Modeling steady state SO(2)-dependent changes in capillary ATP concentration using novel O(2) micro-delivery methods

Adenosine triphosphate (ATP) is known to be released from the erythrocyte in an oxygen (O(2)) dependent manner. Since ATP is a potent vasodilator, it is proposed to be a key regulator in the pathway that mediates micro-vascular response to varying tissue O(2) demand. We propose that ATP signaling mainly originates in the capillaries due to the relatively long erythrocyte transit times in the capillary and the short ATP diffusion distance to the electrically coupled endothelium. We have developed a computational model to investigate the effect of delivering or removing O(2) to limited areas at the surface of a tissue with an idealized parallel capillary array on total ATP concentration. Simulations were conducted when exposing full surface to perturbations in tissue O(2) tension (PO(2)) or locally using a circular micro-outlet (~100 μm in diameter), a square micro-slit (200 × 200 μm), or a rectangular micro-slit (1000 μm wide × 200 μm long). Results indicated the rectangular micro-slit has the optimal dimensions for altering hemoglobin saturations (SO(2)) in sufficient number capillaries to generate effective changes in total [ATP]. This suggests a threshold for the minimum number of capillaries that need to be stimulated in vivo by imposed tissue hypoxia to induce a conducted micro-vascular response. SO(2) and corresponding [ATP] changes were also modeled in a terminal arteriole (9 μm in diameter) that replaces 4 surface capillaries in the idealized network geometry. Based on the results, the contribution of terminal arterioles to the net change in [ATP] in the micro-vascular network is minimal although they would participate as O(2) sources thus influencing the O(2) distribution. The modeling data presented here provide important insights into designing a novel micro-delivery device for studying micro-vascular O(2) regulation in the capillaries in vivo.