Transient effects on the initial rate of oxygenation of red blood cells

The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O₂ in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.     

Theoretical analysis of engineered cartilage oxygenation: influence of construct thickness and media flow rate

A novel parallel-plate bioreactor has been shown to modulate the mechanical and biochemical properties of engineered cartilage by the application of fluid-induced shear stress. Flow or perfusion bioreactors may improve tissue development via enhanced transport of nutrients or gases as well as the application of mechanical stimuli, or a combination of these factors. The goal of this study was to complement observed experimental responses to flow by simulating oxygen transport within cartilage constructs of different thicknesses (250 μm or 1 mm). Using numerical computation of convection–diffusion equations, the evaluation of the tissue oxygenation is performed. Four culture conditions are defined based on tissue thickness and flow rates ranging from 0 to ∼25 mL min⁻¹. Under these experimental conditions results show a mean oxygen concentration within the tissue varying from 0.01 to 0.19 mol m⁻³ as a function of the tissue thickness and the magnitude of the applied shear stress. More generally, the influence of shear stress varying (via flow rate modification) from 10⁻³ to 10 dynes cm⁻² on the tissue oxygenation is studied. The influence on the results of important physical parameters such as the maximal oxygen consumption rate of cells is discussed. Lastly, the importance of oxygen concentration in the lower chamber and its relevance to tissue oxygenation are highlighted by the model results.     

Role of hemoglobin oxygenation in the modulation of red blood cell mechanical properties by nitric oxide

It has been previously demonstrated that both externally generated and internally synthesized nitric oxide (NO) can affect red blood cell (RBC) deformability. Further studies have shown that the RBC has active NO synthesizing mechanisms and that these mechanisms may play role in maintaining normal RBC mechanical properties. However, hemoglobin within the RBC is known to be a potent scavenger of NO; oxy-hemoglobin scavenges NO faster than deoxy-hemoglobin via the dioxygenation reaction to nitrate. The present study aimed at investigating the role of hemoglobin oxygenation in the modulation of RBC rheologic behavior by NO. Human blood was obtained from healthy volunteers, anticoagulated with sodium heparin (15 IU/mL), and the hematocrit was adjusted to 0.4 L/L by adding or removing autologous plasma. Several two mL aliquots of blood were equilibrated at room temperature (22 ± 2 °C) with moisturized air or 100% nitrogen by a membrane gas exchanger, The NO donor sodium nitroprusside (SNP), at a concentration range of 10^?7–10^?4 M, was added to the equilibrated aliquots which were maintained under the same conditions for an additional 60 min. The effect of the non-specific NOS inhibitor l-NAME was also tested at a concentration of 10^?3 M. RBC deformability was measured using an ektacytometer with an environment corresponding to that used for the prior incubation (i.e., oxygenated or deoxygenated). Our results indicate an improvement of RBC deformability with the NO donor SNP that was much more pronounced in the deoxygenated aliquots. SNP also had a more pronounced effect on RBC aggregation for deoxygenated RBC. Conversely, l-NAME had no effect on deoxygenated blood but resulted in impaired deformability, with no change in aggregation for oxygenated blood. These findings can be explained by a differential behavior of hemoglobin under oxygenated and deoxygenated conditions; the influence of oxygen partial pressure on NOS activity may also play a role. It is therefore critical to consider the oxygenation state of intracellular hemoglobin while studying the role of NO as a regulator of RBC mechanical properties.     

Morphological and physiological factors affecting oxygen uptake and release by red blood cells

The kinetics of oxygen uptake and release by human, salamander (Amphiuma means), and artificially constructed red cells were measured under a variety of physiological conditions using stopped-flow, rapid mixing techniques. The results were analyzed quantitatively using the generalized, three-dimensional disc model that was developed in two previous publications (Vandegriff, K. D., and Olson, J. S. (1984) Biophys. J. 45, 825-835 and Vandegriff, K. D., and Olson, J. S. (1984) J. Biol. Chem. 259, 12609-12618). The apparent rate of gas exchange is governed primarily by the oxygen flux at the red cell surface. In the case of uptake, this flux is roughly independent of intracellular chemical reaction parameters and inversely proportional to the thickness of the unstirred solvent layer which is adjacent to the red cell surface. For release experiments in the presence of high concentrations of sodium dithionite, the flux at the cell surface is inversely proportional to the oxygen affinity of the intracellular hemoglobin and roughly independent of the thickness of the external unstirred solvent layer. As a result, the effects of cell size, internal heme concentration, and pH are expressed differently in the two types of kinetic experiments. The rate of oxygen uptake depends on roughly the second power of the surface area to volume ratio of the erythrocyte, whereas the rate of release is much less dependent on the size and shape of the red cell. The half-time of oxygen uptake is directly proportional to intracellular heme concentration for cells of equivalent geometries; the half-time of oxygen release is linearly dependent on internal heme concentration but, at low heme concentrations, is determined primarily by the rate of oxygen dissociation from hemoglobin. The rate of cellular oxygenation is roughly independent of pH and internal 2,3-diphosphoglycerate concentration; in contrast, the rate of deoxygenation depends markedly on these conditions. As the pH is lowered or the internal diphosphoglycerate concentration is raised, the overall oxygen affinity of the cell suspension decreases severalfold, and the rate of oxygen release increases by roughly the same extent.     

Nitric oxide scavenging by red blood cells as a function of hematocrit and oxygenation

The reaction rate between nitric oxide and intraerythrocytic hemoglobin plays a major role in nitric oxide bioavailability and modulates homeostatic vascular function. It has previously been demonstrated that the encapsulation of hemoglobin in red blood cells restricts its ability to scavenge nitric oxide. This effect has been attributed to either factors intrinsic to the red blood cell such as a physical membrane barrier or factors external to the red blood cell such as the formation of an unstirred layer around the cell. We have performed measurements of the uptake rate of nitric oxide by red blood cells under oxygenated and deoxygenated conditions at different hematocrit percentages. Our studies include stopped-flow measurements where both the unstirred layer and physical barrier potentially participate, as well as competition experiments where the potential contribution of the unstirred layer is limited. We find that deoxygenated erythrocytes scavenge nitric oxide faster than oxygenated cells and that the rate of nitric oxide scavenging for oxygenated red blood cells increases as the hematocrit is raised from 15% to 50%. Our results 1) confirm the critical biological phenomenon that hemoglobin compartmentalization within the erythrocyte reduces reaction rates with nitric oxide, 2) show that extra-erythocytic diffusional barriers mediate most of this effect, and 3) provide novel evidence that an oxygen-dependent intrinsic property of the red blood cell contributes to this barrier activity, albeit to a lesser extent. These observations may have important physiological implications within the microvasculature and for pathophysiological disruption of nitric oxide homeostasis in diseases.     

Effects of drugs on water permeability of erythrocyte membranes

The method of NMR-relaxation with the manganese doping has been applied to study changes of water permeability of red blood cell membranes affected by various concentrations of chlorhexidine digluconate and dimephosphone. It is shown that both investigated substances suppress the water permeability of the red blood cell membrane in a dose-dependent manner. Half-maximum inhibitory effect of studied substances was reached at the concentrations of 9 μM of chlorhexidine and 400 μM of dimephosphone.     

Endothelin redistributes blood flow through the lamellae of rainbow trout gills

The lamellae of the fish gill are the primary sites for oxygen uptake from the water. Here, only two very thin layers of cells separate the blood from the water. Therefore, energetically costly ion-fluxes will also occur between blood and water, and it has been hypothesised that the blood flow within the lamellae can be regulated through vasoconstriction, but evidence for this has been lacking. Through direct observations of the lamellae of rainbow trout (Oncorhynchus mykiss) in vivo, using epi-illumination microscopy, we show here that an endothelium-derived vasoactive peptide, endothelin-1 (ET-1, 0.2 μg kg⁻¹ or 1.0 μg kg⁻¹), is able to completely constrict the vascular sheet in the lamellae, probably by inducing contraction of pillar cells. This coincided with a dose-dependent increase in ventral aortic blood pressure (rising from 6.6 kPa to 12.0 kPa in response to the high ET-1 dose). However, blood continued to flow through the marginal channel that circumvents each lamella. Thus, ET-1 caused an intralamellar blood shift from the lamellar sheet towards the marginal channels. Vasoconstriction in the lamellae is likely to provide the fish with a mechanism for matching its respiratory surface area with its respiratory needs, thereby minimising ion-fluxes. Accepted: 8 September 1998     

Investigations on oxygen limitations of adherent cells growing on macroporous microcarriers

Macroporous microcarriers are commonly applied to fixed and fluidized bed bioreactors for the cultivation of stringent adherent cells. Several investigations showed that these carriers are advantageous in respect to a large surface area (Griffiths, 1990; Looby, 1990a). When growing a rC-127 cell line on Cytoline 2 (Pharmacia Biotech), no satisfactory product yield could be achieved. A possible limitation in the supply of nutrient components was investigated to explain these poor results. No significant concentration gradients could be detected. Nevertheless, fluorescence staining revealed a decreasing viability, particularly inside the macroporous structure. Therefore, oxygen transfer to and into the carriers was examined by means of an oxygen microprobe during the entire process. Additional mathematical modeling supported these results. The maximum penetration depth of oxygen was determined to be 300 μm. A critical value influencing the oxygen uptake rate of the rC-127 cells occured at a dissolved oxygen concentration of 8% of air saturation. A significant mass transfer resistance within a laminar boundary film at the surface of the carrier could be detected. This boundary layer had a depth of 170 μm. The results showed that even a 40% air saturation in the bulk liquid could not provide an efficient oxygenation of the surface biofilm during the exponential growth phase. Fluorescent staining reveals a poor viability of cells growing inside the carrier volume. Thus, oxygen supply limits the growth of rC-127 cells on macroporous microcarriers. Poor process performance and low product yield could be explained this way. This revised version was published online in July 2006 with corrections to the Cover Date.     

The change of sediment composition during recovery of two Finnish lakes induced by waste water purification and lake oxygenation

Total oxygen deficit occurred regularly during stagnation periods in the deepest part of Lake Kallavesi in the period 1973–1986. The sediment was black and anaerobic during the first sampling in 1987. After beginning of artificial lake oxygenation and efficient purification of waste waters of a paper board mill in 1986 the oxygen deficit decreased gradually and a light brown oxidized uppermost sediment layer appeared and began to thicken. The following changes in the sediment composition were observed during 1987–1996: loss on ignition, total nitrogen and BOD₇ concentrations decreased in the uppermost sediment layer (0–2 cm) and BOD₇ concentration increased in the next sediment layer beneath (2–10 cm). There were no significant change in phosphorus and iron concentrations.Lake oxygen, total phosphorus and suspended solids concentrations fluctuated in a noticeable degree in Lake Huruslahti depending on waste water input and artificial oxygenation during the years 1980–1993. Oxygen condition was good at times of successful waste water elimination and lake oxygenation while deterioration of either resulted oxygen deficiency as well as increase of total phosphorus and suspended solids concentration. Most of the internal load entered with suspended solids during periods of total oxygen deficiency.An explanation for the findings in Lake Huruslahti could be microbiological. Gas formation inside sediment lift organic material towards top of the sediment and into the water, but after the lake recovery the material retain in the sediment. Also in Lake Kallavesi microbiological gas formation resuspended sediment particles with phosphorus into the overlaying water prior to oxygenation. During oxygenation microbiological processes in uppermost sediment utilize the anaerobic metabolic products, organic acids and methane, and block gas formation. Organic substances remain in the top sediment decomposing gradually in the uppermost layer.     

Effect of temperature and irradiance on the uptake of ammonium and nitrate by <Emphasis Type="Italic">Laurencia brongniartii</Emphasis> (Rhodophyta,Ceramiales)

The effects of temperature (20, 24 and 28 °C) and irradiance (15 and 40 μmol photon m⁻² s⁻¹) on the nitrate and ammonium uptake rates of the subtropical red alga, Laurencia brongniartii, were investigated to prepare for tank cultivation. Nitrate uptake followed saturation kinetics and was faster at higher irradiances and temperatures. In contrast, ammonium uptake was linear over the experimental range and was not affected by an increase in temperature. A parameter, β, was calculated to compare substrate uptake rates of nitrate along the linear portion of the uptake curve with that of ammonium. For nitrate, β was lower at low irradiance and higher at high irradiance (β = 0.007 ± 0.003 and 0.030 ± 0.002 [μmol N L⁻¹ (μmol N g_ww⁻¹ d⁻)⁻¹], respectively). However, β was 0.023 ± 0.002 and 0.034 ± 0.002 [μmol N L⁻¹ (μmol N g_ww⁻¹ d⁻¹)⁻¹] for ammonium, suggesting a preference for ammonium over nitrate.     

Diversity of juvenile fish assemblages in the pelagic waters of Lebanon (eastern Mediterranean)

Oxygen consumption rates of nauplii of the brine shrimp Artemia franciscana Kellogg 1906 were determined over a range of salinities from 10 to 110 ppm, in temperatures from 0 to 30°C, using a multi-factorial design. The oxygen micro-sensors employed have a fast response time and are capable of accurately measuring oxygen concentrations at temperatures well below 0°C. Oxygen uptake rate ranged from 0.03 to 0.66 μmol O₂ mg⁻¹ h⁻¹ and was sensitive to changes in both salinity and temperature. Temperature was the dominant factor affecting oxygen consumption rates, which showed a significant increase with increasing temperature. A slight decrease was measured in oxygen consumption with increasing salinity related to differential solubility of oxygen in waters of different salinities. Thermal sensitivity of oxygen consumption determined from calculations of Q ₁₀, indicated physiological adaptation of Artemia nauplii to the ranges of temperatures tested. Handling editor: A. van Kerchove     

Studies on the Germination of Cereals: 3. The Effect of the Covering Layers on the Uptake of Water by the Embryo of the Wheat Grain

The uptake of water by imbibition, vacuolation, and growth ofthe embryo, has been determined when wheat grains were placedunder germination conditions before maturation was completed;and the effect of the covering layers has been investigatedin a red and a white variety at three stages during ripening. The water lost during ripening was replace by imbibition withoutcausing the embryo to expand sufficiently to rupture the coveringlayers. The cells of the coleorhiza and epiblast absorbed waterby vacuolation as soon as they were imbibed; but afurther periodelapsed before the scutellum became imbibed and water uptakewas associated with an increase in embryo dry weight. In both varieties, uptake opf water by the imbibed embryo wasprevented by the inner layer of the pericarp and the tesa inunripe grains, and by the epidermal layer of the pericarp duringthe early staes of ripening. But after the final stage of rapiddesiccation the covering layers of the white grains were rupturedwhen the embryo absorbed water by vacuolation; whereas the coveringlayers of the red grains remained intact and the uptake of waterwas delayed until a sufficient period had elapsed for nutrientsfrom the endosperm to be available for growth ofr the embryo. The varietal difference in germinationj is therefore attributedto the greater strength of the covering layers of the red grains,which are not disrupted during ripening, and prevent expansionof the embryo until the water absorbing capacity has been increasedby the transfer of reserves from the endosperm.     

An in vitro capillary system for studies on microcirculatory O2 transport

An in vitro artificial capillary system has been developed for use in examining the O2 transport properties of free hemoglobin and erythrocytes. The artificial capillary was constructed by casting a thin film of transparent silicone rubber around a strand of tungsten wire that was 24 micron in diameter. After the rubber had polymerized, the wire was removed. Typical dimensions of the silicone rubber film were 170 micron thick, 1 cm wide, 5 mm long in the direction of flow, and a 27-micron lumen diameter. The artificial capillary bed was mounted on a microscope and perfused by either hemoglobin solutions or cell suspensions. Fractional saturation was measured as a function of axial position by a dual-wave-length microspectrophotometer, and the flow rate was regulated precisely by a syringe pump. O2 release experiments were carried out by suffusing the gas space surrounding the artificial capillary film with 100% N2 and perfusing with an oxygenated sample. O2 uptake experiments were carried out by suffusing the gas space with O2-N2 mixtures and perfusing with deoxygenated samples. The axial velocities were varied from 3 to 15 mm/s. The residence time (the time a particular red cell or hemoglobin molecule has spent in the capillary) for 50% oxygenation of a 4 mM (heme) deoxyhemoglobin solution was approximately 0.05 s at 37 degrees C when the gas space surrounding the capillary contained air. The corresponding time for 50% oxygenation of an equivalent red cell suspension was approximately 0.25 s.(ABSTRACT TRUNCATED AT 250 WORDS)     

Oxygen diffusion and consumption in active aerobic granules of heterogeneous structure

The interior structure of aerobic granules is highly heterogeneous, hence, affecting the transport and reaction processes in the granules. The granule structure and the dissolved oxygen profiles were probed at the same granule in the current work for possible estimation of transport and kinetic parameters in the granule. With the tested granules fed by phenol or acetate as carbon source, most inflow oxygen was consumed by an active layer thickness of less than 125 μm on the granule surface. The confocal laser scanning microscopy scans also revealed a surface layer thickness of approximately 100 μm consisting of cells. The diffusivities of oxygen transport and the kinetic constant of oxygen consumption in the active layers only were evaluated. The theoretical models adopted in literature that ignored the contributions of the layered structure of aerobic granule could have overlooked the possible limitations on oxygen transport.     

Diffusing capacity reexamined: relative roles of diffusion and chemical reaction in red cell uptake of O2, CO, CO2, and NO.

This paper presents an analytical expression for the diffusing capacity (Theta(t)) of the red blood cell (RBC) for any reactive gas in terms of size and shape of the RBC, thickness of the unstirred plasma layer surrounding the RBC, diffusivities and solubilities of the gas in RBC and boundary layer, hematocrit, and the slope of the dissociation curve. The expression for Theta(t) has been derived by spatial averaging of the fundamental convection-diffusion-reaction equation for O(2) in the RBC and has been generalized to all cell shapes and for other reactive gases such as CO, NO, and CO(2). The effects of size and shape of the RBC, thickness of the unstirred plasma layer, hemoglobin concentration, and hematocrit on Theta(t) have been analyzed, and the analytically obtained expression for Theta(t) has been validated by comparison with different sets of existing experimental data for O(2) and CO(2). Our results indicate that the discoidal shape of the human RBC with average dimensions of 1.6-mum thickness and 8-mum diameter is close to optimal design for O(2) uptake and that the true reaction velocity in the RBC is suppressed significantly by the mass transfer resistance in the surrounding unstirred layer. In vitro measurements using rapid-mixing technique, which measures Theta(t) in the presence of artificially created large boundary layers, substantially underpredicts the in vivo diffusing capacity of the RBC in the diffusion-controlled regime. Depending on the conditions in the RBC, uptake of less reactive gases (such as CO) undergoes transition from reaction-limited to diffusion-limited regime. For a constant set of morphological parameters, the theoretical expression for Theta(t) predicts that Theta(t,NO) > Theta(t,)(CO(2)) > Theta(t,)(O(2)) > Theta(t,CO).     

Experimental silicon demand by the sponge Hymeniacidon perlevis reveals chronic limitation in field populations

Dissolved silicon (DSi) is a key marine nutrient. Sponges and diatoms are relevant DSi consumers, but sponges appear to have a less efficient uptake system that requires higher ambient DSI concentrations for maximum uptake. We experimentally tested whether a sponge adapted to live at the intertidal (Hymeniacidon perlevis) also shows such a need for high DSi. Under laboratory conditions, sponges were exposed to both the natural DSi concentration (10 μM) and much higher levels (25, 40, and 70 μM) for 36 h, being water samples taken at 6 h intervals to infer DSi uptake. Uptake rates shifted over time (particularly in high DSi treatments) and showed moderate inter-individual variability. Average DSi uptake rate at 70 μM was twice higher than those at 40 and 25 μM, which in turn were not significantly different from each other, but were twice higher than the uptake rate at 10 μM. Therefore, H. perlevis needs, for efficient uptake, ambient DSi concentrations two to four times higher than the maximum available in its natural habitat. From an eco-physiological point of view, it means that the skeletal growth in the populations of H. perlevis is chronically limited by DSi availability, a limitation that may favor sponge evolution toward skeletal slimming.     

Delivery Rate Affects Uptake of a Fluorescent Glucose Analog in Murine Metastatic Breast Cancer

We demonstrate an optical strategy using intravital microscopy of dorsal skin flap window chamber models to image glucose uptake and vascular oxygenation in vivo. Glucose uptake was imaged using a fluorescent glucose analog, 2-[N-(7-nitrobenz-2-oxa-1,3-diaxol-4-yl)amino]-2-deoxyglucose (2-NBDG). SO₂ was imaged using the differential absorption properties of oxygenated [HbO₂] and deoxygenated hemoglobin [dHb]. This study was carried out on two sibling murine mammary adenocarcinoma lines, 4T1 and 4T07. 2-NBDG uptake in the 4T1 tumors was lowest when rates of delivery and clearance were lowest, indicating perfusion-limited uptake in poorly oxygenated tumor regions. For increasing rates of delivery that were still lower than the glucose consumption rate (as measured in vitro), both 2-NBDG uptake and the clearance rate from the tumor increased. When the rate of delivery of 2-NBDG exceeded the glucose consumption rate, 2-NBDG uptake decreased with any further increase in rate of delivery, but the clearance rate continued to increase. This inflection point was not observed in the 4T07 tumors due to an absence of low delivery rates close to the glucose consumption rate. In the 4T07 tumors, 2-NBDG uptake increased with increasing rates of delivery at low rates of clearance. Our results demonstrate that 2-NBDG uptake in tumors is influenced by the rates of delivery and clearance of the tracer. The rates of delivery and clearance are, in turn, dependent on vascular oxygenation of the tumors. Knowledge of the kinetics of tracer uptake as well as vascular oxygenation is essential to make an informed assessment of glucose demand of a tumor.     

A quantitative description in three dimensions of oxygen uptake by human red blood cells

Oxygen uptake by human erythrocytes has been examined both experimentally and theoretically in terms of the influence of unstirred solvent layers that are adjacent to the cell surface. A one-dimensional plane sheet model has been compared with more complex spherical and cylindrical coordinate schemes. Although simpler and faster, the plane sheet algorithm is an inadequate representation when unstirred solvent layers are considered. The cylindrical disk model most closely represents the physical geometry of human red cells and is required for a quantitative analysis. In our stopped-flow rapid mixing experiments, the thickness of the unstirred solvent layer expands with time as the residual turbulence decays. This phenomenon has been quantified using a formulation based on previously developed hydrodynamic theories. An initial 10(-4) cm unstirred layer is postulated to occur during mixing and expand rapidly with time by a (t)0.5 function when flow stops. This formula, in combination with the three-dimensional cylinder scheme, has been used to describe quantitatively uptake time courses at various oxygen concentrations, two different external solvent viscosities, and two different internal heme concentrations.     

Environmental and physiological factors affecting the uptake of phosphate by Chlorobium limicola

The uptake of soluble phosphate by the green sulfur bacterium Chlorobium limicola UdG6040 was studied in batch culture and in continuous cultures operating at dilution rates of 0.042 or 0.064 h^–1. At higher dilution rates, washout occurred at phosphate concentrations below 7.1 μM. This concentration was reduced to 5.1 μM when lower dilution rates were used. The saturation constant for growth on phosphate (K _μ) was between 2.8 and 3.7 μM. The specific rates of phosphate uptake in continuous culture were fitted to a hyperbolic saturation model and yielded a maximum rate (Va _max) of 66 nmol P (mg protein)^–1 h^–1 and a saturation constant for transport (K _t) of 1.6 μM. In batch cultures specific rates of phosphate uptake up to 144 nmol P (mg protein)^–1 h^–1 were measured. This indicates a difference between the potential transport of cells and the utilization of soluble phosphate for growth, which results in a significant change in the specific phosphorus content. The phosphorus accumulated within the cells ranged from 0.4 to 1.1 μmol P (mg protein)^–1 depending on the growth conditions and the availability of external phosphate. Transport rates of phosphate increased in response to sudden increases in soluble phosphate, even in exponentially growing cultures. This is interpreted as an advantage that enables Chl. limicola to thrive in changing environments. Received: 9 February 1998 / Accepted: June 1998     

Hydrodynamic and diffusion considerations of rapid-mix experiments with red blood cells.

From studies of the oxygenation rate of red blood cells (RBC) using rapid-mix techniques, it has been suggested that RBC are surrounded by a stagnant layer of water that does not (or cannot) mix with the rest of the water. A consideration of the appropriate hydrodynamics and convective diffusion rates shows that a mixer can reduce the resolution time to approximately 1 ms (or possibly less) and give a diffusion layer around the TBC that is approximately 1 micron thick. In stopped flow equipment it expands to approximately 4 micron over approximately 10 ms, whereas in continuous flow work the diffusion layers expands slightly less rapidly and less far. Thus the rate of oxygenation of TBC should be slower when measured by stopped flow techniques than by continuous flow apparatus for which the rate will depend weakly on the Reynolds number of the flow in the interrogation tube.