Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden” Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method

Intramembrane Cavitation as a Predictive Bio-Piezoelectric Mechanism for Ultrasonic Brain Stimulation

Low-intensity ultrasonic waves can remotely and nondestructively excite central nervous system (CNS) neurons. While diverse applications for this effect are already emerging, the biophysical transduction mechanism underlying this excitation remains unclear. Recently, we suggested that ultrasound-induced intramembrane cavitation within the bilayer membrane could underlie the biomechanics of a range of observed acoustic bioeffects. In this paper, we show that, in CNS neurons, ultrasound-induced cavitation of these nanometric bilayer sonophores can induce a complex mechanoelectrical interplay leading to excitation, primarily through the effect of currents induced by membrane capacitance changes. Our model explains the basic features of CNS acoustostimulation and predicts how the experimentally observed efficacy of mouse motor cortical ultrasonic stimulation depends on stimulation parameters. These results support the hypothesis that neuronal intramembrane piezoelectricity underlies ultrasound-induced neurostimulation, and suggest that other interactions between the nervous system and pressure waves or perturbations could be explained by this new mode of biological piezoelectric transduction.Comment: One can find the supplemental material at the end of the PDF fil

Form-Function Relations in Cone-Tipped Stimulating Microelectrodes

Metal microelectrodes are widely used in neuroscience research, and could potentially replace macroelectrodes in various neuro-stimulation applications where their small size, specificity, and their ability to also measure unit activity are desirable. The design of stimulating microelectrodes for specific applications requires knowledge on how tip geometry affects function, but several fundamental aspects of this relationship are not yet well understood. This study uses a combined experimental and physical finite elements simulation approach to formulate three new relationships between the geometrical and electrical properties of stimulating cone-tipped tungsten microelectrodes: (1) The empirical relationship between microelectrode 1-kHz impedance and the exposed tip surface area is best approximated by an inverse square-root function (as expected for a cone-tipped resistive interface). (2) Tip angle plays a major role in determining current distribution along the tip, and as a consequence crucially affects the charge injection capacity of a microelectrode. (3) The critical current for the onset of corrosion is independent of tip surface area in sharp microelectrodes

Correlation-Based Analysis and Generation of Multiple Spike Trains Using Hawkes Models with an Exogenous Input

The correlation structure of neural activity is believed to play a major role in the encoding and possibly the decoding of information in neural populations. Recently, several methods were developed for exactly controlling the correlation structure of multi-channel synthetic spike trains (Brette, 2009; Krumin and Shoham, 2009; Macke et al., 2009; Gutnisky and Josic, 2010; Tchumatchenko et al., 2010) and, in a related work, correlation-based analysis of spike trains was used for blind identification of single-neuron models (Krumin et al., 2010), for identifying compact auto-regressive models for multi-channel spike trains, and for facilitating their causal network analysis (Krumin and Shoham, 2010). However, the diversity of correlation structures that can be explained by the feed-forward, non-recurrent, generative models used in these studies is limited. Hence, methods based on such models occasionally fail when analyzing correlation structures that are observed in neural activity. Here, we extend this framework by deriving closed-form expressions for the correlation structure of a more powerful multivariate self- and mutually exciting Hawkes model class that is driven by exogenous non-negative inputs. We demonstrate that the resulting Linear–Non-linear-Hawkes (LNH) framework is capable of capturing the dynamics of spike trains with a generally richer and more biologically relevant multi-correlation structure, and can be used to accurately estimate the Hawkes kernels or the correlation structure of external inputs in both simulated and real spike trains (recorded from visually stimulated mouse retinal ganglion cells). We conclude by discussing the method's limitations and the broader significance of strengthening the links between neural spike train analysis and classical system identification

Subspace Projection Approaches to Classification and Visualization of Neural Network-Level Encoding Patterns

Recent advances in large-scale ensemble recordings allow monitoring of activity patterns of several hundreds of neurons in freely behaving animals. The emergence of such high-dimensional datasets poses challenges for the identification and analysis of dynamical network patterns. While several types of multivariate statistical methods have been used for integrating responses from multiple neurons, their effectiveness in pattern classification and predictive power has not been compared in a direct and systematic manner. Here we systematically employed a series of projection methods, such as Multiple Discriminant Analysis (MDA), Principal Components Analysis (PCA) and Artificial Neural Networks (ANN), and compared them with non-projection multivariate statistical methods such as Multivariate Gaussian Distributions (MGD). Our analyses of hippocampal data recorded during episodic memory events and cortical data simulated during face perception or arm movements illustrate how low-dimensional encoding subspaces can reveal the existence of network-level ensemble representations. We show how the use of regularization methods can prevent these statistical methods from over-fitting of training data sets when the trial numbers are much smaller than the number of recorded units. Moreover, we investigated the extent to which the computations implemented by the projection methods reflect the underlying hierarchical properties of the neural populations. Based on their ability to extract the essential features for pattern classification, we conclude that the typical performance ranking of these methods on under-sampled neural data of large dimension is MDA>PCA>ANN>MGD