Methods for frequency and correlation analyses of neurograms.

Many physiological functions are based on motor rhythmic activities, among them breathing is a vital issue. The method presented here, or 'temporal grid extraction', aims at characterizing the temporal organization of such an activity. Beyond the measurement of the fundamental frequency, defining the successive cycles, some signal processing tools are helpful in order to look for the presence of higher frequency components that potentially structure these cycles. The method is applied to neurograms recorded from frog brainstem preparations, where two cycle types, buccal and lung cycles, may alternate. It relies on:•Continues Wavelet Transform (CWT) for time-frequency maps and frequency profiles•Crosscorrelation analysis for amplitude maps and amplitude profiles•Cycle-by-cycle autocorrelation analysis for autocorrelation maps and autocorrelation profilesUsing this method, the maps and profiles have revealed that a common high frequency clock drives both buccal and lung cycles.

Is there a common drive for buccal movements associated with buccal and lung 'breath' in Lithobates catesbeianus?

In amphibians, there is some evidence that (1) anatomically separate brainstem respiratory oscillators are involved in rhythm generation, one for the buccal rhythm and another for the lung rhythm and (2) they become functionally coupled during metamorphosis. The present analysis, performed on neurograms recorded using brainstem preparations from Lithobates catesbeianus, aims to investigate the temporal organisation of lung and buccal burst types. Continuous Wavelet Transfom applied to the separated buccal and lung signals of a neurogram revealed that both buccal and lung frequency profiles exhibited the same low frequency peak around 1 Hz. This suggests that a common 'clock' organises both rhythms within an animal. A cross-correlation analysis applied to the buccal and lung burst signals revealed their similar intrinsic oscillation features, occurring at approximately 25 Hz. These observations suggest that a coupling between the lung and buccal oscillators emerges at metamorphosis. This coupling may be related to inter-connectivity between the two oscillators, and to a putative common drive.

Neural network model of an amphibian ventilatory central pattern generator.

The neuronal multiunit model presented here is a formal model of the central pattern generator (CPG) of the amphibian ventilatory neural network, inspired by experimental data from Pelophylax ridibundus. The kernel of the CPG consists of three pacemakers and two follower neurons (buccal and lung respectively). This kernel is connected to a chain of excitatory and inhibitory neurons organized in loops. Simulations are performed with Izhikevich-type neurons. When driven by the buccal follower, the excitatory neurons transmit and reorganize the follower activity pattern along the chain, and when driven by the lung follower, the excitatory and inhibitory neurons of the chain fire in synchrony. The additive effects of synaptic inputs from the pacemakers on the buccal follower account for (1) the low frequency buccal rhythm, (2) the intra-burst high frequency oscillations, and (3) the episodic lung activity. Chemosensitivity to acidosis is implemented by an increase in the firing frequency of one of the pacemakers. This frequency increase leads to both a decrease in the buccal burst frequency and an increase in the lung episode frequency. The rhythmogenic properties of the model are robust against synaptic noise and pacemaker jitter. To validate the rhythm and pattern genesis of this formal CPG, neurograms were built from simulated motoneuron activity, and compared with experimental neurograms. The basic principles of our model account for several experimental observations, and we suggest that these principles may be generic for amphibian ventilation.

New insights into sucking, swallowing and breathing central generators: A complexity analysis of rhythmic motor behaviors.

Sucking, swallowing and breathing are dynamic motor behaviors. Breathing displays features of chaos-like dynamics, in particular nonlinearity and complexity, which take their source in the automatic command of breathing. In contrast, buccal/gill ventilation in amphibians is one of the rare motor behaviors that do not display nonlinear complexity. This study aimed at assessing whether sucking and swallowing would also follow nonlinear complex dynamics in the newborn lamb. Breathing movements were recorded before, during and after bottle-feeding. Sucking pressure and the integrated EMG of the thyroartenoid muscle, as an index of swallowing, were recorded during bottle-feeding. Nonlinear complexity of the whole signals was assessed through the calculation of the noise limit value (NL). Breathing and swallowing always exhibited chaos-like dynamics. The NL of breathing did not change significantly before, during or after bottle-feeding. On the other hand, sucking inconsistently and significantly less frequently than breathing exhibited a chaos-like dynamics. Therefore, the central pattern generator (CPG) that drives sucking may be functionally different from the breathing CPG. Furthermore, the analogy between buccal/gill ventilation and sucking suggests that the latter may take its phylogenetic origin in the gill ventilation CPG of the common ancestor of extant amphibians and mammals.

New insights in gill/buccal rhythm spiking activity and CO(2) sensitivity in pre- and postmetamorphic tadpoles (Pelophylax ridibundus).

Central CO(2) chemosensitivity is crucial for all air-breathing vertebrates and raises the question of its role in ventilatory rhythmogenesis. In this study, neurograms of ventilatory motor outputs recorded in facial nerve of premetamorphic and postmetamorphic tadpole isolated brainstems, under normo- and hypercapnia, are investigated using Continuous Wavelet Transform spectral analysis for buccal activity and computation of number and amplitude of spikes during buccal and lung activities. Buccal bursts exhibit fast oscillations (20-30Hz) that are prominent in premetamorphic tadpoles: they result from the presence in periodic time windows of high amplitude spikes. Hypercapnia systematically decreases the frequency of buccal rhythm in both pre- and postmetamorphic tadpoles, by a lengthening of the interburst duration. In postmetamorphic tadpoles, hypercapnia reduces buccal burst amplitude and unmasks small fast oscillations. Our results suggest a common effect of the hypercapnia on the buccal part of the Central Pattern Generator in all tadpoles and a possible effect at the level of the motoneuron recruitment in postmetamorphic tadpoles.

Neural model of frog ventilatory rhythmogenesis.

In the adult frog respiratory system, periods of rhythmic movements of the buccal floor are interspersed by lung ventilation episodes. The ventilatory activity results from the interaction of two hypothesized oscillators in the brainstem. Here, we model these oscillators with two coupled neural networks, whose co-activation results in the emergence of new dynamics. One of the networks is built with "loop chains" of excitatory and inhibitory neurones producing periodic activities. We define two groups of excitatory neurones whose oscillatory antiphasic sums of activities represent output signals as possible motor commands towards antagonist buccal muscles. The other oscillator is a small network with a self-modulated excitatory input to an excitatory neurone whose episodic firings synchronise some neurones of the first network chains. When this oscillator is silent, the output signals exhibit only regular oscillations, and, when active, the synchronisation process reconfigures the output signals whose new features are representative of lung ventilation motor patterns. The biological interest of this formal model is illustrated by the persistence of the relevant dynamical features when perturbations are introduced in the model, i.e. dynamic noises and architecture modifications. The implementation of the networks with clock-driven continuous time neurones provides simulations with physiological time scales.

Automatic ECG wave extraction in long-term recordings using Gaussian mesa function models and nonlinear probability estimators.

This paper describes the automatic extraction of the P, Q, R, S and T waves of electrocardiographic recordings (ECGs), through the combined use of a new machine-learning algorithm termed generalized orthogonal forward regression (GOFR) and of a specific parameterized function termed Gaussian mesa function (GMF). GOFR breaks up the heartbeat signal into Gaussian mesa functions, in such a way that each wave is modeled by a single GMF; the model thus generated is easily interpretable by the physician. GOFR is an essential ingredient in a global procedure that locates the R wave after some simple pre-processing, extracts the characteristic shape of each heart beat, assigns P, Q, R, S and T labels through automatic classification, discriminates normal beats (NB) from abnormal beats (AB), and extracts features for diagnosis. The efficiency of the detection of the QRS complex, and of the discrimination of NB from AB, is assessed on the MIT and AHA databases; the labeling of the P and T wave is validated on the QTDB database.

Oscillation and coding in a formal neural network considered as a guide for plausible simulations of the insect olfactory system.

For the analysis of coding mechanisms in the insect olfactory system, a fully connected network of synchronously updated McCulloch and Pitts neurons (MC-P type) was developed [Quenet, B., Horn, D., 2003. The dynamic neural filter: a binary model of spatio-temporal coding. Neural Comput. 15 (2), 309-329]. Considering the update time as an intrinsic clock, this "Dynamic Neural Filter" (DNF), which maps regions of input space into spatio-temporal sequences of neuronal activity, is able to produce exact binary codes extracted from the synchronized activities recorded at the level of projection neurons (PN) in the locust antennal lobe (AL) in response to different odors [Wehr, M., Laurent, G., 1996. Odor encoding by temporal sequences of firing in oscillating neural assemblies. Nature 384, 162-166]. Here, in a first step, we separate the populations of PN and local inhibitory neurons (LN) and use the DNF as a guide for simulations based on biological plausible neurons (Hodgkin-Huxley: H-H type). We show that a parsimonious network of 10 H-H neurons generates action potentials whose timing represents the required codes. In a second step, we construct a new type of DNF in order to study the population dynamics when different delays are taken into account. We find synaptic matrices which lead to both the emergence of robust oscillations and spatio-temporal patterns, using a formal criterion, based on a Normalized Euclidian Distance (NED), in order to measure the use of the temporal dimension as a coding dimension by the DNF. Similarly to biological PN, the activity of excitatory neurons in the model can be both phase-locked to different cycles of oscillations which remind local field potential (LFP), and nevertheless exhibit dynamic behavior complex enough to be the basis of spatio-temporal codes.

A machine learning approach to the analysis of time-frequency maps, and its application to neural dynamics.

The statistical analysis of experimentally recorded brain activity patterns may require comparisons between large sets of complex signals in order to find meaningful similarities and differences between signals with large variability. High-level representations such as time-frequency maps convey a wealth of useful information, but they involve a large number of parameters that make statistical investigations of many signals difficult at present. In this paper, we describe a method that performs drastic reduction in the complexity of time-frequency representations through a modelling of the maps by elementary functions. The method is validated on artificial signals and subsequently applied to electrophysiological brain signals (local field potential) recorded from the olfactory bulb of rats while they are trained to recognize odours. From hundreds of experimental recordings, reproducible time-frequency events are detected, and relevant features are extracted, which allow further information processing, such as automatic classification.

Formal modeling with multistate neurones and multidimensional synapses.

Multistate neurones, a generalization of the popular McCulloch-Pitts binary neurones, are described; they are intended to model the fact that neurones may be in several different states of activity, while McCulloch-Pitts neurones model two states only: active or inactive. We show that as a consequence, multidimensional synapses are necessary to describe the dynamics of the model. As an illustration, we show how to derive the parameters of formal multistate neurones and their associated multidimensional synapses from simulations involving Hodgkin-Huxley neurones. Our approach opens the way to solve in a more biologically plausible way, two problems that were addressed previously: (1) the resolution of 'inverse problems', i.e. the construction of formal networks, whose dynamics follows a pre-defined spatio-temporal binary sequence, (2) the generation of spatio-temporal patterns that reproduce exactly the 'code' extracted from experimental recordings (olfactory codes at the glomerular level).

Dynamic proximity of spatio-temporal sequences.

Recurrent networks can generate spatio-temporal neural sequences of very large cycles, having an apparent random behavior. Nonetheless a proximity measure between these sequences may be defined through comparison of the synaptic weight matrices that generate them. Following the dynamic neural filter (DNF) formalism we demonstrate this concept by comparing teacher and student recurrent networks of binary neurons. We show that large sequences, providing a training set well exceeding the Cover limit, allow for good determination of the synaptic matrices. Alternatively, assuming the matrices to be known, very fast determination of the biases can be achieved. Thus, a spatio-temporal sequence may be regarded as spatio-temporal encoding of the bias vector. We introduce a linear support vector machine (SVM) variant of the DNF in order to specify an optimal weight matrix. This approach allows us to deal with noise. Spatio-temporal sequences generated by different DNFs with the same number of neurons may be compared by calculating correlations of the synaptic matrices of the reconstructed DNFs. Other types of spatio-temporal sequences need the introduction of hidden neurons, and/or the use of a kernel variant of the SVM approach. The latter is being defined as a recurrent support vector network (RSVN).

The dynamic neural filter: a binary model of spatiotemporal coding.

We describe and discuss the properties of a binary neural network that can serve as a dynamic neural filter (DNF), which maps regions of input space into spatiotemporal sequences of neuronal activity. Both deterministic and stochastic dynamics are studied, allowing the investigation of the stability of spatiotemporal sequences under noisy conditions. We define a measure of the coding capacity of a DNF and develop an algorithm for constructing a DNF that can serve as a source of given codes. On the basis of this algorithm, we suggest using a minimal DNF capable of generating observed sequences as a measure of complexity of spatiotemporal data. This measure is applied to experimental observations in the locust olfactory system, whose reverberating local field potential provides a natural temporal scale allowing the use of a binary DNF. For random synaptic matrices, a DNF can generate very large cycles, thus becoming an efficient tool for producing spatiotemporal codes. The latter can be stabilized by applying to the parameters of the DNF a learning algorithm with suitable margins.

Modelling spatiotemporal olfactory data in two steps: from binary to Hodgkin-Huxley neurones.

Network models of synchronously updated McCulloch-Pitts neurones exhibit complex spatiotemporal patterns that are similar to activities of biological neurones in phase with a periodic local field potential, such as those observed experimentally by Wehr and Laurent (1996, Nature 384, 162-166) in the locust olfactory pathway. Modelling biological neural nets with networks of simple formal units makes the dynamics of the model analytically tractable. It is thus possible to determine the constraints that must be satisfied by its connection matrix in order to make its neurones exhibit a given sequence of activity (see, for instance, Quenet et al., 2001, Neurocomputing 38-40, 831-836). In the present paper, we address the following question: how can one construct a formal network of Hodgkin-Huxley (HH) type neurones that reproduces experimentally observed neuronal codes? A two-step strategy is suggested in the present paper: first, a simple network of binary units is designed, whose activity reproduces the binary experimental codes; second, this model is used as a guide to design a network of more realistic formal HH neurones. We show that such a strategy is indeed fruitful: it allowed us to design a model that reproduces the Wehr-Laurent olfactory codes, and to investigate the robustness of these codes to synaptic noise.

Functionality of divergence and convergence in a model of the insect olfactory system.

Recent studies have shown that the insect olfactory system uses a spatio-temporal encoding of odours in the population of projection neurons in the antennal lobe, and suggest that the information thus coded is spread across a large population of Kenyon cells in the mushroom bodies. At this stage, the temporal part of the code might be transformed into a spatial code, especially via the temporally sensitive mechanisms of paired-pulse facilitation and feedback inhibition with its possible associated rebound. We explore here a simple model of the olfactory system using a three-layer network of formal neurons, comprising a fixed number (three) of projection and inhibitory neurons, but a variable number of Kenyon cells. We show how enlarging the divergence of the network (i.e. the ratio between the number of Kenyon cells to the number of input - projection - neurons) alters the number of different output spatial states in response to a fixed set of spatio-temporal inputs, and may therefore improve its effectiveness in discriminating between these inputs. Such enlarged divergence also reduces the variation of this effectiveness among random realizations of the network connectivity. Our model shows that the discriminative effectiveness first increases with the divergence, and then plateaus for a divergence factor of approximately 20. The maximal average number of different outputs was 470.2, which was computed from some simulations with random realizations of connectivity and with a set of 512 possible inputs. The discriminative effectiveness of the network is sensitive to paired-pulse facilitation, and especially to inhibition with rebound.