Management of synchronized network activity by highly active neurons

Neuromodulatory Compensation of Cortical Neural Activity on Electrodeposited Pt/Ir Modified Microelectrode Arrays for Temperature Transients

Temperature has a profound influence on various neuromodulation processes and has emerged as a focal point. However, the effects of acute environmental temperature fluctuations on cultured cortical networks have been inadequately elucidated. To bridge this gap, we have developed a brain-on-a-chip platform integrating cortical networks and electrodeposited Pt/Ir modified microelectrode arrays (MEAs) with 3D-printed bear-shaped triple chambers, facilitating control of temperature transients. This innovative system administers thermal stimuli while concurrently monitoring neuronal activity, including spikes and local field potentials, from 60 microelectrodes (diameter: 30 μm; impedance: 9.34 ± 1.37 kΩ; and phase delay: -45.26 ± 2.85°). Temperature transitions of approximately ±10 °C/s were applied to cortical networks on MEAs via in situ perfusion within the triple chambers. Subsequently, we examined the spatiotemporal dynamics of the brain-on-a-chip under temperature regulation at both the group level (neuronal population) and their interactions (network dynamics) and the individual level (cellular activity). Specifically, we found that after the temperature reduction neurons enhanced the overall information transmission efficiency of the network through synchronous firing to compensate for the decreased efficiency of single-cell level information transmission, in contrast to temperature elevation. By leveraging the integration of high-performance MEAs with perfusion chambers, this investigation provides a comprehensive understanding of the impact of temperature on the spatiotemporal dynamics of neural networks, thereby facilitating future exploration of the intricate interplay between temperature and brain function.

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal replay, which is critical for memory consolidation. The sudden and repeated occurrences of these burst states during ongoing neural activity suggest metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to stochastic spiking and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesoscopic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie to obtain a "chemical Langevin equation", which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down-states dynamics) by means of phase-plane analysis. An extension of the Langevin equation for small network sizes is also presented. The stochastic neural mass model constitutes the basic component of our mesoscopic model for replay. We show that the mesoscopic model faithfully captures the statistical structure of individual replayed trajectories in microscopic simulations and in previously reported experimental data. Moreover, compared to the deterministic Romani-Tsodyks model of place-cell dynamics, it exhibits a higher level of variability regarding order, direction and timing of replayed trajectories, which seems biologically more plausible and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.

Learning populations with hubs govern the initiation and propagation of spontaneous bursts in neuronal networks after learning

Spontaneous bursts in neuronal networks with propagation involving a large number of synchronously firing neurons are considered to be a crucial feature of these networks both in vivo and in vitro. Recently, learning has been shown to improve the association and synchronization of spontaneous events in neuronal networks by promoting the firing of spontaneous bursts. However, little is known about the relationship between the learning phase and spontaneous bursts. By combining high-resolution measurement with a 4,096-channel complementary metal-oxide-semiconductor (CMOS) microelectrode array (MEA) and graph theory, we studied how the learning phase influenced the initiation of spontaneous bursts in cultured networks of rat cortical neurons in vitro. We found that a small number of selected populations carried most of the stimulus information and contributed to learning. Moreover, several new burst propagation patterns appeared in spontaneous firing after learning. Importantly, these "learning populations" had more hubs in the functional network that governed the initiation of spontaneous burst activity. These results suggest that changes in the functional structure of learning populations may be the key mechanism underlying increased bursts after learning. Our findings could increase understanding of the important role that synaptic plasticity plays in the regulation of spontaneous activity.

Characterization of neuronal viability and network activity under microfluidic flow

BACKGROUND

Microfluidics technology has the potential to allow precise control of the temporal and spatial aspects of solute concentration, making it highly relevant for the study of volume transmission mechanisms in neural tissue. However, full utilization of this technology depends on understanding how microfluidic flow at the rates needed for rapid solution exchange affects neuronal viability and network activity.

NEW METHOD

We designed a tape-based pressurized microfluidic flow system that is simple to fabricate and can be attached to commercial microelectrode arrays. The device is multi-layered, allowing the inclusion of a porous polycarbonate membrane to isolate neuronal cultures from shear forces while maintaining diffusive exchange of solutes. We used this system to investigate how flow affected survival and spiking patterns of cultured hippocampal neurons.

RESULTS

Viability and network activity of the cultures were reduced in proportion to flow rate. However, shear reduction measures did not improve survival or spiking activity; media conditioning in conjunction with culture age proved to be the critical factors for network stability. Diffusion simulations indicate that dilution of a small molecule accounts for the deleterious effects of flow on neuronal cultures.

COMPARISON WITH EXISTING METHODS

This work establishes the experimental conditions for real time measurement of network activity during rapid solution exchange, using multi-layered chambers with reversible bonding that allow for reuse of microelectrode arrays.

CONCLUSIONS

With correct media conditioning, the microfluidic flow system allows drug delivery on a subsecond timescale without disruption of network activity or viability, enabling in vitro reproduction of volume transmission mechanisms.

Inhomogeneities in Network Structure and Excitability Govern Initiation and Propagation of Spontaneous Burst Activity

The mesoscale architecture of neuronal networks strongly influences the initiation of spontaneous activity and its pathways of propagation. Spontaneous activity has been studied extensively in networks of cultured cortical neurons that generate complex yet reproducible patterns of synchronous bursting events that resemble the activity dynamics in developing neuronal networks in vivo. Synchronous bursts are mostly thought to be triggered at burst initiation sites due to build-up of noise or by highly active neurons, or to reflect reverberating activity that circulates within larger networks, although neither of these has been observed directly. Inferring such collective dynamics in neuronal populations from electrophysiological recordings crucially depends on the spatial resolution and sampling ratio relative to the size of the networks assessed. Using large-scale microelectrode arrays with 1024 electrodes at 0.3 mm pitch that covered the full extent of in vitro networks on about 1 cm², we investigated where bursts of spontaneous activity arise and how their propagation patterns relate to the regions of origin, the network's structure, and to the overall distribution of activity. A set of alternating burst initiation zones (BIZ) dominated the initiation of distinct bursting events and triggered specific propagation patterns. Moreover, BIZs were typically located in areas with moderate activity levels, i.e., at transitions between hot and cold spots. The activity-dependent alternation between these zones suggests that the local networks forming the dominating BIZ enter a transient depressed state after several cycles (similar to Eytan et al., 2003), allowing other BIZs to take over temporarily. We propose that inhomogeneities in the network structure define such BIZs and that the depletion of local synaptic resources limit repetitive burst initiation.

Assessing functional connectivity across 3D tissue engineered axonal tracts using calcium fluorescence imaging

OBJECTIVE

Micro-tissue engineered neural networks (micro-TENNs) are anatomically-inspired constructs designed to structurally and functionally emulate white matter pathways in the brain. These 3D neural networks feature long axonal tracts spanning discrete neuronal populations contained within a tubular hydrogel, and are being developed to reconstruct damaged axonal pathways in the brain as well as to serve as physiologically-relevant in vitro experimental platforms. The goal of the current study was to characterize the functional properties of these neuronal and axonal networks.

APPROACH

Bidirectional micro-TENNs were transduced to express genetically-encoded calcium indicators, and spontaneous fluorescence activity was recorded using real-time microscopy at 20 Hz from specific regions-of-interest in the neuronal populations. Network activity patterns and functional connectivity across the axonal tracts were then assessed using various techniques from statistics and information theory including Pearson cross-correlation, phase synchronization matrices, power spectral analysis, directed transfer function, and transfer entropy.

MAIN RESULTS

Pearson cross-correlation, phase synchronization matrices, and power spectral analysis revealed high values of correlation and synchronicity between the spatially segregated neuronal clusters connected by axonal tracts. Specifically, phase synchronization revealed high synchronicity of  >0.8 between micro-TENN regions of interest. Normalized directed transfer function and transfer entropy matrices suggested robust information flow between the neuronal populations. Time varying power spectrum analysis revealed the strength of information propagation at various frequencies. Signal power strength was visible at elevated peak levels for dominant delta (1-4 Hz) and theta (4-8 Hz) frequency bands and progressively weakened at higher frequencies. These signal power strength results closely matched normalized directed transfer function analysis where near synchronous information flow was detected between frequencies of 2-5 Hz.

SIGNIFICANCE

To our knowledge, this is the first report using directed transfer function and transfer entropy methods based on fluorescent calcium activity to estimate functional connectivity of distinct neuronal populations via long-projecting, 3D axonal tracts in vitro. These functional data will further improve the design and optimization of implantable neural networks that could ultimately be deployed to reconstruct the nervous system to treat neurological disease and injury.

Stimulation triggers endogenous activity patterns in cultured cortical networks

Cultures of dissociated cortical neurons represent a powerful trade-off between more realistic experimental models and abstract modeling approaches, allowing to investigate mechanisms of synchronized activity generation. These networks spontaneously alternate periods of high activity (i.e. network bursts) with periods of quiescence in a dynamic state which recalls the fluctuation of in vivo UP and DOWN states. Network bursts can also be elicited by external stimulation and their spatial propagation patterns tracked by means of multi-channel micro-electrode arrays. In this study, we used rat cortical cultures coupled to micro-electrode arrays to investigate the similarity between spontaneous and evoked activity patterns. We performed experiments by applying electrical stimulation to different network locations and demonstrated that the rank orders of electrodes during evoked and spontaneous events are remarkably similar independently from the stimulation source. We linked this result to the capability of stimulation to evoke firing in highly active and “leader” sites of the network, reliably and rapidly recruited within both spontaneous and evoked bursts. Our study provides the first evidence that spontaneous and evoked activity similarity is reliably observed also in dissociated cortical networks.

A spatially resolved network spike in model neuronal cultures reveals nucleation centers, circular traveling waves and drifting spiral waves

We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal connection formation is independent of the distance between neurons, then the nucleation centers do not arise and the synchronization of spiking activity during a network spike occurs spatially uniform throughout the network. Therefore one can conclude that spatial proximity of connections between neurons is important for the formation of nucleation centers. It is also shown that fluctuations of the spatial density of neurons at their random homogeneous distribution typical for the experiments in vitro do not determine the locations of the nucleation centers. The simulation results are qualitatively consistent with the experimental observations.

Spontaneous Activity Characteristics of 3D "Optonets"

Sporadic spontaneous network activity emerges during early central nervous system (CNS) development and, as the number of neuronal connections rises, the maturing network displays diverse and complex activity, including various types of synchronized patterns. These activity patterns have major implications on both basic research and the study of neurological disorders, and their interplay with network morphology tightly correlates with developmental events such as neuronal differentiation, migration and establishment of neurotransmitter phenotypes. Although 2D neural cultures models have provided important insights into network activity patterns, these cultures fail to mimic the complex 3D architecture of natural CNS neural networks and its consequences on connectivity and activity. A 3D in-vitro model mimicking early network development while enabling cellular-resolution observations, could thus significantly advance our understanding of the activity characteristics in the developing CNS. Here, we longitudinally studied the spontaneous activity patterns of developing 3D in-vitro neural network “optonets,” an optically-accessible bioengineered CNS model with multiple cortex-like characteristics. Optonet activity was observed using the genetically encodable calcium indicator GCaMP6m and a 3D imaging solution based on a standard epi-fluorescence microscope equipped with a piezo-electric z-stage and image processing-based deconvolution. Our results show that activity patterns become more complex as the network matures, gradually exhibiting longer-duration events. This report characterizes the patterns over time, and discusses how environmental changes affect the activity patterns. The relatively high degree of similarity between the network's spontaneously generated activity patterns and the reported characteristics of in-vivo activity, suggests that this is a compelling model system for brain-in-a chip research.

Modularity Induced Gating and Delays in Neuronal Networks

Neural networks, despite their highly interconnected nature, exhibit distinctly localized and gated activation. Modularity, a distinctive feature of neural networks, has been recently proposed as an important parameter determining the manner by which networks support activity propagation. Here we use an engineered biological model, consisting of engineered rat cortical neurons, to study the role of modular topology in gating the activity between cell populations. We show that pairs of connected modules support conditional propagation (transmitting stronger bursts with higher probability), long delays and propagation asymmetry. Moreover, large modular networks manifest diverse patterns of both local and global activation. Blocking inhibition decreased activity diversity and replaced it with highly consistent transmission patterns. By independently controlling modularity and disinhibition, experimentally and in a model, we pose that modular topology is an important parameter affecting activation localization and is instrumental for population-level gating by disinhibition.

The capacity to transmit information between connected parts of a neuronal network is fundamental to its function. The organization of network connections (the topology of the network) is therefore expected to play an important role in determining network transmission. Since modular topology characterizes many brain circuits on multiple scales, investigating the role of modularity in activity gating is clearly desirable. By engineering such modular networks in vitro, we were able to perform such an investigation. Under these experimental conditions, we can independently control the degree of modularity, as well as inhibition in the network. We show that a combination of these two properties is highly beneficial from a communication perspective. Namely, it equips connected modules and large modular networks with the capacity to gate and temporally coordinate activity between the different parts of the network.

Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed 'quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.

A topological study of repetitive co-activation networks in in vitro cortical assemblies

To address the issue of extracting useful information from large data-set of large scale networks of neurons, we propose an algorithm that involves both algebraic-statistical and topological tools. We investigate the electrical behavior of in vitro cortical assemblies both during spontaneous and stimulus-evoked activity coupled to Micro-Electrode Arrays (MEAs). Our goal is to identify core sub-networks of repetitive and synchronous patterns of activity and to characterize them. The analysis is performed at different resolution levels using a clustering algorithm that reduces the network dimensionality. To better visualize the results, we provide a graphical representation of the detected sub-networks and characterize them with a topological invariant, i.e. the sequence of Betti numbers computed on the associated simplicial complexes. The results show that the extracted sub-populations of neurons have a more heterogeneous firing rate with respect to the entire network. Furthermore, the comparison of spontaneous and stimulus-evoked behavior reveals similarities in the identified clusters of neurons, indicating that in both conditions similar activation patterns drive the global network activity.

Glutamate mediated astrocytic filtering of neuronal activity

Neuron-astrocyte communication is an important regulatory mechanism in various brain functions but its complexity and role are yet to be fully understood. In particular, the temporal pattern of astrocyte response to neuronal firing has not been fully characterized. Here, we used neuron-astrocyte cultures on multi-electrode arrays coupled to Ca2+ imaging and explored the range of neuronal stimulation frequencies while keeping constant the amount of stimulation. Our results reveal that astrocytes specifically respond to the frequency of neuronal stimulation by intracellular Ca2+ transients, with a clear onset of astrocytic activation at neuron firing rates around 3-5 Hz. The cell-to-cell heterogeneity of the astrocyte Ca2+ response was however large and increasing with stimulation frequency. Astrocytic activation by neurons was abolished with antagonists of type I metabotropic glutamate receptor, validating the glutamate-dependence of this neuron-to-astrocyte pathway. Using a realistic biophysical model of glutamate-based intracellular calcium signaling in astrocytes, we suggest that the stepwise response is due to the supralinear dynamics of intracellular IP3 and that the heterogeneity of the responses may be due to the heterogeneity of the astrocyte-to-astrocyte couplings via gap junction channels. Therefore our results present astrocyte intracellular Ca2+ activity as a nonlinear integrator of glutamate-dependent neuronal activity.

Explorative Data Analysis of In-Vitro Neuronal Network Behavior Based on an Unsupervised Learning Approach

In the present chapter authors want to expose new insights in the field of Computational Neuroscience at regard to the study of neuronal networks grown in vitro. Such kind of analyses can exploit the availability of a huge amount of data thanks to the use of Multi Electrode Arrays (MEA), a multi-channel technology which allows capturing the activity of several different neuronal cells for long time recordings. Given the possibility of simultaneous targeting of various sites, neuroscientists are so applying such recent technology for various researches. The chapter begins by giving a brief presentation of MEA technology and of the data produced in output, punctuating some of the pros and cons of MEA recordings. Then we present an overview of the analytical techniques applied in order to extrapolate the hidden information from available data. Then we shall explain the approach we developed and applied on MEAs prepared in our cell culture laboratory, consisting of statistical methods capturing the main features of the spiking, in particular bursting, activity of various neuron, and performing data dimensionality reduction and clustering, in order to classify neurons according to their spiking properties having showed correlated features. Finally the chapter wants to furnish to neuroscientists an overview about the quantitative analysis of in-vitro spiking activity data recorded via MEA technology and to give an example of explorative analysis applied on MEA data. Such study is based on methods from Statistics and Machine Learning or Computer Science but at the same time strictly related to neurophysiological interpretations of the putative pharmacological manipulation of synaptic connections and mode of firing, with the final aim to extract new information and knowledge about neuronal networks behavior and organization.

Engineered neuronal circuits: a new platform for studying the role of modular topology

Neuron–glia cultures serve as a valuable model system for exploring the bio-molecular activity of single cells. Since neurons in culture can be conveniently recorded with great fidelity from many sites simultaneously, it has long been suggested that uniform cultured neurons may also be used to investigate network-level mechanisms pertinent to information processing, activity propagation, memory, and learning. But how much of the functionality of neural circuits can be retained in vitro remains an open question. Recent studies utilizing patterned networks suggest that they provide a most useful platform to address fundamental questions in neuroscience. Here we review recent efforts in the realm of patterned networks’ activity investigations. We give a brief overview of the patterning methods and experimental approaches commonly employed in the field, and summarize the main results reported in the literature. The general picture that emerges from these reports indicates that patterned networks with uniform connectivity do not exhibit unique activity patterns. Rather, their activity is very similar to that of unpatterned uniform networks. However, by breaking the connectivity homogeneity, using a modular architecture, it is possible to introduce pronounced topology-related gating and delay effects. These findings suggest that patterned cultured networks may serve as a new platform for studying the role of modularity in neuronal circuits.

Optical validation of in vitro extra-cellular neuronal recordings

Simultaneous calcium imaging and extra-cellular recordings from cultured cortical rat neurons were performed to directly map the efficacy of extra-cellular recordings with microelectrodes. For the first time, we can associate extra-cellular recordings with neuronal activity of specific neurons in the vicinity of the electrode. We demonstrate that recorded cells can be identified by correlating the electrical signals and the calcium response. Our data demonstrate that in sparse cultures, microelectrodes record exclusively from cells which reside at very close proximity to the recording electrode. Moreover, we show that recording appears to be limited to only a partial subset of the cells residing in this range. We further show that even in cases of strong neuron-electrode coupling, extra-cellular signals recorded from single, well-identified neurons vary in shape over time rendering spike sorting and network activity rate analysis incongruous. As multi-electrode array technology is becoming increasingly widespread, the visualization technique we report here will help users better understand the limits of this versatile and useful method.

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.

Innate synchronous oscillations in freely-organized small neuronal circuits

Background

Information processing in neuronal networks relies on the network's ability to generate temporal patterns of action potentials. Although the nature of neuronal network activity has been intensively investigated in the past several decades at the individual neuron level, the underlying principles of the collective network activity, such as the synchronization and coordination between neurons, are largely unknown. Here we focus on isolated neuronal clusters in culture and address the following simple, yet fundamental questions: What is the minimal number of cells needed to exhibit collective dynamics? What are the internal temporal characteristics of such dynamics and how do the temporal features of network activity alternate upon crossover from minimal networks to large networks?

Methodology/Principal Findings

We used network engineering techniques to induce self-organization of cultured networks into neuronal clusters of different sizes. We found that small clusters made of as few as 40 cells already exhibit spontaneous collective events characterized by innate synchronous network oscillations in the range of 25 to 100 Hz. The oscillation frequency of each network appeared to be independent of cluster size. The duration and rate of the network events scale with cluster size but converge to that of large uniform networks. Finally, the investigation of two coupled clusters revealed clear activity propagation with master/slave asymmetry.

Conclusions/Significance

The nature of the activity patterns observed in small networks, namely the consistent emergence of similar activity across networks of different size and morphology, suggests that neuronal clusters self-regulate their activity to sustain network bursts with internal oscillatory features. We therefore suggest that clusters of as few as tens of cells can serve as a minimal but sufficient functional network, capable of sustaining oscillatory activity. Interestingly, the frequencies of these oscillations are similar those observed in vivo.

Synchronization transitions on scale-free neuronal networks due to finite information transmission delays

We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.