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J Appl Physiol 99: 2173-2180, 2005. First published July 28, 2005; doi:10.1152/japplphysiol.00470.2005
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Krogh’s diffusion coefficient for oxygen in isolated Xenopus skeletal muscle fibers and rat myocardial trabeculae at maximum rates of oxygen consumption

Willem J. van der Laarse,1 Ariane L. des Tombe,1 Brechje J. van Beek-Harmsen,1 Marleen B. E. Lee-de Groot,1 and Richard T. Jaspers2

1Department of Physiology, Institute for Cardiovascular Research, VU University Medical Center, and 2Institute for Fundamental and Clinical Human Movement Sciences, Vrije Universiteit, Amsterdam, The Netherlands

Submitted 25 April 2005 ; accepted in final form 22 July 2005


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The value of the diffusion coefficient for oxygen in muscle is uncertain. The diffusion coefficient is important because it is a determinant of the extracellular oxygen tension at which the core of muscle fibers becomes anoxic (Po2crit). Anoxic cores in muscle fibers impair muscular function and may limit adaptation of muscle cells to increased load and/or activity. We used Hill’s diffusion equations to determine Krogh’s diffusion coefficient (D{alpha}) for oxygen in single skeletal muscle fibers from Xenopus laevis at 20°C (n = 6) and in myocardial trabeculae from the rat at 37°C (n = 9). The trabeculae were dissected from the right ventricular myocardium of control (n = 4) and monocrotaline-treated, pulmonary hypertensive rats (n = 5). The cross-sectional area of the preparations, the maximum rate of oxygen consumption (O2 max), and PO2crit were determined. D{alpha} increased in the following order: Xenopus muscle fibers D{alpha} = 1.23 nM·mm2·mmHg–1·s–1 (SD 0.12), control rat trabeculae D{alpha} = 2.29 nM·mm2·mmHg–1·s–1 (SD 0.24) (P = 0.0012 vs. Xenopus), and hypertrophied rat trabeculae D{alpha} = 6.0 nM·mm2·mmHg–1·s–1 (SD 2.8) (P = 0.039 vs. control rat trabeculae). D{alpha} increased with extracellular space in the preparation (Spearman’s rank correlation coefficient = 0.92, P < 0.001). The values for D{alpha} indicate that Xenopus muscle fibers cannot reach O2 max in vivo because PO2crit can be higher than arterial PO2 and that hypertrophied rat cardiomyocytes can become hypoxic at the maximum heart rate.

heart muscle; critical oxygen tension; maximum rate of oxygen consumption

THE ENERGY SOURCE FOR MUSCLE contraction and relaxation is ATP. Most ATP in heart and skeletal muscle cells is produced by oxidative phosphorylation. Muscle performance, especially in heart and respiratory muscles, is critically dependent on continuous oxygen supply. The required rate of oxygen supply to muscle mitochondria can be maintained only when the oxygen tension outside muscle cells is kept above a critical value (17, 30, 39, 40).

According to Hill (16), the extracellular PO2 at which the core of a cylindrical cell becomes anoxic (PO2crit) at themaximum rate of oxygen consumption (O2 max; in nmol·mm–3·s–1) is given by:

(1)
where CSA is the cross-sectional area of the cell (mm2), D is the diffusion coefficient for oxygen in the muscle cell (mm2/s), and {alpha} is the solubility of oxygen in the muscle cell (mM/mmHg). D{alpha} is known as Krogh’s diffusion coefficient. Using Eq. 1 and literature values for D{alpha}, we have previously calculated from the CSA and the oxidative capacity that PO2crit equals 14 Torr (SD 7) for different muscle cells of rodents and frogs, whose CSA and O2 max varied about hundredfold (44). In normal human skeletal muscle, PO2crit was 29 Torr (SD 12), and, in patients suffering from chronic heart failure, New York Heart Association class III, PO2crit was significantly lower: 13 Torr (SD 2) (5). These values are between the half-saturation value of blood with oxygen (12, 37) and close to the predicted end-capillary venous PO2 during maximum exercise (36), including the patients with chronic heart failure (20), indicating that oxygen supply and demand are closely matched. The calculated PO2crit values given above are upper values because myoglobin-facilitated oxygen diffusion (46) is not taken into account. Myoglobin knockout mice are viable but demonstrate several adaptations to prevent cellular hypoxia (14, 31). It has been calculated previously that myoglobin can decrease PO2crit of different mammalian muscle cells by 18–60% (15, 42).

Equation 1 allows potentially useful predictions of metabolic consequences of muscle adaptation to increased load or contractile activity and of muscle adaptations to reduced oxygen supply, e.g., when the CSA of cardiomyocytes increases and the capillary density in the heart decreases due to chronic hypertension. We have shown recently that cytochrome c can be released from the mitochondria into the cytosol in pressure-overloaded rat myocardium (43). Validation of Eq. 1 is a requirement to test the hypothesis that cytochrome c release is due to the development of hypoxic cores.

Equation 1 is based on the following assumptions: 1) the cross section of the fiber is a circle, and oxygen diffuses in the radial direction only; 2) oxygen consumption (O2) is distributed homogeneously in the cells; 3) O2 by mitochondria is independent of local intracellular PO2; and 4) myoglobin-facilitated oxygen diffusion is negligible. According to Eq. 1, the value of PO2crit is inversely related to D{alpha}, which is usually determined in whole muscle at rest, not inside contracting muscle cells at O2 max. D{alpha} may depend on fat content, extracellular space, and unknown factors (2, 9, 19).

The aim of the present experiments was to validate Eq. 1 and to determine D{alpha} at O2 max under conditions in which myoglobin-facilitated oxygen diffusion is negligible and in muscle preparations of different composition. This was done by determination of PO2crit, O2 max, and the CSA of isolated single skeletal muscle fibers of Xenopus and of control and hypertrophied rat myocardial trabeculae in which extracellular space varied.


   MATERIALS AND METHODS
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 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Animals and preparations.   The local Animal Experimental Commission approved the experiments, which were conducted according to the guidelines stipulated by the American Physiological Society on the use of experimental animals. Xenopus laevis females (body length ~10 cm) were cooled on ice and killed by decapitation. The heads were immediately frozen in liquid nitrogen to end electrical activity in the brain and freeze-dried before they were discarded. The iliofibularis muscle was dissected and placed in oxygenated Ringer solution (in mM: 116.5 NaCl, 2.0 KCl, 1.9 CaCl2, 2 Na2HPO4, 0.1 EGTA; pH 7.2). After recovery, the muscle was transferred to a dissection trough, and single, high-oxidative type 2 or 3 fibers were isolated by using small forceps and scissors under dark-field illumination (25). Small rings, made from 50-µm-diameter platinum wire, were tied to the tendons using 20-µm nylon thread. The fibers were dissected 1 day before the experiment and were kept overnight at 7°C.

Male Wistar rats, body weight 200–300 g, were used. Five rats were injected subcutaneously with 40 mg monocrotaline/kg body wt, when body weight was 170–190 g, to induce pulmonary hypertension and myocardial fibrosis (18, 26). The rats were used 3–4 wk after the injection, when body weight was decreasing by ~2%/day. The rats were anesthetized with ether, and the hearts were excised and perfused with Tyrode solution (in mM: 120 NaCl, 5 KCl, 1.2 MgSO4, 2 Na2HPO4, 27 NaHCO3, 1 CaCl2, 10 glucose, and 20 butanedione monoxime, equilibrated with 5% CO2–95% O2, pH 7.2–7.3 at 10°C). Starting in the pulmonary artery, the right ventricle was carefully opened, and a 1.5- to 3-mm long trabecula without side branches was isolated. Small hooks with rings were tied to the ends as described above.

O2 and force measurements.   The preparation was transferred to a glass chamber, volume 170 µl, as described in detail previously (11). One end of the preparation is hooked to the pivot of a spinner, located at the bottom of the chamber, and the other end is hooked to a tungsten wire, which leaves the chamber through a capillary and is suspended from a force transducer (AE 801, SensoNor, Horten, Norway). The spinner circulates the solution in the chamber; the response time (95%) of the system is ~4 s. After mounting of the preparations in the chamber, the Ringer solution used for dissection of Xenopus fibers was replaced by bicarbonate-buffered Ringer solution (in mM: 100 NaCl, 20 NaHCO3, 2.0 KCl, 1.9 CaCl2, 0.1 EGTA, equilibrated with mixtures of 5% CO2 in N2 and 5% CO2 in O2, to adjust PO2 in the chamber and keep CO2 at 5%; pH = 7.2). The Tyrode solution used for dissection of myocardial trabeculae was replaced by the Tyrode solution given above without butanedione monoxime, but with 2 mM CaCl2, and equilibrated with the same gas mixture described above to adjust the PO2 in the chamber. Equilibration with different gas mixtures was done at the experimental temperatures: 20°C for Xenopus and 37°C for rat trabeculae. The solutions were exchanged between each series of contractions using a syringe pump to flush the chamber. PO2 in the chamber was determined with a polarographic oxygen electrode, which was constructed following the design of Kimmich and Kreuzer (21). The sensitivity of the oxygen electrode was determined by pumping Ringer or Tyrode solution with known oxygen concentrations through the chamber. Solubilities of oxygen in Ringer solution at 20°C of 30.15 ml/l and in Tyrode solution at 37°C of 22.73 ml/l were used in the calculations (3). The dark current of the oxygen electrode was determined after the experiment in 5% CO2 in N2. The preparations were stimulated by end-to-end stimulation with squarewave pulses, with duration 0.4 ms and 30% above threshold. After mounting, the preparations were stimulated at 0.2 Hz and were stretched to optimum length (i.e., the length at which twitch force was maximal). Then three or four experiments were conducted at high PO2 in the chamber to determine the twitch frequency at which the Xenopus fibers reach O2 max and to determine the highest PO2 in the chamber at which O2 max could not be reached anymore. Stimulus trains lasted 4 min to prevent fatigue (35, 45). Starting PO2 values were lowered by 10–30 Torr for each following a series of twitches. PO2crit was calculated as the mean of the lowest PO2 at which O2 max was reached and the highest PO2 at which O2 max could not be reached.

Rat trabeculae were stimulated at 10 Hz, which corresponds to the maximum heart rate in rats (23) and is usually the highest rate possible without activation failure in vitro. PO2crit was determined in the same way as for Xenopus muscle fibers, but starting PO2 values were reduced by ~100 Torr for the next series.

Time between stimulus trains was 20–30 min in all cases. After the last series of hypoxic contractions, PO2 was raised to the initial hyperoxic value, to check the stability of the preparation. Force and PO2 signals were analog-to-digital converted and sampled by a computer at 1,000 and 1 Hz, respectively.

After the O2 measurements, the length of the preparation in the experimental chamber and the diameters of the preparation were measured under a microscope using an ocular scale. The smaller and larger diameters were measured at x100 magnification at three different places along the length by rotating the preparation along the longitudinal axis. The CSA and the volume of the preparation were calculated, assuming an elliptical cross section. Force was normalized by the CSA and O2 by the volume of the preparation.

O2 of the preparation was calculated from the decrease of the oxygen tension in the chamber. A second-order polynomial function was used to correct for oxygen loss from the chamber when the preparation was not stimulated. The parameters of the equation of the baseline were determined from oxygen decay in the chamber before the stimulation period and after the recovery period (11). After correction of oxygen loss from the chamber, O2 of the preparation was determined from the slope of the curve determined by linear regression on measurements taken during the last 2 min of the 4-min stimulation period. Oxygen loss from the chamber without a preparation for PO2 between 300 and 700 Torr was 30.7 ± 3.0 (SE)·PO2 fmol/s at 37°C, where SE denotes standard error (r = 0.85, P < 0.0001). At lower PO2 values, oxygen disappears from the chamber mainly due to consumption by the oxygen electrode (0.6–0.9 pmol/s at 121 Torr and 20°C). At subatmospheric PO2 values required for experiments with Xenopus muscle fibers, oxygen could leak into the chamber. In such cases, the mean of the change in oxygen tension before and after the stimulation period was used to correct O2.

Distribution of mitochondria and extracellular space.   After the O2 measurements, the preparations were embedded in 15% gelatin in dissection solution, pH 7.2, and frozen in liquid N2. Cryostat sections were cut and incubated for succinate dehydrogenase activity in a medium consisting of 37.5 mM sodium phosphate buffer, pH 7.6, 75 mM sodium succinate, 0.4 mM tetranitroblue tetrazolium, and 5 mM Na3N, as described previously (Xenopus: 16-µm-thick sections for 45 min at 20°C, Ref. 45; rat trabeculae: 5-µm-thick sections for 7 min at 37°C, Ref. 8). The relationship between O2 at 10 Hz and the succinate dehydrogenase activity of the control trabeculae has been described elsewhere (8). The preparations were used to determine the mitochondrial distribution in the muscle fibers and to determine extracellular space in the trabeculae. Extracellular space was determined by using a microscope densitometer (26) and the threshold option in NIH Image to produce a binary image of the preparation. The mean gray value of the image is used to calculated extracellular space. This rapid procedure yields the same results as manual image editing used previously (compare with Fig. 3, A, C, F, and H in Ref. 8). Extracellular space included endothelial cells, fibroblasts, and leukocytes in the trabeculae.



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  		Fig. 3. Paired determinations of O2 (A–C) and force production (D–F) of a hypertrophied rat trabecula at 10 Hz and 37°C. A and D, and B and E: experiments under hyperoxic conditions at different starting PO2. C and F: experiment in hypoxia. This trabecula was also stimulated at a starting PO2 of 300 Torr and reached critical PO2 (PO2crit) during the stimulus train, indicated by a decrease of O2 during the last minute of the stimulus train (not shown). The trabecula started to contract spontaneously (at 3 Hz) when PO2 in the chamber decreased <204 Torr. See legend to Fig. 1 for details.

 
Calculation of D{alpha}.   D{alpha} for oxygen was calculated by using an equation similar to the one in the Introduction, derived for preparations with an elliptical cross section (16):

(2)
where l and m are the larger and the smaller diameter of the preparation, respectively. For clarity, we define a shape factor b as the ratio of larger and smaller diameter, b {equiv} l/m, and use CSA = {pi}lm/4 = {pi}bm2/4, where CSA is the area of the ellipsoid. Substituting l2 = b2m2 and m2 = 4CSA/{pi}b into equation 2, and rearranging, gives:

(3)
This equation is the same as Eq. 1 when the cross section of the preparation is a circle, i.e., when b = 1.

Statistics.   Unless stated otherwise, values are given as means with standard deviation (SD). Two-sided t-tests with unequal variances were used to determine differences between means. SPSS 9.0 (SPSS, Chicago, IL) was used for multivariate linear regression analysis. P < 0.05 was considered significant.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Figure 1 shows O2 and twitch force production of a Xenopus muscle fiber. Experiments started at high PO2 in the chamber (i.e., 21% oxygen, PO2 = 159 Torr). Starting PO2 was lowered between stimulation periods until a clear drop in the rate of O2 was observed, indicating that oxygen availability is rate limiting. Under hypoxic conditions, the rate of O2 during the stimulation period decreased because PO2 in the chamber decreased. Three type 3 and three type 2 fibers were stimulated at 6 and 4 Hz, respectively. O2 max of type 3 was 0.13 mM/s (SD 0.04), and O2 max of type 2 was 0.058 mM/s (SD 0.014). Both O2 max and force production of the muscle fibers recovered completely after a series of hypoxic twitch contractions.



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  		Fig. 1. Paired determinations of oxygen consumption (O2) (A–C) and force production (D–F) of a single Xenopus type 2 muscle fiber at 4 Hz and 20°C. A and D, and B and E: experiments under hyperoxic conditions at different starting PO2. C and F: experiment at hypoxic PO2. The rate of O2 was calculated from the slope of the tracing of the decay of the oxygen tension in the chamber (scale on left side of panels). The noisy O2 traces are smoothed derivatives of the oxygen tension decay tracings, corrected for oxygen loss from the chamber and normalized by the volume of the preparation (scale on the right side of the panels). Note the O2 decrease during the stimulus train in hypoxia (C). Force was normalized by the cross-sectional area (CSA) of the preparation and was sampled from 30 s before stimulation started until 30 s after the end of stimulation.

 
Comparison of Fig. 1, A and B, and 1C shows that the O2 increase at the onset of the stimulus train was insensitive to hypoxia. Similar results were found for the other Xenopus fibers. These results are in agreement with Kindig et al. (22), who measured intracellular PO2 changes in Xenopus fibers as a function of extracellular PO2.

Figure 2 shows results of a control rat trabecula. Passive force of control trabeculae increased during 10-Hz stimulation under hypoxic conditions (Fig. 2F). The contracture recovered during reoxygenation of the preparation, but, after reoxygenation, active force production of the trabeculae was depressed, whereas O2 at 10 Hz was not changed. O2 at 10 Hz was 0.58 mM/s (SD 0.01) in four control trabeculae when oxygen was not rate limiting.



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  		Fig. 2. Paired determinations of O2 (A–C) and force production (D–F) of a control rat trabecula at 10 Hz and 37°C. A and D, and B and E: experiments under hyperoxic conditions at different starting PO2. C and F: experiment in hypoxia. Note the increase in passive force induced by hypoxia and the decrease of O2 during the stimulus train in hypoxia. See legend to Fig. 1 for details.

 
Figure 3 shows results of a hypertrophied trabecula. O2 at 10 Hz was 0.74 mM/s (SD 0.20) in five hypertrophied trabeculae when oxygen was not rate limiting. Hypertrophied trabeculae did not develop a contracture, despite stimulation-induced hypoxia. O2 at 10 Hz of hypertrophied trabecula was not different from control.

O2 of Xenopus muscle fibers and control trabeculae at rest were below the detection limit, i.e., indistinguishable from the rate of oxygen loss from the chamber without a preparation, but O2 of hypertrophied trabeculae at rest was considerable: 0.43 mM/s (SD 0.17). O2 at rest by hypertrophied trabeculae requires further study.

PO2crit of the preparations was calculated as the mean of the lowest oxygen tension at which the O2 max was reached and the highest oxygen tension at which the maximum rate could not be reached. PO2crit as a function of bO2 max CSA/2{pi} (1 + b2) is shown in Fig. 4. Equation 3 predicts that this relationship is proportional with slope 1/D{alpha}. For Xenopus and control trabeculae similar, proportional relationships are found, indicating that Hill’s diffusion model applies to these preparations. However, hypertrophied trabeculae deviate from these relationships. D{alpha} increased in the order: Xenopus muscle fibers D{alpha} = 1.23 nM·mm2·mmHg–1·s–1 (SD 0.12), control rat trabeculae D{alpha} = 2.29 nM·mm2·mmHg–1·s–1 (SD 0.24) (P = 0.0012 vs. Xenopus), and hypertrophied rat trabeculae D{alpha} = 6.0 nM·mm2·mmHg–1·s–1 (SD 2.8) (P = 0.039 vs. control rat trabeculae). Note that D{alpha} varied considerably in hypertrophied trabeculae.



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  		Fig. 4. The relationship between PO2crit and bO2 max CSA/2{pi}(1 + b2) (see Eq. 3), where b is shape factor, and O2 max is maximum O2. Single Xenopus muscle fibers are shown in both A and B ({blacktriangleup}). Control trabeculae ({blacklozenge}) and hypertrophied trabeculae ({square}) are shown in B. The regression lines are forced through the origin. According to Eq. 3, the slope of the line corresponds to 1/D{alpha}, where D is the diffusion coefficient and {alpha} is the solubility of oxygen. Xenopus: 20°C, rat: 37°C.

 
Effect of extracellular space on D{alpha}.   After the O2 measurements, cross sections were cut from the preparations and incubated for succinate dehydrogenase activity to determine mitochondrial distribution and extracellular space. The images and examples of the analyses are shown in Fig. 5. Succinate dehydrogenase activity was distributed fairly homogeneously in the type 2 and 3 Xenopus fibers selected for the experiments. Extracellular space in control trabeculae is 17.5% (SD 2.7) of the CSA and is significantly (P = 0.04) larger in hypertrophied trabeculae, 30% (SD 10), which confirms fibrosis. Figure 6 shows the relationship between D{alpha} and extracellular space in the preparation. Spearman’s rank correlation coefficient = 0.92 is significant (P < 0.001) also when D{alpha} in Xenopus muscle fibers is corrected for the difference in experimental temperature (see DISCUSSION).



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  		Fig. 5. Images from cross sections of the preparations incubated for succinate dehydrogenase activity used to determine mitochondrial distribution. A Xenopus type 2 muscle fiber (A and D), a control rat trabecula (B and E), and a hypertophied rat trabecula (C and F) are shown. The absorbance at 660 nm (A660) due to succinate dehydrogenase activity along the larger diameter (the line in A) in the Xenopus fiber is shown in D. Binary images (E and F) of the trabeculae shown in B and C, respectively, were used to determine extracellular space. Scale bar = 0.1 mm.

 


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  		Fig. 6. The relationship between Krogh’s diffusion coefficient for oxygen (D{alpha}) and extracellular space in the preparation. Symbols are as defined in Fig. 4 legend.

 
Multivariate linear regression analysis of the nine trabeculae detects two significant, independent determinants of PO2crit (R2 = 0.78, P = 0.011):

(4)
where SE denotes standard error. CSA of the preparations was 0.026 mm2 (SD 0.011; range 0.015–0.046 mm2). O2 of the preparations was 0.67 mM/s (SD 0.16), and the ratio of larger and smaller diameter (b in Eq. 3) was 1.54 (SD 0.40). The variation of the latter two factors was relatively small, and their regression coefficients were not significant.


   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
We have tested a simple model for oxygen diffusion in muscle preparations and used the model to determine values for D{alpha} at O2 max. The results on single muscle fibers and myocardial trabeculae indicate that the model is valid when extracellular space in the preparation is 20% of the volume of the preparation or less.

O2 max of Xenopus type 2 and 3 muscle fibers was similar to the values reported before in phosphate-buffered Ringer solution (45), and O2 at 10 Hz of myocardial trabeculae of the rat under hyperoxic conditions is similar to the rate expected on the basis of mitochondrial enzyme activity (33), when differences between volume densities among dog, pig, and rat are taken into account (1, 4).

For Xenopus, the predicted proportionality of PO2crit and O2 max·CSA is found (the correction factor for deviations from a circular CSA is ignored in this discussion for simplicity), indicating that Hill’s diffusion equation predicts PO2crit in these cells accurately. D{alpha} for Xenopus muscle fibers is 45% smaller than the value for whole frog sartorius muscle at 20°C reported by Mahler et al. (28). This difference can possibly be explained by the effect of extracellular space on D{alpha}, which might have played a role in the experiments of Mahler et al., or other experimental differences, like muscle fiber type (see below). D{alpha} for Xenopus fibers is close to the original value for frog’s abdominal wall reported by Krogh (24), which corresponds to 1.37 nM·mm2·mmHg–1·s–1.

D{alpha} in myocardial trabeculae is larger than D{alpha} in Xenopus muscle fibers. There are several known factors that could explain this difference: myoglobin concentration, experimental temperature, and composition of the preparation, e.g., differences in extracellular space or fat content (6, 9). These factors are discussed briefly below.

Myoglobin-facilitated diffusion.   Myoglobin is undetectable in Xenopus muscle fibers and in Xenopus heart (unpublished observation), whereas it is ~0.25 mM in right ventricular cardiomyocytes of control and monocrotaline-treated, pulmonary hypertensive rats (8). According to a Hill-type diffusion model, which does take myoglobin-facilitated oxygen diffusion into account (32, 34), this concentration can reduce PO2crit of individual control and hypertrophied cardiomyocytes by 25 and 30%, respectively (42). Using the same model and values for the diffusion coefficients of myoglobin, oxygen dissociation constant of myoglobin used by van Beek-Harmsen et al. (42), and the mean parameter values for the present preparations given above, we find for control and hypertrophied trabeculae that myoglobin-facilitated diffusion would reduce PO2crit by <1%. This indicates that myoglobin-facilitated diffusion is negligible in isolated myocardial trabeculae, even when myoglobin could diffuse freely.

According to the model, the cause of the difference between the effect of myoglobin on PO2crit of trabeculae on the one hand and cardiomyocytes on the other is the difference in size. Because PO2crit of trabeculae is high compared with PO2crit of individual cardiomyocytes, myoglobin in trabeculae is saturated with oxygen, except in cardiomyocytes in the core of the trabecula at PO2crit. This agrees with similar conclusions of Loiselle (27) and Dutta et al. (10). We conclude that myoglobin-facilitated diffusion cannot explain the difference between D{alpha} of Xenopus muscle fibers and rat trabeculae.

Temperature.   The effect of temperature on D{alpha} is believed to be small, ~1%/°C, because the D increases with temperature and the {alpha} decreases with temperature (16). The present experiments were carried out at physiological temperature, 20 and 37°C, for Xenopus (29) and rat, respectively. Using the temperature dependency of D{alpha} in frog sartorius muscle (28), the value for D{alpha} of Xenopus at 37°C would be ~10% larger than at 20°C, i.e., 1.35 nM·mm2·mmHg–1·s–1 (SD 0.13), which is still smaller than D{alpha} in control (P = 0.0017) and in hypertrophied trabeculae (P = 0.02). Because the fat content in Xenopus type 2 and 3 fibers is probably larger than the fat content of the Rana sartorius muscle (38), it may be that the temperature dependency of D{alpha} in Rana determined by Mahler et al. (28) does not apply to Xenopus type 2 and 3 fibers (for discussion see Ref. 10). Using the temperature dependency of D{alpha} for hamster retractor muscle, 2.6%/°C (6) D{alpha} for Xenopus type 2 and 3 fibers would be 1.97 nM·mm2·mmHg–1·s–1 (SD 0.19) at 37°C, which is not significantly different from D{alpha} in control trabeculae. Volume density of mitochondria in the hamster retractor muscle, which may be related to the solubility of oxygen in muscle, is 11.4% (41), similar to the volume density of mitochondria in Xenopus type 2 and 3 fibers, 11.1 and 17.4%, respectively (32). The temperature dependency of D{alpha} in Xenopus muscle remains to be determined.

Extracellular space.   The relative volume occupied by cardiomyocytes in hypertrophied trabeculae is smaller than in control trabeculae. Assuming that the diffusion coefficients for oxygen inside normal and hypertrophied cardiomyocytes is the same, the results indicate that extracellular space facilitates oxygen transport in contracting muscle preparations. An increase of D{alpha} with extracellular space can be due to a larger D{alpha} in the extracellular space compared with sarcoplasm: D{alpha} in water is 2.4 times and in 15% gelatin 2 times larger than in muscle (24). It is also a possibility that the extracellular fluid is mixed by the contraction-relaxation cycles. Sarcomeres in trabeculae with fixed ends shorten by ~20% due to series elasticity (7). Because the volume of muscle cells is independent of muscle length, muscle shortening must distort extracellular space. This will cause at least some mixing of extracellular fluid and seems to be the simplest explanation for the relationship between D{alpha} and extracellular space in trabeculae.

Mixing of the extracellular fluid will reduce angular variations of intercellular oxygen tension due to discrete capillary sources in vivo. Federspiel (13) calculated that these angular variations do not penetrate deeply into myoglobin-containing fibers. This complication in the application of Hill’s equations for oxygen diffusion may, therefore, be negligible in working muscle. To what extent D{alpha} depends on muscle shortening remains to be investigated. In the meantime, Eq. 4 can be useful in the design of experiments on myocardial trabeculae.

In conclusion, the results indicate that Hill’s model for oxygen diffusion is valid for single muscle fibers without myoglobin and a fairly homogeneous mitochondrial distribution consuming oxygen at the maximum rate. PO2crit at O2 max of these cells is close to arterial PO2 (12), suggesting that O2 max of Xenopus muscle fibers cannot be reached in vivo.

Extracellular space in multicellular, contracting myocardial trabeculae facilitates oxygen diffusion. Because control trabeculae have the smallest amount of extracellular space, the value for D{alpha} in these preparations provides an upper limit for D{alpha} for oxygen inside cardiomyocytes consuming oxygen at the maximum rate: 2.29 nM·mm2·mmHg–1·s–1 (SD 0.24). D{alpha} in single Xenopus muscle fibers, adjusted to 37°C, may be a lower limit for D{alpha} in cardiomyocytes: 1.35 nM·mm2·mmHg–1·s–1 (SD 0.13) or 1.97 nM·mm2·mmHg–1·s–1 (SD 0.19), depending on temperature dependency.

Taking D{alpha} = 2 nM·mm2·mmHg–1·s–1 (corresponding to 2·10–5 ml O2·cm–1·atm–1·min–1), mean O2 at 10 Hz corrected for extracellular space given above and a CSA of 120 and 380 µm2 for control and hypertrophied cardiomyocytes (8), PO2crit according to Eq. 1 (without myoglobin) is 3.1 and 16.2 Torr in control and hypertrophied cardiomyocytes, respectively. The latter value is close to the predicted critical end-capillary PO2 (30) and will lead to hypoxia in hypertrophied cardiomyocytes. Cytochrome c is released from mitochondria in all cardiomyocytes with CSA larger than 600 µm2 in the right ventricular wall of rats with monocrotaline-induced pulmonary hypertension (43). The present results indicate that cytochrome c release in these cells may be triggered by hypoxia.


   GRANTS
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
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This study was supported by Netherlands Heart Foundation Grants 94.003 and 00.191.


   FOOTNOTES
 

Address for reprint requests and other correspondence: W. J. van der Laarse, Dept. of Physiology, Institute for Cardiovascular Research, Van der Boechorststraat 7, 1081 BT Amsterdam, The Netherlands (e-mail: wj.vanderlaarse{at}vumc.nl)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

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