Transfer of oxygen into haemoglobin solution

Spaan, Jae Jos

doi:10.1007/bf00586101

Cited by 19 publications

(12 citation statements)

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“…The intercept of the curves with the vertical axis is close to zero (t* ~ 0.15). In case of D* = 0 the slope is 0.5 in accordance with the advancing front equation not corrected for physically dissolved oxygen (e.g., Spaan, 1973). Neglecting the small intercept of the curves at H = 0 one may describe the curves of Fig.…”

Section: Parametric Analysissupporting

confidence: 55%

“…(1) and (2) were presented previously (Spaan, 1973). If the hemoglobin is not mobile the saturation profile in general shows a quite steep course, and the profiles are steeper at higher values o f / 1 .…”

Section: The Oxygenation Of Hemoglobin Layers Of Finite or Semi-infinmentioning

confidence: 70%

“…We will assume that the reaction of oxygen with hemoglobin is infinitely fast. The transfer equation describing this oxygenation process (Spaan, 1973) is in dimensionless form: …”

Section: The Oxygenation Of Hemoglobin Layers Of Finite or Semi-infinmentioning

confidence: 99%

“…The oxygen driving pressure P~ is expressed in units of kPa (1 kPa = 7.5 mm Hg). The finite slab oxygenation was calculated numerically according to Spaan (1973) In this equation 7 ~ is to be calculated by the finite layer model [boundary conditions ofeq. (2)].…”

Section: The Oxygenation Of Hemoglobin Layers Of Finite or Semi-infinmentioning

confidence: 99%

“…These studies were extended and confirmed by Kutchai (1971 a, b) who, however, concluded that oxygen diffusion facilitated by oxyhemoglobin was of minor importance only. Spaan (1973) used advancing front equations corrected for the physically dissolved oxygen, and suggested a facilitating contribution by oxyhemoglobin and a possibility of determining values of both oxygen and hemoglobin diffusion coefficients from oxygenation experiments. Thews (1957) applied an approximate solution of the diffusion equations based on simplifying assumptions to the data of Kreuzer (1950) and Klug et al (1956) and found good agreement of the values of the oxygen diffusion coefficient between his calculations and previous approaches where a comparison was possible.…”

Section: Introductionmentioning

confidence: 99%

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A theoretical analysis of nonsteady-state oxygen transfer in layers of hemoglobin solution

1980

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Section: Parametric Analysissupporting

confidence: 55%

Section: The Oxygenation Of Hemoglobin Layers Of Finite or Semi-infinmentioning

confidence: 70%

“…We will assume that the reaction of oxygen with hemoglobin is infinitely fast. The transfer equation describing this oxygenation process (Spaan, 1973) is in dimensionless form: …”

Section: The Oxygenation Of Hemoglobin Layers Of Finite or Semi-infinmentioning

confidence: 99%

Section: The Oxygenation Of Hemoglobin Layers Of Finite or Semi-infinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A theoretical analysis of nonsteady-state oxygen transfer in layers of hemoglobin solution

1980

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Facilitated transport via carrier—mediated diffusion in membranes: Part II. Mathematical aspects and analyses

1974

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Part I1 of this review is concerned with the mathematical analysis of facilitated transport. An exposition is given of the most generally useful techniques for obtaining asymptotic or approximate solutions to one-dimensional carrier-mediated diffusion in membranes, involving multiple permeant and carrier species which undergo one or more chemical reactions. Primary emphasis is devoted to the limiting regimes of weakly-perturbed membranes (small driving forces) and slow or fast reactions (small or large Damkohler numbers). Many of the results appearing in the literature are unified and extended, and a systematic procedure for using these to estimate membrane performance is put forth. Finally, some areas for further work are identified.In the absence of convection and electric-field effects, it appears possible now to estimate mathematically, with some confidence, the steady state performance characteristics of highly complex carrier-mediated membranes, given the requisite kinetic, equilibrium, and diffusion constants. In many cases, predictions can be obtained by relatively straightforward and rapid analytical methods, based on asymptotic or approximate formulae.The most useful and generally applicable results appear to be, roughly in the order of complexity and applicability, 1. The classical type of reaction-equilibrium approximation for investigating nonlinearities in the driving force or concentration gradients and the effects of transport parameters and binding constants, 2. The linearized-kinetic formulae for investigating reaction-rate limitations and nonequilibrium departures from l,.provided the linear approximation is valid in the equilibrium regime, that is, provided it gives reasonably accurate prediction of equilibrium fluxes under the im-posed driving force, and, if not, 3. A strong boundary-layer analysis, based on extensions proposed here of an approximate method due to Kreuzer and Hoofd (1972) and Smith et al. (1973), to replace 2, together with 4. Near-diffusion or slow-reaction, perturbation formulae to determine the approximate lower limits of validity of 3.At the very least, it appears that such formulae can provide useful information about the likely operational regimes and some valuable guidelines for the application of more difficult, numerical methods or the development of special approximate methods.In the summary, suggestions are made for some further theoretical work, including extensions to other interesting geometric configurations and to unsteady operation, as well as to systems with electric-field and convection effects.Only that notation from Part I which is most directly relevant to Part 11, is included here. Some of the mathematical symbols of Part 11, defined only in isolated contexts, are not listed here. No notational distinction is generally made between dimensional quantities x, D, k, . . . and their dimensionless counterparts r / L ,

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Steady state diffusion of oxygen in red blood cell and model suspensions

1976

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Experimental measurements were made of the steady oxygen permeation rate through films of nonreactive and reactive dispersions, including suspensions of red blood cells. The data compare well with a theoretical analysis which incorporates a one-step reversible reaction within the dispersed phase. In the absence of reaction, the red cell permeability could be treated as that of a concentrated hemoglobin solution. For reactive suspensions of red cells or water-in-oil emulsions containing hemoglobin at 25OC, substantial facilitation of oxygen transport occurred when oxyhemoglobin gradients were steep, but both the data and the theory exhibited considerably less facilitation than would be suggested by an equilibrium analysis.The rate of oxygen transport in red blood cells and through whole blood is of biophysical and physiological interest. A quantitative understanding of this process is important in the design and analysis of extracorporeal blood oxygenators because the blood phase invariably constitutes the dominant resistance to mass transfer. The red cell contains a concentrated solution of hemoglobin in which the diffusion coefficient of oxygen is substantially reduced from its value in water or plasma, and it is surrounded by a membrane which may, in addition, offer a significant resistance to oxygen diffusion. Within the red cell, oxygen reacts reversibly with hemoglobin to form oxyhemoglobin, and the parallel diffusion of oxyhemoglobin may augment oxygen transport above that expected from purely physical diffusion. Although the topic is venerable, uncertainty still surrounds the relative importance of these factors.Experimental measurements were made of steady state oxygen permeation through red blood cell and model suspensions. Results were compared with a theoretical model for oxygen transport through a dilute suspension of spheres in the interior of which the reaction O2 + Hb * HbOz occurs. The objectives were to assess the rela- SCOPE CONCLUSIONS AND SIGNIFICANCEAgreement between theory and data was excellent for nonreactive synthetic suspensions (Figure 4); the same was true for nonreactive red cell suspensions (Figure 5) when the red cell oxygen permeability was taken to be that of a hemoglobin solution at the same concentration as the red cell interior and the cell membrane resistance was ignored. The average permeability of red cell suspensions (Figures 7, 8, 9) depended upon oxygen partial pressure boundary conditions. Substantial facilitation occurred in the presence of a large oxyhemoglobin gradient relative to the oxygen gradient. The data fell midway between the predicted limits for a nonreactive suspension tive importance of the mechanisms influencing transport, in particular the extent of facilitated oxygen transport in the red cell, and to evaluate the adequacy of the theoretical model and available physicochemical parameters.Measurements were made with one-dimensional supported vertical films of known thickness under quasisteady conditions. Volume fraction of dispersed phase was varied over a...

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Transfer of oxygen into haemoglobin solution

Cited by 19 publications

References 11 publications

A theoretical analysis of nonsteady-state oxygen transfer in layers of hemoglobin solution

A theoretical analysis of nonsteady-state oxygen transfer in layers of hemoglobin solution

Facilitated transport via carrier—mediated diffusion in membranes: Part II. Mathematical aspects and analyses

Steady state diffusion of oxygen in red blood cell and model suspensions

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