PHYSICAL REVIEW E 89, 062710 (2014) Noise-induced organized slow fluctuations in networks of neural areas with interarea feed-forward excitation and inhibition Dongmyeong Lee, 1 Seunghwan Kim, 2, 3 and Tae-Wook Ko 4 , * 1 Center for Neuroscience, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea 2 Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea 3 Asia Pacific Center for Theoretical Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea 4 National Institute for Mathematical Sciences, Daejeon 305-811, Republic of Korea (Received 17 February 2014; revised manuscript received 11 April 2014; published 23 June 2014) Slow coherent spontaneous fluctuations (<0.1 Hz) in functional magnetic resonance imaging blood-oxygen- level-dependent signals have been observed for a resting state of the human brain. In this paper, considering feed-forward inhibition in addition to excitation between brain areas, which we assume to be in up (active) or down (quiescent) states, we propose a model for the generation and organization of the slow fluctuations. Connectivity with feed-forward excitation and inhibition between the areas makes the system have multiple stable states and organized slow fluctuations manifest as noise-induced slow transitions between the states. With various connectivities, we observe slow fluctuations and various organizations, including anticorrelated clusters, through numerical simulations. DOI: 10.1103/PhysRevE.89.062710 PACS number(s): 87.19.lj, 05.45.−a, 87.19.lf , 87.19.lc I. INTRODUCTION Slow coherent spontaneous fluctuations (<0.1 Hz) in functional magnetic resonance imaging (fMRI) blood-oxygen- level-dependent (BOLD) signals, which are an indirect mea- sure of underlying neuronal activity, have been observed for an awake resting state of the human brain without attention- demanding cognitive tasks [1–7]. Functional connectivity analysis measuring the correlation between the time series from brain areas identifies clusters of brain areas showing correlated fluctuations. This is not specific to the resting human brain, but such clusters have been observed in anesthetized brains of humans [8], monkeys [9,10], and rats [11] and in resting brains of monkeys [12] and rats [13–15]. Moreover, it was shown that the resting human brain contains anticorrelated clusters, one of which is composed of brain areas exhibiting task-related activations while the other is composed of those exhibiting task-related deactivations [4]. These observations support that the resting-state BOLD fluctuation is not a noise but reflects intrinsic spontaneous neuronal activity and the functional architecture of the brain and the functional role of the activity has been investigated in connection with the functions such as memory, coordination of neural activity, and prediction [5–7,16]. In this regard, brain malfunctions of patients with brain disorders such as Alzheimer’s disease, schizophrenia, and autism manifest as alteration of the resting- state brain functional connectivity [16–20]. The mechanism for the generation of the coherent fluc- tuation is the key to understanding the functional role and the alteration of the activity, but it has not been fully explained. Through comparisons of functional and anatomical connectivities, it has been shown that functional connectivity of the resting state is constrained by anatomical connectiv- ity [5,9,16,21–25]. With anatomical connectivity as one of the key factors, several mechanisms for the resting-state activity have been proposed [24–31], including the organized slow * Corresponding author: twko@nims.re.kr evolution of synchronization and desynchronization of fast dynamics [24,25], noise-driven exploration of the dynamic repertoire around an equilibrium [27–29], noise-driven transi- tions between multistable cluster synchronization states [30], and correlation of slow neural activity fluctuations inside clusters of entrained brain areas [31]. Signal transmission delays between brain areas are considered as one of the key factors in Refs. [27,30,31]. However, interarea feed-forward inhibition has rarely been considered in the previous modeling studies of resting- state fluctuations. Local inhibitory dynamics and excitation- inhibition gain control are major determinants of self- organized activity in the brain [32,33]. Although most interarea or extrinsic connections are excitatory ones mediated by gluta- mate, many connections target inhibitory interneurons within the cortex [32,33]. In particular, backward or descending connections in cortical hierarchies may preferentially target inhibitory interneurons especially in the superficial cortical layers [34,35]. These feed-forward inhibitory influences are crucial for self-organized and critical fluctuations and will play an important role in our approach to modeling the resting-state brain activity. In this study, motivated by the slowness of the fluctuation and the existence of anticorrelated clusters, we propose an explanation of the resting-state activity as noise-induced slow transitions between multistable states, in which each brain area can be in one of the two competing states, the so-called up (active) and down (quiescent) states [36–39], on networks with feed-forward inhibition between some of the areas. A recent fMRI study focusing on the brain areas called the amygdala and the infralimbic cortex (IL) supports this idea and showed that the feed-forward inhibitory interaction between the two ar- eas, which has been confirmed neurobiologically, could cause the anticorrelated relationship between the areas [15]. Another supporting study showed that pharmacological disruption of excitatory neurotransmission causes reduction in task-related activation and deactivation during a working memory task and this can be explained in the frame of reciprocal inhibition between brain areas exhibiting task-related activation and 1539-3755/2014/89(6)/062710(10) 062710-1 ©2014 American Physical Society