A parameter identification problem arising from a model of canalicular bile formation.
A parameter identification problem arising from a model of canalicular bile formation.
复制标题
胆管形成模型产生的参数识别问题。
DOI：
10.1007/bf00166146
复制
发表时间：
1993
影响因子：
1.9
通讯作者：
Forker,EL
中科院分区：
文献类型：
--
作者：
Chicone,CC;Cai,ZS;King,PD;Forker,EL
我们建立了一个胆汁形成的简单数学模型，并分析了该模型的一些特征，为未来的生理实验设计提供了建议。数学模型的结果是一个依赖于几个物理参数的泛函微分方程系统的边值问题。根据边界值的可观测性，我们可以定性和定量地确定其中一些物理参数。这一鉴定表明，通过物理实验，人们可以推断出一些目前还不能直接观察到的胆汁转运现象。将平面上常微分方程组的二次方程组的边值问题转化为过渡时间问题，利用二次方程组的一些特殊性质求解数学参数辨识问题。
We develop a simple mathematical model for bile formation and analyze some features of the model that suggest the design for future physiological experiments. The mathematical model results in a boundary value problem for a system of functional differential equations depending on several physical parameters. From the observability of the boundary values we can identify, both qualitatively and quantitatively, some of these physical parameters. This identification then suggests physical experiments from which one could infer some of the bile transport phenomena that are not, at present, directly observable. The mathematical parameter identification problem is solved by converting the boundary value problem to a transition time problem for a quadratic system of ordinary differential equations on the plane where we are able to employ some special properties of quadratic systems in order to obtain a solution.