Cerebral oxygenation and optimal vascular brain organization

Abstract

The cerebral vascular network has evolved in such a way so as to minimize transport time and energy expenditure. This is accomplished by a subtle combination of the optimal arrangement of arteries, arterioles and capillaries and the transport mechanisms of convection and diffusion. Elucidating the interaction between cerebral vascular architectonics and the latter physical mechanisms can catalyse progress in treating cerebral pathologies such as stroke, brain tumours, dementia and targeted drug delivery. Here, we show that brain microvascular organization is predicated on commensurate intracapillary oxygen convection and parenchymal diffusion times. Cross-species grey matter results for the rat, cat, rabbit and human reveal very good correlation between the cerebral capillary and tissue mean axial oxygen convective and diffusion time intervals. These findings agree with the constructal principle.

Keywords: diffusion and convection time; mammalian vascular architecture; optimal; oxygen.

Figure 1.

Erythrocyte to cerebral tissue oxygen transport. Top-left inset (a) depicts a corrosion cast of human cortical capillary vessels (adapted from [2]). The geometry of the framed straight capillary, measuring about 50 μm in length and 12 μm in diameter, is mapped on the bottom cartoon (b), which portrays oxygen efflux from erythrocytes moving from left to right, suspended in plasma, to tissue cells. Top right (c) magnification illustrates oxygen dissociating from haemoglobin molecules, encapsulated in erythrocytes, into the plasma. Once in the plasma, free oxygen molecules cross the endothelial cell wall junctions to be transported, by free and facilitated diffusion, to tissue cells to fuel aerobic and, possibly, anaerobic glycolysis. Bottom and top-right inserts are not to scale. (Online version in colour.)

Figure 2.

Mean oxygen convection and diffusion times for Rattus norvegicus, Felis silvestris catus, Oryctolagus cuniculus and Homo Sapiens. Mean arterial capillary level diffusion and convection times were evaluated from Monte Carlo calculations. Least-squares fit of the mean convective and diffusive times yielded a straight line with equation y = 0.95x − 0.02 and R = 0.897 which demonstrates strong agreement with line y = x. Standard deviation error bars were used.