Italian Institute of Technology, Department of Robotics, Brain and Cognitive Sciences, I-16163 Genoa, Italy

Max Planck Institute for Biological Cybernetics, D-72076 Tübingen, Germany

Imaging Science and Biomedical Engineering, University of Manchester, Manchester M13 9PT, UK

Abstract

Background

Information theory is an increasingly popular framework for studying how the brain encodes sensory information. Despite its widespread use for the analysis of spike trains of single neurons and of small neural populations, its application to the analysis of other types of neurophysiological signals (EEGs, LFPs, BOLD) has remained relatively limited so far. This is due to the limited-sampling bias which affects calculation of information, to the complexity of the techniques to eliminate the bias, and to the lack of publicly available fast routines for the information analysis of multi-dimensional responses.

Results

Here we introduce a new C- and Matlab-based information theoretic toolbox, specifically developed for neuroscience data. This toolbox implements a novel computationally-optimized algorithm for estimating many of the main information theoretic quantities and bias correction techniques used in neuroscience applications. We illustrate and test the toolbox in several ways. First, we verify that these algorithms provide accurate and unbiased estimates of the information carried by analog brain signals (i.e. LFPs, EEGs, or BOLD) even when using limited amounts of experimental data. This test is important since existing algorithms were so far tested primarily on spike trains. Second, we apply the toolbox to the analysis of EEGs recorded from a subject watching natural movies, and we characterize the electrodes locations, frequencies and signal features carrying the most visual information. Third, we explain how the toolbox can be used to break down the information carried by different features of the neural signal into distinct components reflecting different ways in which correlations between parts of the neural signal contribute to coding. We illustrate this breakdown by analyzing LFPs recorded from primary visual cortex during presentation of naturalistic movies.

Conclusion

The new toolbox presented here implements fast and data-robust computations of the most relevant quantities used in information theoretic analysis of neural data. The toolbox can be easily used within Matlab, the environment used by most neuroscience laboratories for the acquisition, preprocessing and plotting of neural data. It can therefore significantly enlarge the domain of application of information theory to neuroscience, and lead to new discoveries about the neural code.

Background

Information theory

Information theory has been used widely for the analysis of spike trains from single neurons or from small populations

Another problem, which is particularly prominent when computing information quantities for multiple parallel recordings of neural activity, is the speed of computation. Multielectrode recordings now allow the simultaneous measurement of the activity of tens to hundreds of neurons, and fMRI experiments allow a broad coverage of the cerebral cortex and recording from a large number of voxels. Therefore speed of calculation is paramount, especially in cases when information theory is used to shed light on the interactions between pairs or small groups of recorded regions. In fact, the number of these subgroups (and thus the time needed to compute their information or interaction) increases fast with the number of recorded regions.

This article aims at meeting the demand for fast and publicly available routines for the information theoretic analysis of several types of brain signals, by accompanying and documenting the first release of the

**Information Breakdown ToolBox**. This file contains the m-files and executables which constitute the Information Breakdown Tool-Box (ibTB). The most up-to-date version of the code can be also obtained at the following site:

Click here for file

Definitions and meaning of neural Entropies and Information

Before proceeding to describe the implementation of the Toolbox and to discuss its use, in the following we will briefly define the basic information quantities and describe their meaning from a neuroscientific perspective.

Consider an experiment in which the experimental subject is presented with _{s }stimuli _{1},...** r **is recorded and quantified in a given post-stimulus time-window. The neural response can be quantified in a number of ways depending on the experimental questions to be addressed and on the experimenter's hypotheses and intuition. Here, we will assume that the neural response is quantified as an array

Unless otherwise stated, we will assume that the neural response in each element of the response array is discrete. If the signal is analogue in nature – such as for LFP or EEG recordings – we assume it has been discretized into a sufficient number of levels to capture the most significant stimulus-related variations. For example, the power at

Having defined the response, we can quantify how well it allows us to discriminate among the different stimuli by using Shannon's mutual information

The first term in the above expression is called the

** r**) being the probability of observing

where ** r**|

The mutual information has a number of important qualities that make it well suited to characterizing how a response is modulated by the stimulus. These advantages have been reviewed extensively ** R**) takes into account the full stimulus-response probabilities, which include all possible effects of stimulus-induced responses and noise. Thus, its computation does not require the signal to be modeled as a set of response functions plus noise and can be performed even when such decomposition is difficult. Third, because information theory projects all types of neural signals onto a common scale that is meaningful in terms of stimulus knowledge, it is possible to analyze and combine the information given by different measures of neural activity (for example: spike trains and LFPs) which can have very different signal to noise ratios.

The contribution of correlations between different neural responses to the transmitted information

Neural signals recorded from different sites are often found to be correlated. For example, spikes emitted by nearby neurons are often synchronous: the probability of observing near-simultaneous spikes from two nearby neurons is often significantly higher than the product of the probabilities of observing the individual spikes from each neuron

The ubiquitous presence of correlations of neural activity across both space and time has raised the question of what is the impact of this correlation upon the information about sensory stimuli carried by a combination of distributed sources of neural activity (see

Different types of correlations affecting information

Before we describe the information theoretic tools for quantifying the impact of correlations on coding, it is useful to briefly define the types of correlations usually considered in the studies of neural population activity.

The most commonly studied type of correlation of neural activity is what is traditionally called "noise correlation", that is the covariation in the trial-by-trial fluctuations of responses to a fixed stimulus ** r**|

The conditional probability _{ind}(** r**|

Many authors further distinguish noise correlations (which, as explained above, exclude sources of correlations due to shared stimulation) from "signal correlations"

The importance of separating noise from signal is, as revealed by theoretical studies, that signal and noise correlations have a radically different impact on the sensory information carried by neural populations (see below). In particular, signal correlations always reduce the information, whereas noise correlations can decrease it, increase it or leave it unchanged, depending on certain conditions

Information Breakdown

We next describe and define briefly several mathematical techniques to quantify the impact of correlations of information. Several different approaches have been proposed (see ** R**) and decomposes it into a number of components, each reflecting a different way into which signal and noise correlations contribute to information transmission. We decided to focus on the information breakdown formalism partly because it was developed by one of the authors of this article, and partly because it naturally includes several of the quantities proposed by other investigators

The information breakdown writes the total mutual information into a sum of components which are related to different ways in which correlations contribute to population coding

The meaning and mathematical expression of each of the components is summarized in Figure

Components of the information breakdown

**Components of the information breakdown**. This figure shows a schematic representation of the terms of the information breakdown of Ref. ** R**) and breaks it down into the sum of two terms:

_{lin }is the sum of the information provided by each element of the response array. This is a useful reference term because if all the elements of the array were totally independent (_{lin}.

**R**) and _{lin }is called synergy. Positive values of synergy denote the presence of synergistic interaction between elements of the response array, which make the total information greater than the sum of that provided by each element of the response array. Negative values of synergy (called "redundancy") indicate that the elements of the response array carry similar messages, and as a consequence information from the response array is less than the sum of the information provided by each individual element. The synergy can be further broken into the contributions from signal and from noise correlations, as follows.

_{sig-sim }is negative or zero and quantifies the amount of redundancy specifically due to signals correlation. We note that the negative of _{sig-sim }equals the quantity named Δ_{signal }which was defined in Ref.

_{cor }quantifies the total impact of noise correlation in information encoding. Originally introduced in ** R**) in the presence of noise correlations and the information

_{cor-ind}, reflects the contribution of stimulus-independent correlations. In general, if noise and signal correlations have opposite signs, _{cor-ind }is positive. In this case, stimulus-independent noise correlations increase stimulus discriminability compared to what it would be if noise correlations were absent _{cor-ind }is negative and stimuli are less discriminable than the zero noise correlation case. In the absence of signal correlation, _{cor-ind }is zero, whatever the strength of noise correlation.

_{cor-dep }is a term describing the impact of stimulus modulation of noise correlation strength. _{cor-dep }is non-negative, and is greater than zero if and only if the strength of noise correlation is modulated by the stimulus. _{cor-dep }was first introduced in Ref. _{cor-dep }is an upper bound to the information lost by a downstream system interpreting the neural responses without taking into account the presence of correlations

All quantities in the information breakdown can be expressed in terms of the six quantities ** R**),

The components of the information breakdown can be quantified from the above quantities as follows:

Implementation

Computing environment

Our

Data input/output

The main routine in the toolbox is ** R**),

Structure of the main routines in the ToolBox

**Structure of the main routines in the ToolBox**. The core function is

As shown in Figure

Finally, ** R**),

Direct Method

The Direct Method

To describe this algorithm, let's consider, as an example, the calculation of the response probability ** r**). Its direct estimator is given by

where ** r**) is the number of times the response

The steps required for computing ** R**) according to (7) are the following. First the routine has to run through all of the

for

read ** r **in current trial

** r**) →

end loop

for ** r **from 1 to

end loop

A problem with this approach comes from the rapid growing of _{r }as _{r }= ^{L}. One can thus see that estimating the information quantities according to this two-loops method becomes prohibitive for _{c }and

where ℋ(** R**) = ∑

First of all, Equation (8) suggests that, instead of normalizing each count ** r**) and then summing over

Equation (8) tells us even more. Suppose that an additional trial is provided in which the response ** R**) is increased by an amount

This observation suggests that, instead of computing the final value of ** r**) we can update ℋ(

for

read ** r **in current trial

ℋ(** R**) → ℋ(

** r**) →

end loop

normalize ℋ(** R**)

where the length of the loop is determined only by the number of available trials.

The previous procedure can be extended to the direct computation of ** R**|

Finally, let's describe the computation of ** R**) and

where we used the compact notation _{i}(_{i }= _{ind}(

where _{1}(_{2}(_{1}(_{2}(

The number of products required to compute _{ind}(_{ind}(** r**),

Since

Bias Correction for the Direct Method: plug-in vs bias-corrected procedures

The Direct Method relies on the empirical measure of the response probabilities as histograms of the fraction of trials in which each discrete response value was observed. Naturally, this procedure gives a perfect estimate of the information and entropies only if the empirical estimates of the probabilities equal the true probabilities. However, any real experiment only yields a finite number of trials from which these probabilities have to be estimated. The estimated probabilities are thus subject to statistical error and necessarily fluctuate around their true values. If we just plug the empirical probabilities into the information equations (a procedure often called the "plug-in" procedure in the literature), then the finite sampling fluctuations in the probabilities will lead to a systematic error (bias) in the estimates of entropies and information

Next, we describe and compare four bias correction procedures that we implemented in our toolbox. These procedures, which are among those most widely used in the literature, were selected for inclusion in our toolbox because they are applicable to any type of discretized neural response (whatever its statistics), because they are (in our experience) among the most effective, and because they are guaranteed to converge to the true value of information (or entropy) as the number of trials

Quadratic Extrapolation (QE)

This bias correction procedure

where

Panzeri & Treves (PT) Bias Correction

This correction technique computes the linear term

The Shuffling (sh) Procedure

Obtaining unbiased information estimates is particularly challenging when the response array is multidimensional (** R**) not directly through Eq. (1), but through the following formula:

where _{sh}(** R**|

It should be noted that, if one is interested in breaking down _{sh}(** R**) (rather than

This three shuffled-corrected quantities, _{sh}, _{cor-sh }and _{cor-dep-sh}, converge to the same values of their uncorrected counterparts _{cor }and _{cor-dep}, respectively, for infinite number of trials. However the bias of the shuffle-corrected quantities is much smaller when the number of trials is finite. This is especially critical for the computation of _{cor-dep }which is by far the most biased term of the information breakdown

Bootstrap Correction

The bootstrap procedure ** R**|

Gaussian Method

The Direct Method, being based on empirically computing the probability histograms of discrete or discretized neural responses, does not make any assumption on the shape of the probability distributions. This is a characteristic which makes the Direct Method widely applicable to many different types of data.

An alternative approach to the Direct estimation of information is to use analytical models of the probability distributions; fit these distributions to the data; and then compute the information from these probability models. This method has been applied so far relatively rarely in Neuroscience (e.g.

Under the Gaussian hypothesis, the noise and response entropy and the information are given by simple functions of their variance

where |^{2}(** R**)| and |

Note that the Gaussian Method – which we implemented using a straight computation of variances which are then fed into the above equations – does not necessarily require data discretization prior to the information calculation.

The advantage of the Gaussian Method is that it depends only on a few parameters that characterize the neural response (

Although less severe than in the Direct case, the upward bias of the information calculation due to limited sampling is still present when using the Gaussian Method. When the underlying distributions are Gaussian and when no discretization is used for the responses, an exact expression for the bias of ** R**) and

where _{bias}(·) is defined as

and

Our toolbox allows the computation of Gaussian estimates without bias correction, with the analytical Gaussian bias correction, Eqs. (16,17), and also with the quadratic extrapolation correction QE. However, using simulated data, we found that quadratic extrapolation did not correct well for bias for the Gaussian Method (results not shown). This can be understood by noting that Eqs. (16,17) indicate that a quadratic data scaling may not necessarily describe well the bias in the Gaussian case.

The Gaussian Method can also be used to compute the terms _{lin}, _{sig-sim }and _{cor }of the information breakdown _{ind}(** R**) with

Results and discussion

In the following we present several case studies and tests of the performance of our ibTB Toolbox on analog neural signals, such as EEGs and LFPs. We emphasize that the toolbox can be effectively applied to spike trains as well as to EEGs and LFPs. The reason why we focus our presentation on EEGs and LFPs is that the very same algorithms implemented in our toolbox have been already illustrated and tested heavily on spike trains; therefore the illustration and test on EEGs and LFPs is more interesting. We however report that we have thoroughly tested our toolbox on spike trains. In particular, we have used our Toolbox to successfully replicate a number of previously published spike train information theoretic studies from our group, reported in Refs.

Finite sampling bias corrections of information measures from analog neurophysiological signals

We start by testing the performance of bias correction procedures on simulated data. These procedures have been previously tested on simulated spike trains ** R**) that can be obtained with a given number of response bins

In order to illustrate both the origin and magnitude of the bias, it is useful to start the analysis by considering the sampling behavior of the plug-in Direct estimator (we remind that the plug-in estimator is the one that does not uses any bias correction after plugging the empirically estimated probabilities into the information and entropy equations). Figure ** R**|

Comparison of the sampling properties of different information quantities and of bias correction techniques

**Comparison of the sampling properties of different information quantities and of bias correction techniques**. The estimates of information and entropies obtained with a number of techniques are tested on simulated data and plotted as a function of the number of generated trials per stimulus. Results were averaged over a number of repetitions of the simulation (mean value ± st. dev. over 50 simulations). We generated simulated LFPs which matched the second order statistics of LFPs recorded from primary visual cortex during visual stimulation with color movies (see Appendix A). The neural response ** r **used to compute information was a two dimensional response array

Figure ** R**|

Figure ** R**) is biased upward: it tends to be higher than the true value for small number of trials, and then it converges to the true value as the number of trials grows. This upward sampling bias, which originates from the downward sampling bias of

The performance of two such procedures implemented in our Toolbox (PT and QE) is reported in Figure ** R**), which, in this simulation became accurate for

Figure ** R**|

Finally, we considered the effect of computing information through _{sh}(** R**) (Eq. (12) rather than through

Due to its intrinsically better sampling properties, _{sh}(** R**) has an advantage over

It should be noted that this behavior applies to cases in which (like the one we simulated) correlations among elements of the response array are relatively weak. In conditions when the correlations among elements of the response array are very strong (as it is often case with both LFPs and spikes recorded from the nearby electrodes), then the sampling behavior of _{sh}(** R**) is still qualitatively similar to that reported here, with the main difference that in cases of stronger correlation

In summary, we presented the first detailed test of bias corrections procedures (originally develop for spike trains) on simulated analog neural signals. These simulations (i) confirm that these procedures are effective also on data with statistics close to that of LFPs; (ii) show that in such case it is highly advisable to use _{sh}(** R**) as method to compute information; (iii) indicate that evaluating and subtracting the residual bootstrap errors of

Correlations between different frequency bands of Local Field Potentials in Primary Visual Cortex

In this section we illustrate the Information Breakdown formalism

We used the information-theoretic procedure to compute how the power of LFPs at these different frequencies reflects changes in the visual features appearing in the movie. We divided each movie into non-overlapping time windows of length _{1 }and _{2}. (Thus, the response ** r **was a two dimensional array [

Figure ** R**) carried by the LFP powers about which part of the movie was being presented, as a function of the frequencies

The information conveyed jointly by V1 LFPs at pairs of frequencies and its breakdown in terms of different correlational components

**The information conveyed jointly by V1 LFPs at pairs of frequencies and its breakdown in terms of different correlational components**. The breakdown of the information about naturalistic color movies carried by the power of LFPs at two different frequencies _{1 }and _{2}. Results are plotted as function of _{1 }and _{2}, and averaged over a set of 51 recording sites obtained from primary visual cortex of anaesthetized macaques. All estimates were computed using the Direct Method corrected with the QE bias correction procedure and the bootstrap subtraction. Each analog LFP power response was binned into 6 equi-populated values. **A**: The information, **B**: The linear sum, _{lin}(**C**: The synergy **D**: The signal-similarity term _{sig-sim }**E**: The stimulus-independent noise correlation component _{cor-ind }**F**: the stimulus-dependent correlational component _{cor-dep}.

The first maximum ** R**) occurs when

Let's first consider any two frequencies _{1 }and _{2 }belonging to the low frequency range. A comparison of ** R**) (Figure

We then considered the case in which _{1 }belongs to the the low frequency range while _{2 }is in the high-gamma range. In this case, the powers at _{1 }and _{2 }added up independent information about the external correlates, because the joint information ** R**) (Figure

We finally examined the case in which both _{1 }and _{2 }belong to the high-gamma frequency range. In this case, there is considerable negative synergy (_{sig-sim }is strongly negative), which means that high gamma frequencies have a similar response profile to the movie scenes. The redundancy between high gamma frequencies is further enhanced by a negative effect of stimulus-independent noise correlation _{cor-ind}, Figure _{cor-ind}.

It is interesting to note that the results obtained with the information breakdown are compatible with those obtained on the same dataset using a simpler linear signal and noise correlation

Performance of the Gaussian Method

In this section, we illustrate the accuracy and performance on real LFPs responses of the Gaussian Method. We consider again the calculation of how the LFP power encodes information about naturalistic movies, and we use again the same set of LFPs recorded from the primary visual cortex of an anesthetized macaque in response to a binocularly presented naturalistic color movie ** R**) – about which of the 2.048 s long movie scene in which we divided the movie was being presented – carried by the LFP power at a given frequency

When using the Gaussian Method, we first estimated the power in each stimulus window and trial using the multitaper technique. We then took the cubic root of this power; we fitted the distribution of this response to each stimulus to a Gaussian; and we finally computed the information through Eqs. (13) and (14) subtracting the analytic gaussian bias correction, Eqs. (16) and (17). The reason for applying the cubic root transformation is that multitaper power estimates are asymptotically chi-square distributed

Figure ^{(g) }and the direct information ^{(d) }(the latter computed using a discretization with ^{(g) }= 1.0 · ^{(d)}. This demonstrates that the Gaussian approximation is extremely precise for the response computed from this dataset, consistent with mentioned properties of multitaper spectral estimators.

A comparison of Gaussian and Direct information estimation on V1 LFPs

**A comparison of Gaussian and Direct information estimation on V1 LFPs**. **A**: This panel compares the values of information about naturalistic movies carried by V1 LFPs with the Gaussian and the Direct methods. It shows a scatter plot of the information conveyed about the movie by a single LFP frequency computed either with the Gaussian Method, or as a Direct estimate with data discretized into 8 bins. Data were taken from channel 7 of session D04 of the dataset reported in Ref. **B**: We tested the Gaussian estimates of information on simulated data. We generated simulated LFPs which matched the second order statistics of LFPs recorded from primary visual cortex during visual stimulation with color movies (see Appendix A). The neural response ** r **used to compute information was either a one, a two or a three dimensional response array containing the simulated LFP power at frequencies of 4, 25 and 75 Hz. The estimates of the mutual information carried by the power at either one, two or three frequencies were computed using these data and the Gaussian Method and was plotted as function of the generated number of trials per stimulus (mean value ± the standard deviation over 50 simulations). Solid lines and dotted lines represent Gaussian estimates obtained without and with the subtraction of the analytic gaussian bias correction (see text) respectively.

A comparison between Gaussian and direct estimates may be useful to evaluate the effect of refining the discretization of neural responses. For this dataset, we found that when using more bins to discretize responses for the Direct Method (^{(d) }do not change appreciably (data not shown). However, when decreasing the number of bins to ^{(g) }versus ^{(d) }was again distributed along a line (like in Figure ^{(g) }= 1.1 · ^{(d) }and ^{(g) }= 1.2 · ^{(d)}, respectively. These findings suggest several conclusions. First, differences that could be observed between gaussian and direct estimates were due to loss of information caused by poor discretization when using low number of bins for the Direct estimate. Second, using 8 response bins is sufficient to capture of the information of the LFP power and using less bins leads to very moderate information losses (of the order of 10–20%). Third, this suggests that knowledge of the second order statistics of the root-transformed power-values is sufficient for extracting the bulk of the information from the LFP power fluctuations.

To demonstrate the sampling properties and data robustness of the Gaussian information estimates, we proceed as we did previously for the Direct Method, generating realistically simulated LFPs whose statistical properties closely matched those of real V1 LFPs (see Appendix A for a description of how data were generated). This time we considered the information about the 102 presented movie sequences carried by the power of either one, two or three different simulated LFP frequencies (

Taken together, these results indicate that the Gaussian Method can be an extremely accurate and useful tool for studying the information content of analog neural signals. Because of its great data robustness, we strongly recommend its use on any neural signal whose response probabilities are consistent with Gaussian distributions.

EEGs frequencies encoding visual features in naturalistic movies

We next demonstrate the applicability of our toolbox to the analysis of single-trial EEGs. We considered EEGs recorded from a male volunteer with a 64-channel electrode cap while the subject was fixating the screen during the repeated presentation of a 5 s-long naturalistic color movie presented binocularly. Full details on experimental procedures are reported in Appendix B. We then used our Toolbox to investigate which frequency bands, which signal features (phase or amplitude), and which electrode locations better encoded the visual features present in movies with naturalistic dynamics.

To understand which frequency bands were more effective in encoding the movie, we used a causal bandpass filter (see Appendix B for details) to separate out the range of EEG fluctuations at each electrode into distinct frequency bands (delta: 0.1–4 Hz; theta: 4–8 Hz; alpha: 8–12 Hz; beta: 12–20 Hz). We then extracted, by means of Hilbert transforms of the bandpassed signal, the instantaneous phase and power of the EEG fluctuations in each electrode, frequency band, and trial and examined the time course of amplitude and phase during the movie.

Figure

Information analysis of EEG recordings during vision of naturalistic movies

**Information analysis of EEG recordings during vision of naturalistic movies**. The Figure shows EEG responses, and their information, recorded from a human subject watching 5 s-long repeated presentations of a color movie. Data from Panels (A-D) were taken from an example electrode (whose location is reported by the arrow in Panels E-F). **A**: The time course of the phase of the delta-band (0.1 – 4 Hz) EEG during a single trial (**B**: The same single-trial delta-band EEG from the example electrode was color-coded according to the instantaneous power binned into four equally probable intervals. **C**: Time course of the instantaneous phases of the 0.1 – 4 Hz (delta) EEG from the example electrode over 30 repetitions of the movie. Phase values were color coded into quadrants exactly as illustrated in Panel (A). **D**: Time course of the binned instantaneous power of the 0.1 – 4 Hz (delta) EEG from the example electrode over 30 repetitions of the movie. Power values were color coded into quadrants exactly as illustrated in Panel (B). **E**: The information conveyed by the binned phase in the delta (0 – 4 Hz), theta (4 – 8 Hz), alpha (8 – 15 Hz) and beta (15 – 30 Hz) frequency bands is plotted topographically across the electrode locations. **F**: The same topographic plot for the EEG instantaneous power information.

To compare the reliability of phase and power of the delta-range fluctuations at different points of the movie, we discretized the power of the delta band EEG from electrode PO8 at each time point into four equipopulated bins. We found that power was much less reliable across trials than phase (Figure

Having illustrated the encoding of the movie by EEGs with an example recording channel and a selected EEG frequency range, we next characterized the behavior across all electrodes and over a wider range of EEG frequencies. Results are plotted in Figure

This example demonstrates the capabilities of the information analysis to extract the most informative components of EEG signals even when using complex dynamic stimulation paradigms and illustrates the potentials of this toolbox for single-trial EEG analysis.

In order to allow users to familiarize with the Toolbox, we have included (as Additional File to this Article) the entire dataset of EEG Delta Phases for all 64 channels and all trials, together with a commented script that loads the data and computes information through the appropriate calls to the Toolbox (Additional file

**EEG_TEST**. This file includes the entire dataset of EEG Delta Phases for all 64 channels and all trials, together with a commented script that loads the data and computes information through the appropriate calls to the Toolbox: running the script outputs the results plotted in top left plot of Fig

Click here for file

Comparison with other available toolboxes

Other groups have developed, or are currently developing, toolboxes for the information analysis of neural responses. Here we briefly discuss some of the relative features of current releases of other information theoretic toolboxes, and their complementariness.

Ince and colleagues

Another available information theoretic toolbox for spike train analysis is the

With respect to the two above toolboxes, our new toolbox presents two distinctive features. First, it is the only package which has been tested heavily non only on spike trains but also on analog brain recordings such as LFPs, and EEGs. It also includes algorithms which are specific for these signals, such as the Gaussian Method information calculation and its bias correction. The second distinctive features of our toolbox is the speed of computation. This speed advantage is not only due to the C implementation, but also to the new algorithm for fast entropy calculation that we presented here. By comparing systematically the speed of our toolbox on simulated data with the speed of

Future Directions

This paper accompanies the first release of ibTB, which we will continue to be developed over the coming years. Some features that we are working to implement in future releases include:

•

•

• fMRI analysis. We are currently in the process of testing and adapting our toolbox to its use with BOLD fMRI data. Although we developed

Conclusion

Neuroscientists can now record, simultaneously and from the same brain region, several types of complementary neural signals, such as spike, LFP, EEG or BOLD responses, each reflecting different and complementary aspects of neural activity at different spatial and temporal scales of organization. A current important challenge of computational neuroscience is to provide techniques to analyze and interpret these data

Availability and requirements

• Project name: Information Breakdown ToolBox

• Project home page:

• Operating system: tested on Mac OS X, Windows 32 and 64 bits, Linux

• Programming language: Matlab (toolbox tested on R2008a and successive releases) and C

• Other requirements: Microsoft Visual C++ 2008 Redistributable Package x86 (or x64) for use on Windows 32 bit (or 64 bit) machine. The package is freely downloadable from Microsoft's website and is only required if Visual C++ is not installed.

• Licence: ibTB is distributed free under the condition that (1) it shall not be incorporated in software that is subsequently sold; (2) the authorship of the software shall be acknowledged and the present article shall be properly cited in any publication that uses results generated by the software; (3) this notice shall remain in place in each source file.

• Any restriction to use by non-academics: none.

Abbreviations

fMRI: functional magnetic resonance imaging; LFP: Local Field Potential; ibTB: Information Breakdown ToolBox; EEG: Electroencephalogram; BOLD: Blood-oxygenation-level-dependent

Authors' contributions

CM conceived the fast algorithms, implemented the procedures and wrote the article. KW and VS recorded the EEG data, and commented on the manuscript. NKL recorded the LFP data, and commented on the manuscript. SP supervised the project, co-implemented the procedures and co-wrote the article.

Appendix A – Simulation of LFP responses

We simulated the LFP power of a recording site in primary visual cortex (V1) in response to many different movie scenes. In brief, data were simulated as follows. We selected from the dataset of

Appendix B – Methods of EEG recording during presentations of short naturalistic movies

The EEG was acquired using a 64 channel electrode cap (BrainAmp MR, BrainProducts). Electrode placement followed the International 10–20 System and electrodes were all referenced to a frontal central electrode (FCz). Electrode impedances were kept below 15 KOhms. Horizontal and vertical eye movements were recorded using an electro-oculogram (EOG) with electrodes placed over the outer canthus of the left eye as well as below the right eye. Subjects were comfortably seated in a dimly lit room. EEG recordings were digitally recorded at 1000 Hz with a bandpass of 0.1–250 Hz and stored for offline analysis. A small fixation cross on black background was shown in order to indicate the beginning of the trial. After 2 seconds of fixation, a 5 second movie segment (full field) was presented, followed by 2 seconds of continued fixation, resulting in trials totaling 9 seconds of fixation. A movie clip, consisting of fast moving and colorful scenes from a commercially available movie, was presented 50 times. All data analysis procedures were implemented with the Matlab programming language in combination with the EEGlab analysis toolbox

To obtain bandpassed EEGs from each electrode, we bandpassed the raw EEG signal sampled at 1 KHz with a zero-phase-shift Kaiser filter with sharp transition bandwidth (1 Hz), very small passband ripple (0.01 dB), high stopband attenuation (60 dB), and bandwidth corresponding to the considered band (

Acknowledgements

We thank C. Kayser, A. Belistki, R. Ince, N. Ludtke, A. Mazzoni, F. Montani, M. Montemurro and G. Notaro for many useful discussions and for testing the code, and E. Molinari for useful discussions. This research was supported by the BMI project of the Department of Robotics, Brain and Cognitive Sciences at the Italian Institute of Technology, and by the Max Planck Society.