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A stochastic differential equation model of diurnal cortisol patterns
E N Brown1, P M Meehan, A P Dempster
1Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA 02114, USA. brown@SRLB.mgh.harvard.edu
American Journal of Physiology. Endocrinology and Metabolism
|February 15, 2001
Summary
This study introduces a novel mathematical model to explain the daily fluctuations in plasma cortisol levels. The model integrates hormone secretion, clearance, and measurement errors, offering a unified framework for understanding cortisol dynamics.
Area of Science:
- Endocrinology
- Mathematical Biology
- Physiology
Background:
- Plasma cortisol levels exhibit diurnal variations due to physiological processes.
- These variations are influenced by ultradian secretory events, circadian amplitude modulation, hormone infusion, and hepatic clearance.
- Cortisol immunoassay measurements include inherent error.
Purpose of the Study:
- To develop a unified mathematical model for plasma cortisol diurnal variation.
- To integrate ultradian, circadian, and kinetic properties of cortisol into a single framework.
- To establish a method for parameter estimation and sensitivity analysis.
Main Methods:
- Development of a stochastic differential equation model with measurement error.
- Determination of physiologically consistent parameter ranges from published data.
- Utilizing multivariate Gaussian probability density for parameter summarization.
- Conducting simulation studies to validate model plausibility.
Main Results:
- The model successfully unifies cortisol's ultradian, circadian, and kinetic properties.
- Physiologically plausible parameter ranges were determined.
- The model allows for simultaneous sensitivity analysis of all parameters.
- Simulation studies confirmed the model's validity.
Conclusions:
- A novel mathematical framework accurately represents diurnal cortisol dynamics.
- The model provides a tool for analyzing cortisol secretion and clearance.
- This paradigm is adaptable for studying other endocrine hormone systems.
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