[Method for calculation of molecular oxygen diffusion coefficient from measurement of oxygen diffusion in hemoglobin and myoglobin solutions]

Two-Dimensional Finite Element Model for Oxygen Transfer in Cross-Flow Hollow Fiber Membrane Artificial Lungs

A predictive, two-dimensional model with good absolute accuracy for flow and mass transfer in cross-flow hollow fiber membrane artificial lungs is developed. The proposed model is able to predict the gas transfer to water flowing outside and perpendicular to hollow fibers in the artificial lung. The model uses a finite element technique to solve the Navier-Stokes equations and the convection-diffusion equation on the computational domain of a unit fiber cell. Subsequent stream-wise and cross-wise unit fiber cells are then coupled/assembled to the relationship between the oxygen transfer rate and flow rate of a cross-flow hollow fiber membrane artificial lung. The model is compared to experimental water data obtained by perfusing three commercial artificial lungs with water.

Role of geometry and anisotropic diffusion for modelling PO2 profiles in working red muscle

A 3-dimensional analytical model of O2 diffusion in heavily working muscle is proposed which considers anisotropic, myoglobin (Mb)-facilitated O2 diffusion inside the muscle fiber and a carrier-free layer separating erythrocytes and fiber. The model is used to study the effects of some commonly applied simplifying assumptions (reduced dimensionality, neglected anisotropy) on the resulting PO2 distributions: (1) In order not to underestimate PO2 drops near erythrocytes, modelling O2 transport in 3 dimensions is important. (2) For a capillary-to-fiber ratio of 1, the results from the 2-dimensional version of the present model and from a Krogh-type model which incorporates a carrier-free layer agree well. (3) This is not true if the capillary-to-fiber ratio is 2. (4) In neither case, a Hill-type model furnishes a good description of the PO2 distributions. (5) Anisotropic diffusion may become important under critical O2 supply conditions. For a capillary-to-fiber ratio of 1, a Krogh-type model in which the O2 fluxes within the carrier-free layer are adapted according to Hellums (Microvasc. Res. 13: 131, 1977) yields almost identical PO2 distributions as the present 3-dimensional model.

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

The oxygenation of layers of hemoglobin solutions thick enough to ensure chemical equilibrium between oxygen and hemoglobin has been analyzed theoretically assuming simultaneous diffusion of oxygen and oxyhemoglobin. The dimensionless transfer equation was solved for the finite and semi-infinite situation, the parameters being 1) the ratio of bound to physically dissolved oxygen after equilibration (H), 2) the ratio of carrier-mediated to free oxygen flux at steady state (D), and 3) the dimensionless saturation curve (characterized by phi 50). A parametric analysis provided plots of the dimensionless oxygenation time against these three dimensionless parameters. In this way, from the oxygenation times plotted as a function of the reciprocal oxygen driving pressure in any particular hemoglobin solution, the values of the oxygen permeability (or, knowing oxygen solubility, of the oxygen diffusion coefficient) and of the hemoglobin diffusion coefficient can be derived simultaneously.

Mathematical, clinical, and laboratory study of hemodynamic changes in the placental circulation

Various rheological properties of blood were investigated in pregnant and non-pregnant women of similar age. The results from 27 women with abnormal pregnancies were compared to those obtained from 17 non-pregnant women. In abnormal pregnancies we found a reduction of the erythrocyte filtration and a pathological use in red cell aggregation and in the shear resistance of the aggregates. Fractional light transmission (T7/T0) was higher than 1.0, suggesting that pressure gradients in the capillary circulation are not sufficient to disperse red cell aggregates. Thus, rheological factors may be partly responsible for the clinical consequences of pre-eclampsia. Pathological red blood cell aggregation and stagnation are consequences of the changed flow properties in the microcirculation. Even a small decrease of the local pressure gradients in the microcirculation of patients with pre-eclampsia would impair the dispersal of red blood cells and lead to their increased aggregation. Complete occlusion of the placental circulation by these aggregates would impair oxygen transfer at a speed that has been calculated from a diffusion equation based on the concept of the placenta as a hollow cylinder.