A parameter identification problem arising from a model of canalicular bile formation

Area of Science:

• Mathematical Biology
• Physiological Modeling

Background:

• Bile formation is a complex physiological process.
• Understanding bile transport phenomena is crucial but challenging.
• Current methods for observing bile transport are limited.

Purpose of the Study:

• To develop a mathematical model for bile formation.
• To identify physical parameters influencing bile formation.
• To suggest designs for future physiological experiments to study bile transport.

Main Methods:

• Formulated a mathematical model for bile formation.
• The model resulted in a boundary value problem for functional differential equations.
• Converted the boundary value problem to a transition time problem for quadratic ordinary differential equations.

Main Results:

• Qualitative and quantitative identification of physical parameters from boundary values.
• The mathematical parameter identification problem was solved using properties of quadratic systems.
• The model provides a framework for inferring unobservable bile transport phenomena.

Conclusions:

• The developed mathematical model offers insights into bile formation.
• Parameter identification facilitates the design of targeted physiological experiments.
• This approach enhances the understanding of complex bile transport mechanisms.