Respiration

Physiology

(1975)

GAS TRANSPORT

23, 209-221;

EFFICACY

THEORY

Physiologic,

Publishing

PIIPER and PETER SCHEID

Max-Plan&-lnstitut

by flow of external

between external transport

by blood

According

fiir

experimentelle

Medizin,

of these systems

is applied

differences

shows

that,

in efficiency

when taking

medium

Germany

organs of vertebrates are inin vertebrates: (1) convective

( =ventilation);

( = medium/blood

flow relative

(a) counter-current

limitations

(2) transfer transfer);

of gas

(3) convective

functional

to capillary

system lungs),

and (d) infinite

is analyzed

blood flow four construc-

(fish gills), (b) cross-current pool system

in terms of conductances,

to ventilation,

of gas exchange

to medium/blood

data

obtained

system

(amphibian

relative transfer

partial and

in an elasmobranch

to fish,

salamander.

despite

values

attributable

to analysis

fowl, dog and a lungless

The analysis marked

and

The theory

dome&ic

air or water

pool system (mammalian

performance

differences

perfusion.

of external

may be distinguished:

The gas transfer

medium,

and blood by diffusion

Giittingen,

flow ( = perfusion).

lungs), (c) ventilated

pressure

respiratory medium

to the arrangement

tion principles (avian skin).

respiratory

Amsterdam

DATA

Abstract. The general functional principles encountered in respiratory vestigated. Generally three steps are involved in external gas exchange transport

Company,

OF GILLS, LUNGS AND SKIN:

AND EXPERIMENTAL

JOHANNES Abteilung

North-Holland

distinct

actually

differences

attained

inhomogeneities

Amphibians

efficiencies

less pronounced,

into account

of these systems, and

which are neglected

may

be even

the less

in this study.

Gas exchange

Birds Comparative Fishes

in maximum

are much

Gas exchange

organs

Models

physiology

Skin breathing

In a previous study (Piiper and Scheid, 1972) the principles of a comparative functional analysis of external gas exchange organs in vertebrates were presented. In the present paper this analysis is extended and completed. In particular the following additions have been made: (1) A barrier to diffusion is assumed to be interposed between medium and blood so that medium/blood equilibration is in part limited by diffusion. (2) A fourth model, termed as ‘infinite pool’, is introduced for representing cutaneous gas exchange which is particularly prominent in amphibians. Accepted for

publication

(I November

1974.

209

210

J. PIIPER

AND

P. SCHEID

Theory MODELS

The four types of external gas exchange organs and the corresponding idealized models, along with partial pressure profiles, are depicted in fig. 1. The model for alveolar lung, which was designated in the preceding paper (Piiper and Scheid, 1972) as ‘uniform pool’, has been renamed ‘ventilated pool’. It is felt, however, that this designation, as well as that of ‘infinite pool’, is not entirely satisfactory. REQUIRED

QUANTITIES

For the description of gas transfer in all these models the quantities listed below are required (in parentheses, typical units illustrating the dimensions). The terminology, the system of quantities and the dimensions used are those suggested by Piiper et al. (1971). (1) Transfer rate, 64, i.e. the amount of gas transferred per unit time (mmol. min- ‘). (2) Partial pressure of gas, P, in inspired medium (Pi), in expired medium (Pe), in blood entering (Pv) and in blood leaving (Pa) the gas exchange organ (torr = mm Hg). (3) Capacitance coefficient, fi, defined as increment in concentration per increment !%tl GILL!5

AWN

LUNG

AMPHIBIAN SKIN

m-b

7s

INFINITE F’CXA

Fig.1.Schematicrepresentationof the models.

In the bottom

four types of external gas exchange organs and of the corresponding row, the equilibration of P,, is indicated. For symbols, see text.

GAS TRANSPORT

EFFICACY OF GILLS, LUNGS AND SKIN

211

in partial pressure( = dC/dP) for both medium p,,,, and blood, /& (mmol. l- ‘. torr- ‘). For gaseous media and for exclusively physical solution in liquids, /I is independent of P; but for CO, and 0, in blood (and for CO, in fresh water or sea water containing carbonate) p is dependent upon P (see Discussion). (4) Flow rate of medium (gas or water), \i,,,, and of blood, \i, (ml.min-‘). (5) Conductance, G (mmol . min -’ ‘torr- ‘); defined as transfer rate, i’& per driving partial pressure difference AP:

For convective transport conductance by ventilation (=medium flow) and by perfusion (= blood flow), G,,,, and Gprrf, the following relationships are easily derived from Fick’s principle : (2)

Gven, = \‘,A

(3)

GM = %P,

Conductance for diffusive transport between medium and blood, Gdirr, equivalent to diffusing capacity D, depends on Krogh’s diffusion constant, K, exchange surface area, A, and diffusion pathway, x, according to Fick’s law of diffusion:

(4)

G,if‘

=K

. ’ X

ASSUMPTIONS

The analysis is restricted to conditions allowing derivation of simplest relationships. The following assumptions are made: (1) The systems are in perfect steady state, implying constancy in time of Pi and Pv, and of \i, and ir,. (2) The /I,,, and fib values are constant, independent of P. (3) The systems are perfectly homogeneous. The, deviations from these conditions in real gas exchange organs will be considered in the Discussion. DERIVATIONS

In a system allowing gas transfer from a flowing medium into flowing blood three elementary processes, each describable by a differential equation. must be considered at any site of medium/blood contact. (1) The transfer rate by diffusion between the two media depends on the partial pressure difference (Pm- Pb) and the diffusive conductance of the infinitesimal element considered, dGdi,,. For a gas transferred from medium into blood. e.g. O,, one obtains : (5)

dti = (Pm-Pb)*dG,i,,

212

J. PIIPER AND P. SCHEID

(2) This transfer rate causes a partial pressure drop in the medium, dPm, across the length of the element in the direction of medium flow: d&l = -G,,,;dPm

(6)

(3) An analogous the element:

relationship,

with reversed sign, holds for blood traversing

dti = G,,,r*dPb

(7)

By adequate combination and integration of these three differential equations, relationships describing the gas transfer in all models are obtained. The mathematical procedures are elementary, being more complex only in the case of the crosscurrent system that has previously been described in detail (Scheid and Piiper, 1970). RESULTS OF CALCULATIONS

The results obtained by integrating eqs. (5), (6) and (7) for the various models can be expressed and standardized in several ways. We chose to consider the following parameters: (a) Relative partial pressure differences, Ap (b) Limitations, L (c) Total conductance, G,,,.

I

9_

9-T

="Pyc,

I

P-P pcrf

9-t

I

I

M

A

Z=l-L. Mdiffo.

dlfi

(X-e-zXl-e-y'X)I AU-•-') X-e-Z

1 -em'

l-e+

I

*)

l-~-~'~

,_

l-z’

, - e-1lx

x = %e,dGpert

Y = GditflGpcrt z =

') Xdl:Aml;

Xwl:A=X

Y.(l-l/X)

e-’ I

X

l_eez’

l-e-'

I

I

X.(1 - l wZ')

X(1-e-')

(X-e-z)(l-e-y)I

p&l-b

I

X.e+ XI l-eey

e-‘-X.(1 - eozi I

I

0 I

X+ I-emY

I

I I.

X*1-e" X(l-e-Y)

X(1-e-")

X.emz-l X -emz

%a ~_=%enl

I

X-esz

-k&A&,

Y

1-,-Y

,_c-2’

x-c-* X(1-e-')

UrAp

1

1-c-=

x*1-c-y

4

I

1

I

(X/Y*l)(l-e-") X*1-e+

I

(X+1)(1-e -")

l-e" -

Y

, _ .-v

X* l-e4

Z'= l/X .(l- e-")

Fig. 2. Formulas for the relative pressure differences, Ap, and limitations, L

I

GAS TRANSPORT EFFICACY OF GILLS, LUNGS AND SKIN

213

(a) The partial pressures in outflowing medium and blood, Pe and Pa, are compared with those in inflowing medium and blood, Pi and Pv, in terms of relative partial pressure differences, Ap, to be attributed to each of the three elementary processes, ventilation, perfusion and medium/blood transfer, and defined in the following way: (8)

Advent = E

(9)

Apprrr = s

(10)

Pe-Pa AP,~ = ~ Pi-Pv

Solving differential eqs. (5), (6) and (7) yields relationships of Apven,, Apperf, and Aptr for each model, which can be expressed as functions of the conductance ratios G,,,,/Gp,,r and Gdiff/Gperf. These equations for the four models are presented in fig. 2 (upper half) and depicted in fig. 3. The values for the infinite pool system can be read from fig. 3C at G,_,+cc. (b) A suitable measure for limitation, L, imposed on gas exchange by each of the three elementary processes, ventilation, perfusion and diffusion, is the relative difference between the maximum transfer rate, I’&,,,, achieved by eliminating the respective limitation by increasing the corresponding conductance to infinity, and the actual transfer rate, klact:

(11) ti,,, can be obtained as the transfer rate at infinite value of the respective conductance. For example, for ventilation, a,,,,,= h;i,,,, (at Gvent+co); this will be termed tivent m. Ventilation limitation, Lvent= 1 - *

Perfusion limitation,

Diffusion limitation,

ventco

Lperf = 1 - +

Ldiff = 1 -

perf

a,

dlff

cc

*

The equations for each of these L values for the four models are presented in fig. 2 (lower half). (c) Application of eq. (1) to the whole system yields a total conductance, G,,,,, equal to transfer rate divided by the total .partial pressure difference between inflowing medium and inflowing blood:

0.2

1.0

0.2..

OJ

0.1

a2

1

I

I

005

-02

1

20 co

11

l

+-f-

-&A _:::-::l 1! i __+

1

2

I

5 GmdGpti

I

10

-1.0

0.05

a1

;

, a2

1 Gwn,f%rt

0.5

I

! I 2

5

,

10

d rl 20' m

-1.0 ao6

-0.8

a0

a2

0.4

,

Qo5

0.f

a0

Ql

0.1

Fig. 3. Relative partial pressures (ordinate) as fuhctions of conductance ratios GIen,jGDerf (abscissa) and C&,/G,,,, (parameter). A, counter-current system; B, cross-current system; C. ventiiated pool system.

0.5

/

I....

_...

__.~

...I )_. _..^,

20

0.2

0.6

a8

0.8

I

a2

l_i5

i

0.2

I a5

1

,... .!,.,. a0

1.0

2b

0.2

a4

46

10

Pi - Pv O’O

PC-P,

g'p,

pi-p, Pi- Py

a8

1.0

2

;

5

f

10

lb

r 20

_ ...

1 20

20 _I

i

GAS TRANSPORT

EFFICACY

OF GILLS,

LUNGS

215

AND SKIN

Gtr,, can easily be obtained from either eq. (2) or (3) in combination eq. (8) or (9):

with either

G,,, = CL,,, *APE,,, G,“, = Gperf 7A~,,err

(13) (14)

For standardized Pi- Pv, G,,,* is a relative measure for h.4. G,,, a measure of gas exchange efficiency. Thus, for given values of GdiFf, differences in gas transfer efliciency between the various assessed from differences in G,,,,. The dependence of G ,,,, on G,,,,, Gperf and G,irf is determined presented in fig. 2 and is visualized in fig. 4 for a few selected sets of G,,,,, Gperi and G,;,r.

can be taken as Gventr Gperf and models can be by the formulae of combinations

08

Fig. 4. Representation arbitrary.

of the total conductance,

G,,,, as function

of G,,,,,

Gperf and Gdiff. Units of G

The parameter kept constant (= 1) marked at the left upper corner of each figure. I, countercurrent system; II, cross-current system; III, ventilated pool system.

Conductance values have been plotted on both abscissa and ordinate for the sake of simplicity, thus limiting the plots to a value of unity for the respective third conductance, Gperf in A and C, and G,,,, in B. It should be noted that this latter restriction is overcome and the plots of fig. 4 may be used for any set of the three conductance values if ordinate, abscissa and curve parameter are divided by Gperr in A and in C, and by G,,, in B. Therefore, fig. 4 can be used for calculating G,,, values from actual values, such as given in table 1. COMPARISON

OF MODELS:

SOME CHARACTERISTIC

FEATURES

(1) For any given set of values of G,,,,, Gperr and G,i,, the sequence of decreasing gas transfer efficiency is: counter-current > cross-current > ventilated pool,

216

J. PIIPER AND P. SCHEID

(2) The infinite pool model for cutaneous gas exchange is formally a particular case of all models with Gven,+co. (3) In the extreme conditions of G_,+cc or Gperf-+~ all systems behave identically. (4) But with Gdi,, -+cc (no resistance to diffusion) and for given finite values for both G,,,, and Gperf the differences in performance between the systems become maximally pronounced. (5) If two of the three conductances become infinite, the total conductance, G,,,,, is equal to the remaining, finite, conductance in all systems: G ven,+a

and Gperr+ ~0: Gtot = Gdirr

G vent+m and Gdirr+m :Gt,,,=Gperr G perr+m and Gdirr+a Application

to experimental

:Gtot=GV,,,

data

The theoretical approach described above is applied to experimental data by calculating the conductances, G, the relative partial pressure differences, Ap, and the limitations, L, for four animals each representing one gas exchange system. (1) Larger spotted dogfish (Scyliorhinus stellaris, Elasmobronchii) for fish gills/ counter-current system; (2) Domestic hen (Gallus domesticus) for parabronchial lungs/cross-current system; (3)DogW anis f ami l iaris ) f or alveolar lung/ventilated pool system; (4) Common Dusky Salamander (Desmognathusfiscus, Plethhtidae), a lungless and gill-less salamander, for skin breathing/infinite pool system. CALCULATIONS

Gperf was calculated from oxygen uptake, Mo,, and arterio-venous partial pressure difference, Pa - Pv, using eq. (1). The GV,,t/Gp,,r ratio was obtained from the simple relationship ensuing from combination of eqs. (2) and (3) with Fick’s principle: (15)

$=

PG

perf

Thereafter the Gdiff/Gperf ratio could have been read as parameter in the plots presented in fig. 3A-C. However, it was preferred to use the G,irr=D values calculated previously from the experimental data taking into account inhomogeneity effects. The Gdiff/Gperf ratio was then obtained as: (16)

z=

D.paE;lPV

The particular problems in handling the data of each of the animal species deserve some comments.

GAS TRANSPORT EFFICACY OF GILLS, LUNGS AND SKIN

217

(1) Dogfish. The underlying data are mean values obtained in resting unanesthetized dogfish (Baumgarten-Schumann and Piiper, 1968; Piiper and Baumgarten-Schumann, 1968). The Gdiff values were obtained by a particular Bohr integration technique taking into account curvature of blood O2 and CO, dissociation curves.and of sea-water COZ dissociation curve. (2) Domestic hen. The data are mean values obtained by Scheid and Piiper (1970) in unanesthetized hens breathing 3% CO;! and 13% O2 in Nz. This hypercapnic-hypoxic mixture was chosen with the aim of placing both CO, and O2 exchange in a more linear range of the blood dissociation curves. For Pe, the PEmaxC02and PEmino values were used. (3) Dog. Mean valies of experiments on anesthetized dogs, artificially ventilated with 1l-12% O2 in N,, were used (Haab et al., 1964, second series of experiments). The ideal-alveolar Po, and Pco2 were considered as Pe, the end-capillary P,, and P as Pa. Therefore, Gdifr for CO2 is infinite (by definition of ideal-alveolar Pz::). Pvco2 had to be assumed. (4) Salamander. The estimation of cutaneous blood flow ( = \i,) and of cutaneous G diff was based on differences in elimination rate of the soluble inert test gas Freon 22 into atmosphere from living and dead animals (Gatz et al., in preparation). Gdifr and Gperr for O2 and COZ were calculated from the values for Freon 22 on the basis of blood dissociation curves, and solubility and diffusivity in tissues (Piiper et al., in preparation). RESULTS: SOME EMERGING FEATURES

The measured and calculated values are presented in table 1. The following relationships and trends become apparent: ( 1) Gv,nt/Gperf ratios are not very far from unity, ranging from 0.18 to 1.17. For skin breathing, the ratio is infinity due to assumedly complete lack of ventilation (stratification) limitation. (2) Gdirr/Gperr ratio is 2 or higher (up to co) for lungs, about 0.5 for dogfish gills, and about 0.25 for skin breathing. Accordingly Idirr increases in the same sequence. (3) For air-ventilated lungs, Gvent/Gperr for O2 is higher than for COZ, due to the lower slope of blood OX as compared with blood CO2 dissociation curve, fib. Therefore, this difference would be even more pronounced in normoxia where fib,, is further reduced. For fish, such differences are less or even reversed due to high /?mcoz relative to firno*. PROBLEMS IN APPLICATION

The real gas exchange organs deviate more or less from the ideal model and the assumptions on which the analysis is based (see above). The main discrepancies and uncertainties are the following: (1) Uncertainty of Pi, Pe, Pa, \j,,, and 3,. With dead space, inherent to all lungs, the correct choice of Pi, Pe and \i, may be difficult. In mammalian lungs,

218

J. PllPER AND I’. SCHEID TABLE 1

Characteristics of respiratory gas transfer in animals with gill. lung and skin breathing. For references see text. Type

Gills

Parabronchial lungs

Alveolar lungs

Skin

Animal Weight(g) Condition

dogfish 2180 normoxia -__--

domestic hen 1600 hypoxia -I hy~r~apnia

dog

salamander 6.1 normoxia _.___-___.-~

Gas

CO,

CO.?

Mo2 (mmol.min-‘)

0.062

0.06s

0.85

1.09

6.07

6.70

0.16

0.19

0.10

O.(H)2

0.11

0.034

0.88

0.48

0.17

0.009

0.2 19.1 39. I 46 0.18

81 38.7 36.9 22.9 0.33 3.0 0.74 0.24 0.01 0.26 0.82 0.01

0.2

0,

25000 hypoxia ~-.CO2

02

_-__. 0,

CO, 0, ~~ _._ ___. .--_

$;:,_min+ torr-‘) Pi (torr) Pe (,torr) Pa (torr) Pv (torr) Gren,/Gnrtr Gdilf/G,Mf AP,,,, Apprr, Aptt L“C”, L pcrr L,iff

0.7 I .25 2.0 2.6 1.09 0.45 0.29 0.31 0.40 0.14 0.15 0.69

149 57 49 10 0.42 0.5 I 0.64 0.27 0.09 0.33 0.09 0.36

20.6 43.4 38.8 46.8 0.35 (25) 0.94 0.33 -0.27 0.67 0.06 (0)

92.2 65.1 69.3 37.6 1.17 1.85 0.51 0.60 -0.11 0.29 0.35 0.11

(=) 0.85 0.15 (0) 0.85 0.15

-. --

(0)

5.2 4.2 X 0.30 0 0.26 0.74 0 0.14 0.74

152 61 40 z 0.22 0 0.20 0.80 0 0.10 0.80

it is convenient to use inspired and alveolar P in conjunction with alveolar ventilation (see above). In avian lungs the situation is much more complex, Pi and Pe probably changing from inspiration to expiration, and effective parabron~hial ii being a highly elusive quantity. Pa may be affected by venous admixture in all gas exchange organs. In mammals pulmonary capillary blood flow in connection with end-capillary P may be used (see above). (2) Vuriabiiity of‘,& For both CO2 and O2 in blood, fl is not constant, i.e. not independent of P, and this is also the case for &oz in sea water. Use of ‘mean’ p values inevitably leads to errors of varied magnitude. In order to overcome, in part, these difficulties, inspired gas mixtures have been used in the experiments on hens and dogs that allowed operation in a partial pressure range in which the dissociation curves for 0, and CO, are close to linear. However, the G,,,, and Gperf values obtained for these conditions are expected to deviate from normal values. An advantage of using hypoxic mixtures is that, due to the greater slope of the 0, dissociation curve, the effects of functional inhomogeneities on O2 transfer are much reduced (see below). (3) Cyctic c~~~ge.~of & and F& Ventilation of lungs and gills is not continuous

GAS TRANSPORT EFFICACY OF GILLS, LUNGS AND SKIN

219

and constant, but cyclic. Neglect of oscillations in flow necessarily leads to increased ineffeciency when compared to constant flow, and this increased inefficiency may falsely be attributed to low Gnifr. The same applies, although to a lesser extent, to blood flow. (4) Functionul inhonzogeneity. The effects of inhomogeneity ( = unequal distribution of ir,, Qj, and D) in reducing gas exchange efficiency in alveolar lungs are well known. The effects of inhomogeneities in other systems can be shown to be qualitatively similar, also leading to reduced efficiency. If the inhomogeneities are neglected, their effects appear as a reduction of the calculated Gdim i.e. the inefficiency is again falsely attributed to inefftcient diffusion properties. (5) ~e~~zing qf Gdiff (=D). All resistance to transfer between medium and capillary blood is attributed to resistance in a ‘membrane’. In reality diffusion resistance in medium and blood and the slowness of reaction of O2 with hemoglobin and the slowness of the various complex reactions involved in liberation of CO2 from blood may also be rate-limiting, particularly at the low temperatures encountered in gas exchange organs of poikilothermic vertebrates. Thus there are several reasons for considering even a partially corrected Gdirr value as a minimum value for diffusive conductance.

GAS EXCHANGE

LIMITATIONS DERIVING

FROM LlMlTATlONS OF THE GAS EXCHANGE

SYSTEM It has been shown that the gas exchange efficacy, expressed as G,,, at given G,,,, G perf and Gdiff, is generally highest for the counter-current system, followed, in sequence, by the cross-current and the ventilated pool systems. It could be argued that the phylogenetic development of the different gas exchange organs in different groups of vertebrates was a functional adaptation to the needs in their different environments. Thus it could be supposed that a cross-current system would not be efficient enough to allow fish to survive as diffusion resistance in water imposes a considerable resistance to diffusion (Scheid and Piiper, 1971). However, when actual values of G,,,,. (table 1 with fig. 4) are compared with respective maximum values, it becomes evident that in most cases the actual efficiency is much below the maximum value due to mismatching of the values for the conductances. This would mean that full advantage is not being taken of the capabilities of a given gas exchange system. On the other hand, as can be seen from fig. 4, the differences in efficiency of the systems blur increasingly as their efficiency deviates from the maximum value. It may therefore be asked, to what extent could the gas exchange in the lungs of the bird or the mammal of table 1 be increased by replacing their lung system by the counter-current system. This question may be answered by calculating the relative increase in G,,,, Agtot, that leads from the value in the actual system, GJact), to that in a counter-current system, G,,,(CC), operating at the same values of G,,,,, Gperf: and G,i,,:

220

J. PIIPER

(17)

&to, =

Gdact)-

AND P. SCHEID

G,,(CC)

GSCC)

Using eq. (14) this can be written as: (18)

Ag,o, =

Ap,&act)Apperr(CC) A~perr(CC)

Table 2 contains Ag,,, for both CO, and O2 for the species listed in table 1. It can be seen that the bird of table 1, having a counter-current rather than a crosscurrent lung, would increase CO, output and O2 uptake by 9 and 12x, respectively. Similarly the dog of table 1 would increase CO2 and O2 exchange by 11 and 27x, respectively, in case its alveolar lung would be replaced by a counter-current system. TABLE Comparison

of gas exchange

in actual

A&,>,

system with that of a counter-current

Cross-current:

Ventilated

domestic

dog

co, Agv,,, (%)

2

1.09 12

hen

02 1.12 64

co2 1.17 25

system. See text.

pool:

0, 1.27 57

We can now ask whether this increase in total conductance could be gained rather by a better matching of the conductance values of the actual system than by the fictitious change into a counter-current system. Since Lven, is generally most pronounced for both O2 and COz, an increase in G,,,, should have marked effects on increasing G,,,. Table.2 presents the relative increase in G,,,,, AgVent,that would result in the same relative increase in Gtot as did the transition to the countercurrent system. It can be seen that for both bird and mammal an increase of ventilation by about 50% would make up for the inherent imperfection of the actual gas exchange system compared with the counter-current system. Conclusion

Although the gas exchange systems of vertebrates can be arranged into an order of increasing efficiency, the actual values of the efficiency depend to a large degree on the values of ventilation, perfusion and diffusion conductances. At experimental values of these parameters, G,,,, in most cases is substantially less than its maximum possible value (i.e. predicted for Gdiff= a). This deviation can either be attributed to diffusion limitation, described by finite Gdirr, or to the effects of functional inhomogeneities in the gas exchange organ. The problems that arise when attempting to distinguish between these two possibilities are well known for

GAS TRANSPORT

EFFICACY

OF GILLS,

LUNGS

221

AND SKIN

mammalian lungs and are expected to be qualitatively similar for other gas exchange organs. In any case, the differences in efficiency between the various vertebrates studied are small for experimental conditions under which the experiments reported here were conducted. At the moment it is not known whether the efficiency values rise in extreme physiological conditions (exercise, high altitude flight, etc.) so that the differences due to the type of the gas exchange organs become more accentuated and eventually allow us to understand why a particular type has been adopted by a particular group. References Baumgarten-Schumann,

D. and J. Piiper stellaris).

dogfish (Scyliorhinus Gatz,

R. N., E. C. Crawford, exclusively

Haab,

Jr. and

skin-breathing

(1968). J. Piiper

salamander

P., G. Due, R. Stuki and J. Piiper

diffusion

pour I’oxygene

Piiper,

(Scyliorhinus

J., P. Dejours,

physiology.

stellaris).

P. Haab

Respir. Physiol.

Piiper.

J., R. N. Gatz

Scheid,

(1968).

Scheid,

(1970).

Kinetics

of inert

,fuscus) (in

Les echanges

gas

equilibration

in an

preparation.for Respir. Physiol.).

gazeux

en hypoxie

et la capacite

de

He/u. Physiol. Acta 22: 203-227.

Effectiveness

of 0,

and CO,

exchange

in the gills of

(1971).

Concepts

and basic quantities

in gas exchange

gas transfer

efficacy of models

for fish gills. avian

lungs and

14: 115-124. Jr. (1975).

(Desmognathusfuscus) Analysis

Gas transport

characteristics

in an exclusively

(in preparation).

of gas exchange

in the avian

lung:

theory

and experiments

fowl. Respir. Physiol. 9: 246-262.

P. and J. Piiper (1971).

through

unanesthetized

13: 292-304.

and E. C. Crawford,

salamander

P. and J. Piiper

in the domestic

(1964).

and H. Rahn

lungs. Respir. Physiol.

skin-breathing

in the gills of resting

Respir. Physiol. 5: 338-349.

Piiper, J. and P. Scheid (1972). Maximum mammalian

(1975).

(Desmognarhus

chez le chien narcotisi.

Piiper, J. and D. Baumgarten-Schumann the dogfish

Gas exchange

Respir. Physiol. 5: 3 177325.

Theoretical

fish gills. Respir. Physiol.

analysis

13: 3055318.

of respiratory

gas equilibration

in water

passing