.

Seagar, A. D., J. M. Gibbs, and F. M. David, ‘‘Interpretation of venous occlusion plethsmographicmeasurements using a simple model.’’, Med. Biol. Eng. Comput., 1984, 22, 12–18.

Shankar, R., and J. G. Webster, ‘‘Noninvasive measurement of compliance in leg arteries.’’ IEEE

Trans. Biomed. Eng., 1991, 38, 62–67.Shankar, T. M. R., and J. G. Webster, ‘‘Design of an automatically balancing electrical impedance

plethysmography.’’ J. Clin. Eng., 1984, 9, 129–134.Shercliff, J. A., The Theory of Electromagnetic Flow Measurement. Cambridge: Cambridge

University Press, 1962.Swanson, D. K., ‘‘Measurement errors and origin of electrical impedance changes in the limbs.’’

Ph.D. dissertation, Department of Electrical and Computer Engineering, University ofWisconsin, Madison, Wisconsin, 1976.

Trautman, E. D., and M. N. D’ambra, ‘‘Cardiac output, thermodilution measurement of.’’ In J. G.Webster (ed.), Encyclopedia of Medical Devices and Instrumentation, 2nd ed., New York;Wiley, Vol. 2, 2006, pp. 25–35.

Valentinuzzi, M. E., and J. C. Spinelli, ‘‘Intracardiac measurements with the impedance tech-nique.’’ IEEE Eng. Med. Biol. Magazine, 1989, 8 (1), 27–34.

Webster, J. G. (ed.), Electrical Impedance Tomography. Bristol, England: Adam Hilger, 1990.


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