A mathematical model of tissue axial and radial diffusion in the microvasculature for intravascular microscopy and phosphorescence quenching data

Abstract

This study aims to extend earlier Krogh Cylinder Models of an oxygen profile by considering axial diffusion and analytically solving Fick's Law Partial Differential Equation with novel boundary conditions via the separation of variables. We next prospectively collected a total of 20 animals, which were randomly assigned to receive either fresh or two-week-old stored red blood cell (RBC) transfusions and PQM oxygen data were measured acutely (90 min) or chronically (24 h). Transfusion effects were evaluated in vivo using intravital microscopy of the dorsal skinfold window chamber in Golden Syrian Hamsters. Hamsters were initially hemorrhaged by 50% of total blood volume and resuscitated 1-h post hemorrhage. PQM data were subsequently collected and fit the derived 2D Krogh cylinder model. Systemic hemodynamics (mean arterial pressure, heart rate) were similar in both pre and post-transfusion with either stored or fresh cells. Transfusion with stored cells was found to impair axial and radial oxygen gradients as quantified by our model and consistent with previous studies. Specifically, we observed a statistically significant decrease in the arteriolar tissue radial oxygen gradient after transfusion with stored RBCs at 24 h compared with fresh RBCs (0.33 ± 0.17 mmHg μ m-1 vs, 0.14 ± 0.12 mmHg μ m-1; p = 0.0280). We also observed a deficit in the arteriolar tissue oxygen gradient (0.03 ± 0.01 mmHg μ m-1 fresh vs. 0.018 ± 0.007 mmHg μ m-1 stored; p = 0.0185). We successfully derived and validated an analytical 2D Krogh cylinder model in an animal model of microhemodynamic oxygen diffusion aberration secondary to storage lesions.