Annals of Biomedical Engineering, Vol. 31, pp. 121–131, 2003 0090-6964/2003/31�2�/121/11/$20.00Printed in the USA. All rights reserved. Copyright © 2003 Biomedical Engineering Society

Spatial Distribution of Human Respiratory System TransferImpedance

R. L. DELLACA,1,2 A. ALIVERTI,1,2 K. R. LUTCHEN,3 and A. PEDOTTI1,2

1Dipartimento di Bioingegneria, Politecnico di Milano, Italy; 2Centro di Bioingegneria, Fondazione Don Gnocchi IRCCS ePolitecnico di Milano, Italy; and 3Department of Biomedical Engineering, Boston University, Boston, MA

(Received 19 December 2001; accepted 29 November 2002)

Abstract—Transfer impedance (Z tr) of the respiratory systemprovides specific information on airways and tissues, but littleis known about its spatial distribution in the different thoraco-abdominal regions. To study Z tr distribution on the chest wallsurface we analyzed five healthy subjects in the supine positionby applying a sinusoidal forcing pressure �4, 8, and 12 Hz� atthe mouth and measuring airway opening pressure and flow.Three-dimensional positions of 68 reflective markers placed onthe chest wall over selected reference points were simulta-neously measured by an optoelectronic motion analyzer. A sub-set of ten points placed on the midline were used to measurechest wall movements in the craniocaudal direction. While themotion of rib cage markers was synchronous, the abdominalmarkers demonstrated surface waves propagating caudally. Theamplitude and phase of these waves were strongly dependenton position and frequency. We used a new method to measuretotal and local chest wall volume variations to compute thedistribution of Z tr over the chest wall. Above 4 Hz we foundthat Z tr was inhomogeneously distributed and strongly depen-dent on position and frequency, mainly in the abdomen wherethe phase was often �180° with high values of modulus. Forthis reason, we conclude that above 8 Hz Z tr represents rib cagemechanics almost exclusively. © 2003 Biomedical Engineer-ing Society. �DOI: 10.1114/1.1541012�

Keywords—Chest wall, Oscillatory mechanics, Abdomen,Forced oscillations, Impedance.

INTRODUCTION

Respiratory transfer impedance (Z tr) data are derivedfrom a noninvasive procedure, and the frequency depen-dence and level of Z tr are sensitive to airway properties,gas compression, and lung and chest wall tissueproperties.14 Until recently, these data were usually ac-quired by creating an oscillating pressure field around asubject’s chest wall (Pcw) as he sat enclosed in a head-out body box.16,17,20,21,25 The corresponding flow at themouth (Vao) was measured and, by definition, the Z tr

�Pcw /Vao . If the forcing signals are small enough to

Address correspondence to Raffaele L. Dellaca, Dipartimento diBioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32,I-20133 Milano Italy. Electronic mail: dellaca@biomed.polimi.it

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keep the respiratory system close to linearity and if theeffect of upper airway shunting is minimized, an alter-native way to measure Z tr can be obtained by applyingforced oscillation at the airway opening (Pao) and mea-suring chest wall flow (Vcw) by a body plethysmograph,then Z tr�Pao /Vcw .19 Recently, a new technique calledoptoelectronic plethysmography �OEP� has proven ca-pable of measuring volume variations of the chest wallaccurately by noninvasive measurements of the displace-ments of passive markers placed on the external surfaceof the chest wall over selected reference points.1,8 Wehave shown that using this technique it is possible totrack flow excursions of the chest wall while imposingpressure oscillations at the airway opening.3 Thus, theOEP method provided the advantage of probing transferimpedance without the subject having to be enclosed in abody chamber and without the need of a flow sensor atthe mouth. Moreover, considering different subsets ofoptical markers placed on the thorax, it is possible topartition the Z tr by measuring the contribution of distinctcomponents of the chest wall to the total Z tr .

Regardless of which method is used, the interpretationof Z tr often requires fitting the data with a simple lumpedelement model in which a single airway compartment ispartitioned from a single tissue compartment by a shuntgas-compression compliance for the air in the lung.16,18

The tissue compartment represents the combined effectsof lung parenchyma and chest wall.

The study of regional pleural expansion during high-frequency ventilation �HFV� at 15 and 30 Hz of excisedlungs using synchronized stroboscopic photography13

showed that while at low frequency �1 Hz� the expansionof the lung was nearly synchronous, during HFV thelung expanded asynchronously. These nonuniformitiessuggested marked inter-regional airflow and elastic wavepropagation in the parenchyma when a high-frequencypressure forcing is applied to the airway opening. Also,during typical breathing conditions it is commonly ac-cepted that the chest wall has at least two and perhapsmore independent mechanical components �as lung-

122 DELLACA et al.

apposed and diaphragm-apposed rib cage and abdomen�,all of which have disparate mechanical properties. Evi-dence for such disparate behavior between the abdomenand rib cage has been published over the frequencyrange from 0 to 4 Hz by Barnas and co-workers.4,5

In our previous study,3 we showed that the frequencydependence of transfer impedances was different for theabdomen and the two rib cage compartments. Thus, thecontribution of the compartments to total Z rs changedwith frequency.

The current study was concerned about how localvariations in chest wall and lung properties �measured aslocal transfer impedance� and elastic wave propagationmight or might not impact measures of total Z tr over afrequency range from 4 to 12 Hz.

We hypothesized that local heterogeneities as well assurface wave propagation, mainly at higher frequencies,are not sufficiently distinct to justify interpretation of Z tr

with more than one lumped tissue compartment for thewhole respiratory system. On the other hand, a techniquethat allows the estimation of the distribution of Z tr overthe chest wall surface could be useful to study, evaluate,and quantify changes in respiratory mechanics inducedby restrictive chest wall diseases or to study heterogene-ity in airways obstruction or during bronchial challenge.Thus, using OEP we developed a new method to mea-sure the degree of heterogeneity in Z tr with higher spatialresolution and the propagation of pressure waves alongthe chest wall during pressure oscillations imposed at themouth.

METHODS

Subjects

Measurements were made in five normal healthy malesubjects, aged from 24 to 30 years �26.4�2.3 SD�,height from 167 to 190 cm �179�9 SD�, weight from 66to 88 kg �77.4�10 SD�. All subjects were nonsmokers.

Forced Oscillations

Waveform propagation phenomena and local transferimpedance of the respiratory system were studied byusing a computer-controlled loudspeaker to apply a sinu-soidal forcing pressure at the mouth. A single sinusoidwaveform was used in order to maximize the signal-to-noise ratio. To obtain the frequency dependence of theresponse, we repeated the measurements on the samesubject changing the forcing frequency. Three differentforcing frequencies were used in this study for move-ment analysis �4, 8, and 12 Hz� while for studying re-gional transfer impedance six frequencies �2, 4, 6, 8, 10,and 12 Hz� were used.

Experimental Measurements

A sinusoidal pressure signal was generated from ananalog-to-digital–digital-to-analog �A/D–D/A� board�DAQ-CARD 1200, National Instruments, Austin, TX�and amplified by a power amplifier �model ProlineEQ552, Eurosound, Milano, Italy� that drove a 25-cm-diam loudspeaker �model HS250, Ciare, Ancona, Italy�mounted on a rigid box of �3 l of internal volume. Thepressure signal generated into the box was transferredthrough a short connecting tube �22 cm long, 19 mm ID�and a mouthpiece to the subject. The pressure at theairway opening (Pao) was measured by a piezoresistivepressure transducer �model SCX01, SenSym, Milpitas,CA�. Airway flow was measured with a pneumot-achograph �model 4700A; Hans Rudolph, Kansas City,MO� connected to a Celesco pressure transducer �modelLCVR, 0–2 cm H2O; Celesco Instruments, Canoga Park,CA�. The frequency response of the pneumotachographwas assessed as suggested in Ref. 7 and it was found tobe flat up to 20 Hz. All signals were sampled at 100 Hzby the same A/D–D/A board used to generate the for-cing signal and synchronized with the kinematicmeasurements.

Chest wall kinematics were measured in the supineposture by an automatic optoelectronic motion analyzer�ELITE system BTS, Milano, Italy�, able to measurewith high accuracy and high temporal resolution �100Hz� the three-dimensional �3D� coordinates of passivemarkers placed on the body surface. This experimentalsetup has been extensively described.3 In previousstudies1–3,10 we analyzed chest wall kinematics in thesupine position using 45 markers, while in the presentapplication we used 68 markers positioned as shown inFig. 1, with a high number of markers placed on theabdomen. In fact, preliminary experiments showed thatduring oscillations at high frequencies ��8 Hz�, someneighboring markers moved in opposite directions,mainly in the abdominal region �vide infra�. Therefore,we decided to increase the number of markers �i.e., thespatial resolution of chest wall surface motion detection�,to describe with more detail possible surface wavepropagation phenomena occurring during oscillations.

Since optoelectronic plethysmography measures vol-umes from the 3D measurement of each marker position,the calibration of the system is not obtained using refer-ence volumes but using 3D objects �for example, grids orbars� of accurately known structure and dimensionsmoved in the working area. In particular, we used agrid-based calibration procedure6 and the calibration ofthe system was then verified measuring the length of acalibration bar �a bar with a marker on each edge whoselength is precisely known to be 200 mm� that was movedin the area where the subject was later analyzed. Thesystem was considered correctly calibrated when the er-

123Local Transfer Impedance in Humans

ror in the measurement of the length of the bar wasfound to be less than 0.2 mm. The capability of thesystem to measure volumes from the measurement of the3D markers position has been extensively validated inour previous works.1,8

PROTOCOL

Each subject was analyzed in the supine position,lying on a bed to facilitate relaxation of the chest wallmuscles. Prior to starting the experiments a 15–20 mintraining period on the oscillation system was performedto accustom the subject to relax the respiratory musclesduring the pressure forcing. During this training period,airway pressure and flow were monitored. The adaptationlasted until the signals became constant in amplitude.After a few breaths, the subject exhaled passively tofunctional residual capacity �FRC�, placed the mouthtightly around the mouthpiece while an operator firmlysupported the cheeks. The subject then stayed relaxed for13 s holding his breath while pressure and 3D markerposition were recorded. Each test was repeated at thedifferent frequencies, with a peak-to-peak pressure valueof about 4 cm H2O. If pressure or flow at the airwayopening presented significant changes during the mea-surement, the data were discarded and the test repeated.

FIGURE 1. Markers position on the chest wall and definitionof the triangles used to describe chest wall surface. Thecentral highlighted markers were used for movement analy-sis. The thick line defines the subset of markers used as anexample in Fig. 2 for the local volume computation proce-dure.

Data Analysis

The accurate measurement of 3D marker coordinatesduring oscillations allowed two different types of analy-sis: motion analysis and regional transfer impedancecomputation. First, we calculated the amplitude ofmarker displacements and the craniocaudal phase shiftsof these amplitudes; second, the chest wall surface wasapproximated by 110 triangles connecting the markers;from the displacement of each triangle during oscilla-tions we estimated ‘‘local’’ volume variations �see be-low�; finally, the transfer functions between the localflow and Pao �local transfer impedance, Zel) were esti-mated to describe the spatial distribution of respiratorysystem transfer impedance.

Motion Analysis

The propagation of the forced wave in the craniocau-dal direction was studied using the amplitude and phaseof the displacement signal of ten markers placed on themidline from the sternal notch to the lower abdomen �seeFig. 1� during oscillations. The relative displacement attime t of the ith marker �si(t)� , whose position wasidentified by the 3D coordinates xi(t), yi(t), zi(t), wascomputed as follows:

si� t ����yi� t ����yi�0 ��2��zi� t ����zi�0 ��2, �1�

where instant 0 identifies the time of the first acquiredimage frame. We considered only displacements in theanteroposterior �z axis� and laterolateral �y axis� direc-tions, because preliminary analysis revealed that cranio-caudal movements along the x axis were not related tothe stimulus and, if considered, the signal-to-noise ratiodecreased.

Propagation of the stimulus was studied in the cran-iocaudal direction along the x axis, using the displace-ment signals of the ten markers of Fig. 1 and consideringthe phase differences between the reference markerplaced over the sternal notch �No. 1� and all the othermarkers �from No. 2 to No. 10�. The phase shift ��1,i

was estimated as the phase angle of the transfer functionbetween the displacement of the reference marker�s1(t)� and the other nine markers �si(t), with i�2 to 10]. The transfer function was estimated bycomputing their fast Fourier transforms �FFTs� �respec-tively, S1( f ) and Si( f ), where f is frequency� and thephase shift was expressed as

124 DELLACA et al.

��1,i�arctg�imm�S1� f ��real�Si� f ���imm�Si� f ��real��S1� f ��

�real�S1� f ��real�Si� f ���imm�S1� f ��imm�Si� f ��, �2�

FIGURE 2. Example of the procedure used to compute local volume changes applied on a subset of markers that defines asmall region of the chest wall surface „Fig. 1, thick line, here reported as the external surface, EXT…. If we consider each trianglethat describes the chest wall surface „for example, the one defined by the markers A, B, and C in Fig. 1… as the base of a prismwith the opposite face defined considering the virtual markers „A�, B�, and C�… it is possible to estimate local volume changesfrom the measurement of the volume of the prism „left…. The virtual markers define the internal surface „INT… and are obtainedusing the mean point P as described in the text. In fact the difference between the prism volume „Vel… in each frame and thevolume computed on the first one gives the element volume change „�Vel…. The volume of the prism is calculated as the sumof the three tetrahedrons „right… defined as follows: „1… base A�-B�-C�, opposite vertex A; „2… base C�-B�-B, opposite vertex A;3… base A-B-C, opposite vertex C�.

where imm� � and real� �, respectively, indicate theimaginary and real part and f is the forcing frequency.

The coherence function between s1(t) and si(t) hasbeen classically obtained as

1,i2 �

�G1,i2 �

G1,1Gi ,i, �3�

where G1,i is the cross spectrum between s1(t) and si(t),while G1,1 and Gi ,i are the autospectra of s1(t) andsi(t), respectively. In the present study we consideredonly values of ��1,i presenting a coherence 1,i

2 �0.9.

Regional Transfer Impedance Computation

As mentioned above, the shape of the chest wall wasdescribed by connecting the markers to form 110 tri-angles �Fig. 1�. To quantify local volume variations, thecontribution due to the motion of each triangle to thetotal chest wall volume change was computed in thefollowing way. The coordinates of the mean positionpoint �P� for the 68 markers were computed by averag-ing the 3D coordinates of all the markers. In this way,we obtained the 3D coordinate of P, which is alwayslocated inside the chest wall. A new projection point foreach marker was then defined to be at an arbitrary dis-tance of 50 mm from the original marker in the directionof point P �Fig. 2�. The resulting projected points were

125Local Transfer Impedance in Humans

connected in the same manner as the original markers toform a set of new triangles that defines a second surfaceinternal to the surface described by the original markersplaced on the chest wall. For each period of acquisition,the coordinates of the projected points were computedonly for the first acquired frame. These points were thenkept fixed for the remaining duration of the acquisition.

As shown in Fig. 2, this procedure allows us to asso-ciate a volume to each triangle by considering the regionof space existing between the external triangle and thecorresponding internal one. During the measurement, thepressure signal applied to the mouth induces volumechanges in the lung and, consequently, the chest wallsurface moves. The markers placed on the chest wallchange their position, and the triangles of the externalsurface move accordingly. This results in a change of thevolume subtended by the external moving triangles andthe internal fixed ones. The volume comprised betweenany external triangle and the corresponding internal onewas computed as the sum of three tetrahedra, as shownin Fig. 2 �right�. The manner in which the volume of thetetrahedron was computed is described in the Appendix.

To increase the signal-to-noise ratio, we consideredregions of the chest wall made by one or more triangles�Fig. 3�, and the volume of these elements was obtainedsimply from the sum of the volumes associated with allthe triangles included in the considered region. Two dif-ferent schemes of triangle fusion were adopted, as shownin Fig. 3. Volume variations of the ith element (�Veli

)

were computed for each sample as the difference be-tween each current value and that occurring on the firstacquired sample. In this way, the sum of all values of�Veli

equaled the total chest wall volume variations

(�Vcw):

FIGURE 3. Definition of the chest wall regions considered toincrease the signal-to-noise ratio. The volumes changes ofthese regions were obtained from the sum of the volumechanges associated with all the triangles included by theregion. In this study we used two different chest wall subdi-visions, one made by six regions „left… and the other by 51„right….

�Vcw��i�1

n

�Veli, �4�

where n, which represents the number of the elements,was fixed to 6 or 51 �see Fig. 3�.

Regional Transfer Impedances

Local transfer impedance relative to the ith element(Zeli

) was computed as the transfer function between thetime derivative of �Veli

and the forcing pressure mea-sured at the mouth:

Zeli�Pao /�Veli

. �5�

The time derivative of �Veliin the above equation was

obtained by multiplying the Fourier transform of thevolume signal by j� . As described in Ref. 3, estimationsof the Zeli

modulus and phase were, respectively, ob-tained as

�Zeli� f ���

�Gpv�

Gvv2 f, �6�

�Zeli� f ��arctg

�p IvR�v IpR�

�pRvR�v Ip I��

2, �7�

where f is the forcing frequency; Gpv is the cross spec-trum between Pao and �Veli

computed for f ; Gvv is the

autospectrum of �Velicomputed for f ; p I and pR are the

imaginary and real parts of the Fourier transform of Pao ,respectively; and v I and vR are the imaginary and realparts of the Fourier transform of �Veli

, respectively.Estimates of Gpv and Gvv were obtained by averaging

different periodograms that were computed by means ofFFT. Segments of 256 samples were taken from theoriginal data with 128 overlapping samples and win-dowed with a Hanning function �8–9 segments for eachtest�. The coherence function of the ith element ( i

2),defined as

i2�

�Gvp2 �

GvvGpp, �8�

was used to warrant reliable local transfer impedancedata, considering only measurements with i

2�0.85.The defined Zeli

modulus is strongly dependent fromthe size of the ith element, and for a uniform chest walldisplacement larger elements produce larger volumechanges. For this reason, Zeli

was normalized (Zeli` ) by

126 DELLACA et al.

dividing it by the area of the corresponding externaltriangle (Ai). Because all the elements are considered assubmitted to the same pressure, i.e., Pao , they resulted inbeing connected in parallel and, therefore, the total Z tr

can be obtained as the parallel of all Zeli:

1

Z tr��

i�1

n1

Zeli

��i�1

n1

Zeli`Ai

. �9�

The different values of Zeli` were finally represented by a

color-scaled map of modulus and phase, providing in thisway the distribution of transfer impedance over all thechest wall surface.

RESULTS

Movement Analysis

Figure 4 shows a representative tracing of the relativedisplacement s(t) of the ten markers placed along themidline, obtained during forced oscillations at 4, 8, and12 Hz. We found a progressive increment of the phaseshift along the craniocaudal direction, both at low andhigh frequency. The phase shift is particularly high in theabdominal compartment, with the four markers placed onthe rib cage showing a more synchronous movement andthis effect is more evident when increasing the fre-quency. During oscillations at 12 Hz the phase shiftsbetween the markers placed on the abdomen are �180°leading to movements in opposite directions in the samecompartment.

Note that some of the displacement signals of Fig. 4contain a short period in which the amplitude of theoscillations are reduced significantly �e.g., 8 Hz, thirdcurve, 12 Hz third, fourth, and fifth curves�. However,

FIGURE 4. Relative displacement of the ten markers placedalong the midline from the sternal notch to the lower abdo-men „see Fig. 1… measured during sinusoidal forced oscilla-tions at 4, 8, and 12 Hz from a representative subjects.Marker No. 1 was the one placed on the sternal notch.

since Pao and Vao were monitored and stable during themeasurement and because only a few traces showed thisphenomenon, these variations were not judged as in-duced by glottis narrowing. Rather, they likely reflectbrief and small increases in thoracoabdominal muscletensions. Also, there is no evidence that these fluctua-tions affected our results. All data processing requiredthe averaging of several �at least 6–7� periodogramscomputed on different segments of data taken from thewhole measurement. We accepted only data with a co-herence value greater than 0.9. Therefore, data were au-tomatically discarded if the variations were responsiblefor significant alterations in spectra estimation. Also,from Fig. 4, it can be noted that the amplitude of therelative displacement is strongly dependent on positionand frequency. Globally, it is higher at low frequencies�4 and 8 Hz� than at 12 Hz. At 4 and 8 Hz the displace-ment is predominant in the abdomen, while at 12 Hz it isin the rib cage. These observations are summarized inFig. 5, where the average values of amplitude �in termsof relative displacement power spectra� and phase shiftshave been represented as a function of position andfrequency.

FIGURE 5. Average valuesÁstandard error of the mean ofmarker displacement represented as a function of position at4 „solid circles…, 8 „gray squares…, and 12 Hz „open triangles….Upper panel: amplitude of relative displacement power spec-tra. Lower panel: phase shifts. Marker Nos. 1–10 are definedin Fig. 1.

127Local Transfer Impedance in Humans

FIGURE 6. Average modulus „upper panels… and phase angle „lower panels… local transfer impedance colored maps obtainedconsidering the chest wall as divided in six regions as indicated in Fig. 3 left. The forcing frequencies were 4 „left…, 8 „center…,and 12 Hz „right….

Local Transfer Impedance

Local transfer impedance maps obtained at the threedifferent frequencies �4, 8, and 12 Hz� are shown in Fig.6. The maps have been obtained averaging, for each ithtriangle, the values of �Zeli

` ( f )� and �Zeli` ( f ) of the dif-

ferent subjects. Figure 6 shows that both the modulusand phase angle of Z tr are heterogeneously distributed onthe chest wall surface, mainly in the craniocaudal direc-tion. Moreover, the phase angles show sharp changeswhen crossing the costal margin, while the moduluspresent a more regular increase.

Figure 7 shows that the phase values become inho-mogeneously distributed at the higher frequencies,mainly in the abdominal region. While at 4 Hz phasevalues are similar all over the chest wall surface, at 8and 12 Hz the lower-central subumbilical part of theabdominal wall showed the highest phase shifts, whichdecreased with distance.

DISCUSSION

The primary purpose of the present paper was to bet-ter understand the regional differences of transfer imped-ance on the chest wall surface. To do this, we initiallyanalyzed the movement of several markers placed on themidline from the sternal notch to the lower abdomen. Wefound that while the markers placed on the rib cagemoved synchronously, the motion of the abdominal wallwas markedly inhomogeneous �as first reported byDuBois et al.11�. We also found that between 4 and 12Hz the motion of the abdomen was more marked thanthat of the rib cage, with a maximum amplitude at about4 Hz in the epigastrium between the costal margin andthe umbilicus �Fig. 5�. At 12 Hz, the amplitude of ab-dominal movements induced by pressure oscillations atthe mouth became comparable to or lower than the ribcage. These findings are in agreement with Barnaset al.,4 who measured chest wall motion during sinu-

128 DELLACA et al.

FIGURE 7. Average phase angle local transfer impedance colored maps obtained considering the chest wall divided in 51regions as indicated in Fig. 3, right. In the upper panel, from left to right, the forcing frequency was 2, 4, and 6 Hz; in the lowerpanel, from left to right, was 8, 10, and 12 Hz.

soidal forcing up to 4 Hz using magnetometers andfound that below 1 Hz the chest wall expanded anddeflated uniformly, while for higher frequencies the ab-dominal wall motion was characterized by larger andnonuniform displacements. In fact, the magnitude andphase of the displacements of the different points of theabdomen were unevenly distributed showing relativelylarge differences in the different abdominal regions. Inour data, the phase angle of marker movement showed amonotonic increase as one moves caudally with thelower part of the chest wall lagging the upper part. Theintersubject variability increased with position in the cau-dal direction and frequency. Moreover, at high frequen-cies ��8 Hz� the wavelengths of surface waves are com-parable to the dimensions of the abdomen, suggestingthat in given times there are markers moving in oppositedirections in the different abdominal regions.

The regional differences in phase �and presumably inregional abdominal pressure� showed that consideringthe abdomen as a unique compartment classically mod-eled as a liquid-filled elastic container, imply excessivesimplification, especially during fast maneuvers, as sug-gested by Decramer et al.9 This phenomenon is particu-larly important during forced oscillations, where more

sophisticated models than a single lumped resistance-inertance-elastance are necessary to describe the mouthpressure-abdominal volume relationship at frequenciesequal to or higher than 8 Hz and the definition of thesenew models requires specific measurements of localchest wall mechanics.

In this study we also defined a new method for study-ing the distribution over the chest wall surface of transferimpedance using optoelectronic plethysmography. Infact, it has been suggested16,17,24 that the transfer imped-ance of the respiratory system is strongly representativeof respiratory mechanics as it allows a quantitative par-titioning between airways and tissue mechanical proper-ties. However, little is known about its distribution in thedifferent thoracoabdominal regions. In 1989 Barnaset al.5 studied transfer impedance of the rib cage and theabdominal compartments �i.e., the transfer functions be-tween compartmental flow and Pao) at low frequencies�0.5–4 Hz� using respiratory inductive plethysmographyto measure compartmental flow. They found that thesetwo compartments are characterized by different transferimpedances, confirming the hypothesis that chest wallmechanical properties are not homogeneously distributedand, therefore, that a complete description of respiratory

129Local Transfer Impedance in Humans

mechanics requires the chest wall to be divided into twoor more compartments.

Recently, we used optoelectronic plethysmography tomeasure the transfer impedance of the chest wall parti-tioned into three compartments �pulmonary rib cage, ab-dominal rib cage, and abdomen� and we found that theirpercentage contribution to total Z tr modulus changedfrom 33%, 13%, and 54% at 1 Hz to 72%, 13%, and15% at 24 Hz, respectively.3 Optoelectronic plethysmog-raphy is a potentially ideal technique to be combinedwith forced oscillation technique �FOT� because, in prin-ciple, it allows the accurate volume measurement of anychest wall compartment one wishes to measure at highsampling rate and without introducing any dynamicaleffect on the measured volumes. In the present paper wedelineate a new volume computation procedure for OEPthat allows the measurement of volume changes due tothe motion of very small chest wall surface elements. Weapplied this procedure to five healthy subjects to com-pute Z tr for each local pathway, as the complex ratiobetween Pao and the small element flow. Averaged trans-fer impedance maps have been plotted as specific modu-lus �modulus divided by element surface� and phasecolor-scale two-dimensional �2D� graphs. These maps,reported in Figs. 6 and 7, clearly show that Z tr is muchmore homogeneous in the upper rib cage than in theabdomen. Moreover, when the frequency increased, theamplitude of the abdominal motion rapidly reduced,mainly in the central part of the compartment. Conse-quently, the abdominal Z tr modulus increased with fre-quency. Phase angles reached very high values in thelower-central part of the abdomen, markedly exceeding180°, probably due to the high inertance of the abdomi-nal contents. All these results confirm that chest wallmechanical properties are characterized by a stronglyheterogeneous spatial distribution.

In particular, Fig. 6 shows that the behavior of thetotal Z tr at high frequency is mainly determined by thelung-apposed chest wall regions because of their lowmodulus. In fact, as frequency increases the modulus ofthe diaphragm-apposed rib cage and the various abdomi-nal regions increase relative to the upper rib cage. Be-cause the gas compression is isothermal for the consid-ered frequency range,12,21 the frequency dependence ofthe modulus and phase of Z tr must be due to the differentmechanical properties determined by different anatomicalstructures.

The upper rib cage �from rib 1 to 6� is tightly attachedto the sternum by short cartilages and, therefore, has alow compliance. It only contains lung under it, whichhas a small inertance. On the other hand, the diaphragm-apposed rib cage is more compliant because it is onlyloosely connected to the sternum through long cartilages,and abdominal contents with high inertance lie beneathit. Finally, the abdomen has no rigid structure around it

and, therefore, it presents a much higher compliance,associated with a high inertance due to the abdominalcontents. We believe that this is the reason why the totalZ tr is so dominated by the Z tr of the lung-apposed ribcage compartment. This hypothesis is also supported bythe differences of local Z tr within the abdomen. In fact,the area of the abdomen close to the midline is associ-ated with the highest compliance �is the farthest fromany rigid structure� and to a very high inertance �in thisarea the anteroposterior diameter of the abdomen reachesits maximum�, and in fact it presents the highest phaseshift �see Figs. 6 and 7�. As far as one moves laterally,the anteroposterior diameter reduces as well as the dis-tance from the vertebrae, and the phase shift of the localZ tr reduces.

It is important to underline that the differences be-tween the abdominal region and the rib cage are verylikely posture dependent. In this study we analyzed thesubjects in the supine position, where the effect of gravi-tational forces increases the relative difference betweenthe regional compliances. It is to be expected that in theupright posture, when abdominal compliance relative tothat of the rib cage decreases a lot, these regional het-erogeneities are reduced. Furthermore, otherstudies14–16,18,19,22,23,25 showed that the Z tr data, if ac-quired over a sufficiently wide range of frequencies �usu-ally from 4 to 64 Hz�, can be used to partition mechani-cal properties of airway and tissue by fitting the datawith the six element model introduced by DuBois.11 Inthat representation, tissue mechanical properties are mod-eled by a single R-I-E compartment, under the assump-tion of unitary behavior of the chest wall. That meansthat despite the measured heterogeneity, a single tissuecompartment is sufficient to describe Z tr data acquiredfrom 4 to 64 Hz. Consequently, either rib cage tissueproperties exert a dominant influence or similar timeconstants between the rib cage and abdomen must exist.

From our results we can conclude that increasing thefrequency, the abdominal Z tr phase angle and modulusincrease as the result of very different mechanical prop-erties from the pulmonary rib cage �discussed above�.These differences are masked in total Z tr by the muchlower modulus of the pulmonary rib cage Z tr that, beingin parallel with the abdomen, strongly dominates theresulting total chest wall mechanical behavior. For thisreason, regional alteration in chest wall mechanical prop-erties cannot be identified from the total Z tr but onlyfrom local measurements, and this technique offers thepossibility of studying how disease can affect heteroge-neity of chest wall mechanics. Important potential appli-cations of this approach might be the study of chest wallmechanics and motion during high-frequency ventilationas well as the measurement of asymmetries in mechani-cal properties in both craniocaudal and laterolateral di-rections in the presence of chest wall restriction andairway obstruction. Another potential application of our

130 DELLACA et al.

method is the assessment of regional mechanical proper-ties at physiological breathing frequencies. In fact, tis-sues properties obtained from Z tr at frequencies greaterthan 2 Hz are likely not relevant to those affecting quietbreathing, and the possibility of describing the spatialdistribution of Z tr around breathing frequencies will helpto better understand the pathophysiology of the respira-tory system.

ACKNOWLEDGMENTS

The writers gratefully acknowledge Antonio Iorio,Gabriele Bonetti, and Andrea Tonoli for their technical

assistance. This study was partially supported by aGlaxoSmithKline grant �Contract No. GEC372-2000�and from grants from the National Institute of Health andNational Science Foundation.

APPENDIX

Tetrahedron Volume Computation

B1 (xB1 ,yB1 ,zB1), B2 (xB2 ,yB2 ,zB2), andB3 (xB3 ,yB3 ,zB3) are the markers defining the base andO (xO ,yO ,zO) the vertex opposite to the base.

The tetrahedron base area �A� was computed as

A�1

2�� det�yB3�yB1 zB3�zB1

yB2�yB1 zB2�zB1�2

�det�zB3�zB1 xB3�xB1

zB2�zB1 xB2�xB1�2

�det�xB3�xB1 yB3�yB1

xB2�xB1 yB2�yB1�2� .

The height � of the tetrahedron is

����AxO�ByO�CzO�D�

�A2�B2�C2,

where

A��yB2�yB1��zB3�zB1���yB3�yB1��zB2�zB1�;

B��xB3�xB1��zB2�zB1���xB2�xB1��zB3�zB1�;

C��xB2�xB1��yB3�yB1���xB3�xB1��yB2�yB1�;

and

D��xB1A�yB1B�zB1C .

The tetrahedron volume V te is then computed as

V te�A�

3.

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