Name
Abstract | ||
|---|---|---|
Most studies devoted to mathematical modelling of oxygen transport to tissue have assumed a constant oxygen consumption, independent of oxygen tension, whilst oxygen concentration remains positive. However, it is more physiologically realistic to allow the oxygen consumption to fall continuously to zero as the oxygen tension falls towards zero for low oxygen tensions. We show that using this more physiologically realistic oxygen consumption in a mathematical model of oxygen transport to tissue gives a significantly different solution to the governing equations when areas of low oxygen tension exist. We then use this method of modelling oxygen consumption to compare the location of regions of low tissue oxygen tension predicted by two previously published mathematical models of oxygen transport. The two models are a partial differential equation (PDE) model, and an ordinary differential equation (ODE) model that is a simplification of the PDE model. We show that most of the predictions of the ODE model are almost identical to those of the PDE model, but there are some significant differences. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.mcm.2004.09.009 | Mathematical and Computer Modelling |
Keywords | Field | DocType |
oxygen transport,mathematical model,physiologically realistic oxygen consumption,myoglobin,constant oxygen consumption,oxygen tension,low oxygen,low oxygen tension,low tissue oxygen tension,pde model,muscle tissue,oxygen consumption,modelling oxygen consumption,partial differential equation,ordinary differential equation,mathematical modelling | Myoglobin,Differential equation,Limiting oxygen concentration,Thermodynamics,Ordinary differential equation,Oxygen,Initial value problem,Mathematical model,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
42 | 9-10 | Mathematical and Computer Modelling |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan Whiteley | 1 | 119 | 13.02 |
| David Gavaghan | 2 | 213 | 30.44 |
| C. E. W. Hahn | 3 | 0 | 0.34 |