A parameter identification problem arising from a model of canalicular bile formation
| Autor: | Carmen Chicone, E. L. Forker, Z. S. Cai, P. D. King |
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| Rok vydání: | 1993 |
| Předmět: |
Osmosis
Differential equation Applied Mathematics Bile Canaliculi Observable Blood Physiological Phenomena Models Biological Agricultural and Biological Sciences (miscellaneous) Parameter identification problem Quadratic equation Control theory Modeling and Simulation Ordinary differential equation Animals Bile Humans Applied mathematics Boundary value problem Observability Transport phenomena Mathematics |
| Zdroj: | Journal of Mathematical Biology. 31:273-289 |
| ISSN: | 1432-1416 0303-6812 |
| DOI: | 10.1007/bf00166146 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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