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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

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Depression diagnostics using a nonlinear mathematical oscillatory model.

L Cveticanin¹, J S Baker²

¹Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia; Doctoral School of Safety and Security Sciences, Obuda University, Budapest, Hungary.

Computer Methods and Programs in Biomedicine

|June 20, 2024

Summary

This summary is machine-generated.

This study models cortisol variation using a nonlinear oscillator to detect depression. Deterministic chaos in cortisol levels, resulting from long-term stress, indicates potential depressive states.

Keywords:

Adrenocorticotropin Chaos Cortisol Nonlinear vibration Resonance Ultradian rhythm

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Published on: December 10, 2014

Area of Science:

Endocrinology
Mathematical Biology
Psychiatry

Background:

Long-term stress can lead to trauma and depression.
Current depression diagnosis relies on subjective interviews, which may lack reliability.
Disturbances in cortisol levels are early indicators of potential mental health conditions.

Purpose of the Study:

To develop a mathematical model for cortisol variation under stress.
To utilize the model for identifying depressive states.
To improve the timeliness and accuracy of depression diagnosis.

Main Methods:

Modeled cortisol concentration changes as a nonlinear oscillator, incorporating ultradian rhythms.
Developed a mathematical model with two coupled first-order differential equations.
Simulated stress as a pulsating trigonometric function and cortisol production as a cubic nonlinear function, analyzing nonlinear, periodically excited, and chaotic systems.

Main Results:

Cortisol variation exhibits oscillatory behavior without stress.
Intensive stress can induce resonance in cortisol oscillations.
Long-term stress leads to deterministic chaos in cortisol levels, serving as a depression indicator.
Model predictions showed good quantitative agreement with experimental data.

Conclusions:

A nonlinear oscillator model effectively indicates depression.
The model offers both general and individualized diagnostic insights based on personal characteristics.
Cortisol level fluctuations, influenced by stress and individual parameters, are crucial for depression assessment.
Findings support enhanced medical diagnosis and treatment strategies for depression.