Features of diffusion

At the microvascular level the delivery of oxygen to the tissues is achieved by diffusion. The driving force determining the amount of diffusion is the difference in partial pressures of the blood between the capillary and the mitochondria in adjacent cells. The quantity of diffusing agent per unit time (J) is proportional to the surface of diffusion (F), the absolute temperature (T) and the ideal gas constant (R) and inversely proportional to the viscosity of the solvents and the radius (r) of the diffusing particles. The interrelationship of these parameters is expressed as diffusion coefficient (D) in the equation of Stokes and Einstein as follows: D = RT / 6% r -q. The first law of diffusion was established by Fick in 1855:

where: C = concentration x = distance of diffusion

Transcapillary diffusion of oxygen can be described by the Krogh cylinder52, a model introduced by Nobel Laureate Krogh in the last century. This unit structure implies that each capillary section provides oxygen supply to a corresponding cylindrical section of surrounding tissue. Oxygen and other metabolites transported within the oxygenated blood will diffuse from the capillary radially towards the tissue to be consumed by the cells. This model is amenable on the assumptions that

• the Krogh cylinder is an appropriate model for the geometry in a given tissue

• the tissue surrounding the cylinder is homogenous and uniform in its metabolic activities

• the axis of the capillary-tissue cylinder is uniform.

Krogh's Cylinder

Krogh's Cylinder

Venule

Arteriole

Figure 1.4-3. Cross section of volume of oxygenated areas around the unique capillary under different conditions: with breathing air, normobaric oxygen (NBO) and hyperbaric oxygen (HBO) according to the Krogh's model

This model allows for a deeper insight into tissue oxygenation although it does not consider geometrical features like branches of the capillary bed, alterations of vascular tone which might constrain capillary blood flow or varying local metabolic demands. Nevertheless, on the basis of this model, key variables of tissue oxygenation may be defined which are the distance between capillaries and the transit time of red blood cells from arteriole to venule.

Thus, the mean distance between capillaries or the mean density of capillaries in a given volume of tissue is a main determinant of tissue oxygenation, which may explain tissue hypoxia despite normal arterial oxygen tension and cardiac output. Above all, the period of time when capillary pO2 exceeds tissue pO2 is also a determinant of tissue oxygenation as well. A shortening of transit time diminishes oxygen delivery to the surrounding tissue.

Partial oxygen pressure continuously declines during the transit of the red blood cells from arteriole to venule, and so does oxygenation of the surrounding tissue. Thus, the cells at the venous end of the capillary are least oxygenated and at risk of hypoxia ("lethal angle"). Three thresholds below normal values may be defined. At a venous pO2 of 25-28mm Hg reactive vasodilation occurs; the PvO2 of 20mm Hg has to be considered critical to tissue oxygenation; and at a PvO2 of 12mm Hg the oxygen pressure approximates zero within the mitochondria.

Under normobaric conditions the pO2 at the arteriole equals the arterial pO2 of about 100mm Hg, the pO2 at the venule being about 34mm Hg. The distance of diffusion equals 100^m at the arteriolar and 36^m at the venular side leading to a diffusion volume with the shape of a truncated cone. In contrast, with exposure to HBO at 303.9kPa (3ata) arteriolar pO2 equals 2000mm Hg and venular pO2 to 100mm Hg on the assumption of constant oxygen consumption. The distance of diffusion equals 247^m at the arteriolar end and to 64^m at the venular end of the capillary, leading to a more than ten-fold increase of oxygen diffusion volume. These theoretical considerations have been confirmed by direct measurements of oxygen

pressure in various tissues .

Nevertheless, the Krogh model remains a simplification because the morphology of the capillaries is not at all uniform, nor the direction of blood flow54'55.

Intracellular utilization of oxygen is mainly achieved within the mitochondria finally leading to adenosine triphosphate (ATP) generation. The determinant of oxidative phosphorylation is mitochondrial pO2. The minimum intramitochondrial driving pressure of oxygen to maintain oxidative phosphorylation is considered to be less than 0.5mm Hg56. A mean tissue PO2 of 15mm Hg indicates tissue dysoxia57. Diffusion barriers58 may impair the diffusion from capillary to mitochondria, such as anatomical barriers like abnormal structure and/or thickness of the erythrocyte membrane, arterial/venous shunts, or physical barriers such as altered haemoglobin-O2 affinity or RBC velocity.

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