Avalanche criticality in individuals, fluid intelligence, and working memory.

The critical brain hypothesis suggests that efficient neural computation can be achieved through critical brain dynamics. However, the relationship between human cognitive performance and scale-free brain dynamics remains unclear. In this study, we investigated the whole-brain avalanche activity and its individual variability in the human resting-state functional magnetic resonance imaging (fMRI) data. We showed that though the group-level analysis was inaccurate because of individual variability, the subject wise scale-free avalanche activity was significantly associated with maximal synchronization entropy of their brain activity. Meanwhile, the complexity of functional connectivity, as well as structure-function coupling, is maximized in subjects with maximal synchronization entropy. We also observed order-disorder phase transitions in resting-state brain dynamics and found that there were longer times spent in the subcritical regime. These results imply that large-scale brain dynamics favor the slightly subcritical regime of phase transition. Finally, we showed evidence that the neural dynamics of human participants with higher fluid intelligence and working memory scores are closer to criticality. We identified brain regions whose critical dynamics showed significant positive correlations with fluid intelligence performance and found that these regions were located in the prefrontal cortex and inferior parietal cortex, which were believed to be important nodes of brain networks underlying human intelligence. Our results reveal the possible role that avalanche criticality plays in cognitive performance and provide a simple method to identify the critical point and map cortical states on a spectrum of neural dynamics, ranging from subcriticality to supercriticality.

Effects of channel blocking on information transmission and energy efficiency in squid giant axons.

Action potentials are the information carriers of neural systems. The generation of action potentials involves the cooperative opening and closing of sodium and potassium channels. This process is metabolically expensive because the ions flowing through open channels need to be restored to maintain concentration gradients of these ions. Toxins like tetraethylammonium can block working ion channels, thus affecting the function and energy cost of neurons. In this paper, by computer simulation of the Hodgkin-Huxley neuron model, we studied the effects of channel blocking with toxins on the information transmission and energy efficiency in squid giant axons. We found that gradually blocking sodium channels will sequentially maximize the information transmission and energy efficiency of the axons, whereas moderate blocking of potassium channels will have little impact on the information transmission and will decrease the energy efficiency. Heavy blocking of potassium channels will cause self-sustained oscillation of membrane potentials. Simultaneously blocking sodium and potassium channels with the same ratio increases both information transmission and energy efficiency. Our results are in line with previous studies suggesting that information processing capacity and energy efficiency can be maximized by regulating the number of active ion channels, and this indicates a viable avenue for future experimentation.

Energy-efficient neural information processing in individual neurons and neuronal networks.

Brains are composed of networks of an enormous number of neurons interconnected with synapses. Neural information is carried by the electrical signals within neurons and the chemical signals among neurons. Generating these electrical and chemical signals is metabolically expensive. The fundamental issue raised here is whether brains have evolved efficient ways of developing an energy-efficient neural code from the molecular level to the circuit level. Here, we summarize the factors and biophysical mechanisms that could contribute to the energy-efficient neural code for processing input signals. The factors range from ion channel kinetics, body temperature, axonal propagation of action potentials, low-probability release of synaptic neurotransmitters, optimal input and noise, the size of neurons and neuronal clusters, excitation/inhibition balance, coding strategy, cortical wiring, and the organization of functional connectivity. Both experimental and computational evidence suggests that neural systems may use these factors to maximize the efficiency of energy consumption in processing neural signals. Studies indicate that efficient energy utilization may be universal in neuronal systems as an evolutionary consequence of the pressure of limited energy. As a result, neuronal connections may be wired in a highly economical manner to lower energy costs and space. Individual neurons within a network may encode independent stimulus components to allow a minimal number of neurons to represent whole stimulus characteristics efficiently. This basic principle may fundamentally change our view of how billions of neurons organize themselves into complex circuits to operate and generate the most powerful intelligent cognition in nature. © 2017 Wiley Periodicals, Inc.

Functional connectivity and information flow of the respiratory neural network in chronic obstructive pulmonary disease.

Breathing involves a complex interplay between the brainstem automatic network and cortical voluntary command. How these brain regions communicate at rest or during inspiratory loading is unknown. This issue is crucial for several reasons: (i) increased respiratory loading is a major feature of several respiratory diseases, (ii) failure of the voluntary motor and cortical sensory processing drives is among the mechanisms that precede acute respiratory failure, (iii) several cerebral structures involved in responding to inspiratory loading participate in the perception of dyspnea, a distressing symptom in many disease. We studied functional connectivity and Granger causality of the respiratory network in controls and patients with chronic obstructive pulmonary disease (COPD), at rest and during inspiratory loading. Compared with those of controls, the motor cortex area of patients exhibited decreased connectivity with their contralateral counterparts and no connectivity with the brainstem. In the patients, the information flow was reversed at rest with the source of the network shifted from the medulla towards the motor cortex. During inspiratory loading, the system was overwhelmed and the motor cortex became the sink of the network. This major finding may help to understand why some patients with COPD are prone to acute respiratory failure. Network connectivity and causality were related to lung function and illness severity. We validated our connectivity and causality results with a mathematical model of neural network. Our findings suggest a new therapeutic strategy involving the modulation of brain activity to increase motor cortex functional connectivity and improve respiratory muscles performance in patients. Hum Brain Mapp 37:2736-2754, 2016. © 2016 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Prediction and control of focal seizure spread: Random walk with restart on heterogeneous brain networks.

Whole-brain models offer a promising method of predicting seizure spread, which is critical for successful surgical treatment of focal epilepsy. Existing methods are largely based on structural connectome, which ignores the effects of heterogeneity within the regional excitability of brains. In this study we used a whole-brain model to show that heterogeneity in nodal excitability had a significant impact on seizure propagation in the networks and compromised the prediction accuracy with structural connections. We then addressed this problem with an algorithm based on random walk with restart on graphs. We demonstrated that by establishing a relationship between the restarting probability and the excitability for each node, this algorithm could significantly improve the seizure spread prediction accuracy in heterogeneous networks and was more robust against the extent of heterogeneity. We also strategized surgical seizure control as a process to identify and remove the key nodes (connections) responsible for the early spread of seizures from the focal region. Compared to strategies based on structural connections, virtual surgery with a strategy based on a modified random walk with extended restart generated outcomes with a high success rate while maintaining low damage to the brain by removing fewer anatomical connections. These findings may have potential applications in developing personalized surgery strategies for epilepsy.

Optimal Organization of Functional Connectivity Networks for Segregation and Integration With Large-Scale Critical Dynamics in Human Brains.

The optimal organization for functional segregation and integration in brain is made evident by the "small-world" feature of functional connectivity (FC) networks and is further supported by the loss of this feature that has been described in many types of brain disease. However, it remains unknown how such optimally organized FC networks arise from the brain's structural constrains. On the other hand, an emerging literature suggests that brain function may be supported by critical neural dynamics, which is believed to facilitate information processing in brain. Though previous investigations have shown that the critical dynamics plays an important role in understanding the relation between whole brain structural connectivity and functional connectivity, it is not clear if the critical dynamics could be responsible for the optimal FC network configuration in human brains. Here, we show that the long-range temporal correlations (LRTCs) in the resting state fMRI blood-oxygen-level-dependent (BOLD) signals are significantly correlated with the topological matrices of the FC brain network. Using structure-dynamics-function modeling approach that incorporates diffusion tensor imaging (DTI) data and simple cellular automata dynamics, we showed that the critical dynamics could optimize the whole brain FC network organization by, e.g., maximizing the clustering coefficient while minimizing the characteristic path length. We also demonstrated with a more detailed excitation-inhibition neuronal network model that loss of local excitation-inhibition (E/I) balance causes failure of critical dynamics, therefore disrupting the optimal FC network organization. The results highlighted the crucial role of the critical dynamics in forming an optimal organization of FC networks in the brain and have potential application to the understanding and modeling of abnormal FC configurations in neuropsychiatric disorders.

Faded Critical Dynamics in Adult Moyamoya Disease Revealed by EEG and fMRI.

Criticality is considered a dynamic signature of healthy brain activity that can be measured on the short-term timescale with neural avalanches and long-term timescale with long-range temporal correlation (LRTC). It is unclear how the brain dynamics change in adult moyamoya disease (MMD). We used BOLD-fMRI for LRTC analysis from 16 hemorrhagic (H MMD) and 34 ischemic (I MMD) patients and 25 healthy controls. Afterwards, they were examined by EEG recordings in the eyes-closed (EC), eyes-open (EO), and working memory (WM) states. The EEG data of 11 H MMD and 13 I MMD patients and 21 healthy controls were in good quality for analysis. Regarding the 4 metrics of neural avalanches (e.g., size (α), duration (ß), κ value, and branching parameter (σ)), both MMD subtypes exhibited subcritical states in the EC state. When switching to the WM state, H MMD remained inactive, while I MMD surpassed controls and became supercritical (p < 0.05). Regarding LRTC, the amplitude envelope in the EC state was more analogous to random noise in the MMD patients than in controls. During state transitions, LRTC decreased sharply in the controls but remained chaotic in the MMD individuals (p < 0.05). The spatial LRTC reduction distribution based on both EEG and fMRI in the EC state implied that, compared with controls, the two MMD subtypes might exhibit mutually independent but partially overlapping patterns. The regions showing decreased LRTC in both EEG and fMRI were the left supplemental motor area of H MMD and right pre-/postcentral gyrus and right inferior temporal gyrus of I MMD. This study not only sheds light on the decayed critical dynamics of MMD in both the resting and task states for the first time but also proposes several EEG and fMRI features to identify its two subtypes.

Reconfigured functional network dynamics in adult moyamoya disease: a resting-state fMRI study.

Treatment of vascular cognitive impairment (VCI) in adult moyamoya disease (MMD) is still unclear because of its unveiled neural synchronization. This study introduced a dynamic measurement of connectivity number entropy (CNE) to characterize both spatial and temporal dimensions of network interactions. Fifty-one patients with MMD were recruited (27 with VCI and 24 with intact cognition), as well as 26 normal controls (NCs). Static network properties were first examined to confirm its aberrance in MMD with VCI. Then, the dynamic measurement of CNE was used to detect the deteriorated flexibility of MMD with VCI at global, regional, and network levels. Finally, dynamic reconfiguration of flexible and specialized regions was traced across the three groups. Graph theory analysis indicated that MMD exhibited "small-world" network topology but presented with a deviating pattern from NC as the disease progressed in all topologic metrics of integration, segregation, and small-worldness. Subsequent dynamic analysis showed significant CNE differences among the three groups at both global (p < 0.001) and network levels (default mode network, p = 0.004; executive control network, p = 0.001). Specifically, brain regions related to key aspects of information processing exhibited significant CNE changes across the three groups. Furthermore, CNE values of both flexible and specialized regions changed with impaired cognition. This study not only sheds light on both the static and dynamic organizational principles behind network changes in adult MMD for the first time, but also provides a new methodologic viewpoint to acquire more knowledge of its pathophysiology and treatment direction.

Maximal flexibility in dynamic functional connectivity with critical dynamics revealed by fMRI data analysis and brain network modelling.

OBJECTIVE: The exploration of time-varying functional connectivity (FC) through human neuroimaging techniques provides important new insights on the spatio-temporal organization of functional communication in the brain's networks and its alterations in diseased brains. However, little is known about the underlying dynamic mechanism with which such a dynamic FC is flexibly organized under the constraint of structural connections. In this work, we explore the relationship between critical dynamics and FC flexibility based on both functional magnetic resonance imaging data and computer models. APPROACH: First, we proposed the connectivity number entropy (CNE), which was an entropy measure for the flexibility of FC. Through an analysis of resting-state fMRI (rs-fMRI) data from 95 healthy participants, we explored the correlation between CNE and long-range temporal correlations (LRTCs), which can represent the critical dynamics. Then, we employed a whole-brain computer model based on diffusion tensor imaging (DTI) to further demonstrate this relationship. MAIN RESULTS: We found that the most flexible FC is present when the brain is operating close to the critical point of a phase transition. Additionally, around this point, our model can yield the best prediction for the regional distribution of CNE because structural information is reflected the most by the CNE through critical dynamics. SIGNIFICANCE: Our results not only reveal the underlying dynamic mechanism for the organization of time-dependent FC but also provide a possible pathway to model the flexible functional organization in the human brain and may have potential application in the analysis of altered dynamic FC in diseased brains.

Detection of subthreshold pulses in neurons with channel noise.

Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal-processing properties of the neuron. We study the response of a stochastic Hodgkin-Huxley neuron to transient input subthreshold pulses. It is found that the average response time decreases but variance increases as the amplitude of channel noise increases. In the case of single-pulse detection, we show that channel noise enables one neuron to detect the subthreshold signals and an optimal membrane area (or channel noise intensity) exists for a single neuron to achieve optimal performance. However, the detection ability of a single neuron is limited by large errors. Here, we test a simple neuronal network that can enhance the pulse-detecting abilities of neurons and find that dozens of neurons can perfectly detect subthreshold pulses. The phenomenon of intrinsic stochastic resonance is also found at both the level of single neurons and the level of networks. At the network level, the detection ability of networks can be optimized for the number of neurons comprising the network.

Transient dynamics for sequence-processing neural networks: effect of degree distributions.

We derive an analytic evolution equation for overlap parameters, including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely retrieved critical loading ratio alpha_{c}=N;{-12} is obtained, where N is the network size. In the presence of random networks, our theoretical predictions agree quantitatively with the numerical experiments for delta, binomial, and power-law degree distributions.

Emergence of synchronization induced by the interplay between two prisoner's dilemma games with volunteering in small-world networks.

We studied synchronization between prisoner's dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization, and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of the coupling factor on the amplitude of oscillation of cooperator density.

Efficient Coding and Energy Efficiency Are Promoted by Balanced Excitatory and Inhibitory Synaptic Currents in Neuronal Network.

Selective pressure may drive neural systems to process as much information as possible with the lowest energy cost. Recent experiment evidence revealed that the ratio between synaptic excitation and inhibition (E/I) in local cortex is generally maintained at a certain value which may influence the efficiency of energy consumption and information transmission of neural networks. To understand this issue deeply, we constructed a typical recurrent Hodgkin-Huxley network model and studied the general principles that governs the relationship among the E/I synaptic current ratio, the energy cost and total amount of information transmission. We observed in such a network that there exists an optimal E/I synaptic current ratio in the network by which the information transmission achieves the maximum with relatively low energy cost. The coding energy efficiency which is defined as the mutual information divided by the energy cost, achieved the maximum with the balanced synaptic current. Although background noise degrades information transmission and imposes an additional energy cost, we find an optimal noise intensity that yields the largest information transmission and energy efficiency at this optimal E/I synaptic transmission ratio. The maximization of energy efficiency also requires a certain part of energy cost associated with spontaneous spiking and synaptic activities. We further proved this finding with analytical solution based on the response function of bistable neurons, and demonstrated that optimal net synaptic currents are capable of maximizing both the mutual information and energy efficiency. These results revealed that the development of E/I synaptic current balance could lead a cortical network to operate at a highly efficient information transmission rate at a relatively low energy cost. The generality of neuronal models and the recurrent network configuration used here suggest that the existence of an optimal E/I cell ratio for highly efficient energy costs and information maximization is a potential principle for cortical circuit networks. SUMMARY: We conducted numerical simulations and mathematical analysis to examine the energy efficiency of neural information transmission in a recurrent network as a function of the ratio of excitatory and inhibitory synaptic connections. We obtained a general solution showing that there exists an optimal E/I synaptic ratio in a recurrent network at which the information transmission as well as the energy efficiency of this network achieves a global maximum. These results reflect general mechanisms for sensory coding processes, which may give insight into the energy efficiency of neural communication and coding.

Spike-Threshold Variability Originated from Separatrix-Crossing in Neuronal Dynamics.

The threshold voltage for action potential generation is a key regulator of neuronal signal processing, yet the mechanism of its dynamic variation is still not well described. In this paper, we propose that threshold phenomena can be classified as parameter thresholds and state thresholds. Voltage thresholds which belong to the state threshold are determined by the 'general separatrix' in state space. We demonstrate that the separatrix generally exists in the state space of neuron models. The general form of separatrix was assumed as the function of both states and stimuli and the previously assumed threshold evolving equation versus time is naturally deduced from the separatrix. In terms of neuronal dynamics, the threshold voltage variation, which is affected by different stimuli, is determined by crossing the separatrix at different points in state space. We suggest that the separatrix-crossing mechanism in state space is the intrinsic dynamic mechanism for threshold voltages and post-stimulus threshold phenomena. These proposals are also systematically verified in example models, three of which have analytic separatrices and one is the classic Hodgkin-Huxley model. The separatrix-crossing framework provides an overview of the neuronal threshold and will facilitate understanding of the nature of threshold variability.

Energy-efficient population coding constrains network size of a neuronal array system.

We consider the open issue of how the energy efficiency of the neural information transmission process, in a general neuronal array, constrains the network size, and how well this network size ensures the reliable transmission of neural information in a noisy environment. By direct mathematical analysis, we have obtained general solutions proving that there exists an optimal number of neurons in the network, where the average coding energy cost (defined as energy consumption divided by mutual information) per neuron passes through a global minimum for both subthreshold and superthreshold signals. With increases in background noise intensity, the optimal neuronal number decreases for subthreshold signals and increases for suprathreshold signals. The existence of an optimal number of neurons in an array network reveals a general rule for population coding that states that the neuronal number should be large enough to ensure reliable information transmission that is robust to the noisy environment but small enough to minimize energy cost.

Optimal size of stochastic Hodgkin-Huxley neuronal systems for maximal energy efficiency in coding pulse signals.

The generation and conduction of action potentials (APs) represents a fundamental means of communication in the nervous system and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in transferring pulse signals with APs. By analytically solving a bistable neuron model that mimics the AP generation with a particle crossing the barrier of a double well, we find the optimal number of ion channels that maximizes the energy efficiency of a neuron. We also investigate the energy efficiency of a neuron population in which the input pulse signals are represented with synchronized spikes and read out with a downstream coincidence detector neuron. We find an optimal number of neurons in neuron population, as well as the number of ion channels in each neuron that maximizes the energy efficiency. The energy efficiency also depends on the characters of the input signals, e.g., the pulse strength and the interpulse intervals. These results are confirmed by computer simulation of the stochastic Hodgkin-Huxley model with a detailed description of the ion channel random gating. We argue that the tradeoff between signal transmission reliability and energy cost may influence the size of the neural systems when energy use is constrained.

The role of coincidence-detector neurons in the reliability and precision of subthreshold signal detection in noise.

Subthreshold signal detection is an important task for animal survival in complex environments, where noise increases both the external signal response and the spontaneous spiking of neurons. The mechanism by which neurons process the coding of signals is not well understood. Here, we propose that coincidence detection, one of the ways to describe the functionality of a single neural cell, can improve the reliability and the precision of signal detection through detection of presynaptic input synchrony. Using a simplified neuronal network model composed of dozens of integrate-and-fire neurons and a single coincidence-detector neuron, we show how the network reads out the subthreshold noisy signals reliably and precisely. We find suitable pairing parameters, the threshold and the detection time window of the coincidence-detector neuron, that optimize the precision and reliability of the neuron. Furthermore, it is observed that the refractory period induces an oscillation in the spontaneous firing, but the neuron can inhibit this activity and improve the reliability and precision further. In the case of intermediate intrinsic states of the input neuron, the network responds to the input more efficiently. These results present the critical link between spiking synchrony and noisy signal transfer, which is utilized in coincidence detection, resulting in enhancement of temporally sensitive coding scheme.

Neural mechanisms underlying breathing complexity.

Breathing is maintained and controlled by a network of automatic neurons in the brainstem that generate respiratory rhythm and receive regulatory inputs. Breathing complexity therefore arises from respiratory central pattern generators modulated by peripheral and supra-spinal inputs. Very little is known on the brainstem neural substrates underlying breathing complexity in humans. We used both experimental and theoretical approaches to decipher these mechanisms in healthy humans and patients with chronic obstructive pulmonary disease (COPD). COPD is the most frequent chronic lung disease in the general population mainly due to tobacco smoke. In patients, airflow obstruction associated with hyperinflation and respiratory muscles weakness are key factors contributing to load-capacity imbalance and hence increased respiratory drive. Unexpectedly, we found that the patients breathed with a higher level of complexity during inspiration and expiration than controls. Using functional magnetic resonance imaging (fMRI), we scanned the brain of the participants to analyze the activity of two small regions involved in respiratory rhythmogenesis, the rostral ventro-lateral (VL) medulla (pre-Bötzinger complex) and the caudal VL pons (parafacial group). fMRI revealed in controls higher activity of the VL medulla suggesting active inspiration, while in patients higher activity of the VL pons suggesting active expiration. COPD patients reactivate the parafacial to sustain ventilation. These findings may be involved in the onset of respiratory failure when the neural network becomes overwhelmed by respiratory overload We show that central neural activity correlates with airflow complexity in healthy subjects and COPD patients, at rest and during inspiratory loading. We finally used a theoretical approach of respiratory rhythmogenesis that reproduces the kernel activity of neurons involved in the automatic breathing. The model reveals how a chaotic activity in neurons can contribute to chaos in airflow and reproduces key experimental fMRI findings.

Role of axonal sodium-channel band in neuronal excitability.

Action potential initiation (API) is a crucial step in neural information integration and communication. A stable site of API is beneficial for neural coding. A specialized band with a high density of sodium channels in the axon initial segment has been proved as the primary site of API. In this paper we investigate the role of a dense sodium-channel band in the threshold and the location of API of a neuron with a multicompartment model. It is shown that the threshold of the injected current for API is enhanced by a farther distance between the stimulated site and the band and lowered by an increase of the sodium-channel density and the bandwidth. There exists an optimal location of the dense sodium-channel band, which enables the lowest threshold for API. In the case of an excitable dendrite, the site of API shifts from the band to the stimulated dendritic site with increasing stimuli strength. A larger bandwidth and higher sodium-channel density elevate the stability of the sodium-channel band as the site of API and an optimal band position enables the highest stability.

Response of Morris-Lecar neurons to various stimuli.

We studied the responses of three classes of Morris-Lecar neurons to sinusoidal inputs and synaptic pulselike stimuli with deterministic and random interspike intervals (ISIs). It was found that the responses of the output frequency of class 1 and 2 neurons showed similar evolution properties by varying input amplitudes and frequencies, whereas class 3 neuron exhibited substantially different properties. Specifically, class 1 and 2 neurons display complicated phase locking (p : q, p > q, denoting output action potentials per input spikes) in low-frequency sinusoidal input area when the input amplitude is above their threshold, but a class 3 neuron does not fire action potentials in this area even if the amplitude is much higher. In the case of the deterministic ISI synaptic injection, all the three classes of neurons oscillate spikes with an arbitrary small frequency. When increasing the input frequency (both sinusoidal and deterministic ISI synaptic inputs), all neurons display 1 : 1 phase locking, whereas the response frequency decreases even fall to zero in the high-frequency input area. When the random ISI synaptic pulselike stimuli are injected into the neurons, one can clearly see the low-pass filter behaviors from the return map. The output ISI distribution depends on the mean ISI of input train as well as the ISI variation. Such different responses of three classes of neurons result from their distinct dynamical mechanisms of action potential initiation. It was suggested that the intrinsic dynamical cellular properties are very important to neuron information processing.