An algorithm for identifiable parameters and parameter bounds for a class of cascaded mammillary models

Area of Science:

• Pharmacokinetics and Systems Biology
• Mathematical Modeling of Biological Systems
• Chemical Kinetics

Background:

• Mammillary models are crucial for understanding drug and metabolite kinetics.
• Structural identifiability is a key challenge in analyzing these complex models.
• Previous methods lacked explicit algorithms for multi-input, multi-compartment systems.

Purpose of the Study:

• To address the structural identifiability problem in unidirectionally interconnected n-compartment linear mammillary models.
• To develop an explicit algorithm for parameter estimation in these complex kinetic systems.
• To enable determination of parameter combinations, bounds, pool sizes, and production rates.

Main Methods:

• Development of an explicit algorithm tailored for n-compartment linear mammillary models.
• Application of the algorithm to a six-compartment model of thyroxine (T4) and triiodothyronine (T3) dynamics.
• Utilizing input forcing and output measurements from central compartments.

Main Results:

• The algorithm successfully provides identifiable parameter combinations and their bounds.
• Steady-state pool sizes and production rates were determined.
• Physiological parameter values, including T4 to T3 conversion rates and individual T4/T3 production rates, were elucidated.

Conclusions:

• The developed algorithm effectively solves the structural identifiability problem for this class of models.
• Stimulus-response measurements in plasma alone are sufficient for determining key physiological parameters.
• This approach has significant implications for drug kinetics and interconversion processes.