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Steady pressure-flow relationship in a cast of the upper and central human airways
Int. J. Bio-MediaalComputing, 20 (1987) 211-224 Elsevier Scientific Publishers Ireland Ltd.
211
STEADY PRESSURE-FLOW RELATIONSHIP IN A CAST OF THE UPPER AND CENTRAL HUMAN AIRWAYS*
ABDELLAZIZ BEN JEBRIA, ZOUHEIR TABKA and PIERRE TECHOUEYRES Laboratoire de Physiologic, Universitd de Bordeaux-II, 146, rue Leo-Saignat, 33076.Bordeaux Cedex (France) (Received October 19th, 1986)
Pressure drops across the upper (larynx) and central airways of a human lung cast were measured at steady state inspiratory and expiratory flows. Air, He-O, and SF6a, gas mixtures were used at tracheal Reynolds’ numbers ranging from 145 to 30 000. The pressure-flow characteristics of the model were analysed using standard pressure-flow diagrams and Moody plots. We found that the asymmetry between inspiratory and expiratory resistances, observed in the central airways (larynx excluded), was markedly reduced in the presence of the larynx. However, static pressure differences were greater across the entire model of the upper and central airways than across the model of the five generations of the trachea-bronchial tree (without larynx) at the same flow-rates. In addition, our results showed that the presence of the larynx tended to reduce the zone of fully developed laminar flow in the Moody diagram with the higher density gas, while extending the zone of turbulent flow even for the low density gas at low Reynold’s numbers.
Keywords: Resistance; Pressure; Flow; Upper airways; Central airways; Cast model
Introduction
Among the interesting biomechanical aspects of the lung, gas flow and airway resistance have received much attention. However, few attempts have been made to analyse the effect of the larynx on the pressure-flow relationships in the airways. Since the pioneer work of Rohrer (1915) on the gas flow pattern in the human airways, a number of other mathematical models have been proposed by different authors (Jeager and Matthys, 1970; Pedley ef al., 1970; Jaffrin and Kesic, 1974; Drazen et al., 1976; Wood et al., 1976; Pedley, 1977; Isabey and Chang, 1981) aimed at producing better predictions of the pressure-flow relationships in the pulmonary tract. All these studies have demonstrated that airways resistance depends on three fundamental factors, namely: the bulk flow-rate, the physical properties of the gas (density and viscosity) and the airway geometry (length, diameter and.orientation). *This work was supported by a grant from INSERM (No. 84.5.001). 0 1987 Elsevier Scientific Publishers Ireland Ltd. 0020-7101/87/$03.50 Printed and Published in Ireland
212
A. Ben Jebti et al.
In addition, it has also been shown (Ma&em and Mead, 1967) that most of the pressure loss occurs in the airways with diameters of more than 2 mm. Airflow velocity in the larynx is very high, since this organ has the smallest cross-sectional area of any part of the upper airways. Moreover, the repeated branching tube network of the bronchial tree and the irregular geometry of these airways are the main features required for an analysis of gas flow patterns in the .lung (Chang and El Masry, 1982; Isabey, 1982). Because it is in these complex airways where pulmonary resistance is the greatest, the aerodynamic behaviour of this zone of the laryngo-tracheo-bronchial tree is of particular importance. However, in vivo experimental evidence (Jeager and Matthys, 1968; Stanescu et al., 1972; Brancatisano et al., 1983) has shown that the movements of the vocal cords are tightly coupled to the pattern of volume change within the respiratory cycle. This additional factor makes analysis of the aerodynamic aspects of the pressure-flow relationship more difficult. In addition, the influence of the elastic properties of the lung parenchyma on the tidal air distribution (Mead, 1969) and the continuously changing airway dimensions during in vivo experiments further complicate in vivo experimental investigations. We were therefore interested in an aerodynamic analysis of the steady pressureflow relationship in a cast model of the larynx and the five generations of the tracheobronchial tree. Absolute noncompliant models of the upper and central human airways were used in this study to eliminate some of the factors occurring in intact lungs which have an effect on airway resistance. We wanted to single out the effect of the larynx on the pressure-flow relationships by comparing the experimental responses obtained both with and without larynx.
Methods Laryngo-trachea-bronchial tree casts The anatomical model of the airways used in this study was made up of two parts: the larynx and the first five generations of the trachea-bronchial tree of man. The larynx with the vocal cords are shown in Fig. 1. This model is rigid, and it was initially constructed in two halves as it was intended for teaching purposes. The photograph shown in Fig. 1 was taken before joining the two halves of the model. It was slightly modified for the present experiments. The diameter of the upper opening of the larynx is 2.4 cm; the base and height (antero-posterior diameter) of the triangularly shaped vocal cords are 0.8 and 2.4 cm, respectively. Thus, the cross-sectional area is 1.0 cm2, the perimeter is 5.7 cm, and the hydraulic radius (2 area/perimeter) is 0.35 cm. The hollow model of the central airways was made from a relatively rigid synthetic rubber resin compound, moulded around a solid human lung cast (Piercan, le Latex de France). A front view of this model is shown in the photograph of Fig. 2. It can be seen that the irregularly divided branching tube network of this hollow cast represents
Pressure flow in human
oinvoys
Fig. 1. Photograph of the rigid cast of the larynx before using it for experiments. parts of the model were joined together, the vocal cords were of triangular shape.
213
When the two
the real geometry of the central airways of the human lung quite accurately. Moreover, the first five generations after the trachea are we11defined and well represented (not constrictions at exits of terminal branches). The dimensions of each of the airways from the trachea down to those of 5 mm diameter and 10 mm length, are
214
A. Ben Jebti et al.
Fig. 2. Front view of the hollow cast of human central airways. The model accurately rep1rc:sents the first five generations of the trachea-bronchial tree.
given in the diagram of Fig. 3. The volume of the hollow cast (132 cm3) was Imea.S,ured by filling it with water with airway orifices closed; the cumulative volume waS also calculated from the dimensions shown in Fig. 3, which only differed sligbttly from the measured value. The calculated value was 134 cm3.
Pressure flow in human airways I
Fig. 3. Schematic diagram showing the morphometric data of the model of the central airways. Figures in each circle are diameters (top) and lengths (bottom) of each branch (cm).
Rocedure and data acquisition
Because the main aim of the study was to show the influence of the larynx on the pressure-flow relationship in the airways, two sets of experiments were carried out on the model: in the first set, measurements were made on the central airways by excluding the larynx, and the pressure difference was measured between the trachea and the spherical box where the airway cast was tightly enclosed; in the second set, the larynx was included, and the pressure difference was then measured between the upper opening of the larynx and the spherical box. A diagram of the apparatus and respiratory tract is shown in Fig. 4. The end opening of the larynx was connected to the trachea of the central airways cast, while a 2.4cm diameter cylindrical PVC tube (same diameter as trachea) was attached to the upper orifice of the larynx. A large rubber bag was used as a tank containing the desired gas mixtures - either air, He-O2 or SF60s. A constant flow-rate was maintained in both inspiration and expiration using a standard vacuum cleaner. During inspiration, the vacuum cleaner was connected to the spherical box and the rubber bag was linked to the pneumotachograph; for expiratory flow the vacuum cleaner and the rubber bag were transposed. This was to avoid unstable output air temperature when a vacuum cleaner is used as an air compressor. In the range of the flow-rates used, no collapse has been seen during the experiments.
A. Ben Jebria e! al.
216
t
AIR
Fig. 4. Diagram of experimental set-up. The system shown here was used for steady expiratory flow measurements. For inspiration measurements, the suction pump and the rubber bag were transposed.
Flow-rate was measured using a Fleisch pneumotachograph (No. 3) coupled to a differential pressure transducer (Validyne MP45 ?: 2 cm HzO). The pneumotachograph was calibrated using a gas-meter and a stopwatch, for each gas studied {air, 21% O2 and 79% He, 21% O2 and 79% SF6) under identical conditions to those of the experimental procedure, both during htspiration and expiration; the length of tubing between flow meter and trachea or larynx was 10 cm. The pressure drop (AP) across the model of the airways (with and without larynx) was measured using variable reluctance transducers (Schlumberger: CH5112/0 and H5130 with 2 and 10 cm Hz0 diaphragm, respectively) with a demodulator (CA iOh5). A wide range of steady flow-rates was used for all three gas mixtures: (0.16-9 l/s), (0.15-7 l/s) and (0.2-2 l/s) corresponding to air, He-O? and SF6-02 mixtures, respectively. This corresponds to Reynolds’ numbers ranging approximately from 145 to 30 000.
Pressureflow in human airways
211
Results
The data were expressed in two different ways, a classical pressure-flow curve, and a plot of the dimensionless pressure drop (AP/OS $3) vs. Reynolds number (log-log plot), usually called a Moody diagram; CO is the mean velocity in the zeroth generation (trachea) of the model, and p is the density of the gas used. The Moody diagram allows one to infer that the airways behave ‘as if they were a single pipe containing a flow which is laminar, transitional or turbulent. Figure 5 shows the pressure-flow curves obtained with air, both with and without the larynx. The inspiration and expiration curves are quite different, and in the absence of the larynx there was a greater pressure drop on expiration. Also the pressureflow relationship on inspiration was largely linear. When the larynx was included in the model the pressure drops on inspiration and expiration were more alike. The relationship between pressure and flow was also only linear at very low flow rates. The pressure drop was greater in both directions when the larynx was included.
i/ (IS’)
9
a 7
-with
6
larynx
-...... without
larynx
5 4 3 2
I
1
234567 AP(cm H~O)
Fig. 5. Comparison of two pressure-flow curves obtained in the central airways (without larynx) and in the complete model of the laryngo-trachea-bronchial tree. Results for experiments using
A. Ben Jebnk et al,
218
-*----_
31
, , ,,,,,
1.1 3 2
3loz4 5 678Qld
1
1111111 4 5 678Qwd
REYNOLDS
2.10'
NUMBER(Ci&/v)
Fig. 6. Moody plot of dimensionless pressure drop against tracheal Reynolds number for expiratory air flow. The normalized pressure drops were computed on the basis of measured pressure difference between: (i) trachea and the spherical box (central airways) and (ii) the upper opening of the larynx and the spherical box (upper and central airways).
3 (Is-‘) 7 INSPIRATION
6 5 4 3 2 1 10 9
9
7
9
5
4
3
2
9
1 . ,
, 1
1
2345678
APkm I+O)
2
/.”
./ *.../ /-...-
EXPIRATION
Fig. 7. Steady pressure-flow diagram obtained in the complete model of the upper and central airways. Effect of gas physical properties.
Pressureflow in humon oirwoys
219
Figure 6 shows a plot of the dimensionless pressure drops for steady expiratory flows against tracheal Reynolds number, both with and without larynx. If we assume that the Moody diagram demonstrates that the model behaves ‘as if it was a single tube with laminar, transitional or turbulent flow, then, in the absence of a larynx, the pressure changes were consistent with laminar flow up to a Reynolds number (Re) of 600 (slope = -1). Above a Re of 7000, the dimensionless pressure drop was independent of Re, corresponding to completely turbulent flow (slope = 0). The region between these two values of Re corresponded to transitional flow with a slope of approximately -0.5. However, in the presence of the larynx the curve was approximately parallel to the x-axis. The second part of the study concerned the effect of gas physical properties on the pressure-flow relationship in the complete larynx and central airway model. The standard pressure-flow plots for air, helium and sulphur hexafluoride mixtures are shown in Fig. 7. It can be seen that the curve is highly dependent on the nature of the gas. Figure 8 shows the same results expressed as a Moody diagram for both expiration
REYNOLDS
NUMBER
(&do/v)
Fig. 8. Moody diagram of dimensionless pressure drop against tracheal Reynolds number, for inspiratory and expiratory air flows, He-O, and SF6-0, in the complete model of .the laryngotrachea-bronchial tree.
A. Ben Jebria et al.
220
and inspiration. For the helium mixture three zones could be distinguished: developed laminar, through transitional to turbulent flows (from left to right). Developed laminar flow was only seen at very low flow rates. For air, however, there was a complete absence of fully developed laminar flow, and transitional flow started at Re below 1500, with turbulent flow above this value. For the sulphur hexafluoride mixture, quasi-turbulent flow was predominant. In summary, the heavier the gas the more turbulent was the flow, even at low Re.
We investigated the inspiratory and expiratory pressure-flow relationships in a model of the human laryngo-trachea-bronchial tree. We showed that the presence of the larynx considerably altered the flow patterns, and hence the pressure-flow relationships. This, also could not exclude the hypothesis advanced by Chang and El Masry (1982) that the effect of the larynx is to increase the pressure drop required to produce a given flow. In the main, the results without larynx agree with the findings of Slutsky et al. (1980) and Isabey and Chang (1981) as can be seen in Table I. However, when the
TABLE I COMPARISON BETWEEN THE SLOPES ALONG WITH THE CORRESPONDING Re IN THE MOODY DIAGRAM OBTAINED IN THIS WORK AND THOSE OF OTHER INVESTIGATORS Re No.
Slopes Present With
<2004OO >7000 >10000 *Isabey and Chang (1981). bSlutsky et al. (1980).
Other
work Without larynx
Without larynx -1* -lb
-0.12
-1 -0.5 * -0.5b
-0.12
-0.5
0 0
0
0* Ob
investigations
Pressure flow in human airways
221
larynx was included in the model, the dimensionless pressure drop decreased slightly, up to a Re of 2000, then continued essentially parallel to X-axis (Fig. 6). This showed that the larynx does affect air flow, as has been suggested by Pedley er al. (1977) and demonstrated by Dekker (1961). We also confirmed the theoretical predictions (Pedley et al., 1970; Drazen et al., 1976; Pedley et al., 1977) and the experimental findings in dog and man (Maio and Farhi, 1967; Drazen etul., 1976), that the airway resistance increases with increasing gas density. It was highest for SF6-O2 and lowest for He-Oz. We found a difference between the inspiratory and expiratory patterns, which was markedly enhanced by omitting the larynx from the model. Figure 9 shows the ratio of expiratory to inspiratory pressure drop (ME/API) plotted against flow rate. If the expiratory and inspiratory flows have the same distribution this ratio should be equal to unity for all flow rates. However, it can be seen from Fig. 9 that, in the experiments carried out on the model without the larynx, this ratio was greater than unity and increased with increasing flow rate. In the presence of the larynx, on the other hand, this ratio remained roughly constant, albeit above unity, whatever the flow rate. Schroter and Sudlow (1969) have demonstrated using a single bifurcation, that the pattern of inspiratory flow is quite different from that of expir-
10,
APE/N _ (dimensionless)
??
a_
e-0
6,
I’
/
./ NO
4,
without
,JC
larynx
,/ u/O /. with
2_ 0. -‘o.‘.~.o...o 0 0
I 1
larynx
.a ,.., 0 .. . 0 ..f..I 0 . ...* 0 ..*. O’.... O.......‘..‘O 1 2
1 3
I 4 0 (Is-‘)
Fig. 9. Expiratory to inspiratory pressure drop ratio versus air flow-rate in the airway model, both with and without larynx. Note the obvious asymmetry between inspiratory and expiratory resistances without larynx. Much greater symmetry is observed with the larynx in the gas circuit.
222
A. Ben Jebria et al.
atory flow, indicating pressure drop differences. In fact pressure drop is a result of two influences, the static pressure drop due to viscous dissipation of energy (Pedley et aZ., 1970) and the drop due to change in kinetic energy. If these two components can be separated, the viscous dissipation of energy component could be described in terms of a frictional coefficient (Jaffrin and Keseic, 1974; Slutsky ef al., 1980). This would be represented by the total pressure drop minus the pressure difference due to change in kinetic energy, divided by the kinetic energy term (CF = (A?‘ToT AFKE)/OS ~20). In this case, a Moody plot would represent the dimensionless pressure drop, and the corresponding inspiratory and expiratory curves would approach each other. Airway kinetic energy is highly dependent on velocity profiles. In a model without the larynx (Patra and Afify, 1983), these profiles have been demonstrated to be different between inspiration and expiration. The asymmetry that we observed between inspiratory and expiratory pressure drops (in the absence of the larynx) may therefore stem from velocity profile effects, as reflected by the kinetic energy differences. When the larynx was added to the central airways, its narrow opening induced a rapid increase in airflow velocity with a corresponding increase in turbulence. We suggest that the reduced differences between inspiratory and expiratory flow resistances (Fig. 9) were due to increased turbulence. The fraction of the resistance in the large airways would be increased, and therefore one would expect to find flat velocity profiles in both directions in the presence of the !arynx. As has been pointed out by Pedley et al. (1970) it is important to measure velocity profiles in the airways in order to determine the relative contributions of viscous dissipation of energy, and kinetic energy effects (Reynolds and Lee, 1981). Measurement of velocity profiles in a model with and without larynx can also throw light on the influence of the larynx on the relative contributions of these two terms. The second series of experiments confirmed that the heavier the gas, the greater was the airways resistance. Even though airway bifurcations may cause flow separation without turbulence per se, sharp asymmetric branchings in the central airways associated with the narrow opening of the larynx may cause turbulence at low Reynolds numbers. Since there is a 5-fold change in kinematic viscosity between SF6-O2 and air, and an lg-fold difference between SF& and He-02, the turbulence effect should be more marked with sulfur hexafluoride than with air, which should be more marked than for helium. The results presented in Fig. 8 show that for the gas heavier than air the fully developed laminar flow zone disappeared, and that for the gas lighter than air, the zone of turbulent flow was enlarged. In conclusion, it can be seen from the model that the upper airways play a significant part in total airway aerodynamics and resistance. The geometry of these structures has a determining influence on the entry flow conditions to the rest of the system. However, more in vitro, and if possible in vivo experiments will be required before satisfactory theoretical predictions can be made on pressure-flow relationships I
Pressure flow in human airways
223
Acknowledgmenta The authors thank Simon P. Jarman for reviewing, and Nadine Capdeville for typewriting the manuscript. References Brancatisano, T., Collett, P.W., and Engel, L.A., 1983, Respiratory movements of the vocal cords, J. Appl. Physiol.: Respir. Environ. Exercise Physiol., 54, 1269-1276. Chang, H.K., and El Masry, O.A., 1982, A model study of flow dynamics in human central airways. Part I: Axial velocity profiles, Respir. Physiol., 49,75 -95. Dekker, E., 1961, Transition between laminar and turbulent flow in human trachea, J. AppL Physiol., 16, 1060-1064. Drazen, J.M., Loring, S.H. and Ingram, R.H., 1976, Distribution of pulmonary resistance: effects of gas density, viscosity, and flow rate, J. Appl. Physiol., 41.388-395. Isabey, D. and Chang, H.K., 1981, Steady and unsteady pressure-flow relationships in central airways, J. Appl. Physiol.: Respir. Environ. Exercise Physiol., 51, 1338-1348. Isabey, D., 1982, Steady and pulsatile flow distribution in a multiple branching network with physiological applications, J. Biomech., 15, 395-404. Jaeger, M.J. and Matthys, H., 1968, The pattern of flow in the upper human airways, Respir. Physiol., 6.113-127.
Jaeger, M.J. and Matthys, H., 1970, The pressure flow characteristics of the human airways, In Airway Dynamics, Physiology and Pharmacology, A Bouhuys, Thomas Springfield, IL, pp. 21-32. Jaffrin, M.Y. and Kesic, P., 1974, Airway resistance: a fluid mechanical approach, J. Appl. Physiol., 36, 354-361.
Macklem, P.T. and Mead, J.. 1967, Resistance of central and peripheral airways measured by a retrograde catheter, J. Appl. Physiol., 22, 395 -40 1. Maio, D.A. and parhi, L.E., 1967, Effect of gas density on mechanics of breathing. J. Appl.
Physiol ,23,687-693. Mead, J., 1969, The distribution Circulatory
and
Respiratory
of gas flow in the lungs, in Cibo Foundation Symposium on Transport, G.E.W. Wolstenholm and J. Knight (Ed.),
Mass
Churchill, London, pp. 204-209. Patra, A.L. and Afify, E.M., 1983, An experimental study of velocity distribution in a human lung cast,J. Biomech. Eng., 105,381-388. Pedley, T.J., Schroter, R.C., and Sudlow, M.F., 1970, Energy losses and pressure drop in models of human airways, Respir. Physiol., 9.371-386. Pedley, T.J., Schroter, R.C. and Sudlow, M.F., 1970, The prediction of pressure drop and variation of resistance within the human bronchial airways, Respir. Phvsiol., 9. 387-405. Pedley, T.J., Schroter. R.C., and Sudlow, M.l:.. 1977, Gas flow and mising in the airways, in Bioengineering Aspects ofthe Lung, J.B. West (Ed.), Dekker, New York, pp. 163-265. Pedley, T.J., 1977, Pulmonary fluid dynamics, Annu. Rev. Fhtid Mech.. 9. 229-274. Reynolds, D.B. and Lee, J.S., 1981, Steady pressure-flow relationship of a model of the canine bronchial tree, J. Appl. Physiol.: Respir. Environ. Exercise Physiol.. 5 1, 1072 - 1079. Rohrer, F., 1915, Der stromungswiderstand ln den menschlichen atemwegen und der Einfluss der Unregelmassigen verzweigung des bronchial Systems auf den Atmungsverlauf in Verschifdenen Lungenbezirken. Pflugers Arch., 162,225 -299.
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Schroter, R.C. and Sudlow, M.F., 1969, Flow patterns in models of the human bronchial airways, Respir. Physiol., I, 341-355. Slutsky, A.S., Berdine, G.G. and Drazen, J.M., 1980, Steady flow in a model of human central airways, J. Appl. Physiol.: Respir. Environ. Exercise Physiol., 49,411-423. Stanescu, DC., Pattijn, J., Clement, J. and Van De Woestijne, K.P. 1972, Glottis opening and airway resistance, J, Appl. Physiol., 32, 460-466. Wood, L.D.H., Engel, L.A., Griffin, P., Despas, P. and Macklem, P.T., 1976, Effect of gas physical properties and flow on lower pulmonary resistance,/. Appl. Physiol., 41,234-244.
211
STEADY PRESSURE-FLOW RELATIONSHIP IN A CAST OF THE UPPER AND CENTRAL HUMAN AIRWAYS*
ABDELLAZIZ BEN JEBRIA, ZOUHEIR TABKA and PIERRE TECHOUEYRES Laboratoire de Physiologic, Universitd de Bordeaux-II, 146, rue Leo-Saignat, 33076.Bordeaux Cedex (France) (Received October 19th, 1986)
Pressure drops across the upper (larynx) and central airways of a human lung cast were measured at steady state inspiratory and expiratory flows. Air, He-O, and SF6a, gas mixtures were used at tracheal Reynolds’ numbers ranging from 145 to 30 000. The pressure-flow characteristics of the model were analysed using standard pressure-flow diagrams and Moody plots. We found that the asymmetry between inspiratory and expiratory resistances, observed in the central airways (larynx excluded), was markedly reduced in the presence of the larynx. However, static pressure differences were greater across the entire model of the upper and central airways than across the model of the five generations of the trachea-bronchial tree (without larynx) at the same flow-rates. In addition, our results showed that the presence of the larynx tended to reduce the zone of fully developed laminar flow in the Moody diagram with the higher density gas, while extending the zone of turbulent flow even for the low density gas at low Reynold’s numbers.
Keywords: Resistance; Pressure; Flow; Upper airways; Central airways; Cast model
Introduction
Among the interesting biomechanical aspects of the lung, gas flow and airway resistance have received much attention. However, few attempts have been made to analyse the effect of the larynx on the pressure-flow relationships in the airways. Since the pioneer work of Rohrer (1915) on the gas flow pattern in the human airways, a number of other mathematical models have been proposed by different authors (Jeager and Matthys, 1970; Pedley ef al., 1970; Jaffrin and Kesic, 1974; Drazen et al., 1976; Wood et al., 1976; Pedley, 1977; Isabey and Chang, 1981) aimed at producing better predictions of the pressure-flow relationships in the pulmonary tract. All these studies have demonstrated that airways resistance depends on three fundamental factors, namely: the bulk flow-rate, the physical properties of the gas (density and viscosity) and the airway geometry (length, diameter and.orientation). *This work was supported by a grant from INSERM (No. 84.5.001). 0 1987 Elsevier Scientific Publishers Ireland Ltd. 0020-7101/87/$03.50 Printed and Published in Ireland
212
A. Ben Jebti et al.
In addition, it has also been shown (Ma&em and Mead, 1967) that most of the pressure loss occurs in the airways with diameters of more than 2 mm. Airflow velocity in the larynx is very high, since this organ has the smallest cross-sectional area of any part of the upper airways. Moreover, the repeated branching tube network of the bronchial tree and the irregular geometry of these airways are the main features required for an analysis of gas flow patterns in the .lung (Chang and El Masry, 1982; Isabey, 1982). Because it is in these complex airways where pulmonary resistance is the greatest, the aerodynamic behaviour of this zone of the laryngo-tracheo-bronchial tree is of particular importance. However, in vivo experimental evidence (Jeager and Matthys, 1968; Stanescu et al., 1972; Brancatisano et al., 1983) has shown that the movements of the vocal cords are tightly coupled to the pattern of volume change within the respiratory cycle. This additional factor makes analysis of the aerodynamic aspects of the pressure-flow relationship more difficult. In addition, the influence of the elastic properties of the lung parenchyma on the tidal air distribution (Mead, 1969) and the continuously changing airway dimensions during in vivo experiments further complicate in vivo experimental investigations. We were therefore interested in an aerodynamic analysis of the steady pressureflow relationship in a cast model of the larynx and the five generations of the tracheobronchial tree. Absolute noncompliant models of the upper and central human airways were used in this study to eliminate some of the factors occurring in intact lungs which have an effect on airway resistance. We wanted to single out the effect of the larynx on the pressure-flow relationships by comparing the experimental responses obtained both with and without larynx.
Methods Laryngo-trachea-bronchial tree casts The anatomical model of the airways used in this study was made up of two parts: the larynx and the first five generations of the trachea-bronchial tree of man. The larynx with the vocal cords are shown in Fig. 1. This model is rigid, and it was initially constructed in two halves as it was intended for teaching purposes. The photograph shown in Fig. 1 was taken before joining the two halves of the model. It was slightly modified for the present experiments. The diameter of the upper opening of the larynx is 2.4 cm; the base and height (antero-posterior diameter) of the triangularly shaped vocal cords are 0.8 and 2.4 cm, respectively. Thus, the cross-sectional area is 1.0 cm2, the perimeter is 5.7 cm, and the hydraulic radius (2 area/perimeter) is 0.35 cm. The hollow model of the central airways was made from a relatively rigid synthetic rubber resin compound, moulded around a solid human lung cast (Piercan, le Latex de France). A front view of this model is shown in the photograph of Fig. 2. It can be seen that the irregularly divided branching tube network of this hollow cast represents
Pressure flow in human
oinvoys
Fig. 1. Photograph of the rigid cast of the larynx before using it for experiments. parts of the model were joined together, the vocal cords were of triangular shape.
213
When the two
the real geometry of the central airways of the human lung quite accurately. Moreover, the first five generations after the trachea are we11defined and well represented (not constrictions at exits of terminal branches). The dimensions of each of the airways from the trachea down to those of 5 mm diameter and 10 mm length, are
214
A. Ben Jebti et al.
Fig. 2. Front view of the hollow cast of human central airways. The model accurately rep1rc:sents the first five generations of the trachea-bronchial tree.
given in the diagram of Fig. 3. The volume of the hollow cast (132 cm3) was Imea.S,ured by filling it with water with airway orifices closed; the cumulative volume waS also calculated from the dimensions shown in Fig. 3, which only differed sligbttly from the measured value. The calculated value was 134 cm3.
Pressure flow in human airways I
Fig. 3. Schematic diagram showing the morphometric data of the model of the central airways. Figures in each circle are diameters (top) and lengths (bottom) of each branch (cm).
Rocedure and data acquisition
Because the main aim of the study was to show the influence of the larynx on the pressure-flow relationship in the airways, two sets of experiments were carried out on the model: in the first set, measurements were made on the central airways by excluding the larynx, and the pressure difference was measured between the trachea and the spherical box where the airway cast was tightly enclosed; in the second set, the larynx was included, and the pressure difference was then measured between the upper opening of the larynx and the spherical box. A diagram of the apparatus and respiratory tract is shown in Fig. 4. The end opening of the larynx was connected to the trachea of the central airways cast, while a 2.4cm diameter cylindrical PVC tube (same diameter as trachea) was attached to the upper orifice of the larynx. A large rubber bag was used as a tank containing the desired gas mixtures - either air, He-O2 or SF60s. A constant flow-rate was maintained in both inspiration and expiration using a standard vacuum cleaner. During inspiration, the vacuum cleaner was connected to the spherical box and the rubber bag was linked to the pneumotachograph; for expiratory flow the vacuum cleaner and the rubber bag were transposed. This was to avoid unstable output air temperature when a vacuum cleaner is used as an air compressor. In the range of the flow-rates used, no collapse has been seen during the experiments.
A. Ben Jebria e! al.
216
t
AIR
Fig. 4. Diagram of experimental set-up. The system shown here was used for steady expiratory flow measurements. For inspiration measurements, the suction pump and the rubber bag were transposed.
Flow-rate was measured using a Fleisch pneumotachograph (No. 3) coupled to a differential pressure transducer (Validyne MP45 ?: 2 cm HzO). The pneumotachograph was calibrated using a gas-meter and a stopwatch, for each gas studied {air, 21% O2 and 79% He, 21% O2 and 79% SF6) under identical conditions to those of the experimental procedure, both during htspiration and expiration; the length of tubing between flow meter and trachea or larynx was 10 cm. The pressure drop (AP) across the model of the airways (with and without larynx) was measured using variable reluctance transducers (Schlumberger: CH5112/0 and H5130 with 2 and 10 cm Hz0 diaphragm, respectively) with a demodulator (CA iOh5). A wide range of steady flow-rates was used for all three gas mixtures: (0.16-9 l/s), (0.15-7 l/s) and (0.2-2 l/s) corresponding to air, He-O? and SF6-02 mixtures, respectively. This corresponds to Reynolds’ numbers ranging approximately from 145 to 30 000.
Pressureflow in human airways
211
Results
The data were expressed in two different ways, a classical pressure-flow curve, and a plot of the dimensionless pressure drop (AP/OS $3) vs. Reynolds number (log-log plot), usually called a Moody diagram; CO is the mean velocity in the zeroth generation (trachea) of the model, and p is the density of the gas used. The Moody diagram allows one to infer that the airways behave ‘as if they were a single pipe containing a flow which is laminar, transitional or turbulent. Figure 5 shows the pressure-flow curves obtained with air, both with and without the larynx. The inspiration and expiration curves are quite different, and in the absence of the larynx there was a greater pressure drop on expiration. Also the pressureflow relationship on inspiration was largely linear. When the larynx was included in the model the pressure drops on inspiration and expiration were more alike. The relationship between pressure and flow was also only linear at very low flow rates. The pressure drop was greater in both directions when the larynx was included.
i/ (IS’)
9
a 7
-with
6
larynx
-...... without
larynx
5 4 3 2
I
1
234567 AP(cm H~O)
Fig. 5. Comparison of two pressure-flow curves obtained in the central airways (without larynx) and in the complete model of the laryngo-trachea-bronchial tree. Results for experiments using
A. Ben Jebnk et al,
218
-*----_
31
, , ,,,,,
1.1 3 2
3loz4 5 678Qld
1
1111111 4 5 678Qwd
REYNOLDS
2.10'
NUMBER(Ci&/v)
Fig. 6. Moody plot of dimensionless pressure drop against tracheal Reynolds number for expiratory air flow. The normalized pressure drops were computed on the basis of measured pressure difference between: (i) trachea and the spherical box (central airways) and (ii) the upper opening of the larynx and the spherical box (upper and central airways).
3 (Is-‘) 7 INSPIRATION
6 5 4 3 2 1 10 9
9
7
9
5
4
3
2
9
1 . ,
, 1
1
2345678
APkm I+O)
2
/.”
./ *.../ /-...-
EXPIRATION
Fig. 7. Steady pressure-flow diagram obtained in the complete model of the upper and central airways. Effect of gas physical properties.
Pressureflow in humon oirwoys
219
Figure 6 shows a plot of the dimensionless pressure drops for steady expiratory flows against tracheal Reynolds number, both with and without larynx. If we assume that the Moody diagram demonstrates that the model behaves ‘as if it was a single tube with laminar, transitional or turbulent flow, then, in the absence of a larynx, the pressure changes were consistent with laminar flow up to a Reynolds number (Re) of 600 (slope = -1). Above a Re of 7000, the dimensionless pressure drop was independent of Re, corresponding to completely turbulent flow (slope = 0). The region between these two values of Re corresponded to transitional flow with a slope of approximately -0.5. However, in the presence of the larynx the curve was approximately parallel to the x-axis. The second part of the study concerned the effect of gas physical properties on the pressure-flow relationship in the complete larynx and central airway model. The standard pressure-flow plots for air, helium and sulphur hexafluoride mixtures are shown in Fig. 7. It can be seen that the curve is highly dependent on the nature of the gas. Figure 8 shows the same results expressed as a Moody diagram for both expiration
REYNOLDS
NUMBER
(&do/v)
Fig. 8. Moody diagram of dimensionless pressure drop against tracheal Reynolds number, for inspiratory and expiratory air flows, He-O, and SF6-0, in the complete model of .the laryngotrachea-bronchial tree.
A. Ben Jebria et al.
220
and inspiration. For the helium mixture three zones could be distinguished: developed laminar, through transitional to turbulent flows (from left to right). Developed laminar flow was only seen at very low flow rates. For air, however, there was a complete absence of fully developed laminar flow, and transitional flow started at Re below 1500, with turbulent flow above this value. For the sulphur hexafluoride mixture, quasi-turbulent flow was predominant. In summary, the heavier the gas the more turbulent was the flow, even at low Re.
We investigated the inspiratory and expiratory pressure-flow relationships in a model of the human laryngo-trachea-bronchial tree. We showed that the presence of the larynx considerably altered the flow patterns, and hence the pressure-flow relationships. This, also could not exclude the hypothesis advanced by Chang and El Masry (1982) that the effect of the larynx is to increase the pressure drop required to produce a given flow. In the main, the results without larynx agree with the findings of Slutsky et al. (1980) and Isabey and Chang (1981) as can be seen in Table I. However, when the
TABLE I COMPARISON BETWEEN THE SLOPES ALONG WITH THE CORRESPONDING Re IN THE MOODY DIAGRAM OBTAINED IN THIS WORK AND THOSE OF OTHER INVESTIGATORS Re No.
Slopes Present With
<200
Other
work Without larynx
Without larynx -1* -lb
-0.12
-1 -0.5 * -0.5b
-0.12
-0.5
0 0
0
0* Ob
investigations
Pressure flow in human airways
221
larynx was included in the model, the dimensionless pressure drop decreased slightly, up to a Re of 2000, then continued essentially parallel to X-axis (Fig. 6). This showed that the larynx does affect air flow, as has been suggested by Pedley er al. (1977) and demonstrated by Dekker (1961). We also confirmed the theoretical predictions (Pedley et al., 1970; Drazen et al., 1976; Pedley et al., 1977) and the experimental findings in dog and man (Maio and Farhi, 1967; Drazen etul., 1976), that the airway resistance increases with increasing gas density. It was highest for SF6-O2 and lowest for He-Oz. We found a difference between the inspiratory and expiratory patterns, which was markedly enhanced by omitting the larynx from the model. Figure 9 shows the ratio of expiratory to inspiratory pressure drop (ME/API) plotted against flow rate. If the expiratory and inspiratory flows have the same distribution this ratio should be equal to unity for all flow rates. However, it can be seen from Fig. 9 that, in the experiments carried out on the model without the larynx, this ratio was greater than unity and increased with increasing flow rate. In the presence of the larynx, on the other hand, this ratio remained roughly constant, albeit above unity, whatever the flow rate. Schroter and Sudlow (1969) have demonstrated using a single bifurcation, that the pattern of inspiratory flow is quite different from that of expir-
10,
APE/N _ (dimensionless)
??
a_
e-0
6,
I’
/
./ NO
4,
without
,JC
larynx
,/ u/O /. with
2_ 0. -‘o.‘.~.o...o 0 0
I 1
larynx
.a ,.., 0 .. . 0 ..f..I 0 . ...* 0 ..*. O’.... O.......‘..‘O 1 2
1 3
I 4 0 (Is-‘)
Fig. 9. Expiratory to inspiratory pressure drop ratio versus air flow-rate in the airway model, both with and without larynx. Note the obvious asymmetry between inspiratory and expiratory resistances without larynx. Much greater symmetry is observed with the larynx in the gas circuit.
222
A. Ben Jebria et al.
atory flow, indicating pressure drop differences. In fact pressure drop is a result of two influences, the static pressure drop due to viscous dissipation of energy (Pedley et aZ., 1970) and the drop due to change in kinetic energy. If these two components can be separated, the viscous dissipation of energy component could be described in terms of a frictional coefficient (Jaffrin and Keseic, 1974; Slutsky ef al., 1980). This would be represented by the total pressure drop minus the pressure difference due to change in kinetic energy, divided by the kinetic energy term (CF = (A?‘ToT AFKE)/OS ~20). In this case, a Moody plot would represent the dimensionless pressure drop, and the corresponding inspiratory and expiratory curves would approach each other. Airway kinetic energy is highly dependent on velocity profiles. In a model without the larynx (Patra and Afify, 1983), these profiles have been demonstrated to be different between inspiration and expiration. The asymmetry that we observed between inspiratory and expiratory pressure drops (in the absence of the larynx) may therefore stem from velocity profile effects, as reflected by the kinetic energy differences. When the larynx was added to the central airways, its narrow opening induced a rapid increase in airflow velocity with a corresponding increase in turbulence. We suggest that the reduced differences between inspiratory and expiratory flow resistances (Fig. 9) were due to increased turbulence. The fraction of the resistance in the large airways would be increased, and therefore one would expect to find flat velocity profiles in both directions in the presence of the !arynx. As has been pointed out by Pedley et al. (1970) it is important to measure velocity profiles in the airways in order to determine the relative contributions of viscous dissipation of energy, and kinetic energy effects (Reynolds and Lee, 1981). Measurement of velocity profiles in a model with and without larynx can also throw light on the influence of the larynx on the relative contributions of these two terms. The second series of experiments confirmed that the heavier the gas, the greater was the airways resistance. Even though airway bifurcations may cause flow separation without turbulence per se, sharp asymmetric branchings in the central airways associated with the narrow opening of the larynx may cause turbulence at low Reynolds numbers. Since there is a 5-fold change in kinematic viscosity between SF6-O2 and air, and an lg-fold difference between SF& and He-02, the turbulence effect should be more marked with sulfur hexafluoride than with air, which should be more marked than for helium. The results presented in Fig. 8 show that for the gas heavier than air the fully developed laminar flow zone disappeared, and that for the gas lighter than air, the zone of turbulent flow was enlarged. In conclusion, it can be seen from the model that the upper airways play a significant part in total airway aerodynamics and resistance. The geometry of these structures has a determining influence on the entry flow conditions to the rest of the system. However, more in vitro, and if possible in vivo experiments will be required before satisfactory theoretical predictions can be made on pressure-flow relationships I
Pressure flow in human airways
223
Acknowledgmenta The authors thank Simon P. Jarman for reviewing, and Nadine Capdeville for typewriting the manuscript. References Brancatisano, T., Collett, P.W., and Engel, L.A., 1983, Respiratory movements of the vocal cords, J. Appl. Physiol.: Respir. Environ. Exercise Physiol., 54, 1269-1276. Chang, H.K., and El Masry, O.A., 1982, A model study of flow dynamics in human central airways. Part I: Axial velocity profiles, Respir. Physiol., 49,75 -95. Dekker, E., 1961, Transition between laminar and turbulent flow in human trachea, J. AppL Physiol., 16, 1060-1064. Drazen, J.M., Loring, S.H. and Ingram, R.H., 1976, Distribution of pulmonary resistance: effects of gas density, viscosity, and flow rate, J. Appl. Physiol., 41.388-395. Isabey, D. and Chang, H.K., 1981, Steady and unsteady pressure-flow relationships in central airways, J. Appl. Physiol.: Respir. Environ. Exercise Physiol., 51, 1338-1348. Isabey, D., 1982, Steady and pulsatile flow distribution in a multiple branching network with physiological applications, J. Biomech., 15, 395-404. Jaeger, M.J. and Matthys, H., 1968, The pattern of flow in the upper human airways, Respir. Physiol., 6.113-127.
Jaeger, M.J. and Matthys, H., 1970, The pressure flow characteristics of the human airways, In Airway Dynamics, Physiology and Pharmacology, A Bouhuys, Thomas Springfield, IL, pp. 21-32. Jaffrin, M.Y. and Kesic, P., 1974, Airway resistance: a fluid mechanical approach, J. Appl. Physiol., 36, 354-361.
Macklem, P.T. and Mead, J.. 1967, Resistance of central and peripheral airways measured by a retrograde catheter, J. Appl. Physiol., 22, 395 -40 1. Maio, D.A. and parhi, L.E., 1967, Effect of gas density on mechanics of breathing. J. Appl.
Physiol ,23,687-693. Mead, J., 1969, The distribution Circulatory
and
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of gas flow in the lungs, in Cibo Foundation Symposium on Transport, G.E.W. Wolstenholm and J. Knight (Ed.),
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Churchill, London, pp. 204-209. Patra, A.L. and Afify, E.M., 1983, An experimental study of velocity distribution in a human lung cast,J. Biomech. Eng., 105,381-388. Pedley, T.J., Schroter, R.C., and Sudlow, M.F., 1970, Energy losses and pressure drop in models of human airways, Respir. Physiol., 9.371-386. Pedley, T.J., Schroter, R.C. and Sudlow, M.F., 1970, The prediction of pressure drop and variation of resistance within the human bronchial airways, Respir. Phvsiol., 9. 387-405. Pedley, T.J., Schroter. R.C., and Sudlow, M.l:.. 1977, Gas flow and mising in the airways, in Bioengineering Aspects ofthe Lung, J.B. West (Ed.), Dekker, New York, pp. 163-265. Pedley, T.J., 1977, Pulmonary fluid dynamics, Annu. Rev. Fhtid Mech.. 9. 229-274. Reynolds, D.B. and Lee, J.S., 1981, Steady pressure-flow relationship of a model of the canine bronchial tree, J. Appl. Physiol.: Respir. Environ. Exercise Physiol.. 5 1, 1072 - 1079. Rohrer, F., 1915, Der stromungswiderstand ln den menschlichen atemwegen und der Einfluss der Unregelmassigen verzweigung des bronchial Systems auf den Atmungsverlauf in Verschifdenen Lungenbezirken. Pflugers Arch., 162,225 -299.
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Schroter, R.C. and Sudlow, M.F., 1969, Flow patterns in models of the human bronchial airways, Respir. Physiol., I, 341-355. Slutsky, A.S., Berdine, G.G. and Drazen, J.M., 1980, Steady flow in a model of human central airways, J. Appl. Physiol.: Respir. Environ. Exercise Physiol., 49,411-423. Stanescu, DC., Pattijn, J., Clement, J. and Van De Woestijne, K.P. 1972, Glottis opening and airway resistance, J, Appl. Physiol., 32, 460-466. Wood, L.D.H., Engel, L.A., Griffin, P., Despas, P. and Macklem, P.T., 1976, Effect of gas physical properties and flow on lower pulmonary resistance,/. Appl. Physiol., 41,234-244.