Oxygen transport in heterogeneous tissue

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume.

Mathematical modelling of oxygen transport-limited follicle growth

Mathematical modelling was used to investigate oxygen transport in the developing ovarian follicle. In contrast to previous findings, the results show that oxygen can reach the oocyte in large preantral follicles. This is largely due to the inclusion of fluid voidage in the model and improved estimates of oxygen diffusion coefficients through the granulosa. The results also demonstrate that preantral follicles will eventually reach a size beyond which further growth will result in the follicle becoming increasingly anoxic. The predicted size range at which this occurs is consistent with the size range at which antrum formation is observed in many mammals. This suggests that the antrum formation stage of follicular growth may be pivotal to the further development and ultimate fate of the follicle, and that antrum formation itself may represent a mechanism by which the follicle can overcome oxygen limitations. This was supported through extension of the model to the antral follicle, which showed that antrum formation can provide a way in which the follicle can continue to grow and yet avoid becoming hypoxic. The results of the model were consistent with observed follicle development.

Mathematical modelling of oxygen concentration in bovine and murine cumulus–oocyte complexes

Immature oocytes benefit from nutrient modification of the follicular environment by the surrounding cumulus mass. However, the oxygen concentration that the oocyte may be exposed to could be lower than the antral follicular concentration due to the metabolism of surrounding cumulus cells. Using metabolic data previously determined, we have developed a mathematical model of O2diffusion across the bovine and murine cumulus–oocyte complex. From this we have determined that across a physiological range of external pO2, less than 0.25% and 0.5% O2is removed by cumulus cells within the bovine and murine cumulus–oocyte complex respectively. Our model differs from others as it: incorporates a term that allows for nonlinear variation of the oxygen consumption rate with oxygen concentration; considers two regions (oocyte and cumulus) sharing a common boundary, both of which consume oxygen at different non linear rates. Cumulus cells therefore remove little O2, thus sparing this essential gas for the oocyte, which is dependent on ATP generation via oxidative phosphorylation.

Oxygen gradients in CHO cells: measurement and characterization by electron spin resonance

The concentration of oxygen within cells is important in many physiological and pathological processes, but such oxygen-dependent processes are generally studied as a function of the concentration of extracellular oxygen, due to a lack of suitable methods. Using a newly developed technique based on ESR spectroscopy, we show that respiration stimulation of a cell suspension can result in a significant difference between average intracellular and extracellular concentrations of oxygen. These results indicate that studies of oxygen-dependent phenomena in cells may require measurement of intracellular oxygen concentrations and imply that there are mechanisms in cells that restrict the free diffusion of oxygen.

Analysis of intracellular oxygenation of isolated adult cardiac myocytes

The influence of cellular shape, cellular O2 consumption rate, and intracellular diffusion coefficient for O2 on the magnitude of intracellular O2 gradients during hypoxia was analyzed with the model of Boag (Curr. Top. Radiat. Res. 5: 141-195, 1969) to determine whether these parameters could account for the experimentally measured O2 dependence curves for myoglobin (Mb) oxygenation and cytochrome a + a3 oxidation in heart cells. The analysis shows that the intracellular diffusion coefficient for O2 must be below 4 X 10(-6) cm2/s for a substantial intracellular gradient to occur. The intracellular diffusion coefficient was calculated from the difference in half-maximal oxidation (P50) values for isolated Mb and intracellular Mb and was found to be 1.76 X 10(-6) cm2/s. Use of this value and appropriate geometric models satisfactorily described the O2 dependence of Mb oxygenation and cytochrome a + a3 oxidation in cells over an eightfold range of O2 consumption rates. However, the analysis does not account for the correspondence of intracellular P50 values of Mb oxygenation and cytochrome a + a3 oxidation. This implies that there exists an intracellular heterogeneity of either Mb distribution, mitochondrial distribution, or mitochondrial respiratory characteristics. Such heterogeneity would further contribute to diffusion limitation of O2 supply during hypoxia and could be a major factor underlying the cardiac myocyte structure-function relationship.

Effect of mitochondrial clustering on O2 supply in hepatocytes

Isolated rat hepatocytes were treated with digitonin to selectively disrupt the plasma membrane and allow study of the O2 dependence of mitochondria within the cell cytoskeleton, but without cytosol. Half-maximal oxidation of cytochrome c occurred at 2.0 microM O2 in treated cells incubated under State 3 conditions, whereas in intact cells it was 6.0 microM and in isolated mitochondria (State 3) 0.69 microM. the intermediate value for treated cells indicates that both the geometry of mitochondrial packing and the intracellular diffusion coefficient are important in determining intracellular mitochondrial O2 dependence. Analysis of intracellular diffusion, assuming that the mitochondrial clustering increases the effective mitochondrial radius, indicates that an intracellular diffusion coefficient of between 10(-6) and 4 X 10(-6) cm2 . s-1 and an effective mitochondrial radius of approximately 2 micron would account for the observed intracellular O2 dependence of mitochondrial function.

Oxygen dependence of cellular metabolism: the effect of O2 tension on gluconeogenesis and urea synthesis in isolated rat hepatocytes

The dependencies of gluconeogenesis and urea synthesis on oxygen concentration were measured in suspensions of isolated rat hepatocytes and compared with the O2 dependence of cellular energy supply (reduction of cytochrome c, respiratory rate, mitochondrial [NAD+]/[NADH], lactate production, and [ATP]/[ADP] [Pi]). As the oxygen concentration was decreased, production of both glucose and urea declined; the changes were observable at 20 microM oxygen and below, with the apparent Km values for both processes of near 5 microM. The similar dependence of gluconeogenesis and urea synthesis on oxygen concentration indicates that the two pathways have equal access to the cellular ATP supply, i.e., there is no evidence that either pathway is preferentially turned off to spare ATP for the other. The cellular energy state had an oxygen dependence similar to that of glucose and urea synthesis. It is suggested that the behavior of gluconeogenesis and urea production is a reflection of homeostatic regulation of cellular metabolism which is designed to respond to changes in [ATP]/[ADP][Pi].

Intracellular oxygen supply during hypoxia

The intracellular supply of O2 to mitochondria was studied in single-cell suspensions of rat hepatocytes by measuring the O2 dependence of oxidation of cytochromes. Values were obtained by adding standardized O2-containing solutions to anaerobic cell suspensions and observing absorbance changes at wavelength pairs specific for cytochromes a + a3, c + c1, and b561 + b566. Half-maximal oxidation, calculated relative to aerobic cells, occurred at 3.5, 6.2, and 4.9 microM O2, respectively. These values are similar to those for changes in cellular ATP/ADP, lactate/pyruvate, and NADH/NAD+ but are much higher than corresponding values for isolated mitochondria. Analysis of these data indicate that the diffusion coefficient in the region of mitochondria in situ is considerably smaller than the extracellular diffusion coefficient and suggests that a significant O2 gradient in the vicinity of mitochondria occurs under hypoxic conditions. These results suggest that the rate of O2 diffusion may be a critical factor for intracellular O2 supply to mitochondria during hypoxia.

Spatio-temporal micromeasurements of the oxygen uptake in the developing chick embryo

A method has been developed for the determination of the oxygen uptake of small areas (0.01 mm2) in an entire chick embryo cultured in vitro under defined metabolic conditions. It is based on the recordings of the spectral changes of the hemoglobin used as oxygen source for the respiring tissue (Barzu and Borza, 1967). Rapid scanning of the hemoglobin absorbance over the preparation allows a comparison of the O2 uptake of various regions. Values of the order of 10(-2) 1 O2 . min-2 are measured in less than 10 sec with a spatial resolution of 100 micron. The differentiation of embryonic tissue is not disturbed by the measurements. The O2 diffusion in the media and in the tissue has been analyzed by digital simulation. The O2 uptake of the Hensen's node was measured from embryos starting at the stage of definitive primitive streak (stage 4) up to the stage of 10 somites. It increases from 0.6 to 1.1 nl . h-1 with a marked acceleration between stages 4 and 5. The values corrected for the protein content of the Hensen's node at stage 4, 5, 6 and 8 are 32, 30 and 28 microliter . mg-1 . h-1 respectively. The first scanning results show different patterns of the O2 utake at the level of the Hensen's node and of the neural plate. At stage 6-7, the corrected O2 uptake is 30 microliter . mg-1 . h-1 for . the former and 43 microliter . mg-1 . h-1 for the latter.