ch54MEASUREMENT TECHNIQUES IN RESPIRATORY MECHANICS

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The assessment of respiratory mechanics begins with themeasurement of variables whose correlations containinformation about the mechanical functioning of the respi-ratory system. These variables are usually pressures and

flows, or volumes, of gas made at appropriate sites. Theamount of detail that can be gleaned about the mechanicalfunction of the respiratory system depends on which partic-ular variables are measured and the conditions under whichthey are measured. Although the modern history of meas-urement in respiratory mechanics extends back at least 100years, novel methods and approaches are still being devel-oped as advances in instrumentation and computer technol-ogy continue to extend the boundaries of what is possible.

This review of measurement in respiratory mechanicsbegins with the general theory of measurement as it appliesto modern electronic transducers and the acquisition of databy digital computer. It then proceeds to consider how this

theory is applied to the measurement of respiratory pres-sures, flows, and volumes. Finally, it is shown how thesemeasurements are used in combination to collect informa-tion from which respiratory mechanics are determined.

MEASUREMENT THEORY

The general measurement situation is depicted in Figure 54-1,which shows the steps involved in converting a biologicsignal into a string of numbers stored on a computer. Ateach step we have the potential for errors to occur, repre-sented as additive noise. First we consider the issuesinvolved in transducing the biologic signal into an electricalsignal. This is performed by a transducer. We then considerthe process of digitizing the electrical signal so that it can bemanipulated in digital form on a computer, which is howany subsequent data analysis is carried out.

TRANSDUCERSA transducer is something that converts energy from oneform to another, although for the present purposes werestrict ourselves to the more particular definition of theconversion being between some biologic quantity we areinterested in and a voltage. Ideally, we would like the voltageto be a perfect representation of the biologic quantity, but

this is never the case in practice. It is therefore crucial tounderstand the imperfections of the transducer to be used inany particular application and whether or not these imper-fections are going to limit the amount of information that

can be extracted from the measured signals.

Static Properties of Transducers We first consider thevarious static properties that characterize a transducers per-formance. These are properties that do not depend on howrapidly the measured signal is varying, which is equivalentto saying that the transducer has no trouble keeping up withthe signal. One such property is linearity, which refers to theextent to which the voltage v produced by a transducer canbe represented in terms of the biologic signal s by an equa-tion of the form

v as b (54-1)

where a and b are constants (solid line in Figure 54-2).Manufacturers of transducers usually specify the linearity ofa transducer in terms of its full-scale output. A value of 1%is typical. Although linearity is a desirable trait, with theavailability of digital computers it is not essential. Suppose,for example, that v is not a linear function ofs as in Equation54-1 but is instead a curvilinear function of s that can beaccurately represented as a polynomial (dashed line inFigure 54-2). If the polynomial coefficients are known (say,from a prior calibration experiment) it is a simple matter touse a computer to invert the equation to obtain s as a func-tion ofv, allowing the recorded voltage to be related back tothe value of the original biologic signal.

Another important static property of a transducer is hys-teresis, which refers to the extent to which the voltage corre-sponding to a biologic signal differs depending on whetherthe immediately preceding value was below or above thecurrent value (Figure 54-3). Hysteresis is obviously a badthing and is unfortunately extremely difficult to correct for,so one should always try to select a transducer with minimalhysteresis.

In selecting a transducer for a particular application, itis important to make sure it has the appropriate resolutionand dynamic range, which determine the smallest andlargest changes in the biologic signal that can be accurately

CHAPTER 54

MEASUREMENT TECHNIQUES INRESPIRATORY MECHANICS

Jason H. T. Bates


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624 Clinical Respiratory Physiology

measured. Related to the issue of resolution is the signal-to-noise ratio. What the transducer in Figure 54-1 actuallyrecords in response to a biologic signal is a voltage plusnoise. The latter must be substantially lower than anyimportant changes that are to be recorded in the biologicsignal (by preferably at least an order of magnitude).

Dynamic Properties of Transducers We now considerthe somewhat more complicated issue ofdynamic propertiesof transducers. These refer to those characteristics thatdetermine how well a transducer can respond to a changingbiologic signal. Most transducers are low-pass systemsbecause they can respond faithfully to slowly varying signals

but have increasing difficulty keeping up as the signalincreases in frequency. Some transducers are high-pass sys-tems because they faithfully record high frequencies but donot respond when frequency is very low. Transducers arecharacterized in general by the way in which they respondto input signals that vary sinusoidally. Provided that thetransducers are linear, their voltage outputs to an input sinewave will also be sinusoidal with the same frequency butwill in general be altered in amplitude by a factor A andshifted in phase by an amount . That is, if the input sinewave is sin(2ft), then the output will be Asin(2 ft )(Figure 54-4). The values ofA and depend on frequency

and together constitute the frequency response of thetransducer.

DIGITAL DATAACQUISITIONOnce a transducer has converted a biologic signal into avoltage, it must be recorded in some permanent medium forsubsequent analysis and display. In the early days of physi-ology (ie, until about 20 years ago), physiologic recordingwas achieved by have a writing instrument move laterally

over a suitable recording medium as it scrolled by. In theearly part of the twentieth century, the writing instrumentwas a rigid pointer and the scrolling medium was a cylindri-cal drum covered in soot. This was eventually replaced bythe electronic chart recorder, consisting of one or more ink

pens writing on a roll of paper moving past at constantspeed. Each experiment produced a (frequently large) stackof paper that then had to be analyzed manually if calcula-tions were to be made from the recorded signals.

Since the advent of the modern laboratory digitalcomputer, however, these earlier analog recording deviceshave been replaced by digital computers that both recordand analyze experimental data. The speed and flexibility ofcomputers, together with their universal availability, haverevolutionized the way that physiologic research is done.

Everything is thus now done digitally, beginning withthe recording of the analog voltage signal arriving from

the transducer. Conversion of an analog signal to digitalform is known as digitization and is accomplished with ananalog-to-digital (A-D) converter. Figure 54-5 shows what isinvolved. The analog (continuous) voltage signal is sampledat regularly spaced intervals by the A-D converter, andthe resulting set of voltage values is stored in the computeras a set of numbers. These numbers and their locationsin time then constitute our representation of the originalsignal.

Resolution and Discretization Error A major considera-tion when digitizing signals is the resolution of the A-D con-verter, which defines the smallest difference in voltage level

that it can distinguish in the incoming analog signal. A-D

TransducerAnalog-digitalconverter

Computer

Biologicsignal

Voltage Digitalsignal

Noise Noise

FIGURE 54-1 The general measurement scenario.

Biological signal

Voltage

FIGURE 54-2 Characteristics of a linear (solid line) and nonlinear(dashed line) transducer.

Biologic signal

Voltage

FIGURE 54-3 Hysteresis. The voltage output by a transducer inresponse to a particular value of the input biologic signal dependson whether the value was approached from above or below.

Transducer

Input Output

1.0 A

FIGURE 54-4 If an input to a linear transducer is sin(2ft), itsoutput in general will beAsin(2ft ), where the values ofA and characterize the frequency response of the transducer.


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Measurement Techniques in Respiratory Mechanics 625

converters are set up to receive voltages within a specifiedrange, such as 10 to 10 volts. This voltage range isdivided into N equally spaced bins numbered 0 to N1(Figure 54-6). Nis determined by the number ofbits in theA-D converter. A 12-bit A-D converter has 212 4,096 bins,a 16-bit converter has 216 65,536 bins, and so on. Thus, for

example, a 12-bit converter with a 10-volt input range canresolve voltage differences of 20/4,096 0.0049 volts.

The finite resolution of an A-D converter means that caremust be taken to ensure that it is able to resolve the smallestdifferences in voltage required by the experimenter. Forexample, suppose one is measuring flow of gas entering apatients lungs during mechanical ventilation. If the flowreaches 2,000mL.s1 during both inspiration and expira-tion, then the range of flows encountered is 4,000mL.s1. Ifthis flow signal is recorded on a 12-bit A-D converter, theresulting digitized signal has a maximum resolution of4,000/4,096 0.98mL.s1. However, it only achieves this

resolution if the entire dynamic range of the A-D converteris used. This only occurs if the analog signal producedby the flow transducer is amplified so that a flow of2,000mL.s

1produces the lowest voltage the A-D

converter can receive (eg, 10 volts), and similarly a flow

of 2,000 mL.s1 produces the highest receivable voltage(eg, 10 volts).

This may not be the case. A common error in the labora-tory occurs when the voltage signal coming in from thetransducer is not amplified enough to make use of many ofthe discrete bins in the A-D converter. As an example, sup-pose that the flow signal of 2,000 to 2,000 mL.s1

results in a voltage signal that only occupies the range of

0.1 to 0.1 volts. Now only the middle 1% of the availablebins (numbers 2,028 to 2,069) of the A-D converter areused, giving a 100-fold reduction in flow resolution. Inextreme examples of this situation, the discrete levels of theA-D converter will be apparent in a plot of the resulting volt-age signal (Figure 54-7). The errors incurred in havinginsufficient vertical resolution in an A-D converter are calleddiscretization errors.

Sampling Theorem and Aliasing Another major ques-tion that arises when digitizing analog signals is how fre-quently to sample the signal. A continuous signal iscomposed of an infinite number of infinitesimally spaced

points yet must somehow be represented by a finite numberof digitized values. Obviously, if a signal is changing rapidly,then sampling its value infrequently will cause the detailbetween the samples to be lost. On the other hand, samplinga long signal too rapidly might result in an unmanageablylarge number of data points. Thus, one might be inclined tothink that the choice of sampling rate represents a tradeoffbetween capturing detail in the original signal on the onehand and avoiding being overwhelmed by the volume ofdata on the other. Fortunately, however, we are saved bysomething known as the sampling theorem (often associatedwith engineers Shannon and Nyquist).

To understand the sampling theorem, it is necessary to

first understand what is meant by thefrequency content of asignal. Any analog signal can be expressed as the sum of aseries of sine wave functions of appropriate frequency,amplitude, and phase. Furthermore, this collection of fre-quencies, amplitudes, and phases is unique to that signal,which means they define it distinctly from all other possiblesignals. A signal can be decomposed into its individual sinewave components by the Fourier transform. A simple exam-ple is given in Figure 54-8, which shows the four sine wavesmaking up a signal that looks considerably more complexthan any of its individual components. The frequencycontent of a signal thus refers to the unique spectrum of

1

0

0.210.430.500.500.420.330.330.370.480.520.590.58..

.t

V(t)

t

FIGURE 54-5 Digitization. An analog voltage signal V(t) issampled every t seconds to produce a series of numbers that arestored in a computer for subsequent analysis.

-10 volts

+10 volts

0

4095

Analog signal Digitized signal

FIGURE 54-6 Digitization of the 10 volt analog range by a 12-bitA-D converter. The 20-volt span of possible input signals isassigned to 4,096 numbers representing successive increments of4.9 millivolts.

FIGURE 54-7 Discretization error. The left panel shows an analogsignal faithfully captured by a set of digitized points. The right

panel shows points occupying discrete levels corresponding toadjacent bins of the A-D converter.


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sinusoidal components from which it is composed. Inparticular, if the frequency content of a signal is such thatnone of its sinusoidal components has a frequency greaterthan some maximum frequency, then the signal is said to beband limited.

The sampling theorem says that it is possible to captureall the information in a band-limited analog signal by sam-pling the signal at a rate at least twice the highest frequencyin the signal itself. Thus, for example, if Fourier analysis ofa signal reveals that it contains no components with fre-quencies greater thanf0, then we need not sample the signalany faster than 2f0 (known as the Nyquist rate). Intuitively,this makes sense because sampling a sine wave at its Nyquistfrequency means collecting another sample from the signalevery time it changes direction. If we know we are samplinga sine wave, then from this set of points we can reconstruct

the intervening continuous signal segments by fitting a sinewave to the points. Thus, by sampling an analog signal at orabove the Nyquist rate, we lose no informationthe entireoriginal continuous signal can be reconstructed from thesampled points alone.

The sampling theorem in principle means we lose noth-ing in moving from a continuous to a digital environment.However, there is a practical issuewhat iff0 is so high that

we still end up with an unmanageably large number ofdata points when we satisfy the sampling theorem?Unfortunately, we cannot drop the sampling rate below2f0 and hope to merely sacrifice some detail in the retainedsamples. The high frequencies in the analog signal do notsimply disappearthey turn up in the digitized data but atwrong (much lower) frequencies! This is a particularlyinsidious problem known as aliasing, and experimentersmust always be careful to avoid it, especially if the powerspectra of the collected data are of interest. Aliasing canlead to completely erroneous spectral characterization ofa signal and at the very least degrades the signal-to-noiseratio of a measurement. Figure 54-9 shows how aliasing

occurs; a sine wave is sampled at a frequency below theNyquist rate to yield a set of points that look as if theyrepresent a different sine wave of a much lower frequency.Obviously, aliasing can be avoided by sampling at or abovethe Nyquist rate. However, in practice it is usually necessaryto force the analog signal to be band limited to somemanageablef0. This is done by passing the signal through ahigh-quality low-pass electronic filter before it is digitized.Such filters are known as antialiasing filters. It is importantto remember that filtering for antialiasing must be doneprior to digitization of the signal. Once aliasing occurs,no amount of digital filtering after the fact can fix theproblem.

Fourier transform

FIGURE 54-8 An analog signal can be decomposed (by theFourier transform) into its component sine waves, each with itsown frequency, amplitude, and phase.

FIGURE 54-9 A sine wave (solid line) is sampled (dots) below theNyquist rate, yielding a set of data points defining a different sinewave (dashed line) at a lower frequency.


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MEASUREMENT OF RESPIRATORY SIGNALS

Having established the general considerations for measuringsignals in the laboratory, we now move on to consider thosesignals specific to the study of mechanical lung function.

PRESSUREThe measurement of pressure is central to the study of res-piratory physiology because it is pressure that generates theflow of gas needed to ventilate the lungs.

Pressure Transducers Pressure transduction is based onthe graded deformation of some mechanical element whosealtered configuration is read by some electronic means(Figure 54-10). Until about 15 years ago, the mainstay ofpressure measurement in the respiratory physiology labora-tory was the variable reluctance transducer in which a thinmetal disk is placed between the primary and secondarycoils of a transformer excited by several kHz of alternatingelectric current. A pressure difference either side of the diskcauses it to deform in a way that alters the magnetic flux

linkage between the transformer coils, thereby changing theinduced voltage in the secondary coil. The change in voltageis then transformed into a DC voltage proportional to thepressure difference. These transducers are sensitive andaccurate. They also typically have a frequency response thatis flat to 20 Hz or more, depending on the length of the tub-ing connecting its ports to the sites of pressure measure-ment.1 However, they are somewhat cumbersome and can bedamaged by over pressurization.

In recent years, respiratory pressure measurement hasbeen taken over by the piezoresistive transducer,2 inwhich the pressure-sensitive element changes its electricalresistance as it deforms. If a constant voltage (or current)

is passed through the piezoresistive element when it isconfigured to be one of the four arms of a suitably bal-anced Wheatstone bridge, the voltage across the bridge isthen proportional to the change in the elements resistance.A medium-gain amplifier followed by an antialiasingfilter are the only remaining elements required to producean electrical signal proportional to pressure that is readyfor digitization. When piezoresistive pressure transducerswere first used in respiratory physiology in the 1980s,they tended to suffer from baseline drift, were affected byorientation and temperature, and were not very sensitive.These problems have now been essentially overcomeallowing piezoresistive transducers to be exploited for

their several advantages. These include an extremelyhigh-frequency response (typically flat to several hundredHz), robustness (they can be pressurized to many times theirnominal full-scale range without damage), and the factthat they can be manufactured using solid-state technologyto be very small and light. Piezoresistive transducers arealso much cheaper than their variable reluctance counter-parts and require simpler electronic signal conditioning

circuitry.

Measuring Pressure at the Airway Opening The assess-ment of pulmonary function frequently requires that thepressure in a flowing stream of gas be measured, such as atthe entrance to the endotracheal tube in a mechanically ven-tilated patient. Gas always flows down a pressure gradient,so at each point along the stream of flowing gas there is adriving pressure pushing the gas downstream of it. The goalis to determine this driving pressure. The easiest way is toinsert a perpendicular tap into the tube and connect it to apressure transducer (Figure 54-11). This provides what isknown as lateral pressure (Plat), and it corresponds to the

pressure exerted perpendicular to the direction of flow asthe gas moves past the point of measurement. It turns out,however, that Plat is less than the pressure driving the gasalong the tube because of a phenomenon known as theBernoulli effect, which occurs because of the principle ofconservation of energy; the faster gas is moving along thetube, and consequently the larger its kinetic energy, the moreit loses in potential energy, manifest as a drop in Plat. Plat under-estimates true driving pressure, in a tube of cross-sectional areaA with flow V, by an amount Pb given by the formula

(54-2)

where is the density of the gas and is a factor determinedby the flow velocity profile. For example, if the profile is flat(the linear velocity of the gas molecules is the same at everypoint in the tube cross section) then 1 and 2 if theprofile is parabolic.

If the gas in the tube were stationary, then Plat wouldequal driving pressure, a condition that can always beachieved by connecting a pressure transducer to a small tube

Pb V

.2

2A2

Pressuresource

Deformableelement

FIGURE 54-10 Pressure transducer. The application of a pressuredeforms an element whose configuration is converted into an elec-trical signal proportional to the degree of deformation.

Plat

Pstat

V

.

FIGURE 54-11 Lateral pressure (Plat) measured through a lateraltap, and static pressure (Pstat) measured with a Pitot tube.


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that enters the flow stream laterally and then bends until itsopen end faces directly into the oncoming flow (see Figure54-11). Such a device, called a Pitot tube, measures the staticpressure (Pstat) in a small parcel of gas that has been broughtto rest by abutting up against the tube opening. Pb is thedifference between Pstat and Plat. That is,

Plat Pstat Pb (54-3)

The problem for respiratory pressure measurement causedby the Bernoulli effect is apparent from Equation 54-2,which shows that Pb depends on the square of flow dividedby cross-sectional area. When the area is large enough, Pbis negligible. However, as the area decreases there comes apoint at which Pb starts to become important, comparedwith Pstat. Indeed, Equation 54-3 shows that for small tubeareas Plat may even become negative. Thus, it is importantin any application in which lateral pressures are measured tobe sure that the Bernoulli effect is not significantly affectingthe measurement of the desired quantity, namely drivingpressure.3 The Bernoulli effect may also be an important fac-tor influencing the measurement of pressures at the distal

end of an endotracheal tube in an intubated patient.4

Esophageal and Gastric Pressures Two other pressuresof great practical importance in the study of respiratoryphysiology are those in the esophagus and stomach.Esophageal pressure (Pes) is a useful surrogate for pleuralpressure, the esophageal lumen being separated from thepleural space by only soft tissue. Gastric pressure (Pga)measures the pressure exerted on the diaphragm by theabdominal contents, which is important for understandingactive expiration. The difference between Pes and Pga is thepressure across the diaphragm, which is important in stud-ies of respiratory muscle function.5

Both Pes and Pga can be measured using a balloon-tippedcatheter (Figure 54-12). A thin-walled latex balloon, a fewcentimeters in length, is sealed over a thin plastic catheter,typically about 100cm long. The balloon is passed into theesophagus, usually via the nose. Once in place in either theesophagus or stomach, a small volume of air is injected intothe balloon and a pressure transducer is connected to theproximal end of the catheter. The volume of air in the bal-loon must be sufficient to prevent the walls of the balloonfrom occluding all the multiple holes in the end of the

catheter, but not so much that there is tension in the balloonwalls. The correct placement of the balloon is gauged fromthe nature of the recorded pressure signals. When the bal-loon is in the stomach, spontaneous inspiration produces apositive deflection in the recorded Pga. As the balloon iswithdrawn and enters the esophagus, the inspiratory pres-sure swings will suddenly become negative. At this point,when inspiratory efforts are made against an occluded air-

way (the so-called occlusion test), the deflections in Pesshould match those in pressure measured at the airwayopening (Pao). Thus, a regression of Pes versus Pao shouldyield a slope of unity.6 In practice, slopes that differ from 1.0by up to 10% are common. Although the occlusion testrequires that the subject be able to breathe spontaneously, ithas been shown that the esophageal balloon also works wellduring paralysis.7 The frequency response of the esophagealballoon is obviously somewhat compromised by the fact thatpressure changes in the esophageal lumen must be transmit-ted through the air inside a long thin catheter to a pressuretransducer some distance away. However, a reasonably goodresponse to 30Hz has been observed.8 Pes has also been meas-

ured using catheter-tip piezoresistive transducers, which havebeen shown to perform well9 and have a much betterfrequency response than balloon catheter systems. In smallanimals, Pes can be measured using a water-filled catheter.

10

Alveolar Pressure In experimental animals it is possibleto measure alveolar pressure directly using a techniqueknown as the alveolar capsule.11 The chest is opened andretracted to expose the pleural surface of the lung to whicha small plastic capsule is fixed (Figure 54-13). The capsulehas a cylindrical chamber leading down to a small windowon the pleural surface encircled by a flange. If the pleuralsurface is first swabbed with alcohol and dried, the flange

can be secured to it with cyanoacrylate glue. Small punctureholes are then made in the pleural surface within the capsulewindow. If the holes are made carefully to a depth of 1 to

10 cm

100 cm

Pressuretransducer

Latex balloonPlasticcatheter

FIGURE 54-12 An esophageal balloon catheter. Note the multipleholes in the walls of the catheter inside the balloon.

Pressuretransducer

Pleural surface

Capsule

Terminalairways

Sub-pleuralalveoli

FIGURE 54-13 The alveolar capsule.


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2 mm, preferably with a cautery needle, bleeding is minimaland the subpleural alveoli are brought into contact with the

capsule chamber. A small piezoresistive pressure transducercan then be lodged in the chamber to give a direct recordingof subpleural pressure. In large animals, such as dogs, sev-eral alveolar capsules can be installed at different sites overthe lung surface.1214 A single alveolar capsule can even beused in an animal as small as a mouse.15

FLOWPneumotachographs The mainstay of flow measurementin respiratory physiology is the pneumotachograph, whichis a calibrated resistance (R) across which a differential pres-sure is measured (Figure 54-14). When gas flows throughthe pneumotachograph, there is a pressure drop (P) from

the upstream side of the resistance to the downstream sidethat increases as flow (V) increases, thus

P RV (54-4)

IfR is independent ofVover the range of flows of interestthen the pneumotachograph is said to be linear. Manufac-turers strive for linearity and always quote the linear rangeof a pneumotachograph. However, if the device is nonlinear,so that R depends on V, it is a simple matter to invertEquation 54-4 on a computer and calculate Vfrom a measure-ment ofP, provided that the relationship ofR toVis known.

The frequency response of a pneumotachograph dependson the construction of its resistive element. Some consist ofa honeycomb arrangement of conduits, whereas others con-sist of a wire screen. The honeycomb type is less likely tobecome partially blocked by secretions but has a poorer fre-quency response than the screen type. Either type should beheated to above body temperature during prolonged use toavoid breath condensate from settling on the resistive ele-ment and changing its resistance (and hence altering the cal-ibration of the device). Pneumotachographs can have a goodfrequency response above 20 Hz with a resonance occurringat around 70Hz, provided that the associated differentialtransducer has a response at least that good and is connectedwith the shortest possible lengths of tubing.1 The frequency

response of a pneumotachograph degrades rapidly as thetubing connecting the transducer to the lateral taps eitherside of the resistance element increases in length. Inad-equate frequency response can be corrected for to a signifi-cant extent by digital compensation, giving an effectivelyflat frequency response to more than 100Hz.16

Another consideration for pneumotachographs concernstheir dynamic common-mode rejection characteristics. If the

two ports of the pneumotachograph are both subjected to thesame change in pressure, ideally the device should register aflow of zero. This is not always the case, however, particu-larly if the physical dimensions of the two ports are differentand if the input impedance of the pressure transducer is notvery large compared with that of the system under investiga-tion when flow oscillates at a high frequency. Digital compen-sation methods can improve the situation to a certain extent.17

Poor dynamic common-mode rejection is a significant prob-lem for pneumotachographs used with very small animals.18

Other Devices for Measuring Flow Although the resis-tive pneumotachograph is the mainstay for measuring flow

in respiratory applications, other devices have been used.For example, ultrasonic transducers based on differences intime-of-flight of sound propagating into the direction flowversus away from it have an excellent frequency responseand avoid the problems of a resistive element becomingclogged with secretions.19 Devices based on the rate of cool-ing of a heated wire are also in use.20

VOLUMEDirect Measurement of Volume The volume of gas enter-ing the lungs can be measured directly with a spirometerattached to the mouth or from the pressure or flows emanat-ing from a whole body plethysmograph when the subject

breathes through a conduit connected to outside the plethys-mograph. A more convenient but less accurate plethysmo-graphic method is provided by the changes in trunk volumeassessed with an inductance plethysmograph.21 Recently, amore accurate but expensive optical plethymograph has beendeveloped that allows the detailed measurement of thoracicmovement during breathing.22 However, for many applica-tions requiring the assessment of lung function, the easiestway to assess changes in lung volume is to integrate the flowmeasured at the mouth with a pneumotachograph.

Integration of Flow Before the advent of the modern lab-oratory digital computer, integration was typically achievedin real time using an electronic circuit based on the chargingof a capacitor. Nowadays, integration is performed digitallyon a computer. The digitized flow signal consists of a seriesof data points {V1,V2,V3, } separated by equal time intervalst. A simple formula for numerical integration is thetrapezoidal rule, which involves approximating the areaunder a section of a curve by a trapezoid. This meansapproximating the curve betweenV1 andV2 by a straight line(Figure 54-15) and calculating the area A under it as

(54-5) AV V

t+ 1 22

V

.

Differential pressuretransducer

Resistive element

FIGURE 54-14 The pneumotachograph.


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The areaA under a section of curve is then simply the sumof all the individual As, thus

(54-6)

There are other more accurate, and more complicated,numerical integration schemes. However, the key thing isthat t should be small enough so that the errors involvedin approximating the true curve between points isnegligible. This can be tested for by integrating the datausing progressively smaller values for t, until the results donot change.

MEASUREMENT OF LUNG FUNCTION

Now that a set of respiratory data has been collected andstored on a computer, as described above, we are faced withthe task of having to interpret it. How this is done dependsvery much on the nature of the data collected. In most cases,however, the assessment of lung function from respiratorydata is based on some model idealization of the real systemunder study. The model is only useful if it behaves like thereal system to a satisfactory degree. It is therefore crucial tounderstand what model is being invoked whenever lungfunction is being assessed so that the suitability of the modelcan be evaluated. In most applications, the model concernedis very simple, typically involving only a single compart-ment. In some cases, the model may be very complicatedwith multiple alveolar compartments and airway branchesrepresented. Regardless of the level of model complexity,however, it is crucial that any investigation of mechanicallung function begin with an understanding of the mathe-matical model being invoked.

FORCED EXPIRED FLOWHaving just expounded on the importance of models in theanalysis of lung function data, it turns out that the tradi-tional mainstay of clinical pulmonary function testing, the

A A

VV V V

V

ii

n

nn

+ + + + +

=

1

12 3 12 2

tt

forced expiration, yields quantities that are usually treated aspurely empirical. The forced vital capacity (FVC) and theforced expiratory volume in 1 second (FEV1) are widelyused either individually or as a ratio to diagnose a variety ofcommon lung pathologies. The great advantage of the forcedexpiration is that it can be performed easily in an outpatientsetting, requiring nothing more than a device for measuringflow (or volume) and some cooperation from the subject.

The measuring device must be able to measure flows ofgreater than 10 L.s1 with a frequency response that cap-tures the rapid onset of flow at the start of a maximal forcedexpiration beginning from total lung capacity. There arecommercially available systems designed specifically for thistask, either by direct spirometric measurement of exhaledvolume or by pneumotachograph measurement of flow.

The clinical utility of forced expired flows arises from thephenomenon of flow limitation, whereby exhaled flowreaches a maximum value independent of further increasesin expiratory muscle activity. Subjects with normal musclefunction can reach this limiting flow over most of the vitalcapacity range. The limiting flow is reduced in obstructive

lung disease, and the relationship of flow to exhaled volumeassumes shapes that are characteristic of various lungpathologies. Detailed accounts of the flow-volume curve andits relation to pulmonary disease can be found in standardtexts.23 Unfortunately, the underlying mechanical mecha-nisms in the lung responsible for producing the flow-volume loop are complex and nonlinear, so parameters suchas FVC and FEV1 are not easily related to a model of the res-piratory system. Consequently, making the link betweenfunction and lung structure from forced expired flows hasnot been straightforward. In other words, although parame-ters such FVC and FEV1 are sensitive to both obstructiveand restrictive lung disease, it is unclear how to deduce the

site or nature of an abnormality from the values of theseparameters, although some sophisticated computer model-ing studies have attempted to elucidate the relationshipsbetween the forced expired flow-volume loop and the phys-ical properties of the lungs.24 Nevertheless, the convenienceof measuring forced expired flows and their diagnostic util-ity make this technique the most clinically important of alllung function measurements.

METHODS BASED ON THE SINGLE-COMPARTMENTMODELThe model of respiratory or pulmonary mechanics most fre-quently employed as the basis for lung function measure-ments is that of a single elastic compartment served by asingle flow-resistive airway (Figure 54-16). This modelassumes that the lungs are homogeneously ventilated andthat all alveolar pressures are equal to each other at all times.

Plethysmography Whole-body plethysmography com-plements the measurement of forced expired flows as theother major methodology for measuring lung function incurrent clinical use. Plethysmography is used to measuretwo important parameters of lung function, thoracic gas vol-ume (TGV) and airway resistance (Raw), both under theassumption of the single-compartment linear model. The

V (t)

t2

t3

t1

t

.

A1 A2

FIGURE 54-15 Trapezoidal integration of flow involves connect-ing each sampled flow value by straight line and summing the areasunder each trapezoid.


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FIGURE 54-17 Body plethysmograph used to measure A, TGV and B, Raw. Pao is airway opening pressure, Pbox is pressure inside theplethysmograph, and V is mouth flow.


calculation of TGV and Raw using a body plethysmograph iscovered in numerous other articles and books23 and so isdescribed only briefly here.

TGV is measured first by having the subject make breath-ing efforts against a closed airway while the change in air-way opening pressure (Pao) is measured (Figure 54-17A).At the same time, the pressure in the plethysmograph or theflow leaving it (depending on whether it is a pressure or flowbox) provides a measure of changes in total body volume(V). Assuming that the only compressive part of the bodyis the gas in the lungs, Vis equal to the compression of thethoracic gas. Applying Boyles law gives

(54-7)

where we have equated 1 atmosphere to 1,000cm H2O inthe denominator on the left side of Equation 54-7, whichcan be rearranged to give a measure of TGV.

Next, this measurement of TGV is used to estimate Raw byhaving the subject pant while completely enclosed inside

P VTGV

ao

1000

the plethysmograph. Flow (V) is measured at the subjectsmouth with a pneumotachograph while pressure (Pbox)inside the plethysmograph is measured (Figure 54-17B).Pbox varies because of two factors. One of these is that gasinspired from the plethysmograph becomes humidified andheated to body temperature, thereby increasing in volume.This increases the combined volume of the remainingplethysmographic gas and the subjects body and so com-

presses the plethysmographic gas. The other factor is that anegative pressure in the thorax is required for inspirationand the converse for expiration. This results in compressivevolume changes in the thoracic gas that are again manifestas changes in the combined volume of plethysmographic gasand subject. To the extent that the first source of changes inPbox can be ignored, the changes in Pbox can be equated tocompressive changes in thoracic gas volume, which can thenbe used, again via Boyles law, to infer the changes inalveolar pressure (Palv). The difference between Palv and Paodivided byVthen yields a measure ofRaw.

The plethysmographic measurement of TGV and Rawassumes that the lungs are a homogeneously ventilated (ie,

effectively single-compartment) system. This works well innormal lungs but may not in severely diseased lungs inwhich obstructed airways can lead to marked differencesbetween Palv and Pao when panting against a closed airway.

25

An unrestrained version of plethysmography has beenused in an attempt to assess lung function in infants26 andsmall animals.27 This technique involves merely measuringvariations in Pao as the subject breathes while inside the box.Although these pressure swings arguably give informationabout the pattern of breathing,28 they cannot provide mean-ingful information about respiratory mechanical function,29

despite recent claims to the contrary.30,31

Resistance and Elastance The single-compartmentmodel of respiratory mechanics (see Figure 54-16) isdescribed by a simple and extremely useful mathematicalequation if it is linear. If the resistive pressure drop betweenone end of the airway and the other is considered to be pro-portional to the flow of gas (V) through it, then the constantof proportionality (R) is termed resistance. Similarly, theelastic recoil pressure inside the compartment is taken as

FIGURE 54-16 The single-compartment model of the respiratorysystem. R is resistance and E is elastance (see Equation 54-8).

E

R

Pao

Pao

V

.

A B

Pbox Pbox


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proportional to the volume of the compartment above someelastic equilibrium volume, with its constant of proportion-ality (E) termed elastance. Finally, we must account for thepossibility that the pressure (P) applied across the model(from the entrance to the airway through to the outside ofthe elastic compartment) has some finite value P0 when Vand Vare both zero. Simple addition of pressures shows thatP is the sum of the resistive and elastic pressures, thus,

P(t) RV(t) EV(t) P0 (54-8)

where we have written the variables P,V, and Vexplicitly asfunctions of time (t) to remind us that they all vary duringbreathing.

Equation 54-8 is used in respiratory investigations to esti-mate R, E, and P0 via multiple linear regression. This pro-vides those values ofP, V, and Vthat, when used in the rightside of Equation 54-8, provide the closest approximation tothe measured P in the left side. Closest here means inthe least squares sense, which means that the sum of thesquared differences between the measured value ofP and themodel values is minimal. R and E are taken as measures of

the resistance and elastance of the lung or respiratory sys-tem, which in a sense they are. Strictly speaking, however, Rand E are nothing more than the parameters of a simplemodel (see Figure 54-16) that has been forced to match themeasured signals as well as possible. The usefulness ofR andE as reflections of physiology thus lies in the degree towhich the single-compartment linear model accuratelydescribes the behavior of the system under study. In manycases, this accuracy is acceptable, such as the exampleshown in Figure 54-18 of a patient with chronic obstructivelung disease being mechanically ventilated in the intensivecare unit.

When the single-compartment linear model does

describe a set of respiratory data to an acceptable degree ofaccuracy, one is then faced with the task of assigning a phys-iologic interpretation to the values ofR and E it provides. Itmight seem obvious, for example, that R would correspondto the flow resistance of the airway tree. However, this turnsout not to be the case, at least not entirely. Studies with thealveolar capsule in dogs and other animals have allowedtotal lung resistance (ie, R) to be partitioned into airwayresistance and tissue resistance.11,32 The latter has beenshown to depend greatly on the frequency at which thelungs are oscillated and, at normal breathing frequencies,may constitute the great majority ofR.13 It is not until fre-quency gets well above the range of normal breathing (aboveabout 2Hz) that the tissue component ofR decreases to thepoint where R is a good reflection of airway resistancealone.3335 In the intact animal, R also contains a significantcontribution from the chest wall.36

Nonlinear Single-Compartment Models There are situ-ations in which the single-compartment linear model doesnot describe a set of respiratory data with acceptable accu-racy. The model must then be replaced by a more realistic(and invariably more complex) model. An example typicallyoccurs when the volume excursions of the lungs becomelarge or when the stiffness of the lung tissue increases in

certain diseases. In this case, one often finds that thedynamic elastic behavior of the tissues is significantly betterdescribed by a curvilinear function of volume rather than astraight line, as in the linear model. For example, it has beenshown in both humans37 and animals38 that a nonlinearmodel with the equation

P(t) RV(t) E1V(t) E2V2(t) P0 (54-9)

sometimes fits the data significantly better than the linearmodel above (see Equation 54-8). The nonlinear model isstructurally the same as the linear model in that it still hasonly a single compartment being ventilated through a singleairway. The difference is that the elastic properties of the tis-sues surrounding the compartment are nonlinear. Similarly,the linear resistance term in Equation 54-8 can be replacedby two terms representing a flow-dependent resistance asoriginally proposed by Rohrer.38 Which of these modelsshould be used to describe a given set of respiratory data canbe decided using, for example, the F-ratio test applied to themean squared differences between measured P and P pre-dicted by the various models.38

Another use of the single-compartment model ofrespiratory mechanics arises when the stiffness of the lungor respiratory system is assessed from the quasistatic pressure-volume (P-V) curve. The P-V curve is obtained by inflating

0 1 2

0

10

20

30

data

model fit

Time (s)

Pressure

(cmH2O)

0.0

0.5

1.0

Volume(l)

-2

0

2

Flow

(l/s)

FIGURE 54-18 Example of pressure, flow, and volume data over asingle breath from a mechanical ventilated patient in the intensivecare unit. The lower panel also shows the fit to pressure producedby Equation 54-8.


11/16


and deflating the lungs, either continuously or in steps,slowly enough that the resistive pressure drop across theairways can be neglected. The result is a relationship thatembodies the elastic properties of the pulmonary or respira-tory tissues, viewed as a single compartment. The modelinvoked to account for the P-V curve is thus again a single-compartment model, but now it is nonlinear because theelastic recoil pressure inside the compartment increases dis-

proportionately as volume approaches total lung capacity. Acommonly used equation for describing the descending limbof the P-V curve is the exponential expression39

VA BeKP (54-10)

where A, B, and K are constants chosen to make the rightside of the equation match the left side as closely aspossible.

The ascending limb of the P-V curve lies to the right ofthe descending limb (Figure 54-19), reflecting a phenome-non known as hysteresis. The amount of hysteresis dependson the volume range over which Vis cycled and is caused bya number of factors. One of the most important is recruit-

ment of closed airspaces during inspiration that remainopen during expiration. Hysteresis may become markedlyenhanced in pathologies such as acute lung injury.40

METHODS BASED ON MULTICOMPARTMENT MODELSThe single-compartment linear model (see above) generallydescribes respiratory pressure-flow data well when volumeexcursions are modest and the volume oscillations are con-centrated around a single frequency, such as pertains, forexample, during normal breathing or mechanical ventilation.However, the values ofR and E obtained using this modelvary with frequency. In particular, R decreases markedly asfrequency is increased over the range of normal breathing,

whereas E correspondingly increases. The main reason forthis frequency dependence ofR and E in normal lungs is thefact that the respiratory tissues are viscoelastic, that is, theyexert a recoil pressure that is a function not only of volumebut also of volume history.41 In diseased lungs, additionalvariation of R and E with frequency may be caused byregional variations in mechanical function throughout thelung, leading to transient redistribution of gas as the lungsare dynamically inflated and deflated.42,43 In any case, thesingle-compartment linear model no longer suffices as adescription of pulmonary or respiratory mechanics whenmultiple frequencies are involved. Instead, we need toinvoke models featuring two or more compartments toaccount for regional differences in mechanical functionthroughout the lung.44

Interrupter Technique A technique for assessing lungfunction that was first introduced nearly a century agoinvolves the rapid interruption of airflow at the airway open-ing, while pressure just behind the point of interruption ismeasured. Initially, it was thought that this maneuver wouldsimply obliterate any resistive pressure drop across the air-ways, so that the observed sudden change in pressure wouldreflect Raw. However, work over the past two decades hasshown that the sudden change in pressure occurring with

0 5 10 15

-10

0

10

20

30

40

Time (s)

Pressure

(cmH2O)

0.0

0.2

0.4

0.6

0.8

1.0

Volume(ml)

0 10 20 30

0.0

0.2

0.4

0.6

0.8

Volume(l)

Pressure (cmH2O)

A

B

FIGURE 54-19 A, Pressure and volume data obtained from a mouseduring stepwise inflation and deflation of the lungs. B, Ascendingand descending limbs of the quasistatic pressure-volume (P-V)curve derived from the plateaus of the data in Figure 54-19A.

interruption of flow is accompanied by some rapid dampedoscillations and a subsequent further transient change inpressure to a stable plateau (Figure 54-20). The oscillationsare mainly owing to ringing of the gas in the central air-ways,45 whereas the secondary slow pressure change is due


12/16


to the viscoelastic properties of the respiratory tissues whenthe lung is normal12 and may be accentuated by gas redistri-bution in pathologic situations.46 Interpreting the initialrapid and secondary slower pressure changes has been doneon the basis of two-compartment models of respiratorymechanics.44,47,48

The interrupter technique is currently gaining interestamong pediatricians,49 who face a particular challenge intrying to assess lung function in young children and infantsunable to perform the voluntary maneuvers necessary togenerate forced expired flows. However, the interruption offlow is merely a specialized kind of flow perturbation.Understanding the information obtained by applying gen-eral flow perturbations to the lungs is best done in the con-text of the forced oscillation technique and impedance.

Input Impedance The frequency dependence ofR and Ehas led respiratory researchers to move to a more global assess-ment of mechanics based on a quantity known as input imped-ance (Zin). Zin can be determined over a range of frequenciesby subjecting the lungs to an oscillatoryVsignal that containsmultiple frequencies. Zin is then determined by taking the ratioof the Fourier transform ofP to the Fourier transform ofV.This yields a complex function of frequency

Zin(f) R(f) iX(f) (54-11)

with a real part R(f) and an imaginary part X(f), where. The value ofR at each value off is equal to the

resistance of an equivalent single-compartment linearmodel, so the R(f) is called the resistance. X(f) is called thereactance and at each f is related to the elastance of theequivalent single-compartment model by

(54-12)X fE f

f( )

( )=

2

i = 1

Zin is thus nothing more than a description of how R and Evary over a range of frequencies. Zin still requires that thesystem under study be linear. This assumes that whatevervalues ofR and E are obtained at a particular frequency, theirvalues do not depend on the amplitudes of the P, V, and Vsignals used to measure them (which, of course, is neverprecisely the case in practice).

Forced Oscillation Technique The measurement ofZin isachieved by the so-called forced oscillation technique in whicha flow generator (such as a loudspeaker or piston pump) isused to drive an oscillatory flow into the lungs via the airwayopening.50 The frequency range over which the signal oscil-lates determines the kind of information that will be obtainedabout respiratory mechanical function. At frequencies belowabout 2Hz, much ofZin is determined by the rheologic prop-erties of the tissues, as well as regional mechanical hetero-geneities throughout the lung should they exist. Regionalheterogeneities can affect the shape of Zin above 2Hz aswell.42,43 At frequencies of hundreds of Hz one obtains infor-mation about the acoustic characteristics of the airways.51

Whatever the frequency range, the interpretation ofZin in physiologic terms requires some kind of model of thesystem under investigation. For example, normal respiratoryor pulmonary Zin is described very accurately below about20 Hz by a model consisting of a uniformly ventilatedcompartment surrounded by viscoelastic tissue. The com-partment is served by a single airway having a newtonianresistance RN, whereas the viscoelastic tissue has animpedance with real and imaginary parts that both decreasehyperbolically withf. The equation for the impedance of thisconstruct, which is frequently referred to as the constant-phase model, is35

(54-13)

where the parameter is related to the two tissue parame-ters via the relation

(54-14)

Gti characterizes the viscous dissipation of energy in the tis-sues and so is related (but not equivalent to) tissue resist-ance. Hti characterizes the storage of elastic energy in thetissues and is closely related to E. Iis an inertance reflectingthe mass of the gas in the central airways. The four parame-ters RN, I, Gti, and Hti together account for the entire fre-quency spectrum of Zin below 20Hz in a convenient andcompact way. They also allow Zin to be partitioned into acomponent pertaining to the airways (ie, RN and I) and acomponent pertaining to the lung periphery (ie, Gti and Hti).Figure 54-21 shows an example of the fit to Zin provided byEquation 54-13.

Other Respiratory Impedances The calculation ofrespiratory impedance is not limited to Zin obtained from Pand V at the airway opening. Any relevant pressure andflow signals will do, although the impedance obtained will

= 2 1

tanH

Gti

ti

Z f R i fI G iHf

in ti tiN( )( )= + +

22

0.0 0.5 1.0

Pressure(arbitraryuntis)

Time (s)

Initial rapid pressure change

Secondary slowerpressure change

Damped high-frequencyoscillations

Point of flowinterruption

FIGURE 54-20 Schematic representation of airway opening pres-sure recorded during interruption of expiratory flow. An initialalmost instantaneous jump in pressure is accompanied by rapid

damped oscillations, which are followed by a slower further pres-sure change.


13/16


be different in each case. For example, if pressure is oscil-lated around the body surface while flow is measured atthe mouth, the impedance obtained is known as transferimpedance (Ztr). Ztr has been used in numerous studies inboth animals52 and humans.5355 Although in principle Ztrshould give similar information about lung function to Zin,its measurement may be associated with some practicaladvantages. First, when the distal airways of the lungbecome significantly constricted, the flow oscillationsapplied at the mouth to measure Zin may become shuntedto a large degree into the central airways that have a finitecompliance.43 If the amount of flow reaching the lungsbecomes small to the point that it approaches the noise level

of flow measurements at the mouth, then one effectivelyloses the ability to probe the lung periphery. In contrast,when pressure oscillations are applied at the body surface,flow is driven from the lung periphery toward the trachea,and shunting into the central airway compartment isminimized. This means that all flow measured at the mouthcomes from the lung periphery, giving Ztr a signal-to-noiseadvantage over Zin for the investigation of severelyconstricted lungs.

Another recently developed variant of respiratory imped-ance uses the heart as the oscillatory source, producing whathas been termed output impedance.56 When a subjectrelaxes with an open glottis, the beating heart perturbsthe lungs sufficiently to generate a small flow that can bemeasured at the mouth. When the airway opening isoccluded, corresponding pressure oscillations are measuredjust behind the point of occlusion. The impedance deter-mined from these two signals was found to have anessentially zero imaginary part and a real part that corre-sponded closely to the resistance of the conducting airways,as measured by Zin.

56

Yet a further type of respiratory impedance has beenobtained by applying forced oscillations in flow to thelungs of dogs through an alveolar capsule.57 The resultingalveolar input impedance (ZA) between 26 and 200Hz

was found to be well described by a simple model consistingof a subpleural alveolar compartment connecting to therest of the lungs by a terminal airway compartment. Themagnitude ofZA was found, on the basis of an anatomicallyaccurate computer model of the dog lung,58 to correspondto that expected of a single lung acinus. When ZA wasfollowed during the development of bronchoconstriction,the response of the lung periphery was demonstrated to be

extremely heterogeneous both spatially and temporally.59,60

The information obtained about lung mechanical functionthus depends on the site at which flow perturbations areapplied and where pressures and flows are measured. It alsodepends to a great extent on the nature of the flowperturbations themselves. Measuring lung mechanics duringnormal breathing in a conscious subject using an esophagealballoon has the advantage of allowing the subject to remainin a reasonably natural state. However, it suffers from the dis-advantage that the subject is free to choose the breathing pat-tern, which may change with an intervention. This itself willaffect the measurement of mechanics regardless of any truechanges in the intrinsic mechanical properties of the airways

or tissues. Thus, one faces a trade-off between minimizingthe interventional nature of the measurement and controllingfor confounding variables. This situation has been likened tothe uncertainty principle of quantum mechanics.61

SUMMARY

The quantitative study of respiratory mechanics involvesmeasurement at two levels, namely the measurement of theraw signals that carry the mechanical information and themeasurement of key physiologic parameters that embody thisinformation. Measurement of signals requires the use of trans-ducers for recording pressure, flow, and volume and comput-

ers for capturing and storing the data. Measurement ofphysiologic parameters involves matching the measured sig-nals to a suitable mathematical model of respiratory mechan-ics. There are many decisions to be made in achieving theseends, such as which type of transducer to use, how fast tosample the signals, what resolution of analog-to-digital con-verter is required, what kind of perturbation should beapplied to the respiratory system, and what mathematicalmodel should be invoked to interpret the data. There is nouniversally correct decision for any of these issues because theappropriate action to be taken depends on the physiologicquestions being addressed. These questions, whatever theyare, will determine what mathematical model of respiratorymechanics should be invoked, what frequency response char-acteristics are required of the transducers, what data samplingrate is needed, and so on. It is therefore important for the res-piratory scientist to understand the basics of measurementtheory as it applies to both the collection of physiologicsignals and their interpretation through mathematical models.Such an understanding minimizes the risk, for example, ofbeing misled by measurement artifact from a transducer thatis not up to the task required of it or of being confused by theapparently bizarre behavior of a calculated parameterobtained using a model that does not apply to the situation athand.

0 5 10 15 20

-14

-12

-10

-8

-6

-4

-2

0

2

Real part

Imaginary part

Model fit

Impedan

ce(cmH2O.s/m)

Frequency (Hz)

FIGURE 54-21 Fit of constant-phase model (Equation 54-13) toZin data from a mouse.


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