Mathematically modeling the Neurochemistry of Human Sleep-wake Cycles
Lisa Rogers, CIMS
In order to improve upon previously established mathematical models of human sleep/wake system behavior, an analysis, computation and experimental data driven construction of the complex system is presented. The correlations between the chemical and mathematical aspects of specific neuron function is used to determine the mechanics of the sleep/wake cycle. Aspects of circadian biology theory are utilized, with an emphasis on the buildup of restorative REM/NREM oscillations to demonstrate the unfailing circadian regulation process. The construction of the model draws upon limit cycle behavior and stability theory with references to an established background in the laws of mass action. The initial assumptions and predictions are validated by a combination of computational methods and previously established knowledge of the function of human circadian processes. The consequences of qualitative and quantitative analysis are utilized to establish various physiological implications. We use neurotransmitter data from experimentalists to derive equations. We use a linearized stability analysis as well as eigenvalue-finding algorithms to help find coefficients of the system and to determine a reasonable area in which solutions exist. We then use experimental data from normal sleep- wake systems and orexin knockout systems to verify the physiological validity of the equations.