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Abstract
Microelectrode array (MEA) technology has been used in functional neuronal network studies for decades, enabling the analysis of extracellular neuronal activity in both
Keywords
- burst
- EAP
- extracellular action potential
- extracellular electrophysiology
- functional connectivity
- MEA
- microelectrode array
- network burst
- neuron
- signal analysis
- spike
1. Introduction
The neurons belong to electrically excitable cells, as their membrane is capable of rapid impulse conduction: a transient voltage perturbation—the action potential, also called a spike. The brain’s remarkably complex function arises from the electrical activity of billions of neurons. The brain encodes information through the frequencies and timing patterns of action potentials generated by neuronal populations, which is rather difficult to study non-invasively [1, 2, 3].
The electrical properties of neuronal activity allow for distant acquisition through microelectrodes [4, 5]. However, accessing the micro- and mesoscale electrophysiological dynamics of the human brain
Unlike intracellular recordings, MEAs capture activity from multiple neurons across several locations simultaneously [4, 5, 8, 9, 10, 11], offering insights into network function and connectivity, which are crucial properties of neuronal networks. The obtained information about electrophysiological activity and functional interactions of the neurons serves as a proxy measure of synaptic transmissions [11]. Moreover, MEAs offer a non-invasive method to observe the electrical activity of the neuronal cells, thus allowing sequential or time-lapse follow-up of the same network. This approach is especially useful in developmental studies as well as mid- or long-term exposure experiments [3, 12, 13].
MEA analysis of
Figure 1.
A. Schemes of well and electrode alignment of Axion MEA well plates. CytoView MEA 12 has 64 electrodes per well, and CytoView MEA 48 has 16 electrodes per well. Modified from Ref. [17]. B. Custom MEMO MEA plate components and scheme of its three compartments with microtunnels and electrode layout. Modified from Ref. [18]. C. (Left) Immunofluorescent images show neuronal axons penetrating the microtunnels. (Right) Zoomed schematic of a central part of the MEMO MEA plate. The black dots represent the electrodes, and the gray lines between compartments depict the microtunnels designed to enable axonal connections between three neuronal cultures. Each compartment has 24 electrodes. An additional eight electrodes per compartment are located near the entries of the microtunnels. Modified from Ref. [19].
Figure 2.
A. Components of MEA2100-System. Modified from Ref. [23]. B. The block scheme illustrates the main contributors to the noise of the MEA system. Modified from Ref. [4].
Novel culturing paradigms also impose another state-of-the-art subtype of
This chapter focuses on the emerging use of
2. Microelectrode array signals
When an electrode is positioned close enough to a spiking neuron, the recorded extracellular voltage signal typically exhibits a distinct and easily recognizable action potential signature. Since extracellular electrodes do not disrupt neural activity, these recordings offer an accurate and impartial representation of the activity within intact neural circuits [11]. Electrophysiological research with
The voltage signal detected by an MEA electrode results from the linear summation of contributions from current sources, with each contribution weighed inversely to its distance from the electrode. Calculating the voltage signal at the electrode necessitates two key assumptions: (1) neurons can be modeled as a spatial distribution of ion currents and sinks, approximated as monopolar point sources, and (2) the surrounding medium is homogeneous, isotropic, and unbounded. Consequently, the potential
where
The recorded MEA signal incorporates multiple noise sources that degrade the recorded signal. Non-biological noise sources include 1/f or 1/f2 electrode-electrolyte interface noise and thermal noise. Moreover, digital recordings of the voltage signal and electrical stimulation require a connection between the MEA plate electrodes and various hardware, including amplifiers, filters, a digitizer, data transmission cables, a stimulator, and power lines. All these components of MEA systems contribute further to device noise. Signal distortions may also result from phase noise and lossy data compression methods [4, 51, 52, 53]. A block scheme of noise contributors in MEA recordings is shown in Figure 2B.
The biological components of the signal include the spikes and less prominent local field potential (LFP) fluctuations [5]. The LFP component contains hard-to-detect extracellular electric field changes, which originate from subthreshold transmembrane activities of neurons and distant spiking activity. The LFP resides in the lower part of the spectrum of the signal. However, a part of the LFP component is usually considered as biological noise. In such cases, the desired signal and the noise have overlapping spectral characteristics [4, 50, 52, 54, 55, 56]. Although the LFP component is often challenging to analyze, it can still provide valuable insights.
In contrast, spikes buried in the MEA signal serve as precise indicators of neuronal action potentials. The initial step in processing a raw MEA signal typically involves pre-filtering to distinguish between the LFP and spiking components. The spike detection typically begins with the band-pass filtering within a frequency range of approximately 300–3000 Hz, whereas LFP analysis involves low-pass filtering with cutoff frequencies below 300 Hz [5, 56, 60, 61, 62].
Next, we will consider spike detection and consecutive analyses based on the spiking activity.
3. Microelectrode array signal analysis
Typically, the MEA signal analysis includes the detection of neuronal spikes in pre-filtered data, followed by the identification of spike-based features, such as firing rate (Section 3.1) or single-channel bursts and network bursts (NBs; Section 3.2). These analysis steps are visualized in Figure 3. Moreover, additional investigation of functional connectivity measures is often applied to map the functional topology of the networks [63, 64, 65] (Section 3.3). The functional connectivity evaluation methods may utilize both raw MEA data and the detected spikes [63, 64, 65]. Each analysis step is associated with the derivation of numerous feature-specific output parameters, which are then used for scientific inference.
Figure 3.
A. Exemplary signal recorded by a single MEA electrode. The pre-filtered waveform is shown in gray; detected spikes are highlighted with red circles; and periods identified as single-channel bursts are marked by black lines superimposed on the middle of the waveform. B. The raster plot demonstrates a segment of data recorded from 16 electrodes simultaneously. The spike train from each electrode is represented as a row of colored bins in time. Each row corresponds to the spike train of a separate electrode. The rows from all electrodes are stacked on top of each other. The bin color encodes firing rate within the bin: white indicates 0 Hz, and black indicates 40 Hz. Green and red lines denote the start and end of detected NBs, respectively. The data were acquired with the Axion CytoView MEA 48 plate, which has 16 electrodes per well. Modified from Ref. [19].
3.1 Spike detection and sorting
A single neuronal excitation, the extracellular action potential or the spike, is a key feature to extract from the pre-filtered signal of each electrode in an MEA [66], and it can be characterized by two main features: an amplitude peak and a biphasic shape [11]. These two characteristics are essential for designing spike detection algorithms. The segment of the signal induced by a spike in extracellular recordings typically lasts about 3 ms [11].
The typical shape of an extracellularly acquired action potential is considered biphasic. The action potential begins with a rapid influx of Na+ ions, forming a current sink that generates a prominent negative deflection in the extracellular action potential. This is followed by a slower efflux of K+ ions, creating a current source and leading to a smaller positive deflection [4]. However, the final signal shape captured by an electrode tends to depend on its position relative to the neuron’s morphology: with large negative spikes recorded at the perisomatic area and positive spikes at the dendritic area, generated by balancing outward return current as the net membrane current summed over the entire neuron is always zero [4, 45, 67, 68]. Thus, it is rather difficult to conclude which polarity of the spike waveform should be considered characteristic.
One of the simplest spike detection methods involves thresholding based on the amplitude peaks: either negative or both negative and positive. Thresholds can be either static, defined by the user, or adaptive, computed from the data [69, 70]. Static thresholding struggles with the inherent variability in MEA data since noise levels can differ across channels and change over time. To overcome this limitation, adaptive thresholding techniques were introduced. The adaptive threshold is typically set in relation to the noise level, which is estimated from segments of the raw signal that are free of spikes [11]. The most common adaptive method, known as absolute amplitude-based thresholding (ABS), calculates the threshold by estimating the noise’s standard deviation (SD), multiplied by a threshold calculation factor (TCF). This estimation uses the median of the absolute values of the signal to prevent excessively high thresholds [69]. The block diagram of the ABS spike detection method is shown in Figure 4 below.
Figure 4.
Block diagram of the ABS algorithm.
The performance of this algorithm still decreases significantly when the signal-to-noise ratio (SNR) is low [46]. Despite this, the amplitude-based thresholding algorithms remain widely used in both
Figure 5.
Block diagram of the PTSD algorithm.
A different category of spike detection techniques focuses on transforming the signal into a specialized variable, known as the transformation variable or indicator signal, which is subsequently subjected to thresholding. This variable is designed to emphasize the key characteristics of the spikes and separate them from the noise. For instance, the Multiresolution Teager Energy Operator algorithm (MTEO) utilizes the Teager Energy Operator (TEO) concept, also known as Nonlinear Energy Operator (NEO), modified with a resolution parameter to detect various possible widths of action potential amplitude peaks. The discrete TEO is computed by finding the difference between the squared signal value at a given time point and the product of its adjacent samples. The algorithm highlights the transient amplitude changes in the signal. The corresponding equation is provided below:
where
Figure 6.
Block diagram of the MTEO algorithm. Modified from Ref. [54].
On the other hand, the transformation variable can be derived through various types of wavelet decomposition applied to the input signal. A wavelet is the probing function of finite duration, which can be described as a short-lived waveform or localized pulse [80, 81]. Wavelet basis functions typically exhibit biphasic, triphasic, or multiphasic waveforms with compact support, making them similar to action potentials. These functions are translated or slid over the signal to localize the time instants where the signal resembles the wavelet shape or its dilated versions in the time domain, though the exact waveform of the extracellular action potential is not known. The obtained output exhibits local maxima at points where the input signal closely matches the shape of the wavelet function [82, 83]. The wavelet decomposition is usually implemented with a pair of wavelets: a mother wavelet, also called the wavelet function, and a father wavelet, also called the scaling function. The mother wavelet is designed to capture a detailed (or high-frequency) profile of the input, while the father wavelet emphasizes the low-frequency approximation of the input signal. The resulting coefficients are denoted as detail coefficients and approximation coefficients, respectively. This multiresolution approach allows for efficient time-frequency analysis, particularly useful for non-stationary signals like MEA data [84]. A classical multilevel discrete wavelet transform (DWT) shifts to the next decomposition level, also called a scale, by downsampling the obtained coefficients and decomposing them with the same mother and father wavelets. Due to the downsampling, the classical DWT is not a time-invariant transform, which means that the DWT of a signal and the DWT of the same signal shifted in time do not differ in the shift of the coefficients only [46, 84]. A stationary wavelet transform is a time-invariant version of the DWT. Instead of downsampling the obtained coefficients, it moves to the next decomposition level by upsampling the mother and father wavelets [46, 82, 84].
Thus, in spike detection, wavelet-based methods are specifically designed to spotlight the distinctive shapes of spikes within an input signal. The previously published Stationary Wavelet Transform (SWT)-based spike detection algorithm involves denoising wavelet detail coefficients using MAD-based thresholding of each sub-band [82]. Since the signal’s energy is concentrated within a limited number of coefficients while noise is distributed across many coefficients, such thresholding helps eliminate low-energy time-scale points across all scales [82]. The block diagram of the SWT algorithm is presented in Figure 7 below.
Figure 7.
Block diagram of the SWT algorithm. Modified from Ref. [82].
Another technique, the Wavelet-based Teager Energy Operator algorithm (WTEO), combines multilevel DWT using only the father wavelet with the application of the TEO to the resulting approximation coefficients of each sub-band [83]. The TEO outputs are combined with the maximum filter and then thresholded using an SD-based threshold [46, 83]. The block diagram of the WTEO algorithm is presented in Figure 8 below.
Figure 8.
Block diagram of the WTEO algorithm. Adopted from Refs. [46, 83].
Building on a similar principle, the Stationary Wavelet Transform-based Teager Energy Operator method (SWTTEO) utilizes the stationary wavelet transform instead of traditional wavelet decomposition [46]. The block diagram of the SWTTEO algorithm is presented in Figure 9 below.
Figure 9.
Block diagram of the SWTTEO algorithm. Modified from Ref. [46].
However, wavelet-based methods rely on the selection of a suitable wavelet basis—a pair of wavelets whose shape should roughly match that of the spikes, despite the actual spike morphology being unknown. Several alternative advanced methods were developed to avoid using such predefined spike shape characteristics. In those, the spike templates were derived from the MEA signal using higher-order statistical measures and subsequently convolved with the raw signal for spike detection [85, 86]. Alternatively, some recent approaches employed supervised machine learning (ML) techniques for spike detection, such as pre-trained convolutional neural networks (CNNs). These models were trained using a combination of hand-curated datasets and synthetic data, which significantly enhanced detection accuracy. Another strategy involves conducting a preliminary analysis to establish a “ground truth” using conventional spike detection methods, which is then used to train the model [87, 88, 89].
The spike detection algorithms are typically assessed on synthetic datasets crafted to mimic real MEA recordings. However, evaluations using different synthetic datasets often yield markedly different performance ratings for the same algorithms [46, 66, 86].
In certain experimental setups, the spike detection is followed by spike sorting to further analyze the detected spikes. For example, analyzing single-neuron activity requires accurately assigning each detected spike to its originating neuron [11]. This process involves extracting spike events as signal segments spanning over several tens of samples corresponding to the putative spike duration. These segments are then projected into a lower-dimensional space using techniques such as principal component analysis (PCA) or shape-based metrics such as peak-to-peak amplitude or spike width [90, 91]. Clustering algorithms are then applied to sort the spikes. Alternatively, the extracted waveforms can be decomposed using wavelet transforms, with selected wavelet coefficients serving as inputs for further clustering [69, 92]. The challenges imposed on spike sorting techniques arise from various features of MEA recordings, such as the interference of overlapping waveforms, spike shape changes during bursts, drift of neurons relative to their initial positions on the electrodes, and the unknown number of neurons within the electrode’s receptive field [11]. In conventional MEAs, many neurons usually contribute to spikes at the electrode, while in HD MEA setups, a single spike is clearly reflected in several electrode signals [11].
The general logic of the spike detection is rather consistent across standard MEAs, HD MEAs, and multicompartmental MEA setups. However, the choice of a method, its parameterization, and the interpretation of results should reflect the specific characteristics of the MEA plate used, such as electrode size and density, cell type-related activity features, and other aspects of the experimental design.
3.2 Bursts
Bursts reflect network dynamics and are typically characterized by the simultaneous occurrence of frequent neuronal activity. Bursts imply compressed information transfer between neurons, consisting of a series of tightly packed single spikes. Bursts are recorded from single or several electrodes of an MEA and defined as single-channel bursts and NBs, respectively [11, 93, 94]. Although bursting is a key feature commonly used to evaluate neuronal network activity, a clear and universally accepted formal definition of a burst is still lacking in the field after more than 50 years of MEA research. As a result, burst detection strategies within the scientific community remain diverse and are often tailored to specific data at hand [11, 95, 96].
Bursts are believed to play a role in long-term potentiation and other processes related to synaptic transmission. This bursting activity contributes to a consistent and information-rich mode of neuronal communication [11, 93, 97, 98, 99].
The lack of definition of bursts, together with unavailable ground truth MEA data, imposes serious constraints on the performance evaluation of the single-channel burst and NB detection algorithms. The efficiency assessment of the algorithms is usually achieved with synthetic data sets and visual performance estimation [11, 94, 99, 101].
3.2.1 Single-channel burst detection methods
Single-channel burst firing determines distinct developmental patterns in neuronal populations during MEA recordings [7, 98]. Numerous algorithms have been developed for detecting single-channel bursts [99], with many relying on interspike interval (ISI) characteristics within the recorded spike trains. The ISI-based approach may be further constrained with an additional criterion for a minimum number of spikes per burst to avoid detecting very brief single-channel bursts. The ISI threshold used for ISI-based detection can either be a fixed value [98] or be determined from the distribution of ISIs observed in the recorded signal [93, 101].
For example, the adaptive single-channel burst detection algorithm introduced by Pasquale and colleagues [93] constructed the logarithmic histogram of all ISIs of an input spike train. Then all peaks of the histogram were identified. The set of peaks was checked to contain the putative intra-burst peak: a maximum peak with an ISI value below the predefined intra-burst peak threshold. This peak was considered to represent the ISIs of intra-burst spikes. If no such peak was found, the data was marked as non-bursting. If the intra-burst peak was present, the algorithm evaluated the local minima between this peak and all other peaks that corresponded to longer ISI values. The evaluation criterion for the candidate minima was denoted as a
Figure 10.
Two ISI-based single-channel burst detection methods. A. (Left) Logarithmic distribution of ISI with the red star-marked ISI threshold ISIth that was selected at the local minima based on the peaks’ separation criterion. The corresponding peaks are marked with the black star symbols. An intra-burst peak threshold of 100 ms is depicted with the red dashed line. The horizontal axis of the histogram is logarithmic. (Right) Detection outcome: an exemplary spike train with the red spikes classified as belonging to the single-channel burst and the blue spikes marked as the out-burst spikes. The spike train is presented as a point process in time. Reproduced from Ref. [93]. B. Definition of the ISI threshold using the maximum value of the CMA curve of the ISI histogram. The maximum value of CMAm was reached at the bin with ISI value xm, and the ISI threshold xt was defined as the ISI value of the bin that corresponded to the αCMAm value. The defined ISI threshold for burst detection is marked with the red dashed vertical line. The ISI histogram is depicted with gray bars. The axes of the histogram are linear. Reproduced from Ref. [101].
Alternatively, the algorithm created by Kapucu and colleagues [101] computed a non-logarithmic histogram of ISIs and then derived the cumulative moving average (CMA) value for each bin. The maximum CMA value,
On the other hand, there exists a family of so-called surprise-based methods for single-channel burst detection. These algorithms use statistical analysis to distinguish periods of bursting from baseline neuronal firing. Initially, a suitable assumption about the distribution of baseline spike firing times is developed. The bursting regimes are expected to produce evident deviation from this distribution, which is used to identify the single-channel bursts [96, 102, 103].
The spike timing-based detection of the single-channel bursts may, in principle, be applied to any MEA setup. However, the correct implementation of a particular algorithm relies on the general understanding of the origins of the recorded data. For example, with the standard commercial MEAs, it is impossible to infer directly whether the recorded single-channel bursting originates from one bursting neuron or from several active cells near the electrode [11]. Only the sorting of the in-burst spikes may provide an answer in this case.
3.2.2 Network burst detection methods
NB activity is commonly linked to network maturation, with its peak generally aligning with the period of highest synaptic density within a network [11, 93, 94, 104, 105, 106]. Numerous established methods for detecting NBs have been proposed [93, 94, 106, 107, 108, 109]. Based on their underlying detection principles, these methods can be categorized into ISI-based approaches [93, 94, 108], population firing rate (PFR)-based approaches [106, 107], and hybrid methods [109]. PFR integrates the time-varying binned spike firing rates from all involved MEA electrodes into a common firing rate signal.
Some of the listed techniques extrapolate single-channel burst detection results to the network level [93, 108]. Pasquale and colleagues [93] extended their single-channel burst detection logic to the NB detection level. After the single-channel bursts were detected in the signals of all involved electrodes, they pooled the timings of all these bursts into the cumulative burst event train. The logarithmic inter-burst interval (IBI) histogram was constructed using that. The histogram was used to identify the IBI threshold and to detect NBs within the cumulative burst event train. Finally, the criterion for minimum participating channels was applied to the detected NBs to preserve only the NBs with contributions from multiple electrodes [93]. Similarly, Välkki and colleagues [108] identified the single-channel bursts among MEA electrodes using the algorithm by Kapucu and colleagues [101] described above and evaluated their synchronization. The total NB signal was obtained by summing bursting behaviors over channels, which was then thresholded in accordance with the minimum participating channels criterion [108].
Others treat the NB detection as an independent process [94, 106, 107, 109]. For example, Bakkum and colleagues [94] developed a logarithmic ISIN histogram-based method. First, the spike trains from all involved MEA electrodes were combined and sorted into a joint spike train to calculate the logarithmic ISIN histogram of ISIs between N consecutive spikes. Again, the histogram exhibiting two separate peaks was assumed to represent two different firing regimes: in this case, the spikes that belong to NBs and the spikes outside the network firing regime, respectively. Therefore, the threshold for detecting NBs was selected at the minimum point between these peaks in the histogram [94]. Hedrich and colleagues [107] presented the PFR average-based method. The spike trains from all involved MEA electrodes were summed into 5 ms time bins to calculate the PFR, which was then smoothed by a Gaussian kernel with a 100 ms SD. The intervals with a PFR exceeding the slowly varying 1-second PFR average were selected as NB candidates. The candidates were accepted if they fit three criteria: their peak firing rate exceeded three SDs of the PFR, their peak firing rate exceeded 10% of the average of the top five peaks, and at least three electrodes contributed. At the last step, neighboring NBs with IBIs less than 200 ms were merged [107].
Matsuda and colleagues [109] combined ISI-thresholding with a form of PFR-thresholding. In their four-step method, the spike trains from all electrodes were pooled into a joint spike train, where the spikes separated by ISIs less than 4 ms were assigned to NB candidates. NBs with less than 20 spikes were discarded. Neighboring NBs with IBI less than 60 ms were merged. At the last step, only the NBs that accommodate more than 3000 spikes were considered valid [109]. The method involved a number of fixed parameters, which usually limit the adaptivity of the approach to highly variable MEA data.
The detection of NB activity provides an advanced measure of neuronal network functioning. Figure 11 shows the gradual drop in NB counts in a kainic acid (KA)-exposed culture compared to its baseline activity. The data was acquired with an Axion CytoView MEA 48 plate, which has 16 electrodes per well.
Figure 11.
Detected NB counts at baseline and after KA exposure. The raster plots of KA-induced perturbation of NB activity. The upper plot shows baseline spiking activity in a well with detected NBs. The green and red vertical lines represent the starting and ending times of NBs, respectively. The lower plot demonstrates disruption of the NBs into spread tonic firing. No NBs were detected. Modified from Ref. [110].
3.2.3 Detection of network bursts in multi-compartment setups
Application of the NB detection methods to multi-compartment MEA setups possesses additional challenges. While the listed methods are well-documented for standard MEA setups, they are not directly applicable to the data acquired with multi-compartment MEAs. The architecture of multi-compartment MEAs involves multiple potential synchronization levels, requiring specialized analysis tools to fully exploit the data they generate. Without such tailored analysis techniques, the advantages of multi-compartment MEAs over conventional single-network setups may be lost. Overall, the signal analysis for such systems should account for both the spatial separation and the interactions between the interconnected networks to ensure accurate assessment [41].
Previous studies involving multi-compartment MEA data analysis often considered synchronous bursting as a key feature [30, 31, 32, 33, 41]. Typically, these studies first identified local NBs within individual compartments using conventional methods, followed by evaluating the temporal alignment of these NBs within the entire compartmentalized network [30, 31, 32, 41]. For example, a recent work by Vinogradov and colleagues [41] defined three levels of synchronization within a three-compartment network of neurons (Figure 1B–C) recorded with the MEMO MEA plate. The initial detection of NBs was performed separately in each compartment using a custom algorithm developed based on a previously published method [94], which was extended with additional parameters to reflect local network synchrony [41]. The locally detected NBs were then evaluated for temporal alignment to capture their global, circuitry-level synchronization [41]. Beyond the localized NBs occurring within each of the three individual compartments of the device, two additional, more complex synchronization patterns were identified and analyzed. An intermediate circuitry burst (ICB) was characterized as simultaneous activity in two out of three compartments. Furthermore, a circuitry burst (CB) refers to synchronized bursting that encompasses the entire network across all three compartments [41]. The analysis demonstrated that a local network within a single compartment of a MEMO MEA plate could not only generate local NBs but also contribute to both ICBs and CBs observed at the global network levels, as illustrated by the network in compartment B (Figure 12).
Figure 12.
Examples of NB, ICB, and CB detection. The detections are visualized on a combined raster plot of spiking activity in three compartments within a 150-second segment. The data was recorded with the MEMO MEA plate. The green and red vertical lines represent the starting and ending times of detected local NBs, respectively. The purple polygons at the top depict the time intervals of detected CBs involving all three compartments; the orange polygons indicate ICBs with two-compartment synchronization; and the yellow polygons indicate local NBs in a single (B) compartment only. The length of the polygons corresponds to the duration of the corresponding synchronization patterns. Reproduced with modification from Ref. [41].
3.3 Methods for functional connectivity analysis
Beyond analyzing synchronous bursting, various methods have been developed to assess functional connectivity and information propagation in neuronal cultures. One such approach is the spike time tiling coefficient (STTC), which measures the proportion of spike co-occurrences between electrode pairs to determine pairwise correlations in their spiking activity [64, 111]. Similarly, functional connectivity maps can be constructed by analyzing correlations of simultaneous spikes across electrodes [35]. Cross-correlation-based methods have also been employed on compartment-wise firing rates within the network to infer the direction of activity propagation by evaluating the latency of peak correlations [30] or implemented straightforwardly between electrode pairs [31]. An additional alternative approach, known as correlated spectral entropy (CorSE), evaluates functional connectivity by analyzing temporal changes in the power spectra of raw MEA signals. The method involves segmenting the signals into windows, calculating spectral entropies for each window, and then determining connectivity through cross-correlation of the resulting entropy signals [63].
In a work by Hyvärinen and colleagues [112], the rat cortical and human pluripotent stem cell (hPSC)-derived cultures were compared in terms of functional connectivity development using both the CorSE and the STTC methods. The data was acquired with Axion CytoView MEA 12 plates with 64 electrodes per well. Both algorithms indicated earlier onset of functionally interconnected networks in the rodent data [112]. Figure 13 provides the connectivity maps obtained using the CorSE algorithm and shows the dynamics of the average CorSE and STTC values for both culture types over the experimental timeline.
Figure 13.
Functional connectivity development analysis. A. (Up) Functional connectivity maps from an hPSC-derived network over 10 minutes of recording between days 21 and 42 on MEA and (Down) from a rat cortical network between days 14 and 35 on MEA. Each map presents the electrode layout of the Axion CytoView MEA 12 plate as an 8 × 8 array with detected functional connections depicted as lines. An arbitrary CorSE value of 0.7 was used as the connectivity strength threshold for the line plotting. B. Functional connectivity development of the hPSC-derived and rat cortical networks described with the average CorSE values over time. C. The same as described by the average STTC values. The average values were calculated from all electrode pairs for each well. Both the hPSC-derived and rat cortical network data consist of n = 12 networks per group; data are shown as Tukey box plots. A Mann-Whitney U-test was performed to compare the two groups at each time point. Statistical significances are marked as *p < 0.05, **p < 0.01, and ***p < 0.001. Adapted from Ref. [112].
In addition to the correlation-based methods, various event-based and information theory-based approaches have been developed to estimate functional connectivity and causal interactions. Event Synchrony (ES), introduced by Quiroga and colleagues, quantifies synchronization based on the timing proximity of discrete events such as spikes. It assigns synchrony scores based on the coincidence of spike times within a local temporal window, providing an intuitive, symmetric measure of synchrony between two spike trains [113].
Mutual Information (MI) is a widely used metric that quantifies statistical dependencies between signals by comparing the joint probability distribution of events to their marginal distributions [65, 114]. MI has been particularly useful for assessing nonlinear relationships in spike train data [65, 115].
Extending the concept of MI, Transfer Entropy (TE) accounts for the directionality of information flow by incorporating time-lagged dependencies, thus estimating the extent to which past activity in one signal predicts future activity in another [116, 117]. Since TE is asymmetric and captures both linear and nonlinear interactions, making it suitable for analyzing directed functional connectivity [117].
Similarly, Granger causality [118], or its extended models for the frequency domain and multivariate signals [119], evaluates directional influences by relying on autoregressive modeling. It assumes that if a causal relationship exists, the past values of one time series will significantly contribute to the prediction of another. Several works in the field applied the Granger causality method for MEA data [31, 120, 121].
Each of these approaches complements classical correlation-based techniques and can enhance functional network mapping, particularly when directionality and information flow are of interest.
Functional connectivity analysis methods are particularly valuable in the context of multi-compartment MEA systems. Several illustrative examples are listed here. Le Feber and colleagues [30] applied cross-correlation analysis to compartment-specific firing rates within defined time bins, using the latency of peak correlations to infer the direction of activity propagation within a custom two-compartment MEA platform [30]. In another custom two-compartment MEA configuration, DeMarse and colleagues [31] estimated functional connectivity by computing cross-correlation and conditional Granger causality metrics from spike train data across electrode pairs [31]. Likewise, Van de Wijdeven and colleagues [35] generated functional connectivity maps by analyzing the correlations of simultaneous spikes detected across electrodes [35]. The CorSE method was used for evaluation of KA-exposure effects on functional connectivity in a three-compartment setup using previously mentioned MEMO MEA plates [41].
4. Conclusions
MEA technology remains a powerful tool for investigating the functional dynamics of neuronal networks. Precise analysis of electrophysiological signals is crucial for in vitro MEA studies focused on development, disease modeling, and drug testing. In this chapter, we introduced basic steps of neuronal data analysis and provided the corresponding analysis methods. This chapter has reviewed the core methods and current challenges in MEA signal analysis, including the accurate detection of spikes and the identification of bursts, both at single-channel and network levels, and functional connectivity mapping.
By presenting a comprehensive overview of established and emerging analysis strategies, this chapter aims to support researchers in making informed choices when designing experiments and interpreting MEA data. Integrating these analytical approaches enables a deeper understanding of neuronal network behavior and promotes the advancement of
Acknowledgments
The work was supported by the Facility of Electrophysiological Measurements (Faculty of Medicine and Health Technology, Tampere University). The authors also thank Biocenter Finland for the support of the Electrophysiological Measurements facility. This work was supported by the Research Council of Finland and EU H2020-FETOpen (PRIME project).
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