Partial Differential Equation (PDE), Models
Partial differential equation (PDE) models are sets of equations describing the evolution of a physical quantity, not only with time, but also according to a structure variable such as space. They may be used for the physiological modeling of the evolution of a biological substance (e.g., a drug in an organism) submitted to changes, rather than ODE models (q.v.) when some physical or physiological knowledge of the medium containing it is available. Then derivatives are partial, meaning that they are calculated not only with respect to time but also with respect to a structure variable relevant to the representation of the medium. This structure variable may be space, which implies using spatial coordinates in 1, 2, or 3 dimensions; it may also be a physiological variable such as age in the cell division cycle (q.v.) or molecular content, for example, in DNA or cyclins (Perthame 2007). PDEs are often derived from ODEs by adding to the equations a transport term (e.g.,...
- Perthame B (2007) Transport equations in biology. Birkhäuser, BaselGoogle Scholar