publications

2025

1. Chaos

   Mean-field approximation for networks with synchrony-driven adaptive coupling

   N. Fennelly, A. Neff, R. Lambiotte, A. Keane, and Á. Byrne

   2025

   Abs DOI

   Synaptic plasticity plays a fundamental role in neuronal dynamics, governing how connections between neurons evolve in response to experience. In this study, we extend a network model of θ -neuron oscillators to include a realistic form of adaptive plasticity. In place of the less tractable spike-timing-dependent plasticity, we employ recently validated phase-difference-dependent plasticity rules, which adjust coupling strengths based on the relative phases of θ -neuron oscillators. We explore two distinct implementations of this plasticity: pairwise updates to individual coupling strengths and global updates applied to the mean coupling strength. We derive a mean-field approximation and assess its accuracy by comparing it to θ -neuron simulations across various stability regimes. The synchrony of the system is quantified using the Kuramoto order parameter. Through bifurcation analysis and the calculation of maximal Lyapunov exponents, we uncover interesting phenomena such as bistability and chaotic dynamics via period-doubling and boundary crisis bifurcations. These behaviors emerge as a direct result of adaptive coupling and are absent in systems without such plasticity.

2023

1. NeuralComp

   Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

   Benoit Duchet, Christian Bick, and Áine Byrne

   2023

   Abs DOI

   Abstract Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidating how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP and by the lack of low-dimensional description that could provide analytical insights. Phase-difference-dependent plasticity (PDDP) rules approximate STDP in phase oscillator networks, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe part of the phase space for this very high-dimensional system. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multiharmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a family of low-dimensional descriptions based on the mean-field dynamics of each cluster and average coupling weights between and within clusters. Finally, we show that such a two-cluster mean-field model can be fitted to synthetic data to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step toward a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.

2022

1. BrainTop

   Mean-Field Models for EEG/MEG: From Oscillations to Waves

   Áine Byrne, James Ross, Rachel Nicks, and Stephen Coombes

   2022

   Abs DOI

   Neural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

2021

1. JCompNeuro

   Predictive coding models for pain perception

   Yuru Song, Mingchen Yao, Helen Kemprecos, Aine Byrne, Zhengdong Xiao, and 4 more authors

   2021

   Abs DOI

   Pain is a complex, multidimensional experience that involves dynamic interactions between sensory-discriminative and affective-emotional processes. Pain experiences have a high degree of variability depending on their context and prior anticipation. Viewing pain perception as a perceptual inference problem, we propose a predictive coding paradigm to characterize evoked and non-evoked pain. We record the local field potentials (LFPs) from the primary somatosensory cortex (S1) and the anterior cingulate cortex (ACC) of freely behaving rats—two regions known to encode the sensory-discriminative and affective-emotional aspects of pain, respectively. We further use predictive coding to investigate the temporal coordination of oscillatory activity between the S1 and ACC. Specifically, we develop a phenomenological predictive coding model to describe the macroscopic dynamics of bottom-up and top-down activity. Supported by recent experimental data, we also develop a biophysical neural mass model to describe the mesoscopic neural dynamics in the S1 and ACC populations, in both naive and chronic pain-treated animals. Our proposed predictive coding models not only replicate important experimental findings, but also provide new prediction about the impact of the model parameters on the physiological or behavioral readout—thereby yielding mechanistic insight into the uncertainty of expectation, placebo or nocebo effect, and chronic pain.

2. NewJPhys.

   Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models

   Prejaas Tewarie, Bastian Prasse, Jil Meier, Áine Byrne, Manlio De Domenico, and 6 more authors

   2021

   Abs DOI

   Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can be significant coupling between frequency bands (interlayer connectivity). A multilayer network approach offers a solution to analyze frequency-specific networks in one framework. We propose to use a recently developed network reconstruction method in conjunction with phase oscillator models to estimate interlayer connectivity that optimally fits the empirical data. This approach determines interlayer connectivity based on observed frequency-specific time series of the phase and a connectome derived from diffusion weighted imaging. The performance of this interlayer reconstruction method was evaluated in-silico. Our reconstruction of the underlying interlayer connectivity agreed to very high degree with the ground truth. Subsequently, we applied our method to empirical resting-state MEG data obtained from healthy subjects and reconstructed two-layered networks consisting of either alpha-to-beta or theta-to-gamma band connectivity. Our analysis revealed that interlayer connectivity is dominated by a multiplex structure, i.e. by one-to-one interactions for both alpha-to-beta band and theta-to-gamma band networks. For theta–gamma band networks, we also found a plenitude of interlayer connections between distant nodes, though weaker connectivity relative to the one-to-one connections. Our work is an stepping stone towards the identification of interdependencies across frequency-specific networks. Our results lay the ground for the use of the promising multilayer framework in this field with more-informed and justified interlayer connections.

2020

1. MathBiosci

   Piecewise-constant optimal control strategies for controlling the outbreak of COVID-19 in the Irish population

   Lennon Ó Náraigh, and Áine Byrne

   2020

   Abs DOI

   We introduce a deterministic SEIR model and fit it to epidemiological data for the COVID-19 outbreak in Ireland. We couple the model to economic considerations — we formulate an optimal control problem in which the cost to the economy of the various non-pharmaceutical interventions is minimized, subject to hospital admissions never exceeding a threshold value corresponding to health-service capacity. Within the framework of the model, the optimal strategy of disease control is revealed to be one of disease suppression, rather than disease mitigation.

2. Chaos

   Order-indeterminant event-based maps for learning a beat

   Áine Byrne, John Rinzel, and Amitabha Bose

   2020

   Abs DOI

   The process by which humans synchronize to a musical beat is believed to occur through error-correction where an individual’s estimates of the period and phase of the beat time are iteratively adjusted to align with an external stimuli. Mathematically, error-correction can be described using a two-dimensional map where convergence to a fixed point corresponds to synchronizing to the beat. In this paper, we show how a neural system, called a beat generator, learns to adapt its oscillatory behavior through error-correction to synchronize to an external periodic signal. We construct a two-dimensional event-based map, which iteratively adjusts an internal parameter of the beat generator to speed up or slow down its oscillatory behavior to bring it into synchrony with the periodic stimulus. The map is novel in that the order of events defining the map are not a priori known. Instead, the type of error-correction adjustment made at each iterate of the map is determined by a sequence of expected events. The map possesses a rich repertoire of dynamics, including periodic solutions and chaotic orbits.

3. JNeurophys

   Next-generation neural mass and field modeling

   Áine Byrne, Reuben D. O’Dea, Michael Forrester, James Ross, and Stephen Coombes

   2020

   Abs DOI

   The Wilson–Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson–Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson–Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

2019

1. Springer

   A Neural Mass Model for Abnormal Beta-Rebound in Schizophrenia

   Áine Byrne, Stephen Coombes, and Peter F. Liddle

   In Multiscale Models of Brain Disorders, Cham, 2019

   Abs DOI

   Patients with schizophrenia demonstrate robust abnormalities of the synchronisation of beta oscillations that occur in diverse brain regions following sensory, motor or mental events. A prominent abnormality seen in primary motor cortex is a reduction in amplitude of so-called beta-rebound. Here a sharp decrease in neural oscillatory power in the beta band is observed during movement (MRBD) followed by an increase above baseline on movement cessation (PMBR). An understanding of how neural circuits give rise to MRBD and PMBR is clinically relevant to the pathophysiology of schizophrenia. Here we survey a very recent neural mass model for movement-induced changes in the beta rhythm and show that it is an ideal candidate for use in a clinical setting. The model arises as an exact mean-field reduction of a spiking network, has a realistic model of synaptic processing and is able to describe the dynamic changes in population synchrony that can underlie event-related desynchronisation/synchronisation for MRBD/PMBR. A lengthening of the synaptic response time to sensory drive, modelling NMDA receptor hypofunction, shows a reduction in beta-rebound consistent with that seen in schizophrenia.

2. Springer

   Next Generation Neural Mass Models

   Stephen Coombes, and Áine Byrne

   In Nonlinear Dynamics in Computational Neuroscience, Cham, 2019

   Abs DOI

   Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. In this chapter we consider the theta-neuron model that has recently been shown to admit to an exact mean-field description for instantaneous pulsatile interactions. We show that the inclusion of a more realistic synapse model leads to a mean-field model that has many of the features of a neural mass model coupled to a further dynamical equation that describes the evolution of network synchrony. A bifurcation analysis is used to uncover the primary mechanism for generating oscillations at the single and two population level. Numerical simulations also show that the phenomena of event related synchronisation and desynchronisation are easily realised. Importantly unlike its phenomenological counterpart this next generation neural mass model is an exact macroscopic description of an underlying microscopic spiking neurodynamics, and is a natural candidate for use in future large scale human brain simulations.

3. HearingRes

   Auditory streaming and bistability paradigm extended to a dynamic environment

   Áine Byrne, John Rinzel, and James Rankin

   2019

   Abs DOI

   We explore stream segregation with temporally modulated acoustic features using behavioral experiments and modelling. The auditory streaming paradigm in which alternating high- A and low-frequency tones B appear in a repeating ABA-pattern, has been shown to be perceptually bistable for extended presentations (order of minutes). For a fixed, repeating stimulus, perception spontaneously changes (switches) at random times, every 2e15 s, between an integrated interpretation with a galloping rhythm and segregated streams. Streaming in a natural auditory environment requires segregation of auditory objects with features that evolve over time. With the relatively idealized ABA-triplet paradigm, we explore perceptual switching in a non-static environment by considering slowly and periodically varying stimulus features. Our previously published model captures the dynamics of auditory bistability and predicts here how perceptual switches are entrained, tightly locked to the rising and falling phase of modulation. In psychoacoustic experiments we find that entrainment depends on both the period of modulation and the intrinsic switch characteristics of individual listeners. The extended auditory streaming paradigm with slowly modulated stimulus features presented here will be of significant interest for future imaging and neurophysiology experiments by reducing the need for subjective perceptual reports of ongoing perception.

4. JNeurophys

   Firing rate models for gamma oscillations

   Stephen Keeley, Áine Byrne, André Fenton, and John Rinzel

   2019

   Abs DOI

   Gamma oscillations are readily observed in a variety of brain regions during both waking and sleeping states. Computational models of gamma oscillations typically involve simulations of large networks of synaptically coupled spiking units. These networks can exhibit strongly synchronized gamma behavior, whereby neurons fire in near synchrony on every cycle, or weakly modulated gamma behavior, corresponding to stochastic, sparse firing of the individual units on each cycle of the population gamma rhythm. These spiking models offer valuable biophysical descriptions of gamma oscillations; however, because they involve many individual neuronal units they are limited in their ability to communicate general network-level dynamics. Here we demonstrate that few-variable firing rate models with established synaptic timescales can account for both strongly synchronized and weakly modulated gamma oscillations. These models go beyond the classical formulations of rate models by including at least two dynamic variables per population: firing rate and synaptic activation. The models’ flexibility to capture the broad range of gamma behavior depends directly on the timescales that represent recruitment of the excitatory and inhibitory firing rates. In particular, we find that weakly modulated gamma oscillations occur robustly when the recruitment timescale of inhibition is faster than that of excitation. We present our findings by using an extended Wilson-Cowan model and a rate model derived from a network of quadratic integrate-and-fire neurons. These biophysical rate models capture the range of weakly modulated and coherent gamma oscillations observed in spiking network models, while additionally allowing for greater tractability and systems analysis. NEW & NOTEWORTHY Here we develop simple and tractable models of gamma oscillations, a dynamic feature observed throughout much of the brain with significant correlates to behavior and cognitive performance in a variety of experimental contexts. Our models depend on only a few dynamic variables per population, but despite this they qualitatively capture features observed in previous biophysical models of gamma oscillations that involve many individual spiking units.

5. CerebralCortex

   Relationships Between Neuronal Oscillatory Amplitude and Dynamic Functional Connectivity

   Prejaas Tewarie, Benjamin A E Hunt, George C O’Neill, Aine Byrne, Kevin Aquino, and 4 more authors

   2019

   Abs DOI

   Event-related fluctuations of neural oscillatory amplitude are reported widely in the context of cognitive processing and are typically interpreted as a marker of brain “activity”. However, the precise nature of these effects remains unclear; in particular, whether such fluctuations reflect local dynamics, integration between regions, or both, is unknown. Here, using magnetoencephalography, we show that movement induced oscillatory modulation is associated with transient connectivity between sensorimotor regions. Further, in resting-state data, we demonstrate a significant association between oscillatory modulation and dynamic connectivity. A confound with such empirical measurements is that increased amplitude necessarily means increased signal-to-noise ratio (SNR): this means that the question of whether amplitude and connectivity are genuinely coupled, or whether increased connectivity is observed purely due to increased SNR is unanswered. Here, we counter this problem by analogy with computational models which show that, in the presence of global network coupling and local multistability, the link between oscillatory modulation and long-range connectivity is a natural consequence of neural networks. Our results provide evidence for the notion that connectivity is mediated by neural oscillations, and suggest that time–frequency spectrograms are not merely a description of local synchrony but also reflect fluctuations in long-range connectivity.

6. NeuroImage

   How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes

   Prejaas Tewarie, Romesh Abeysuriya, Áine Byrne, George C. O’Neill, Stamatios N. Sotiropoulos, and 2 more authors

   2019

   Abs DOI

   Functional networks obtained from magnetoencephalography (MEG) from different frequency bands show distinct spatial patterns. It remains to be elucidated how distinct spatial patterns in MEG networks emerge given a single underlying structural network. Recent work has suggested that the eigenmodes of the structural network might serve as a basis set for functional network patterns in the case of functional MRI. Here, we take this notion further in the context of frequency band specific MEG networks. We show that a selected set of eigenmodes of the structural network can predict different frequency band specific networks in the resting state, ranging from delta (1–4 Hz) to the high gamma band (40–70 Hz). These predictions outperform predictions based from surrogate data, suggesting a genuine relationship between eigenmodes of the structural network and frequency specific MEG networks. We then show that the relevant set of eigenmodes can be excited in a network of neural mass models using linear stability analysis only by including delays. Excitation of an eigenmode in this context refers to a dynamic instability of a network steady state to a spatial pattern with a corresponding coherent temporal oscillation. Simulations verify the results from linear stability analysis and suggest that theta, alpha and beta band networks emerge very near to the bifurcation. The delta and gamma bands in the resting state emerges further away from the bifurcation. These results show for the first time how delayed interactions can excite the relevant set of eigenmodes that give rise to frequency specific functional connectivity patterns.

7. PLoSCompBio

   A neuromechanistic model for rhythmic beat generation

   Amitabha Bose, Áine Byrne, and John Rinzel

   2019

   Abs DOI

   When listening to music, humans can easily identify and move to the beat. Numerous experimental studies have identified brain regions that may be involved with beat perception and representation. Several theoretical and algorithmic approaches have been proposed to account for this ability. Related to, but different from the issue of how we perceive a beat, is the question of how we learn to generate and hold a beat. In this paper, we introduce a neuronal framework for a beat generator that is capable of learning isochronous rhythms over a range of frequencies that are relevant to music and speech. Our approach combines ideas from error-correction and entrainment models to investigate the dynamics of how a biophysically-based neuronal network model synchronizes its period and phase to match that of an external stimulus. The model makes novel use of on-going faster gamma rhythms to form a set of discrete clocks that provide estimates, but not exact information, of how well the beat generator spike times match those of a stimulus sequence. The beat generator is endowed with plasticity allowing it to quickly learn and thereby adjust its spike times to achieve synchronization. Our model makes generalizable predictions about the existence of asymmetries in the synchronization process, as well as specific predictions about resynchronization times after changes in stimulus tempo or phase. Analysis of the model demonstrates that accurate rhythmic time keeping can be achieved over a range of frequencies relevant to music, in a manner that is robust to changes in parameters and to the presence of noise.

8. PRE

   Next-generation neural field model: The evolution of synchrony within patterns and waves

   Áine Byrne, Daniele Avitabile, and Stephen Coombes

   2019

   DOI

2017

1. JCompNeuro

   A mean field model for movement induced changes in the beta rhythm

   Áine Byrne, Matthew J Brookes, and Stephen Coombes

   2017

   DOI