Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver
| Autor: | E. Benjamin Randall, Nicholas Z. Randolph, Mette S. Olufsen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Adult Valsalva Maneuver medicine.medical_treatment Models Neurological Blood Pressure Dynamical Systems (math.DS) Autonomic Nervous System Instability Quantitative Biology - Quantitative Methods General Biochemistry Genetics and Molecular Biology 03 medical and health sciences symbols.namesake Postural Orthostatic Tachycardia Syndrome 0302 clinical medicine Transcritical bifurcation Control theory Heart Rate Valsalva maneuver medicine FOS: Mathematics Humans Mathematics - Dynamical Systems Quantitative Methods (q-bio.QM) 030304 developmental biology Mathematics Hopf bifurcation 0303 health sciences General Immunology and Microbiology Applied Mathematics General Medicine Delay differential equation Models Theoretical Nonlinear system Autonomic nervous system Modeling and Simulation FOS: Biological sciences symbols General Agricultural and Biological Sciences 030217 neurology & neurosurgery |
| Popis: | Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may signify (i) an attempt to return to homeostasis or (ii) system dysfunction. In this study, we analyze a nonlinear, nonautonomous, nonhomogeneous open-loop neurological control model describing the autonomic nervous system response to the Valsalva maneuver. Unstable modes have been identified as a result of parameter interactions between the sympathetic delay and time-scale. In a two-parameter bifurcation analysis, we examine both the homogeneous and nonhomogeneous systems. Discrepancies between solutions result from the presence of the forcing functions which stabilize the system. We use analytical methods to determine stability regions for the homogeneous system, identifying transcendental relationships between the parameters. We also use computational methods to determine stability regions for the nonhomogeneous system. The presence of a Hopf bifurcation within the system is discussed and solution types from the sink and stable focus regions are compared to two control patients and a patient with postural orthostatic tachycardia syndrome (POTS). The model and its analysis support the current clinical hypotheses that patients suffering from POTS experience altered nervous system activity. Mathematical Biosciences, 2019 |
| Databáze: | OpenAIRE |
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