Abstract
Bipolar disorder is a common psychiatric dysfunction characterized by recurring episodes of mania and depression. Despite its prevalence, the causes and mechanisms of bipolar disorder remain largely unknown. Recently, theories focusing on the interaction between emotion and behavior, including those based on dysregulation of the so-called behavioral approach system (BAS), have gained popularity. Mathematical models built on this principle predict bistability in mood and do not invoke intrinsic biological rhythms that may arise from interactions between mood and expectation. Here we develop and analyze a model with clinically meaningful and modifiable parameters that incorporates the interaction between mood and expectation. Our nonlinear model exhibits a transition to limit cycle behavior when a mood-sensitivity parameter exceeds a threshold value, signaling a transition to a bipolar state. The model also predicts that asymmetry in response to positive and negative events can induce unipolar depression/mania, consistent with clinical observations. We analyze the model with asymmetric mood sensitivities and show that large unidirectional mood sensitivity can lead to bipolar disorder. Finally, we show how observed effects of lithium- and antidepressant-induced mania can be explained within the framework of our proposed model.
Highlights
Bipolar disorder is characterized by cycling between manic and depressive episodes (Geller & Luby, 1997)
We propose a continuous-time model based on interactions between the dynamical variables of mood m(t), expectation v(t), and reality r(t): dm dt ηm( f m ηv( f m
These results suggest that the mood sensitivity controls a spectrum of personality responses, from normal to cyclothymic, and is a key determinant in triggering bipolar disorder as its threshold is exceeded
Summary
Bipolar disorder is characterized by cycling between manic and depressive episodes (Geller & Luby, 1997). The models describe mood as being formed from an intrinsically oscillatory brain circuit and explain self-reported mood scores as well as the effects of medication Following these studies, a natural step is to clarify the mechanism of the oscillations and distinguish key differences between normal individuals and patients with bipolar disorder (see Goldbeter, 2011). The mood in our model directly reflects the prediction-error history but is susceptible to the effects of a higher order recovery term −k3m3, distinguishing it from both Eldar and Niv (2015) and Eldar et al (2016) This difference represents two mechanisms for bounding the mood: explicitly specifying the limits of the mood through the tanh function and limiting the mood through a general (allowed by symmetry) cubic “force” term in the dynamics. The system (1, 2) is solved by explicit fourth to fifth order Runge–Kutta solvers (Dormand & Prince, 1980), carried out by the ode function in MATLAB
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