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.
Whiteley
Jonathan P
JP
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
Gavaghan
David J
DJ
Hahn
Clive E W
CE
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