Mathematical modelling of oxygen transport to tissue.
The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co-axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non-linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non-dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically.
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
Jonathan P
JP
Whiteley
David J
DJ
Gavaghan
Clive E W
CE
Hahn
D002196:Capillaries / Q000502:physiology; D006454:Hemoglobins / Q000378:metabolism*; D008954:Models, Biological; D009211:Myoglobin / Q000378:metabolism*; D009716:Numerical Analysis, Computer-Assisted; D010100:Oxygen / Q000097:blood / Q000378:metabolism*
D006454:Hemoglobins; D009211:Myoglobin; D010100:Oxygen