Oxygen Deficient Metabolism in Organs: A Link to Combustion Science



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In an attempt to better understand and model transport of oxygen, O2, from capillaries to living cells in surrounding tissue, the group combustion (O2 deficient) concept from the field of combustion science in engineering is applied to the biological field of microvascular O2 transport from capillaries to cells immersed in interstitial fluid (IF). The conventional Krogh model represents typical biological models, considering tissue cylinder with uniform oxygen source/sink term (US) (m''', g/s/cm^3) and O2 transport from capillary on axis (COA) towards the surface; engineering models consider cylinders with O2 supplied from the surface of cylinder (COS); in addition, they present i) transport (diffusion) and ii) kinetics limited sink rates and profiles for O2. Diffusion limitation causes m''' to be proportional to local O2 concentration. Thus, the present work modifies COS engineering models for COA cases and considers only diffusion limited transport of O2 to metabolic cells from IF. O2 profiles and resulting specific metabolic rates, SMRs (W/g), are generated for four models: I) COA with oxygen dependent consumption source term (O2) (COA-O2), II) COA-US, III) COS-O2, and IV) COS-US. In order to validate the current approach, the model results are verified with the following different types of experimental data: A) If SMRs (mq W/g) are given by the allometric law, kbmk^kq=am for organ k, then COS models under limiting conditions suggest -1/3<bk<0 where bk=0 for small organs following isometric law and -1/3 for large organs while COA models suggest -2/3<bk<0 under similar conditions. Most experimental data for vital organs yield -0.27<bk<0 which suggests better correlation with COS models. B) Measured capillary-IF interface pressure of O2 (pO2,cap-IF) for rat mesentery system as given by Tsai et. al. is about 38 mmHg while predicted pO2,cap-IF is 54.5, 38.1, 55.3 and 46.2 mmHg for COA-O2, COS-O2, COA-US and COS-US respectively. C) Further, SMR for the average human liver is about 0.01 W/g as given by Wang et. al. (2010) while the COA-O2, COS-O2, COA-US and COS-US models yield 0.006, 0.032, 0.003 and 0.022 W/g respectively. COS models are of the same order magnitude as the experimental value while COS-US model is closest.