Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick’s Law Model of Diffusion

To investigate the impact of experimental interventions on living biological tissue, ex vivo rodent brain slices are often used as a more controllable alternative to a live animal model. However, for meaningful results, the biological sample must be known to be healthy and viable. One of the gold-standard approaches to identifying tissue viability status is to measure the rate of tissue oxygen consumption under specific controlled conditions. Here, we work with thin (400 μm) slices of mouse cortical brain tissue which are sustained by a steady flow of oxygenated artificial cerebralspinal fluid (aCSF) at room temperature. To quantify tissue oxygen consumption (Q), we measure oxygen partial pressure (pO2) as a function of probe depth. The curvature of the obtained parabolic (or parabola-like) pO2 profiles can be used to extract Q, providing one knows the Krogh coefficient Kt, for the tissue. The oxygen trends are well described by a Fick’s law diffusion–consumption model developed by Ivanova and Simeonov, and expressed in terms of ratio (Q/K), being the rate of oxygen consumption in tissue divided by the Krogh coefficient (oxygen diffusivity × oxygen solubility) for tissue. If the fluid immediately adjacent to the tissue can be assumed to be stationary (i.e., nonflowing), one may invoke conservation of oxygen flux K·(∂P/∂x) across the interface to deduce (Kt/Kf), the ratio of Krogh coefficients for tissue and fluid. Using published interpolation formulas for the effect of salt content and temperature on oxygen diffusivity and solubility for pure water, we estimate Kf, the Krogh coefficient for aCSF, and hence deduce the Kt coefficient for tissue. We distinguish experimental uncertainty from natural biological variability by using pairs of repeated profiles at the same tissue location. We report a dimensionless Krogh ratio (Kt/Kf)=0.562±0.088 (mean ± SD), corresponding to a Krogh coefficient Kt=(1.29±0.21)×10−14 mol/(m·s·Pa) for mouse cortical tissue at room temperature, but acknowledge the experimental limitation of being unable to verify that the fluid boundary layer is truly stationary. We compare our results with those reported in the literature, and comment on the challenges and ambiguities caused by the extensive use of ‘biologically convenient’ non-SI units for tissue Krogh coefficient.