Gas exchange efficacy of high-frequency oscillatory ventilation studied by helium washout from dog lungs

Respiration Physiology (1986) 63, 307-325 Elsevier

307

GAS EXCHANGE EFFICACY OF HIGH-FREQUENCY OSCILLATORY V E N T I L A T I O N S T U D I E D BY H E L I U M W A S H O U T F R O M D O G L U N G S

M I C H A E L M E Y E R , H O R S T R I E K E and C H R I S T I A N

HOOK

Abteilung Physiologie, Max-Planck-lnstitut far Experimentelle Medizin. Gi~ttingen, F.R.G.

Abstract. The gas exchange efficacy of high-frequency oscillatory ventilation (HFOV) was assessed from an analysis of helium washout from lungs in anesthetized paralyzed supine dogs. Piston stroke volumes (Vs) were varied from 20 to 40 ml, frequencies (f), from 10 to 40 Hz and mean airway opening pressures from 2 to 10 cm H20. The time course of washout could be described as the sum of three exponential components. Based on a series model comprising a proximal and a distal lung compartment, two component conductances, a 'distal' conductance (Gd) and a 'proximal' conductance (Gp) and an overall conductance of the lung (GL) could be calculated. Gd, Gp and GL increased with fup to a maximum value remaining constant or decreasing at higher f; the frequency at which the maximum occurred depending on Vs and on the diameter of the endotracheal tube (ET). With increasing Vs generally the G values increased, but decreased at higher fwith the smaller ET. The insoluble inert gas washout is shown to be a useful method for assessing the ventilatory gas exchange conductance of lungs during HFOV. Conductance Convection

Inert gases Lung washout

Model analysis Ventilation

High-frequency oscillatory low tidal volume ventilation ( H F O V ) has been d e m o n s t r a t e d to provide adequate alveolar ventilation in both experimental animals and humans. Theories o f gas t r a n s p o r t m e c h a n i s m s in H F O V have considered the c o m b i n e d action o f turbulent flow and diffusion ('augmented dispersion', Fredberg, 1980; Slutsky et al., 1980), 'direct alveolar ventilation' ( K a m m et aL, 1984), axial distribution o f transit times o f gas moving through the d e a d space (Mitzner et aL, 1984), parallel convective flow ('Pendelluft', Lehr, 1980), and a s y m m e t r y o f flow profiles ('convective streaming', Scherer et al., 1984) to be o f m a j o r importance. A c c o r d i n g to predictions derived from these models, the rate o f gas exchange (e.g. C O 2 elimination rate) is mainly determined by the i m p o s e d oscillatory flow rate, i.e. the p r o d u c t o f frequency and tidal volume, f. VT (Fredberg, 1980; Slutsky et aL, 1980), with additional specific effects o f VT (Slutsky

Accepted for publication 4 November 1985 0034-5687/86/$03.50 © 1986 Elsevier Science Publishers B.V. (Biomedical Division)

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et al., 1980). The concepts have been reviewed recently (Chang, 1984; Drazen et al., 1984). Measurements of CO2 elimination rate in the transient state of short-term HFOV (Slutsky et aL, 1980, 1981 ; Rossing et al., 1981, 1982) or of arterial Pc'o2 in steady state (Bohn etal., 1980; Wright etal., 1981; Ngeow and Mitzner, 1982; Rieke etal., 1983) have been ambiguous in regard to the effects of f and VT. In view of current model predictions, these data may be suggestive of the inadequacy of present theories. But interpretation of data may also suffer from the uncertainty about the functional characteristics of the different HFOV systems that may vary because of the particular arrangement of the circuit. Multiple-breath inert gas washout has been analyzed conventionally in terms of two or three compartment models to quantitate ventilation distribution in the lung. In the present study, it is attempted, by calculation of physiologically relevant parameters from insoluble test gas washout kinetics, to assess the efficacy of gas transport by HFOV. It will be demonstrated that the analysis of inert gas washout provides useful information upon parameters relevant for quantifying ventilatory efficiency of HFOV that are otherwise inaccessible to direct measurement.

Methods

Six mongrel dogs (mean body weight 19+ 2 kg) were surgically anesthetized with sodium pentobarbital (20 mg/kg i.v.), supplemented as needed, and muscle paralysis was maintained by alcuronium (1 mg/hr i.v., initial dose 0.25 mg/kg). The animals were studied in supine position and were allowed to recover upon completion of the experiment. High-frequency ventilation circuit. A hydraulically operated piston-type high-frequency ventilator provided with servo positioning control of piston combined with a highimpedance balanced bias flow circuit was used. This apparatus, similar to that used by Slutsky et al. (1981), permits control of frequency, stroke volume, and lung volume. A constant air flow (~'F) of 10 L/min was supplied at the tip of the endotracheal tube (length 40 cm, inner diameter 8 or 10 ram) about 5 cm from the carina. Locating the bias flow entry point near the carina enhances the effectiveness of HFOV by eliminating the gas transport resistance imposed by the endotracheal tube. By controlled suction (vacuum) at the proximal end of the endotracheal tube mean pressure at the airway opening was kept at + 1 cm H20 throughout the various settings. The details of the HFOV circuit along with data on respiratory gas transport in dogs during steady state were reported in a previous communication (Rieke et al., 1983). Experimentalprocedures. After equilibration of lung gas with the inert gas He (bias flow containing 1Yo He in air) washout of He was initiated by instantaneous changeover of the bias flow to test gas-free air. The partial pressures (P) of He, 02, CO2, and N e in

HE WASHOUT DURING HFOV

309

exiting lung gas were continuously monitored by a high-performance respiratory mass spectrometer (redesigned Varian M3, cfi Scheid, 1983) sampling close to the proximal end of the endotracheal tube. Output of the mass spectrometer during He washout was stored on flexible disk (50 Hz A/D frequency, MINC 11, Digital Equipment) for later off-line analysis. Washouts were recorded in duplicate at oscillator stroke volumes (Vs) of 20, 30, and 40 ml and frequencies (f) of 10, 20, 30, and 40 Hz, varied at random. Each animal was studied twice. In the first session (series I) a large endotracheal tube (10 mm ID) was used. In the second session (series H) the experimental protocol was repeated with a smaller endotracheal tube (8 mm ID). In addition, measurements at mean airway opening pressures (Pao) of 2, 6, and 10 cm H20 (f = 20 Hz, Vs = 20 ml) were performed in series I experiments. The experimental data of series H were obtained in the same study in which steady-state gas transport of 0 2 and CO 2 was determined (cfi Rieke et al., 1983). The experimental protocol was typically conducted within 8 hr while the animals were ventilated by HFOV without interruption.

Model and calculations. Partial pressures of He (PHe(t)) were numerically normalized, the washin equilibrium partial pressure (PHe(o)) assigned to unity. The He washout kinetics (fig. 1)revealed three exponential components described by their rate constants (k I > kii > kHi ) and amplitude coefficients (= intercepts, A~, m l i , and Ain). 10

@

PHe

0.5

2O

t

{see]

I •' 0

I

I 60

®

-5

0

20

40

t

I 60

(sec)

Fig. 1 Time course of He washoutduring HFOV. A. Linear scale. B. Semilogarithmicscale.

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M. MEYER et al.

Lung volume (VL) was obtained by integration of the washout curve: ts

VL = p

(l)

P(t)'dt t()

In practice, integration is restricted to a limited washout time interval (t o - tj ). The remainder (t~ - t~ ) was obtained by extrapolation of the monoexponential component ki~~ predominating the late part of the washout. The He washout curve was interpreted as arising from a set of three compartments arranged in series (fig. 2A). The lung is divided into a distal compartment (volume V~ ) and a proximal compartment (volume V2). A third compartment (V3) is attributed to the volume of the endotracheal tube (20 ml and 30 ml for smaller or larger ET, respectively). Homogeneous gas mixing is assumed in each compartment. Gas transport between V~ and V2 is quantified by the 'distal conductance' (Gd), defined as transfer rate (l~I) per unit partial pressure difference (AP), that between V2 and V~ by the 'proximal' conductance (Gp'), and a third conductance (Gy) is attributed to gas transport between V3 and the atmosphere. In compartment 3 lung gas is continuously mixed with fresh gas. Only a fraction of the fresh gas flow (bias flow) is delivered to V2 while the remainder is vented through the endotracheal tube. The three-compartment model can be remodeled to a two-compartment model where compartment 3 is eliminated and Gp' and Gy are replaced by a single 'proximal' conductance, Gp (fig. 2B). The conductance can be expressed in terms of an effective ventilation which would be required at the boundary to produce gas mixing across the boundary. The 'proximal' conductance (Gp) divided by the capacitance coefficient of the gas phase (fig) yields the effective fresh gasflow to the lung (VH), i.e. the effective

@

Gd

V1

Gp

V~

Gy

V3 N

VF

P2 ~ P3-

P,

Po

® Od Gp DISTAL ~ PROXIMALLY' .

Vl

.

.

.

.

V2 ~ VF P2 ~ Po

l i ° P;

Fig. 2. Compartment lung model used for analysis of inert gas washout during HFOV. A. Three-compartment series lung model. B. Modified two-compartment lung model. See text for details and Appendix.

HE WASHOUTDURING HFOV

311

fresh gas ventilation of the proximal compartment (VF1 = Gp/flg). The capacitance

coefficient fig of a medium for a gas x is defined as the increment of quantity of gas species x in unit volume of gas mixture per increment of partial pressure P× with dimensions ml STPD. L - ~• Torr- ~and, for any gas species at 37 ° C, has the numerical value 1.16 (cf Piiper et aL, 1971). Similarly, GpTflg yields the effective ventilation of the proximal compartment (V2) that may be used to calculate the effective oscillatory tidal volume ( V T e ff = ~12/f). The unknown variables V~, V2, Gd and Gp can be calculated from the slow (klli) and intermediate (kn) exponential rate constants and the zero-time intercept (Am) of the slow component, as shown in the Appendix. The overall ventilatory conductance of the lung (GL) is calculated from the following relationship:

dc

+

Results

Washout rate constants. Typical values at 20 Hz oscillation frequency and 30 ml stroke volume for the exponential constants, k~, k n, kin, and the coefficient A m were 1.09, 0.32, 0.07 sec- 1, and 0.27, respectively. For simplicity the raw data for the various settings are not presented in extenso. Generally, the washout rate constants and coefficients were larger in series I than in series H (smaller endotracheal tube). The variables k m and AIn were markedly affected by f and Vs; the effects were less pronounced for kii and insignificant for kx. Lung volumes. Mean lung volumes (VL) obtained in the different conditions are shown in fig. 3 for series I and series H experiments. Considerable changes were encountered

with varying both f and Vs and were more pronounced for the smaller endotracheal tube in spite of constant mean airway opening pressure throughout all settings. Volume of compartments. The fractional volume of the distal compartment (VI/VL)is shown in fig. 4 as function of oscillation frequency (f). The V~/VL ratio decreased when f or Vs were increased (fig. 4A) but, above 30 Hz, increased again. A similar relationship was found in series I I but the frequency dependence of VI/VL was less pronounced (fig. 4B). The complementary mirror image of fig. 4 yields the associated changes of fractional volume (V2/VL)of the proximal compartment. Gas transport conductances. The 'distal' conductance (Gd) plotted against the product f. Vs (X)osc)is shown in fig. 5 (upper panel) for the larger (A) and smaller (B) endotracheal tube. Gd increased almost linearly with ~'osc when the range of Vos¢ was low. A tendency to level off with higher values of ~'os~ became apparent when the larger tube

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M. MEYER et al.

13f

,o , ~

,At,

8 mm

13

12 VL (L)11

12 VL {L) 11

10

10

0.9

09

08

0.8

T

B;

MEANS t SE

07

~10

20

J "0

30

07

L 10

J 30

20

z,O

f [Hz)

F i g . 3.

f (Hz]

Lung volume calculated f r o m H e washout as function of oscillation frequency for different stroke volumes. A . Series I ( 1 0 m m t u b e ) . B. Series I1 (8 m m tube).

was used. The results for the smaller tube reveal a distinct maximum for Gd depending on Vs. Moreover, for a given value of'V'osc (e.g. 0.8 L/sec) Gd was greater when Vs was large and f was low indicating that f and Vs had quantitatively different effects. The 'proximal' gas transport conductance (Gp) increased with Vosc but for the small-diameter tube, similar to Gd, discrete maximum values were observed upon transition to higher 'Vosc with shifting of the critical frequency to lower values (fig. 5, middle panel). The ventilatory lung conductance (GL) displays a pattern qualitatively similar to that of Gd and Gp as a result of increasing the product f. Vs (fig. 5, lower panel). Again the effects of size of the endotracheal tube become apparent.

(~.... =lOmm

(~

¢ .... = S m m

@

Vs [ml)

06

06 )

Vl / VL 04

04

02

0.2 MEANS z SE

10

L

20

l

I

30

f lHzl F i g . 4.

I --

~0

0

]

10

,

210

t_

i _

30

~

f (Hz)

Volume of distal lung compartment relative to overall lung volume,

~o

T vs

0

1.0

1.5

VOX IL/se4 6-

6

2-

@

0

05

1.5

10. v05c

0

0

MEANS t SE

Bmm I

I

I

0.5

10.

1.5

VOX

ILked

ILlSd

3-

3GL

@lOmm 01 0

MEANS t SE

05

15

10. v05c

ILlsed

Fig. 5. ‘Distal’ gas transport conductance (upper panel), ‘proximal’ gas transport conductance (middle panel), and overall gas transfer conductance of the lung as function of frequency-stroke volume product

314

M. M E Y E R etal.

Effective fresh gasflow and tidal volume. The effective fresh gas flow to the lungs (9~) calculated from the proximal conductance ( vl = G~/flg) was found to be in the range of 35 to 60% of the bias fresh gas flow to the system (VF) that was constant at 10 L/rain in all conditions. The effective volume of fresh gas delivered to the lung on each

10

10

6

6

VFL

{

VFL

(ml)

4

(ml)

Vs I~(I

05i

° -

1'0

115 VOSC (L/sec) •

0

10I

05i

i 1,5

.

VosC

(L/sec)

T

20 VT'" (m[)

20- T I

VTe" (mr) 15

15r ~ imH

10

10

5

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~/

10

30

"

40 f (Hz)

I

ao

}

5

NEANS "_ SE

20

±

0 10

MEANS ~ SE

20

30

40 f [Hz)

Fig. 6. Effective osci||atory tidal volume and effective fresh gas volume delivered on each oscillatory stroke.

315

HE W A S H O U T D U R I N G HFOV

TABLE 1 Effect of lung volume on model parameters. Changes of lung volume were achieved by varying mean airway pressure (Pao) at constant frequency (20 Hz) and stroke volume (20 ml). Endotracheal tube 10 m m ID. Mean values + SE, n = 6 (number of experiments). P~,o (cm HzO )

2

VL (L) V 1 (L) V~/VL Gd (ml. rain - l .Torr - 1 ) Gp (ml' rain- 1. T o r r - t) GL (ml. m i n - 1 . T o r r - 1)

0.83 0.50 0.58 1.87 5.4 1.39

6 + + + + + +

0.11 0.11 0.07 0.17 0.9 0.16

1.00 0.66 0.64 1.89 4.9 1.36

10 + 0.11 +_ 0.11 + 0.04 + 0.20 +_ 0.7 + 0.16

1.21 0.81 0.68 1.94 5.2 1.41

+ 0.13 _+ 0.07 + 0.04 + 0.20 + 0.6 + 0.15

oscillatory stroke (VF1) was in the range of about 8 to 2 ml decreasing with increasing product f. Vs (fig. 6, upper panel). The effective oscillatory tidal volume (VTeff = GpTflg • f) was estimated at about 50~o of the oscillator stroke volume (Vs) for low frequencies, further decreasing at higher frequencies (fig. 6, lower panel).

Effect of lung volume. The effects of changes in lung volume (VL) achieved by varying mean airway opening pressures (Pao) at constant f. Vs are compiled in table 1. V~/VL slightly increased with lung volume whereas the 'distal' (Gd) and 'proximal' (Gp) conductances, and lung conductance (GL) remained essentially unchanged.

Discussion

Critique of experimental methods. A major problem is of course that we, like others, were unable to precisely determine the effective tidal volume delivered to the animal on each oscillatory stroke. Because direct measurement of tidal volume (e.g. by pneumotachography or plethysmography) requires a primary periodic flow reference standard for calibration which for the range of flow rates encountered in this study is not available, an indirect method was employed. The oscillatory stroke volume (Vs) referred to throughout this paper was obtained from a linear potentiometer attached to the oscillating piston. Calibration of effectively displaced gas volume was performed at 1 Hz oscillation frequency by relating its output to the volume displaced into a calibrated syringe. For higher frequencies (10-40 Hz) the entire system (with bias flow attached) was evaluated by connecting the tracheal tube to a rigid isothermal 8-L box carefully engineered to meet the acoustic criteria required and relating box pressure changes (Setra model 237 transducer) to volume changes applying Boyle's law. These indirect measurements of tidal volume revealed no significant differences between the stroke volume of the oscillator and the delivered gas volume for the range of frequencies, volumes and size of endotracheal tubes of interest. In addition, volume changes

316

M. MEYER etal.

measured by a circumferential mercury-in-rubber strain gauge applied to the animal's chest increased in proportion to stroke volume and for a given stroke volume were constant over the range of frequencies used. On the other hand, a precise estimate of the volume displaced by the ventilator is not required because it does not enter the calculation of the parameters derived from He washout kinetics. Particular problems were encountered with the indirect control of lung volume. It was intended to achieve constant lung volume by maintaining mean pressure at the airway opening constant throughout all settings. Measurements of lung volume from integration of the He washout curve demonstrate our failure in this respect. In spite of adequate frequency response of the transducer-monitoring system, mean alveolar pressure and hence lung volume apparently increased with frequency or volume. Artefacts most likely arising from Bernouilli effects when gas velocities are high make measurements of mean airway opening pressure unreliable for continuously controlling lung inflation during HFOV. It is important to note, however, that the variables recovered from He washout probably were little affected by lung volume (see below). Volume of compartments. According to the model of Fredberg (1980) and Slutsky et al. (1980) the well mixed swirling flow regime penetrates farther into the lung if the amplitude of the imposed oscillatory flow is increased by f a n d Vs. In the present model displacement of the zone of transition from dominance of convective to diffusive gas transport processes and hence displacement of the maximum resistance to mass transfer towards more peripheral lung regions should be reflected by an increase of the volume of the proximal lung compartment (V2). Hence, V1/VL which is a complementary measure of the penetration depth of airway transport processes due to convective exchange is expected to decrease with f and Vs. However, changes of overall lung volume associated with f and Vs are also expected to affect V1/VL because the distal alveolar lung zones are more compliant than the upper airways. This hypothesis is confirmed by V~/VL increasing at higher intrapulmonary pressures (cf table 1). The pronounced decline of Vt/VL with f and Vs, regardless a substantial increase in VL, is therefore attributable to farther displacement of the transitory zone to deeper lung regions. The different pattern of VI/VL in series I and H experiments is apparently due to the size of the endotracheal tube. Assuming that f and Vs were essentially the same in both series the flow just distal the endotracheal tube should be same. However, for low f" Vs products ( < 400 ml/sec) V1/VL is slightly smaller in series H compared with series I and the depth of penetration of convective transport cannot be further advanced by increasing oscillation frequency if the diameter of the endotracheal tube is small. The various factors potentially limiting gas mixing efficiency during HFOV will be discussed below. 'Distal' gas transport conductance. The almost linear correlation of Gd with ~'oso up to about 600 ml/sec (fig. 5) is in agreement with theoretical predictions from the models of Fredberg (1980) and Slutsky et al. (1980). These models predict that gas transport by HFOV depends on the applied flow amplitude (product f" Vs). In a later refinement

HE WASHOUT DURING HFOV

317

of the model (Slutsky et al., 1981) allowance was made for the convective purging action of the fresh gas (bias) flow near the airway opening and the alveolar laminar flow zone. This model predicts that for low frequencies ( < 25 Hz) and Vs less than anatomic dead space gas transport varies relatively linearly with f. Vs and is independent of lung volume if the lung expands isotropically. A further feature of this model is the tidal volume dependence of gas transport, i.e. increasing Vs and decreasing f at constant f. Vs results in increased gas transport. The results from this study for Gd are in line with the above concept for low frequencies (cfi fig. 5) as well as for lung volume changes showing practically no effect on Gd (table 1). On the other hand, the present findings suggest that the tidal volume dependence is mainly determined by the size of the endotracheal tube. The effects of the size of the endotracheal tube are further discussed in fig. 7 for the specific 'distal' conductance, Gd/V l, accounting for the fact that changes of f and Vs were associated with changes in VL. For low Vs (20 ml) Gd/V I linearly increased with f but for larger Vs (30 and 40 ml) transition beyond a critical frequency resulted in decreasing Gd/V~ (fig. 7A). With the smaller endotracheal tube Gd/V 1 was clearly reduced at higher frequencies (about 50~o at 40 Hz, fig. 7B). Figure 7C shows that Gd/V~ increased almost linearly with Voso up to a value of 900 ml/sec. However, as a result of the smaller lumen Gd/VI was no longer correlated with ~'osc but varied independently of f and Vs (fig. 7D). "Proximal" gas transport conductance. The 'proximal' gas transport conductance (Gp) that may be used to calculate the effective fresh gas flow to the lung (~/F~) displays a similar relationship to "~osc as found for Gd. However, the relative changes of Gp, respectively of VF~, are smaller than those of Gd. Factors limiting efficacy of gas transport by HFOV. Our results show an apparent inefficiency of HFOV that is particularly relevant at higher frequencies and/or larger stroke volumes. The mechanisms are not entirely clear but the following are considered to be of importance. The impairment of efficiency could result from increased airway distensibility. At higher oscillation frequencies a greater fraction of the oscillatory volume could have been lost by expanding the central airways and thus reducing the effective tidal volume. That the non-rigid upper airways may act as a shunt capacitance in parallel with the distal airways when oscillating frequency increases has recently been demonstrated by cineradiographic studies of airway dynamics in dogs during HFOV (Gavrieli et aL, 1985). Non-linear relationships between frequency and rate of CO2 elimination during HFOV in rabbits have been attributed to the frequency-dependent behavior of respiratory system resistance (Watson and Jackson, 1984). Respiratory system resistance was found to increase in dogs by about 50~o when frequency was increased from 7 to 32 Hz. This finding may be associated with the effects of parallel resistance-inertance inhomogeneities leading to a reduction in cross-sectional area for gas mixing and increasing flow velocities. The net effect of these two factors could theoretically lead to an impairment of gas mixing at higher frequencies.

318

M. MEYER et al. 015

i

015

010

Gd/Vl (sec-'-Torr 11 s

)

J

3o

0 05

.

10 ml'n

MEANS -* SE

]

Ol 10

20

30

z.0

10

20

30

f [Hzl

°,51

z.0 f {Hzl

015

[

//L~30

Vs

Imp)

010

010

Gd/Vl

Od [ V 1

(sec- 1.Torr -1)

[$ec q Torr 1

005

0 0 ~.

/ (C') 10 mm 0 0

05

~D) 8 mm

MEANS,SE ---

10 VOSC

J

: ~--~

0 L

15

0

(L/sec]

05

10

15 VOS C {L/se¢l

Fig. 7. Specific 'distal' gas transport conductance as function of oscillation frequency (A and B) and frequency-stroke volume product (C and D).

Another mechanism affecting the gas mixing efficacy of H F O V is the shape of intra-airway velocity profiles. Blunting of velocity profiles is expected to occur at higher frequencies and would result in decreased gas transport efficiency (Scherer e t al., 1984). The overall effect of these mechanisms is reflected in the estimated effective oscillatory tidal volume (VTeff') that was considerably smaller than the oscillator's

HE WASHOUT DURING HFOV

319

stroke volume (Vs) and decreased with increasing frequency. It is important to emphasize that VTeff as calculated from He washout constitutes the fractional stroke volume that is effective for intrapulmonary gas mixing and transport and should not be confounded with the oscillatory tidal volume at the airway opening. VTeff can be considered as the tidal volume that would be required if none of the above mechanisms leading to impaired gas mixing efficiency was operative. Series model vs parallel model. The multiexponential washout of insoluble gases from lungs is usually interpreted in terms of parallel arrangement of multiple functional compartments with differing ventilation-to-volume ratios. However, the same washout behaviour can equally well be explained by a model comprising multiple compartments arranged in series (Nye, 1974; Wagner and Evans, 1977). In the present analysis we have adopted a series model and the ability of this operational model to approximate the relevant parameters describing gas exchange efficacy needs to be evaluated. A series arrangement of a well-mixed central compartment beyond the trachea and a 'slower' peripheral compartment has been suggested by Lehr et al. (1981) to account for the washout kinetics of tracer boli from excised dog lung lobes. Considering different mechanisms of gas transport in HFOV when more proximal lung airways are compared with most distal airways, well-mixed turbulent flow is assumed to predominate in the conducting airways where gas velocities are high whereas in the lung periphery a gradual transition from turbulent to laminar convection and to diffusion occurs. Convective mixing is expected to be most efficient in the turbulent flow regime but diffusive equilibration becomes important in the peripheral alveolar spaces. Models with series arrangement of compartments have also been used by Knopp etal. (1983) and by Kaethner et al. (1984) to explain inert gas washout from dog lungs. However, because the general anatomical lung structure implies parallel and/or series arrangement of elements evaluation of the experimental data was also performed on the basis of a parallel 2-compartment model (compartments 1 and 2 of fig. 2 arranged in parallel). The results for the calculated volume of the compartments and conductances (series model: V 1, Vz, Gd, Gp, GL; parallel model: V1, V2, G1, G 2, GL) are compiled in table 2. For reasons outlined below, calculations were restricted to the data set of series H (8 mm endotracheal tube) and minimum (min) and maximum (max) values along with overall mean values (mean) obtained from all different settings are presented. For the analysis of experimental washout curves the series and parallel models are mutually exclusive. Differences between the compartment volumes, V~ and V2, become apparent as a result of the underlying model. More important, the overall conductance of the lung (GL) of the parallel model exceeds that of the series model by a factor of about 3.5. The calculation of the specific conductances (series model: Gd/V~ = 4.3, Gp/V 2 -- 9.8; parallel model: G~/V~ = 12.9, G z / V 2 = 1.9) suggests the existence of a small compartment (V~) that is hyperventilated relative to V2 in the parallel model. This distribution of G/V in the parallel model would constitute an inhomogeneity of ventilation that would be in agreement with our previous observation of negligible Pco2

320

M. MEYER et al.

TABLE 2 Volume of compartments and conductances of series and parallel lung model (He washout) and C O 2 conductance of lung determined from CO 2 transport in steady state. Minimum (Min), maximum (Max) and overall mean values (Mean) from series II. Min

Max

Mean

Series Model VI 0.36 V2 0.35 Gp 4.1 Gd 1.0 GL 0.8 Parallel Model VI 0.23 V2 0.49 Gl 3.0 Gz 0.7 GL 3.7

0.60 0.69 6.8 3.1 2.1

0.48 0.53 5.2 2.1 1.5

0.40 0.90 5.4 1.6 7.0

0.31 0.69 4.0 1.3 5.3

GLco 2

5.9

3.8

1.5

differences between alveolar gas and arterial blood during HFOV (Rieke et al., 1983) only, if the perfusion is distributed in proportion to the alveolar ventilation. In the series model the gas transport conductance of the lung (GL) is calculated from Gd and Gp according to eq. (2). Our data show close agreement with recent results of Brusasco et al. (1983) who used a 133Xe closed-circuit (no bias flow) washin technique and a different analytical approach that does not require the assumption of a particular lung model. The frequency dependence of GL was essentially similar to our findings for the smaller tube (fig. 5B, lower panel). At a given product of stroke volume and frequency the average GL was greater at large stroke volume and low frequencies than at low stroke volume and high frequencies. The overall average value of 1.53 ml. min - ' • Torr - i in the present series is in agreement with the value of 1.46 that may be obtained from the data of Brusasco et al. (1983). In contrast to their findings, GL was not found to be dependent of lung volume in the present series (table 1). The overall gas transport conductance GL may be used to predict the ventilation potential of HFOV for elimination of CO2 in steady state. With the average values of 1.47 (series model) or 5.32 (parallel model) and assuming an alveolar-to-inspired CO2 partial pressure difference of 40 Torr one would expect a CO2 elimination rate of 59 ml/min or 213 ml/min, respectively. When these values are compared with the normal CO 2 production of anesthetized dogs during HFOV (75-90 ml/min) the GL data would underestimate (series model), respectively overestimate (parallel model) the CO 2 elimination rate achieved in steady state. The apparent discrepancy becomes more evident when the GL values are compared with the G t c o 2 values obtained from steady state analysis of gas exchange in the same

321

HE W A S H O U T D U R I N G HFOV

experiments (table 2; GLco 2 data taken from Rieke et al., 1983). The mean GLco 2 of 3.8 ml. min - 1. Torr- ~ is about 2.6 times higher than the GLue values for the series model. Conversely, GLHe of the parallel model overestimates GLco: by a factor of about 1.4, Thus the overall conductance (GL) inferred from He washout measurements when based on overly simplistic series or parallel compartment models does not accurately predict the CO 2 elimination that may actually be achieved by HFOV. Evidently in real lungs a large number of branching airways and of serial and parallel compartments is present but the experimental washout curves usually do not provide enough information for more complex models.

Significance of parameters derived from inert gas washout. For quantitative description of gas transport efficacy by HFOV a series lung model was assumed and efficacy described in terms of gas transport conductances of pulmonary compartments. The compartments calculated are not a unique solution to the washout data obtained and are mathematical concepts rather than representations of actual subdivisions of the lung. Thus the compartments and their respective conductances have meaning only as indices of the effectiveness of gas transport that may actually be achieved by HFOV in the various settings. The effective ventilation of the distal compartment, "¢1 (= Gd/flg), which may be considered to entirely represent alveolar ventilation (~/A), displays the same frequencydependent characteristics recently obtained in the same group of animals (8 mm tube) where VA was calculated from steady-state CO 2 data (cf. Rieke et al., 1983). In contrast, only a fraction of the ventilation of the proximal compartment contributes to alveolar ventilation because it is expected to comprise a 'dead space' component. The dead space ventilation component may be estimated from the difference between effective fresh gas flow to the lung and alveolar ventilation: ~/D = V~Fl = VA. Figure 8 shows that the dead space-to-alveolar ventilation ratio (DD/VA) varies between 2.5 and 0.5 as a result of the particular combination of f and Vs (data taken from present series H and from Rieke

3

2 MEANS

.~ SE

Vs lint) 30 40 0

I

10

L

I

2O

i

I

i

3O

L

l.O f (Hz)

Fig. 8. Dead space-to-alveolar ventilation ratio.

322

M. MEYER et al.

et al., 1983). It is important to emphasize that the average value of'Vv~, 4.5 L" min

corresponds well to the total ventilation value that would be required for achieving normal gas exchange during conventional mechanical ventilation (VT = 15 ml/kg, f -- 15 min ~, "~ = 4.5 L/min; assuming 20 kg body weight). We therefore suggest that comparison of gas exchange efficiency between HFOV and CMV should be performed on the basis of equal fresh gas flow to lung (in HFOV) and total ventilation (in CMV), respectively. Calculation of parameters from inert gas washout to quantify the efficacy of gas transport by HFOV reveals important advantages. Unlike assessing gas exchange efficiency in terms of arterial blood gas data in steady state, attainment of steady state conditions for the respiratory gases is not required which is particularly relevant when oscillation frequency and stroke volume are randomly varied over a wide range. Moreover, a precise estimate of the oscillatory tidal volume delivered need not be known. The method appears to be particularly useful when the effects of different settings of the HFOV ventilator or different methods of generating high-frequency oscillations are to be studied.

Appendix List of symbols

(For schematic representation of models see figs. 2A and B)

VL

System volume (lung + endotracheal tube) Volume of distal lung compartment Volume of proximal lung compartment Volume of endotracheal tube (ET) 'Distal' gas transfer conductance 'Proximal' gas transfer conductance Gas transfer conductance between compartment 2 (V2) and compartment 3 (V3) Gas transfer conductance between compartment 3 (Vs) and atmosphere 9v Fresh gas (bias) flow supplied at tip of ET Inert gas partial pressure of compartment i (i = 1, 2, 3) Pi Inert gas partial pressure of bias flow ( = 1 for washin, = 0 for washout) Po kl,n,lll Exponential washout rate constants of fast (k0, intermediate (kn), and slow (kxn) component AI,II,III Amplitude coefficients (zero-time intercepts) of k~, kn, and kiw

Vl V2 V3 Gd Gp Gp' Gy

Mathematical processing of series 3-compartment model The following three linear differential equations describe the time course of P~, P2, and P3 during washout.

dP~

1

dt

VI

Gd(Pl - P2)

(A1)

HE W A S H O U T D U R I N G HFOV

323

dP 2 1 - - = - - [Gd(a~ - P2) - GP'(P2 - a3)] dt V2

(A2)

dP 3 1 - - = - - [GP'(P2 - P3) - Gy(P3 - Po)] dt V3

(A3)

Because the time constants of the fast (k I) and intermediate (kii) component were considerably larger than the slow component kii I the time course o f P 3 (P3(t)), after termination ofki, is predominated by the time course of P2 (P2(t)) of the proximal compartment. Hence, after rapid initial washout of V s, the time course of P3 in compartment V3 that is accessible to measurement by mass spectrometry can be approximated by the following relationship which is obtained if dP3/dt in eq. (A3) is assumed to be zero (quasi steady-state approximation).

P3(t) - Gp'P2(t) + GyPo

Gp' + Gy

(A4)

The 'proximal' gas transfer conductance Gp is defined by

Gp = Gy

_Gp' : Gp' + Gy

(A5)

Combination of eqs. (A4) and (A5) yields

P3(t) = ~yP2(t) + ~

tap'

Po

(A6)

Applying mass balance principle to the 2-compartment lung model of fig. 2B yields the expressions for Pl(t) and P2(t). dP 1 _

Gd

(P1 - P2)

(A7)

dP2 = Gd (PI - P2) + G p (Po - P2) dt V2 V2

(A8)

dt

V1

Solution of this system of linear differential equations yields the following compound exponential functions for PI and P2, Pi(t) = All.i ' exp ( - kii. t) + AIII.i • exp( - kil I • t) The rate c o n s t a n t s

(A9)

k l l and kni are defined by the following expression, /

a + b + c kii Ill

•

- -

2

/(a

+ ~/ -

+ b + e)2

4

a.c

(A10)

in which a, b, and c are the coefficients of the differential eqs. (A7) and (A8): a = Gd/V 1 (A11), b = Gd/V 2 (A12), c = Gp/V 2 (A13).

324

M. M E Y E R et al.

The coefficient A,~.2 (zero-time intercept of slow c o m p o n e n t with rate constant k u) of the normalized gas fractions (i.e. Pi~t o) = 1) is obtained from eqs. (A8) and (A9), (C - kll )

AII.2 =

(A14)

(kll I - k u ) Because Au, z cannot be determined directly, A,,.2 may be transformed into AIL 3 of the accessible slow component of P3¢t) using eq. (A6), Gp A n . 3 = A l l I = ~FF AII,2

(AI5)

The eqs. (A10) - (A15) enable calculation of the u n k n o w n parameters V,, V2, Gd, and Gp. Rearrangement of eqs. ( A I 0 ) and ( A I 5 ) yields

kn+km=

k n . k,n =

Alll

=

x +x+z (v - y) y y X

(A16)

Z

. (v - y) y

(AI7)

z/y - kll z ' ;(kli I - kil ) VF

(A18)

with the following expressions: x = G d (A19); y = V 2 (A20); z = Gp (A21); v = VL - V 3 = V~ + V 2 (A22). Eqs. (A19) - (A22) may be solved algebraically for x, y, and z,

x = k l t ' k t n ( v - Y)'Y

(A23)

z

y =

(A24)

k n + AHI" ~/F(kll I - kn)/z

z =

ktl'kll I 'v

+

AII 1 • Wv(kli

I -

kn)

(A25)

km

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