今日の論文
- Tornoe, ..., Jonsson, et al. (2004) Comp Methods Programs Biomed, "Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations"
- このパッケージの特徴は次の二点だと思う．しかし，このことについて，何らかの検討をした結果，あるいは，議論は述べられていない．何だそれ．
The alogorithm used in lsoda*1 includes automatic selection between methods for stiff and non-stiff systems of ODE's. The definition of a stiff system is a system with two or more eigenvalues where the real parts of the eigenvalues are very different in magnitude. Adam's method is used for solving non-stiff systems of ODE's while the backwards differentiation formula is used for stiff systems.
In order to investigate the possibility of increasing the numerical stability and the rate of convergence of the NLME algorithm, a gradient attribute is included by simultaneous solution to the associated sensitivity equations to be used in the Gauss-Newton non-linear least-squares optimization algorithm.*2
These methods*3 are not able to handle systems with discontinuities arising from multiple doses or infusions. These problems are overcome by using the critical time argument in lsoda and by calling lsoda separately for each discontinuity so that the solver does not attempt to integrate over the discontinuity.
