title: Toward a complex system understanding of bipolar disorder: A chaotic model of abnormal circadian activity rhythms in euthymic bipolar disorder.
abstract: OBJECTIVE
  In the absence of a comprehensive neural model to explain the underlying mechanisms of disturbed circadian function in bipolar disorder, mathematical modeling is a helpful tool. Here, circadian activity as a response to exogenous daily cycles is proposed to be the product of interactions between neuronal networks in cortical (cognitive processing) and subcortical (pacemaker) areas of the brain.
  
  
  OBJECTIVE
  To investigate the dynamical aspects of the link between disturbed circadian activity rhythms and abnormalities of neurotransmitter functioning in frontal areas of the brain, we developed a novel mathematical model of a chaotic system which represents fluctuations in circadian activity in bipolar disorder as changes in the model's parameters.
  
  
  METHODS
  A novel map-based chaotic system was developed to capture disturbances in circadian activity across the two extreme mood states of bipolar disorder. The model uses chaos theory to characterize interplay between neurotransmitter functions and rhythm generation; it aims to illuminate key activity phenomenology in bipolar disorder, including prolonged sleep intervals, decreased total activity and attenuated amplitude of the diurnal activity rhythm. To test our new cortical-circadian mathematical model of bipolar disorder, we utilized previously collected locomotor activity data recorded from normal subjects and bipolar patients by wrist-worn actigraphs.
  
  
  RESULTS
  All control parameters in the proposed model have an important role in replicating the different aspects of circadian activity rhythm generation in the brain. The model can successfully replicate deviations in sleep/wake time intervals corresponding to manic and depressive episodes of bipolar disorder, in which one of the excitatory or inhibitory pathways is abnormally dominant.
  
  
  CONCLUSIONS
  Although neuroimaging research has strongly implicated a reciprocal interaction between cortical and subcortical regions as pathogenic in bipolar disorder, this is the first model to mathematically represent this multilevel explanation of the phenomena of bipolar disorder.
authors.affiliation: Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran.
authors.forename: Fatemeh
authors.initials: F
authors.lastname: Hadaeghi
authors.affiliation: Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran mrhashemigolpayegani@aut.ac.ir.
authors.forename: Mohammad Reza
authors.initials: MR
authors.lastname: Hashemi Golpayegani
authors.affiliation: Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran.
authors.forename: Sajad
authors.initials: S
authors.lastname: Jafari
authors.affiliation: Department of Psychological Sciences, Faculty of Health, Arts and Design, Swinburne University of Technology, Hawthorn, VIC, Australia.
authors.forename: Greg
authors.initials: G
authors.lastname: Murray
mesh_terms: D001714:Bipolar Disorder / Q000503:physiopathology*; D002540:Cerebral Cortex / Q000503:physiopathology*; D002940:Circadian Rhythm / Q000502:physiology; D006801:Humans; D008962:Models, Theoretical; D009415:Nerve Net / Q000503:physiopathology*; D017711:Nonlinear Dynamics; D013493:Suprachiasmatic Nucleus / Q000503:physiopathology*
keywords: Bipolar disorder; chaos theory; circadian pacemaker; cognitive network; computational modeling