Effective and Morphometric Oxygen-Diffusing Capacity of the Gills of the Elasmobranch Scyliorhinus Stellaris

There is a distinct discrepancy in fish between the effective conductance (diffusing capacity or transfer factor) for gill O₂ exchange as determined by physiological methods and morphometric measurements of gill secondary lamellae (cf. Hughes, 1972). One reason for the physiological estimates being lower than the morphometric has been claimed to be the diffusion resistance offered by the water passing through the interlamellar space (Scheid & Piiper, 1971; Hills & Hughes, 1970). The first attempt at a comparison of the effective, physiological conductance for O₂ (D_eff) with morphometric measurements that accounted for resistance in water showed a reasonable agreement between D_eff and preliminary morphometric data for the gills in the elasmobranch Scyliorhinus stellaris (Scheid & Piiper, 1976).

Recently, the morphometric gill data of the same species have been reanalysed and completed, with particular attention paid to corrections for shrinkage and for optical artefacts (Hughes, Perry & Piiper, 1986). The aim of this study is to compare diffusing capacity for O₂ derived from this newer set of morphometric data with D_eff calculated from physiological measurements in the same species both at rest and during swimming activity (Baumgarten-Schumann & Piiper, 1968; Puper & Baumgarten-Schumann, 1968b; Piiper, Meyer, Worth & Willmer, 1977). This comparison is based on the approach used in the previous study (Scheid & Piiper, 1976).

A hypothetical profile across a secondary lamella and the adjacent interlamellar water space is schematically shown in Fig. 1, which is based on the morphometry of Hughes et al. (1986). The profile results from the resistances to O₂ diffusion, in interlamellar water and in the tissue barrier, and to the O₂ uptake resistance offered by the blood. Since the diffusivity of O₂ in water is about twice that in tissue (in terms of both Krogh’s diffusion constant, K, and diffusion coefficient, d = K/ α; where α is the solubility of O₂) but the maximum diffusion pathway in water, equal to one-half the interlamellar distance (b), is about five times the thickness of the water-blood tissue barrier (s), an appreciable part of the total O₂ pressure drop is expected to reside within the interlamellar water.

An attempt will be made to estimate the relative magnitudes of the resistances to O₂ diffusion in interlamellar water and across the water-blood barrier and to compare their sum with in vivo measurements of branchial O₂ transfer. In accordance with customary usage, the reciprocal of O₂ diffusion resistance, i.e. the O₂ conductance or O₂-diffusing capacity, will be used as the characteristic parameter. In particular, we intend to compare the ‘membrane’ 02-diffusing capacity (D_m) with that of interlamellar water (D_w) and both of these with the effective diffusing capacity (D_eff), which includes both components, tissue barrier (‘membrane’) and water.

Calculations are based on measurements of ventilation and gas exchange in Scyliorhinus stellaris at rest and during exercise. In the experiments of Baumgarten-Schumann & Piiper (1968), the animals were quiescently resting; i.e. although awake and unanaesthetized, their metabolic rate was probably close to basal. In the more recent experiments of Piiper et al. (1977) the same species was investigated in conditions of spontaneous periodic swimming and resting periods between swimming bouts. These resting periods can be regarded as a state of alertness, the metabolic rate being above basal. Table 1 shows ventilation and O₂ uptake for these series.

The measurements of Hughes et al. (1986) were used, which were obtained on 12 specimens of Scyliorhinus stellaris with body mass ranging from 0·58 to 2·62 kg. From linear regressions of the logarithms of the morphometric variables against the logarithm of body mass the values for fish of 2·18 and of 2·53 kg, corresponding to the mean body mass of the fish used in physiological measurements (Table 1), were obtained.

The morphometric values required for this study, corrected for shrinkage as well as for the slant and Holmes effects (both due to non-perpendicular sectioning) are presented in Table 2, which also lists the magnitudes of the corrections.

The effective O₂-diffusion conductance of any gas exchange system can be obtained as the ratio of O₂ uptake and mean difference between medium, e.g. water, and blood (cf. Piiper & Scheid, 1975). In Table 1 the effective diffusing capacity (= transfer factor) for O₂ (D_eff) was calculated from experimental data of O₂ uptake and of in inspired water (PI), expired water (PE), mixed venous blood (Pv) and arterial blood (Pa) using three different methods.

1. divided by the arithmetic mean water —blood difference [i.e. (PI+PE—Pa—Pv)/2] (Randall, Holeton & Stevens, 1967).

2. According to the theory of the counter-current model, assuming all resistance to O₂ diffusion to reside in a membrane separating blood and water, and the blood O₂ dissociation curve to be linear (Scheid & Piiper, 1976).

3. The same as method 2, but using the blood O₂-dissociation curve and a graphical Bohr integration technique adjusted to the counter-current model (Puper & Baumgarten-Schumann, 1968b ; cf. Piiper & Scheid, 1984).

Since method 3 is the most accurate in theory, the D_eff values based on this method are used in the present study. The method is shown diagramatically in Fig. 2. D_eff is calculated as

Evidently equation 1 defines a mean Pw—Pb (= Ṁ/D_eff) as a harmonic mean. The same applies to method 2, whereas method 1 uses an arithmetic mean.

The mean D_eff values thus obtained are presented in Table 1.

Unfortunately, no experimental data exist for d, α or K of secondary lamellar tissue for O₂. We adopted the value for human lung tissue (Grote, 1967) extrapolated to 17 and 18·3°C, the average water temperature in the experiments (Table 1). These values are listed in Table 3.

The values for D_m thus calculated from equation 2 are listed in Table 2.

Fig. 3 illustrates the relationship between ε and φ according to model B of Scheid & Piiper (1971) in which water flow is laminar in the interlamellar space (parabolic velocity distribution across the secondary lamellar space). These two curves represent limiting cases of lamellar shape as expressed by the base-to-top taper index, λ, i.e. the ratio of lamellar length at the top to that at the base. For λ = 1·0 (rectangular secondary lamella) the water velocity is independent of the height, whereas there is a hyperbolic flow distribution for λ = 0·5, accounting for the smaller resistance to water flow at the shorter top compared with the bottom.

Using these values for φ, and a mean taper index of λ = 0·75 (Table 4), the corresponding values for the equilibration inefficiency, E, can be obtained from Fig. 3. They are listed in Table 4.

The inefficiency parameter, E, has the meaning of a fractional effective water shunt: it defines what fraction of the respiratory water may be considered as shunted (because the value is unchanged) when the remainder is assumed to equilibrate completely with the secondary lamellae. Scheid & Piiper (1971) have used E to calculate the effective diffusing capacity of interlamellar water, D_w. The equivalent model used for this analysis is shown in Fig. 4B, in which the continuously distributed water velocity of the laminar flow model is replaced by a model with a stagnant water layer lining the secondary lamellar surface and a central core of mixed flow. In this model the central core equilibrates with the wall according to the equation:

The values of D_eff (Table 1), D_m (Table 2) and D_w (Table 4) are compiled and compared in Table 5.

The ratio D_m/D_w is higher than unity, implying that the limitation to O₂ diffusion is greater in interlamellar water than in the water-blood tissue barrier.

In two previous studies on resting fish (Baumgarten-Schumann & Piiper, 1968; Piiper et al. 1977), there were important differences in the conditions under which relevant measurements (e.g. of ventilation) were made. In the former study, the fish were in a prolonged state of inactivity, whereas the animals in the latter study were alert, the relatively short resting periods (averaging about 30 min) being interrupted by spontaneous swimming periods. This is evident from the marked differences in both ventilation and O₂ uptake. Such an increase in D_eff may in part be due to increased water velocity in the interlamellar space, with an associated increase in water diffusing capacity, D_w (see below). On the other hand, it is conceivable that in the resting quiescent condition the full capacity of the gill apparatus is not used, because there is ample functional shunting. This hypothesis is supported by the observations of rapidly changing arterial in some fish, apparently reflecting changing functional inhomogeneity (Piiper & Schumann, 1967).

The present analysis shows, in agreement with the previous study (Scheid & Piiper, 1976), that the resistance to O₂ diffusion in interlamellar water plays an important role in limiting branchial O₂ transfer, both at rest and during swimming activity.

The relative roles of diffusion in interlamellar water and across the water-blood barrier depend on the diffusion distances (Fig. 1) and the diffusion properties of the media. For a first approximation, the average path length for lateral diffusion of O₂ molecules in the interlamellar space may be taken as b/2, and that across the water-blood barrier as s. For Scyliorhinus stellaris the b/2: s ratio is between 2·7 and 3 (Table 2). The ratio of the assumed Krogh diffusion constant for tissue—water (Table 3) is between 0·55 and 0·53. Thus the estimated water/tissue diffusion resistance ratio, corresponding to the D_m/D_w ratio, is expected to be between 1·5 and 1·6, which is in reasonable agreement with the calculated results of Table 5.

The mean diffusion path length decreases with increasing water velocity, because gas exchange becomes restricted to layers close to the secondary lamellar surface. This is why D_w increases and the equivalent stagnant water layer decreases with increasing water flow (Table 5). The exact quantitative relationships are influenced by the flow velocity profile (Scheid & Piiper, 1971).

For the quiescently resting fish, the total morphometric diffusing capacity (D_morph), estimated by the combined membrane-and-water diffusing capacity (D_m+w), is considerably above the effective, physiological diffusing capacity, D_eff. This result, which is in qualitative agreement with the earlier analysis of Scheid & Piiper (1976), is not unexpected since in most reported cases D_morph has been found to be considerably higher, even by an order of magnitude, than the D_eff. This has been repeatedly documented for mammalian lungs (reviewed by Weibel, 1973), but also for reptilian lungs (Perry, 1978) and for avian lungs (Abdalla et al. 1982). Only for the skin of a lungless plethodontid salamander (Piiper, Gatz & Crawford, 1976) and for the pleural membrane of dog lungs (Magnussen, Perry, Willmer & Piiper, 1974) has a reasonable agreement been found. But also in these cases, D_morph was slightly higher than D_eff.

The conventional explanation for D_morph /D_eff>l is that the numerous parallel units in the gas exchange organ are inhomogeneous with respect to ventilation, diffusion and perfusion, which, unless properly accounted for, leads to an underestimation of D_eff. For example, in mammalian lungs, D for O₂ is determined from alveolar-arterial differences; since these are also generated by shunt and unequal distribution of ventilation to perfusion, D for O₂ is underestimated if no appropriate corrections are applied (see Piiper & Scheid, 1980).

For fish gills, there is ample possibility of ventilation-perfusion inhomogeneity due to both morphological and functional factors. Extreme cases are blood shunting (e.g. due to perfusion of intrafilamentary afferent-efferent arterial connections or to perfusion of unventilated lamellae) and water shunting (due to passage of water between rows of secondary lamellae or between tips of filaments). Moreover, part of the O₂ uptake resistance may reside in the blood (diffusion limitation; reaction limitation due to slow oxygenation of haemoglobin).

Whereas the finding that D_m+w/D_eff>l for the quiescently resting fish thus appears to be readily explained, it was unexpected to find a close agreement between D_m+w and D_eff for resting and swimming fish. This would call for a critical examination of all the methods, including morphometric techniques, physical properties, models and physiological measurements, for directional errors potentially leading to an overestimation of D_eff or to an underestimation of D_morph.

One of the basic problems in morphometry is deformation, due in great part to shrinkage and to the finite sectioning thickness. Hughes et al. (1986) have presented a detailed account of the procedures for morphometry and the determination of factors for corrections for deformation (see Table 2).

D_m is proportional to A/s, thus the correction factor is 1·30/1·13 = 1·15. This means that without correction, D_m is underestimated by (1 —1/1·15)× 100 = 13%.

The effects of shrinkage on D_w are more complex. According to equation 4 the anatomical dimensions determining φ are the interlamellar distance (2b) and the length of the secondary lamellae (l), φ being proportional to b²/l. With the correction factors from Table 2 this yields a combined correction factor for φ of 1·15. Thus shrinkage appears to lead to underestimation of φ and ε, and thus to overestimation of D_w.

It is evident from equation 11 that not only the extent, but even more the anisotropy of the shrinkage, i.e. different functional shrinkage of b, h and l, play an important role in influencing the conditions for O₂ diffusion in terms of D_w.

There are only few reports in the literature on measurements of the O₂ diffusion coefficient, d, or of the Krogh diffusion constant for O₂, K (=d× α), in tissues (see Bartels, 1971). Most authors have used the values of Krogh (1918/19) and of Thews & Grote (see Grote, 1967).

There are no measurements on fish gill tissue. We used the values obtained by Grote (1967) on rat lung tissue mainly because they appear to be derived from the most reliable determinations. Not only may the true value for fish gills be different, but also in calculations of D_m for lungs it must be considered that the measurements were performed on slices of degassed whole lung tissue, only a small fraction of which constitutes the gas-blood barrier. A promising approach is determination of D_m from oxygenation and deoxygenation kinetics of red cells in isolated secondary lamellae of fish gills (Hills, Hughes & Koyama, 1982). At present, nothing can be predicted concerning the direction or extent of errors due to the uncertainty about O₂ diffusivity.

For this reason, i.e. lack of reliable data on physical diffusion properties, it appears to be generally preferable to express the results of morphometric studies on mediumblood barrier for gas exchange in terms of the surface area/mean harmonic thickness ratio (A/s; dimension : length) - the ‘anatomical diffusion factor’ of Perry (1978). The value can then be used for functional estimates in conjunction with the appropriate K value, of which more accurate determinations will be available in the future. In addition, the previously reported values for O₂ diffusivity in water are rather unreliable (see Bartels, 1971).

The flat sheet model for calculation of D_m is rather straightforward. But problems arise from making appropriate allowance for the pillar cells, which support the secondary lamellae and reduce the surface area available for gas exchange.

More critical are the assumptions for calculation of D_w. Unfortunately, the required morphometric measurements in large Scyliorhinus stellaris are very limited (Hughes et al. 1986). Moreover, the parabolic flow velocity profile, assumed in the model analysis, may not be fully developed in the interlamellar space. A square-front flow would be more efficient for gas exchange and would therefore yield higher D_w values (Scheid & Piiper, 1971).

Transversal mixing of interlamellar water would greatly increase gas exchange efficiency by reducing the gradient in water (see Fig. 1). However, the flow in the interlamellar space is expected to be fully laminar on the basis of low Reynolds numbers (estimated range 0·1–0·4). But the splitting of flow upon entering the interlamellar spaces may give rise to some transverse mixing which could elevate the O₂ transport efficiency.

The simplified model for isolated quantification of diffusion resistance in interlamellar water (Scheid & Piiper, 1971) does not take into account the change of in secondary lamellar blood, which in reality increases from the mixed venous to the arterial value. Instead, the lamellar is assumed to be constant throughout (Po in equation 3 and Fig. 4). Therefore, the simple additive combination of D_w with D_m, yielding D_m+w (equation 10), and comparison with D derived from a model that accounts for changing in intralamellar blood is clearly incorrect because the models are not consistent. However, a recent theoretical study shows that the error produced by this apparent incompatibility is relatively minor (Scheid, Hook & Piiper, 1986).

We conclude that resistance to O₂ diffusion in the interlamellar water (1/D_W) exceeds that of the secondary lamellar tissue membrane (1/D_m) and that this is particularly pronounced at rest. When comparing morphometric with physiological estimates of the diffusing capacity, the good agreement between the D_eff and D_m+w values may be interpreted to show that the methods and models used are appropriate. On the other hand, local variations of physiological quantities like ventilation, diffusing capacity and blood flow, in part resulting from morphometric inhomogeneity, are expected to reduce gas exchange efficiency, i.e. to decrease D_eff. Possibly some inhomogeneity effects were compensated by physiological control mechanisms. In any case, there seemed to be little space for mechanisms reducing O₂ transfer efficiency, such as blood or water shunts.