Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools

Data-driven and equation-free methods for neurological disorders: analysis and control of the striatum network

The striatum as part of the basal ganglia is central to both motor, and cognitive functions. Here, we propose a large-scale biophysical network for this part of the brain, using modified Hodgkin-Huxley dynamics to model neurons, and a connectivity informed by a detailed human atlas. The model shows different spatio-temporal activity patterns corresponding to lower (presumably normal) and increased cortico-striatal activation (as found in, e.g., obsessive-compulsive disorder), depending on the intensity of the cortical inputs. By applying equation-free methods, we are able to perform a macroscopic network analysis directly from microscale simulations. We identify the mean synaptic activity as the macroscopic variable of the system, which shows similarity with local field potentials. The equation-free approach results in a numerical bifurcation and stability analysis of the macroscopic dynamics of the striatal network. The different macroscopic states can be assigned to normal/healthy and pathological conditions, as known from neurological disorders. Finally, guided by the equation-free bifurcation analysis, we propose a therapeutic close loop control scheme for the striatal network.

The Long Journey from Animal Electricity to the Discovery of Ion Channels and the Modelling of the Human Brain

This retrospective begins with Galvani's experiments on frogs at the end of the 18th century and his discovery of 'animal electricity'. It goes on to illustrate the numerous contributions to the field of physical chemistry in the second half of the 19th century (Nernst's equilibrium potential, based on the work of Wilhelm Ostwald, Max Planck's ion electrodiffusion, Einstein's studies of Brownian motion) which led Bernstein to propose his membrane theory in the early 1900s as an explanation of Galvani's findings and cell excitability. These processes were fully elucidated by Hodgkin and Huxley in 1952 who detailed the ionic basis of resting and action potentials, but without addressing the question of where these ions passed. The emerging question of the existence of ion channels, widely debated over the next two decades, was finally accepted and, a decade later, many of them began to be cloned. This led to the possibility of modelling the activity of individual neurons in the brain and then that of simple circuits. Taking advantage of the remarkable advances in computer science in the new millennium, together with a much deeper understanding of brain architecture, more ambitious scientific goals were dreamed of to understand the brain and how it works. The retrospective concludes by reviewing the main efforts in this direction, namely the construction of a digital brain, an in silico copy of the brain that would run on supercomputers and behave just like a real brain.

Data-driven modelling of brain activity using neural networks, diffusion maps, and the Koopman operator

We propose a machine-learning approach to construct reduced-order models (ROMs) to predict the long-term out-of-sample dynamics of brain activity (and in general, high-dimensional time series), focusing mainly on task-dependent high-dimensional fMRI time series. Our approach is a three stage one. First, we exploit manifold learning and, in particular, diffusion maps (DMs) to discover a set of variables that parametrize the latent space on which the emergent high-dimensional fMRI time series evolve. Then, we construct ROMs on the embedded manifold via two techniques: Feedforward Neural Networks (FNNs) and the Koopman operator. Finally, for predicting the out-of-sample long-term dynamics of brain activity in the ambient fMRI space, we solve the pre-image problem, i.e., the construction of a map from the low-dimensional manifold to the original high-dimensional (ambient) space by coupling DMs with Geometric Harmonics (GH) when using FNNs and the Koopman modes per se. For our illustrations, we have assessed the performance of the two proposed schemes using two benchmark fMRI time series: (i) a simplistic five-dimensional model of stochastic discrete-time equations used just for a "transparent" illustration of the approach, thus knowing a priori what one expects to get, and (ii) a real fMRI dataset with recordings during a visuomotor task. We show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient space; one can use instead the low-frequency truncation of the DMs function space of L2-integrable functions to predict the entire list of coordinate functions in the ambient space and to solve the pre-image problem.

Bayesian inference of a spectral graph model for brain oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Electrophysiological insights into deep brain stimulation of the network disorder dystonia

Deep brain stimulation (DBS), a treatment for modulating the abnormal central neuronal circuitry, has become the standard of care nowadays and is sometimes the only option to reduce symptoms of movement disorders such as dystonia. However, on the one hand, there are still open questions regarding the pathomechanisms of dystonia and, on the other hand, the mechanisms of DBS on neuronal circuitry. That lack of knowledge limits the therapeutic effect and makes it hard to predict the outcome of DBS for individual dystonia patients. Finding electrophysiological biomarkers seems to be a promising option to enable adapted individualised DBS treatment. However, biomarker search studies cannot be conducted on patients on a large scale and experimental approaches with animal models of dystonia are needed. In this review, physiological findings of deep brain stimulation studies in humans and animal models of dystonia are summarised and the current pathophysiological concepts of dystonia are discussed.

Connectome-based prediction of functional impairment in experimental stroke models

Experimental rat models of stroke and hemorrhage are important tools to investigate cerebrovascular disease pathophysiology mechanisms, yet how significant patterns of functional impairment induced in various models of stroke are related to changes in connectivity at the level of neuronal populations and mesoscopic parcellations of rat brains remain unresolved. To address this gap in knowledge, we employed two middle cerebral artery occlusion models and one intracerebral hemorrhage model with variant extent and location of neuronal dysfunction. Motor and spatial memory function was assessed and the level of hippocampal activation via Fos immunohistochemistry. Contribution of connectivity change to functional impairment was analyzed for connection similarities, graph distances and spatial distances as well as the importance of regions in terms of network architecture based on the neuroVIISAS rat connectome. We found that functional impairment correlated with not only the extent but also the locations of the injury among the models. In addition, via coactivation analysis in dynamic rat brain models, we found that lesioned regions led to stronger coactivations with motor function and spatial learning regions than with other unaffected regions of the connectome. Dynamic modeling with the weighted bilateral connectome detected changes in signal propagation in the remote hippocampus in all 3 stroke types, predicting the extent of hippocampal hypoactivation and impairment in spatial learning and memory function. Our study provides a comprehensive analytical framework in predictive identification of remote regions not directly altered by stroke events and their functional implication.

Bayesian Inference of a Spectral Graph Model for Brain Oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which can not be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Exploration of sleep function connection and classification strategies based on sub-period sleep stages

Background

As a medium for developing brain-computer interface systems, EEG signals are complex and difficult to identify due to their complexity, weakness, and differences between subjects. At present, most of the current research on sleep EEG signals are single-channel and dual-channel, ignoring the research on the relationship between different brain regions. Brain functional connectivity is considered to be closely related to brain activity and can be used to study the interaction relationship between brain areas.

Methods

Phase-locked value (PLV) is used to construct a functional connection network. The connection network is used to analyze the connection mechanism and brain interaction in different sleep stages. Firstly, the entire EEG signal is divided into multiple sub-periods. Secondly, Phase-locked value is used for feature extraction on the sub-periods. Thirdly, the PLV of multiple sub-periods is used for feature fusion. Fourthly, the classification performance optimization strategy is used to discuss the impact of different frequency bands on sleep stage classification performance and to find the optimal frequency band. Finally, the brain function network is constructed by using the average value of the fusion features to analyze the interaction of brain regions in different frequency bands during sleep stages.

Results

The experimental results have shown that when the number of sub-periods is 30, the α (8-13 Hz) frequency band has the best classification effect, The classification result after 10-fold cross-validation reaches 92.59%.

Conclusion

The proposed algorithm has good sleep staging performance, which can effectively promote the development and application of an EEG sleep staging system.

Modelling brain dynamics by Boolean networks

Understanding the relationship between brain architecture and brain function is a central issue in neuroscience. We modeled realistic spatio-temporal patterns of brain activity on a human connectome with a Boolean networks model with the aim of computationally replicating certain cognitive functions as they emerge from the standardization of many fMRI studies, identified as patterns of human brain activity. Results from the analysis of simulation data, carried out for different parameters and initial conditions identified many possible paths in the space of parameters of these network models, with normal (ordered asymptotically constant patterns), chaotic (oscillating or disordered) but also highly organized configurations, with countless spatial–temporal patterns. We interpreted these results as routes to chaos, permanence of the systems in regimes of complexity, and ordered stationary behavior, associating these dynamics to cognitive processes. The most important result of this work is the study of emergent neural circuits, i.e., configurations of areas that synchronize over time, both locally and globally, determining the emergence of computational analogues of cognitive processes, which may or may not be similar to the functioning of biological brain. Furthermore, results put in evidence the creation of how the brain creates structures of remote communication. These structures have hierarchical organization, where each level allows for the emergence of brain organizations which behave at the next superior level. Taken together these results allow the interplay of dynamical and topological roots of the multifaceted brain dynamics to be understood.

Brain architecture-based vulnerability to traumatic injury

The white matter tracts forming the intricate wiring of the brain are subject-specific; this heterogeneity can complicate studies of brain function and disease. Here we collapse tractography data from the Human Connectome Project (HCP) into structural connectivity (SC) matrices and identify groups of similarly wired brains from both sexes. To characterize the significance of these architectural groupings, we examined how similarly wired brains led to distinct groupings of neural activity dynamics estimated with Kuramoto oscillator models (KMs). We then lesioned our networks to simulate traumatic brain injury (TBI) and finally we tested whether these distinct architecture groups’ dynamics exhibited differing responses to simulated TBI. At each of these levels we found that brain structure, simulated dynamics, and injury susceptibility were all related to brain grouping. We found four primary brain architecture groupings (two male and two female), with similar architectures appearing across both sexes. Among these groupings of brain structure, two architecture types were significantly more vulnerable than the remaining two architecture types to lesions. These groups suggest that mesoscale brain architecture types exist, and these architectural differences may contribute to differential risks to TBI and clinical outcomes across the population.

A review of motor neural system robotic modeling approaches and instruments

In this review, we are considering an actively developing tool in neuroscience-robotic modeling. The new perspective and existing application fields, tools, and methods are discussed. We try to determine starting positions and approaches that are useful at the beginning of new research in this field. Among multiple directions of the research is robotic modeling on the level of muscles fibers and their afferents, skin surface sensors, muscles, and joints proprioceptors. Some examples of technical implementation for physical modeling are reviewed. They are software and hardware tools like event-related modeling algorithms, reduced neuron models, robotic drives constructions. We observe existing drives technologies and prospective electric motor types: switched reluctance and transverse flux motors. Next, we look at the existing examples and approaches for robotic modeling of the cerebellum and spinal cord neural networks. These examples show practical methods for the model neural network architecture and adaptation. Those methods allow the use of cortical and spinal cord reflexes for the network training and apply additional artificial blocks for data processing in other brain structures that transmit and receive data from biologically realistic models.

Deep brain stimulation for movement disorder treatment: exploring frequency-dependent efficacy in a computational network model

A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus. Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities are derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities (synchronisation index, mean synaptic activity and response efficacy) switch from normal to Parkinsonian conditions. Simulating DBS of the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and Parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.

Short- and Long-Range Connections Differentially Modulate the Dynamics and State of Small-World Networks

The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.

Functional Complex Networks Based on Operational Architectonics: Application on Electroencephalography-Brain-computer Interface for Imagined Speech

A new method for analyzing brain complex dynamics and states is presented. This method constructs functional brain graphs and is comprised of two pylons: (a) Operational architectonics (OA) concept of brain and mind functioning. (b) Network neuroscience. In particular, the algorithm utilizes OA framework for a non-parametric segmentation of EEGs, which leads to the identification of change points, namely abrupt jumps in EEG amplitude, called Rapid Transition Processes (RTPs). Subsequently, the time coordinates of RTPs are used for the generation of undirected weighted complex networks fulfilling a scale-free topology criterion, from which various network metrics of brain connectivity are estimated. These metrics form feature vectors, which can be used in machine learning algorithms for classification and/or prediction. The method is tested in classification problems on an EEG-based BCI data set, acquired from individuals during imagery pronunciation tasks of various words/vowels. The classification results, based on a Naïve Bayes classifier, show that the overall accuracies were found to be above chance level in all tested cases. This method was also compared with other state-of-the-art computational approaches commonly used for functional network generation, exhibiting competitive performance. The method can be useful to neuroscientists wishing to enhance their repository of brain research algorithms.

Construction of embedded fMRI resting-state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling, Isometric Feature Mapping, Diffusion Maps, Locally Linear Embedding and kernel PCA. Furthermore, based on key global graph-theoretic properties of the embedded FCN, we compare their classification potential using machine learning. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the cross correlation metric. We show that diffusion maps with the cross correlation metric outperform the other combinations.

Collective almost synchronization-based model to extract and predict features of EEG signals

Understanding the brain is important in the fields of science, medicine, and engineering. A promising approach to better understand the brain is through computing models. These models were adjusted to reproduce data collected from the brain. One of the most commonly used types of data in neuroscience comes from electroencephalography (EEG), which records the tiny voltages generated when neurons in the brain are activated. In this study, we propose a model based on complex networks of weakly connected dynamical systems (Hindmarsh-Rose neurons or Kuramoto oscillators), set to operate in a dynamic regime recognized as Collective Almost Synchronization (CAS). Our model not only successfully reproduces EEG data from both healthy and epileptic EEG signals, but it also predicts EEG features, the Hurst exponent, and the power spectrum. The proposed model is able to forecast EEG signals 5.76 s in the future. The average forecasting error was 9.22%. The random Kuramoto model produced the outstanding result for forecasting seizure EEG with an error of 11.21%.

Construction of functional brain connectivity networks from fMRI data with driving and modulatory inputs: an extended conditional Granger causality approach

We propose a numerical-based approach extending the conditional MVAR Granger causality (MVGC) analysis for the construction of directed connectivity networks in the presence of both exogenous/stimuli and modulatory inputs. The performance of the proposed scheme is validated using both synthetic stochastic data considering also the influence of haemodynamics latencies and a benchmark fMRI dataset related to the role of attention in the perception of visual motion. The particular fMRI dataset has been used in many studies to evaluate alternative model hypotheses using the Dynamic Causal Modelling (DCM) approach. Based on the use of the Bayes factor, we show that the obtained GC connectivity network compares well to a reference model that has been selected through DCM analysis among other candidate models. Thus, our findings suggest that the proposed scheme can be successfully used as a stand-alone or complementary to DCM approach to find directed causal connectivity patterns in task-related fMRI studies.

Criticality or Supersymmetry Breaking?

In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently found approximation-free supersymmetric theory of stochastics (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation) annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.

Neurocognitive Mechanism of Human Resilience: A Conceptual Framework and Empirical Review

Resilience is an innate human capacity that holds the key to uncovering why some people rebound after trauma and others never recover. Various theories have debated the mechanisms underlying resilience at the psychological level but have not yet incorporated neurocognitive concepts/findings. In this paper, we put forward the idea that cognitive flexibility moderates how well people adapt to adverse experiences, by shifting attention resources between cognition–emotion regulation and pain perception. We begin with a consensus on definitions and highlight the role of cognitive appraisals in mediating this process. Shared concepts among appraisal theories suggest that cognition–emotion, as well as pain perception, are cognitive mechanisms that underlie how people respond to adversity. Frontal brain circuitry sub-serves control of cognition and emotion, connecting the experience of physical pain. This suggests a substantial overlap between these phenomena. Empirical studies from brain imaging support this notion. We end with a discussion of how the role of the frontal brain network in regulating human resilience, including how the frontal brain network interacts with cognition–emotion–pain perception, can account for cognitive theories and why cognitive flexibilities’ role in these processes can create practical applications, analogous to the resilience process, for the recovery of neural plasticity.

Data-Driven Predictive Modeling of Neuronal Dynamics Using Long Short-Term Memory

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions have been of interest to engineers, mathematicians and physicists over the last several decades. With the motivation of developing computationally efficient models of brain dynamics to use in designing control-theoretic neurostimulation strategies, we have developed a novel data-driven approach in a long short-term memory (LSTM) neural network architecture to predict the temporal dynamics of complex systems over an extended long time-horizon in future. In contrast to recent LSTM-based dynamical modeling approaches that make use of multi-layer perceptrons or linear combination layers as output layers, our architecture uses a single fully connected output layer and reversed-order sequence-to-sequence mapping to improve short time-horizon prediction accuracy and to make multi-timestep predictions of dynamical behaviors. We demonstrate the efficacy of our approach in reconstructing the regular spiking to bursting dynamics exhibited by an experimentally-validated 9-dimensional Hodgkin-Huxley model of hippocampal CA1 pyramidal neurons. Through simulations, we show that our LSTM neural network can predict the multi-time scale temporal dynamics underlying various spiking patterns with reasonable accuracy. Moreover, our results show that the predictions improve with increasing predictive time-horizon in the multi-timestep deep LSTM neural network.

A Parametric Time-Frequency Conditional Granger Causality Method Using Ultra-Regularized Orthogonal Least Squares and Multiwavelets for Dynamic Connectivity Analysis in EEGs

OBJECTIVE

This study proposes a new parametric time-frequency conditional Granger causality (TF-CGC) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source electroencephalogram (EEG) signals to reveal dynamic interaction patterns in oscillatory neocortical sensorimotor networks.

METHODS

The Geweke's spectral measure is combined with the time-varying autoregressive with exogenous input (TVARX) modeling approach, which uses multiwavelet-based ultra-regularized orthogonal least squares (UROLS) algorithm, aided by adjustable prediction error sum of squares (APRESS), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves, but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems.

RESULTS

The proposed method is validated on two simulations, and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cortical networks.

CONCLUSION

Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks.

SIGNIFICANCE

The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition.

Observability and synchronization of neuron models

Observability is the property that enables recovering the state of a dynamical system from a reduced number of measured variables. In high-dimensional systems, it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. The observability of a network of neuron models depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, to perform a study of observability using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, to study the emergence of phase synchronization in networks composed of neuron models. This is done performing multivariate singular spectrum analysis which, to the best of the authors' knowledge, has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization: (i) without having to measure all the state variables, but only one (that provides greatest observability) from each node and (ii) without having to estimate the phase.