Frontiers in Applied Mathematics and Statistics (Oct 2020)
Stabilizing Circadian Rhythms in Bipolar Disorder by Chaos Control Methods
Abstract
Bipolar disorder (BD), which involves mood swings between mania and depression, is associated with multiple relapses during long-term treatment and high suicide and morbidity rates. In BD, the circadian rhythms, which are measured by daily mood scores and actigraphic records, are disturbed. Chronotherapy has emerged as a potential treatment for BD because it stabilizes the disturbed circadian rhythms and improves BD symptoms. Concrete treatments include light therapy and combination therapy (light therapy and drugs). However, some patients have difficulty adjusting to light therapy; inappropriate light and duration of treatment increase risks for inducing mixed states and the emergence of conditions, such as hypomania and autonomic hyperactivation. Therefore, it is important to devise methods for optimizing chronotherapy for BD. We aimed to develop feedback signals for the frontal cortex, which were based on the delayed feedback method as one of the chaos control methods, to stabilize the disturbed circadian rhythms of BD. Concrete procedures of this study are indicated as follows: first, circadian rhythms of BD are reproduced using the frontal cortex and hypothalamus neural system, which has been previously proposed. Second, the delayed feedback signal is developed by using bifurcation analysis. Third, the effect of delayed feedback signal is evaluated by index for complexity, and power spectrum under the condition with/without stochastic noise in feedback term. We found that application of the delayed feedback signal to the frontal cortical neural activity induces the periodic state of circadian rhythms from the disturbed complex and is feasible for treating BD. However, when increasing the influence of noise in feedback term, the stabilizing effect is diminished. In conclusion, we developed a stabilizing method for disturbed circadian rhythms of BD using the circadian neural systems. The present study highlights the potential usefulness of the chaos control method for treating BD.
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