A model of countercurrent shunting of oxygen in the intestinal villus

Abstract

This report describes a mathematical model of the countercurrent shunting (CCS) of O2 in the intestinal villus. The anatomic basis for the model is the close proximity of the arteriole and venule between which O2 is free to diffuse. The model divides the villus into four segments from base to tip. Steady-state equations describe the convective and diffusive fluxes of O2 in the arteriolar, capillary, and tissue compartments within each segment. Longitudinal diffusion along the length of the villus is assumed to be negligible. Simulations with the model led to the following observations: 1) CCS shifted the VO2 vs. blood flow curve down and to the right, slightly impairing VO2 at a given blood flow; 2) the base-to-tip PO2 gradient caused by the tissue O2 consumption was reduced by CCS; 3) when blood flow was reduced, the base-to-tip PO2 gradient increased until the tip PO2 fell to zero and then fell with further flow reductions; 4) lowering blood flow initially caused slight increases in shunting but further decreases in flow reduced shunting; 5) in the blood flow range in which VO2 was flow independent, increasing the O2 demand or decreasing the intervascular distance increased shunting because of the greater arteriole-to-capillary O2 concentration gradient and the decreased diffusion distance, respectively; and 6) lowering the hemoglobin's P50 to simulate fetal blood caused slight reductions in shunting and reduced VO2 at a given flow. In summary, the model confirms the potentially deleterious effects of CCS on intestinal oxygenation, and, in contrast to assertions in the literature, it shows that a base-to-tip PO2 gradient is not prima facie evidence of counter-current shunting.