Bipolar oscillations between positive and negative mood states in a computational model of Basal Ganglia

Abstract

Bipolar disorder is characterized by mood swings-oscillations between manic and depressive states. The swings (oscillations) mark the length of an episode in a patient's mood cycle (period), and can vary from hours to years. The proposed modeling study uses decision making framework to investigate the role of basal ganglia network in generating bipolar oscillations. In this model, the basal ganglia system performs a two-arm bandit task in which one of the arms (action responses) leads to a positive outcome, while the other leads to a negative outcome. We explore the dynamics of key reward and risk related parameters in the system while the model agent receives various outcomes. Particularly, we study the system using a model that represents the fast dynamics of decision making, and a module to capture the slow dynamics that describe the variation of some meta-parameters of fast dynamics over long time scales. The model is cast at three levels of abstraction: (1) a two-dimensional dynamical system model, that is a simple two variable model capable of showing bistability for rewarding and punitive outcomes; (2) a phenomenological basal ganglia model, to extend the implications from the reduced model to a cortico-basal ganglia setup; (3) a detailed network model of basal ganglia, that incorporates detailed cellular level models for a more realistic understanding. In healthy conditions, the model chooses positive action and avoids negative one, whereas under bipolar conditions, the model exhibits slow oscillations in its choice of positive or negative outcomes, reminiscent of bipolar oscillations. Phase-plane analyses on the simple reduced dynamical system with two variables reveal the essential parameters that generate pathological 'bipolar-like' oscillations. Phenomenological and network models of the basal ganglia extend that logic, and interpret bipolar oscillations in terms of the activity of dopaminergic and serotonergic projections on the cortico-basal ganglia network dynamics. The network's dysfunction, specifically in terms of reward and risk sensitivity, is shown to be responsible for the pathological bipolar oscillations. The study proposes a computational model that explores the effects of impaired serotonergic neuromodulation on the dynamics of the cortico basal ganglia network, and relates this impairment to abstract mood states (manic and depressive episodes) and oscillations of bipolar disorder.

Keywords: Basal risk sensitivity; Cortico-basal ganglia network; Dopamine dysfunction; Reward hypersensitivity; Serotonin dysfunction.

Fig. 1

Schematic relating important components of models A, B, and C with regards to the construction of utility and the auxillary dynamics

Fig. 2

Model A and B outline: a schematic of the network model of the basal ganglia as block diagram, b schematic of the network model to include the cellular substrates involved in the neural dynamics adapted from Balasubramani et al (2014, 2015a, b). Refer to Balasubramani et al. (2014, 2015b) for details on the network model of the basal ganglia

Fig. 3

Softmax-based phenomenological model behavior: the topmost panel shows the stability of solutions as a function of Ar and k. Solutions were found from the model trajectories; monostable solution could indicate either positive or negative action stability, and oscillations indicate swings between positive and negative actions with varying time periods. Instances of each solution are provided as cases a–c: solutions stabilizing at positive state regime as shown in case a for parameters Ar = 0.001 and k = −500, and solutions stabilizing at negative action as in case b are shown for parameters Ar = 0.001 and k = 500. Oscillations, case c, are shown for parameters Ar = 500, and k = −0.001. The trajectories in cases a–c are illustrated for 13 different initial α’s, and Ar, k are chosen from the bifurcation plot as indicated in the first panel, and fixed for all 13 α initializations

Fig. 4

BG network model behavior: the first panel shows the stability of solutions as a function of A_r and k. Solutions were found from the model trajectories; monostable solution could indicate either positive or negative action stability, and oscillations indicate between among positive and negative actions with varying time periods. Instances of each solution are provided as cases a–c: solutions stabilizing at positive action regime as shown in case a for parameters A_r = 0.001 and k = −500, and solutions stabilizing at negative action as in case b are shown for parameters A_r = 0.001 and k = 500. Oscillations, case c, are shown for parameters A_r = 100, and k = −0.001. The trajectories in cases a–c are illustrated for 13 different initial α’s, and Ar, k are chosen from the bifurcation plot as indicated in the first panel, and fixed for all 13 α initializations

Fig. 5

Reduced dynamical system model behavior: The first panel show the stability of solutions as a function of Ar and k found through bifurcation analysis, with other parameters initialized to a = −6, and μ = 0.6. Monostable solution showing positive, negative ‘x’ stability; and Bipolar oscillations indicate swings between positive and negative states with varying time periods. Instances of each solution are provided as cases a–c: trajectories and phase planes for dynamics stabilizing at positive state regime as shown in case a, at a negative state are shown in case b, oscillations in case c. The trajectories are illustrated for 13 different initial α’s, and Ar, k are chosen from the bifurcation plot as indicated in the first panel, and fixed for all 13 α initializations

Fig. 6

Explaining subject’s data-QIDS score: this figure shows QIDS-SR16 (Quick Inventory of Depressive Symptomology) scores of six patients, that are indicative of analyzing the treatment options for bipolar patients, adapted from Bonsall et al. (2012, 2015) and Rush et al. (2006) and normalized (divided by the max score of 27) for visualization. The model results indicating the proportional selection of negative states are presented for comparison, the data is linearly smoothened with window size of 15, the optimized parameters, Ar, k, and α as indicated in the figure for every subject