Endocrine System Modelling

Summary

Mathematical models of feedback loops predict hormone dynamics and treatment responses.

In depth

Models use differential equations for feedback loops, e.g. glucose-insulin dynamics used in artificial pancreas devices; menstrual cycle models predict ovulation; pharmacokinetic and pharmacodynamic models.

Models predict responses to drugs and guide diagnosis. Closed-loop systems are used in diabetes.

Key idea: feedback loops can be described mathematically.

Mathematical models represent hormone systems as differential equations with feedback. A basic model of the insulin-glucose system, such as the minimal model of Bergman, predicts glucose after a dose and estimates insulin sensitivity.

Models of the HPA axis, thyroid axis and menstrual cycle reproduce oscillations and responses to drugs, showing that delays and nonlinear feedback produce rhythms and bistability. They are used to optimise treatment, as in the artificial pancreas, a closed-loop system with a continuous glucose monitor, algorithm and insulin pump that mimics a pancreas. Parameters are estimated from patient data, and uncertainty is often large.

Example: control theory is applied to dosing hormone therapy.

Key idea: models let us test hypotheses and design personalised therapies.