Oxygen delivery to skeletal muscle has been modeled in a Krogh Tissue Cylinder Model with a mixture of human red blood cells and hemoglobin based oxygen carriers. The model geometry consists of three distinct subdomains representing the capillary, the membrane wall of the capillary, and the skeletal muscle tissue space. Oxygen transport in each of these subdomains is represented by a nonlinear partial differential equation. These PDEs were solved using the finite element method in Comsol Multiphysics 3.2. The oxygen dissociation curves were represented by the four parameter Adair equation, which more accurately models the data at high and low pO₂s. The following parameters were studied in detail: the oxygen affinities of hemoglobin based oxygen carriers (P₅₀s) ranging from 5-55 mmHg; tissue oxygen consumption rates (V_max) ranging from 5-150 μM/s; human red blood cell hematocrits ranging from 0.1-0.5; and capillary inlet pO₂s ranging from 5-115 mmHg.

Our results show that at low inlet pO₂s, high affinity O₂ carriers most effectively deliver O₂ to tissues compared to the low affinity O₂ carriers. Additionally, low affinity O₂ carriers delivered similar amounts of O₂ to the skeletal muscle at normoxic inlet pO₂s compared to human red blood cells and high affinity O₂ carriers. However, the pO₂ tensions in each subdomain were higher for the the oxygen transport simulations conducted with low affinity O₂ carriers. This increased oxygen tension can be the cause of the autoregulatory induced vasoconstriction effect seen in clinical HBOC studies.