|Current Workshop | Overview||Back | Home | Search ||
Computational Neuroscience and the Dynamics of Disease States
Pattern formation in excitable media
Networks of excitable cells, such as those found in the heart and brain, display a wide range of macroscopic spatio-temporal patterns.
These patterns may drive cell activity in non intuitive ways; cardiac cells, which beat periodically in isolation, display bursting behaviour when coupled in a network. Experiments where connectivity and density are varied in monolayer cultures of spontaneously beating heart cells suggest that sharp transitions between patterns can be driven by a gradual change of a control parameter. Further, simulations with simple excitable media models indicate that transitions can be predicted by the interplay between heterogeneity density, connectivity and generic properties of the wavefront.
Peter Magill and Rafal Bogacz
Understanding excessive beta oscillations in Parkinson’s disease
In idiopathic Parkinson’s disease, abnormal beta-band oscillations (13-30Hz) emerge in the firing of neurons in cortico-basal ganglia circuits, and the power/coherence of these oscillations therein correlates with difficulty in the initiation and execution of voluntary movements. During this talk, we will give an overview of our experimental and theoretical research that aims to define how these excessive oscillations are generated and are spread through the basal ganglia. We will first review patterns of neuronal activity recorded in a rat model of Parkinson’s disease that accurately recapitulates the clinical pathophysiology. We will then show how the oscillations are generated in a mathematical model of a circuit composed of two basal ganglia nuclei, the subthalamic nucleus and external globus pallidus. We will also describe how two neuronal populations in globus pallidus may be distinguished in vivo on the basis of their distinct patterns of activity, and how we extend the computational model to include these two populations and predict their functional connectivity. We will conclude by comparing the model’s predictions with unpublished experimental data.
Beauty and the beast - On marrying pretty theories to ugly realities
Modelling diseases of the brain raises the stakes for computational neuroscience. Predictions in this field can have "real world impact" by shaping the kind of treatment patients will receive. Then failures and inaccuracies of our models may inflict more serious suffering than just our own professional disappointment. I will ask whether we are ready for this challenge, from the perspective of my own work in neural population models. I will consider two issues in particular: fidelity to neuroanatomy and -physiology on one hand, and approaches to parameter tuning on the other hand. This will lead to one suggestion how one might arrive at predictions that are potentially "robust" enough to bet other people's health on.
Modeling altered functional connectivity in brain disease states
Modern brain imaging methods allow quantitative study of both local activity dynamics and the interdependency between activities in anatomically distant areas. The latter, known as functional connectivity analysis, is of growing interest in the clinical and experimental neuroscience community. In this talk, I will discuss functional connectivity from a theoretical and modeling viewpoint to highlight some less appreciated aspects of the functional connectivity phenomena important to properly understand any of its observed alterations in disease. I will start with reviewing the methods for quantification of functional connectivity, focusing on comparison of linear and nonlinear measures.
Further, I shall discuss several factors that shape functional connectivity. In particular, I will critically assess the dominant role of the underlying long-range anatomical connectivity, showing how changes in other system properties such as local dynamics can be also responsible for functional connectivity alterations observed in disease states. To illustrate the main points, I will use network models composed of neural populations connected according to anatomically based long-range cortical connectivity pattern. The talk will conclude with open challenges in the field of functional connectivity modeling.
Understanding the dynamics of brain disease states using the Liley model
The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. In particular I will focus on the Liley model for cortical activity that has been particularly successful for describing oscillations consistent with the alpha band of the human EEG spectrum. I will contrast this with a similar (and simpler) Wilson-Cowan style model with delays and highlight the major differences between the two - emphasising the rich dynamic repertoire of the Liley model. Following a bifurcation analysis of the ten dimensional Liley cortical module, I will move on to treat layered two- dimensional sheets with long range axonal connections mediating synaptic interactions. Extensions of the basic formalism to treat adaptive feedback, dendritic structure and inhomogeneous connectivity are described along with open challenges for the development of multi- scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale. This talk will be given as a primer for the subsequent talks by John Terry, Rafal Bogacz, Ingo Bojak and Jaroslav Hlinka.
Transient patterns in a subexcitable medium and their relation to migraine diagnostics and non-medical treatment
Cortical spreading depression (SD) is a massive but transient perturbation in the brain's ionic homeostasis. It is the underlying cause of neurological symptoms during the aura phase in migraine. Recently, animal models also provided evidence for a causal relationship between SD and the headache phase.
Not all phases occur with every migraine attack leading to different diagnostic subforms of migraine. To address this variety, I present a mechanism by which transient SD waves segments are formed in a subexcitable medium. I use a generic reaction-diffusion model of the 2D folded human cortex being weakly susceptible for SD. In the subexcitable regime, the homogeneous steady state is the only attractor. Initial perturbed states can develop into distinct transient pulses caused by a saddle-node ghost of collided traveling pulse solutions that leads to a slow passage through a bottle-neck. The location of the bottle-neck in phase space is associated with a characteristic form (shape, size) of a wave segment, which was also observed with fMRI. An ensemble of initial perturbed states is created based on cortical pinwheel maps in the primary visual cortex and the course of the transient dynamics is investigated. The emerging transient patterns and their classification according to size and duration offered the following hypothesis: the headache phase depends on the instantaneous maximum spread (IMS) of SD, which occurs soon after initiation, possibly due to more convergent diffusion of noxious substances into the meninges with a subsequent delayed nociceptive responses; the aura phase may stay silent when IMS is small (depressed activity may be compensated, in particular, when cortical magnification factor is high). Furthermore, the statistics suggest a negative correlation between headache severity and aura phase and, more generally, the statistics of occurrences of the different classes has the potential to reproduce epidemiological statistics of different diagnostic subforms.
This approaches also offers a model-based analysis of phase-depended stimulation protocols for non-invasive neuromodulation devices to intelligently target migraine.
Wim van Drongelen
Brain Electrical Activity in Pediatric Epilepsy: Characterization and Localization of Events
Epilepsy is a serious neurological disorder characterized by recurrent seizures. It affects 1-2% of the population and about 1/3 of the patients with epilepsy do not respond to treatment. Despite continued introduction of new antiepileptic drugs over the past decades, this fraction of refractory patients has remained the same. This disappointing result is most likely due to poor understanding of the various mechanisms underlying epileptogenesis.
My talk is about temporal and spatial localization of interictal and ictal events in the clinical electroencephalogram (EEG)/electrocorticogram (ECoG), and their characterization. I will present and discuss results of temporal localization of seizures in long term recordings of pediatric patients, source localization of interictal spikes, and the outcome of detrended fluctuation analysis in EEG and ECoG data.
This type of analysis can be considered a first step in the examination of clinical manifestations of epileptiform activity. The outcome may be clinically relevant in that it has the potential to help establish a diagnosis, evaluate presurgical candidates, and evaluate treatment. In addition, localization and characterization procedures may indicate where transitions occur from the interictal to ictal state and thereby aid the investigation of seizure onset and offset.
Computational models as prospectors for anticipation and suppression of epileptic seizures
Epilepsy is a dynamic pathological condition of the human central nervous system featuring unexpected transitions to abnormal states, called seizures, where normal brain functions are impaired. The exact cause of these transitions is still largely unknown and the task to find a reliable method to predict or control these states still pose in majority of the cases a formidable challenge to both clinicians and neuroscientists. The first objective of this talk is to introduce various generic model scenarios of autonomous seizure generation. Computational models dedicated to explain the phenomena fall into three classes – models with parameter fluctuations, models with multiple attractors and models with intermittency. Depending on which scenario is responsible for the transitions to epileptic seizure, the strategy for prediction or control of these adverse events may be quite different. We address two specific questions where computational models can play leading role. First, is it possible to estimate the closeness of the system to the eventual transition, or in other words, the risk of an imminent seizure, and if it is, what is the best way to estimate this risk according to the model’s prescription? The second challenge is to design an optimal seizure suppression algorithm based on direct electric stimulations. We use modified versions of previously developed lumped neuronal model with multiple attractors that has the property of spontaneously switching between two states, representing normal and epileptic behaviour, due to intrinsic or extrinsic perturbations. Seizure generation patterns can be modulated by several intrinsic parameters such as the excitatory couplings between the model lumps and the amount of inhibition. We show that this model can reproduce realistic phenomenological distributions of seizure and inter-ictal time durations. Although in this class of models the exact timing of the seizure onset is unpredictable, the risk of seizure can be reconstructed from features of the activity, measuring for example the inter-ictal correlations between the lumps outputs. Another feature predicted by the models with multiple attractors is that the system’s behaviour can be altered by a brief stimulation pulse when the later is administered at the right time. We introduced in our model a reactive, state-dependent control module that effectively suppresses the paroxysmal activity. The model simulations are used to determine an optimal set of counter-stimulation parameters allowing for maximal effect with minimal stimulation dose.
Epilepsy is the third most common neurologic disorder, affecting 1% of the population worldwide. Despite the availability of over 20 anticonvulsant medications, approximately one third of patients have refractory epilepsy. The need for new therapies and improved understanding of the epileptic neuron and epileptic networks of neurons remains critical for these patients.
My talk is an introduction to the scope of the clinical problem of epilepsy. The epidemiology, semiology of seizures will be presented with clinical examples. Epilepsy in children has many clinical manifestations. The electroencephalogram will be described and its relationship to seizures will be illustrated. Current therapies and their limitations will also be discussed.
Building on this background, a discussion of current research problems and questions will be detailed and some of our collaborative work will be illustrated.
Neural Mass Models: EEG/MEG and hemodynamic signals
Neural Mass Models are being applied to make a bridge between the activity of neuronal networks as reflected in EEG/MEG signals and hemodynamic signals as measured by way of functional MRI (BOLD), in order to gain insight in the working of neuronal networks underlying cognitive processes and pathological conditions. This constitutes a central feature of Dynamic Causal Modelling (DCM)¹.
According to this approach the summed post-synaptic potentials generated by a neural mass model of neuronal networks based on Wilson-Cowan equations² are used in the forward mode to estimate the primary current density distribution of a brain area. This approach has been applied in a number of studies of brain rhythmic activities, both under normal and pathological conditions (epilepsy)³. Here I consider this approach in a wider context. The primary current density can be transformed into the signal recorded at EEG sensors, by applying a linear spatial convolution with the EEG lead field, i.e. the function which relates any source in the brain to the corresponding measurements at the EEG sensors. Simultaneously the summed post-synaptic potentials generated by the neural mass model can be transformed into a local vasomotor feed forward signal that is then further transformed by way of temporal convolution with the hemodynamic response function (HRF) into a simulated BOLD signal4. In this way the information obtained from the EEG signal and from the corresponding fMRI BOLD signal recorded from the same region of interest can be fused. This approach, however, is based on concepts that are still insufficiently established. Namely more research is needed to better understand how neural activities, generated by neural populations with complex geometrical configurations are transformed into cortical current distributions on the one hand, and how they are associated with BOLD signals on the other, as for example In the case of alpha rhythms5. Understanding these basic processes is important to be able to make insightful interpretations of multimodal imaging of brain processes.
1David O, Friston KJ.. 2003. A neural mass model for MEG/EEG: coupling and neuronal dynamics.
Neuroimage. 2003 Nov;20(3):1743-55. Friston, K.J., Harrison, L., Penny, W. 2003. Dynamic causal modeling. NeuroImage 19: 1273 – 1302.
2Wallace E, Benayoun M, van Drongelen W, Cowan JD. Emergent oscillations in networks of stochastic spiking neurons. PLoS One. 2011 May 6;6(5).
3Lopes da Silva F, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN.2003. Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia:44 Suppl 12:72-83
4Valdes-Sosa PA, Sanchez-Bornot JM, Sotero RC, Iturria-Medina Y, Aleman-Gomez Y, Bosch-Bayard J, Carbonell F, Ozaki T. 2008. Model driven EEG/fMRI fusion of brain oscillations. Hum Brain Mapp. 23;30(9):2701-2721
5de Munck JC, Gonçalves SI, Mammoliti R, Heethaar RM, Lopes da Silva FH. 2009.
Interactions between different EEG frequency bands and their effect on alpha-fMRI correlations. Neuroimage.;47(1):69-76.- de Munck JC, Gonçalves SI, Faes TJ, Kuijer JP, Pouwels PJ, Heethaar RM, Lopes da Silva FH. 2008. A study of the brain's resting state based on alpha band power, heart rate and fMRI. Neuroimage;42(1):112-21. - de Munck JC, Gonçalves SI, Huijboom L, Kuijer JP, Pouwels PJ, Heethaar RM, Lopes da Silva FH. 2007. The hemodynamic response of the alpha rhythm: an EEG/fMRI study. Neuroimage;35(3):1142-51.
Seizure onset: Vulnerability at the edge of stability?
An association between multistability and seizure onset has long been recognized. From this perspective seizure onset and cessation are related to stimuli that cause switches between basins of attraction associated with healthy brain dynamics and those associated with the seizure state. Surprisingly little attention has been given to the role played by the unstable boundary that separates the basins of attraction (“separatrix”), particularly in the presence of noise and time delay. Here attention is drawn to a simple model of two neurons with mutual time-delayed feedback in which long-lived oscillatory transients arise whenever the dynamical system is brought sufficiently close to the separatrix. Since this phenomenon does not occur when time delays are absent these transients are referred to as delay-induced transient oscillations (DITOs). The duration of the DITOs can be orders of magnitude longer than the delay. Bistable states arise naturally as a result of slow time scale parameter changes as one brain state is replaced by another. These parameter changes also bring the dynamical nervous system arbitrarily close to the separatrix. Taken together these observations suggest that when brain states change the nervous system generically must become transiently vulnerable to generate transient dynamical behaviors which possibly are related to seizure generation. These observations may explain the observation of increased risk of seizure onset noted in some forms of epilepsy with respect to sleep stage transitions and circadian rhythms.
Jonathan Rubin and Thomas Wichmann
Basal ganglia activity patterns in parkinsonism
Activity patterns in various basal ganglia structures may become significantly altered by the development of parkinsonism. The changes observed include variations in firing rates, enhanced oscillations or burstiness, and increased correlations between outputs of different neurons. We present experimental findings on these alterations, with a focus on bursting activity, the effects of local injections of dopamine--‐related drugs, and responses to deep brain stimulation (DBS) of the subthalamic nucleus (STN), including those manifested in pallidal regions linked synaptically with the STN. Computational models offer the opportunity to test hypotheses about the origins of enhanced bursting, and we discuss two different mechanisms for low--‐rate bursting that arise in the simulated parkinsonian STN. Furthermore, we offer predictions about the downstream implications of parkinsonian increases in STN burstiness, assuming that it is transmitted to the globus pallidus pars interna. These predictions relate to the effects of burstiness on relay performed by thalamic neurons in areas targeted by pallidal outputs and on the transfer of correlations from GPi to thalamus.
Steven J. Schiff
Towards Model–based Control of Epilepsy and Parkinson’s Disease
Since the 1950s, we have developed mature theories of modern control theory and computational neuroscience with almost no interaction between these disciplines. With the advent of computationally efficient nonlinear Kalman filtering techniques, along with improved neuroscience models which provide increasingly accurate reconstruction of dynamics in a variety of important normal and disease states in the brain, the prospects for a synergistic interaction between these fields are now strong. I will review the foundation of Kalman filtering, and then demonstrate how to apply such techniques to standard models from computational neuroscience. We will examine the reconstruction of seizure dynamics from experimental data, and demonstrate the essential role that extracellular potassium dynamics play in these phenomena. In Parkinson's disease, we will explore the prospects of using reduced models of thalamic neurons, and then extend our control explorations to more complete models of basal ganglia dynamics. These techniques are broadly applicable to a wide range of dynamical disease states.
Piotr Suffczynski, Nathan E. Crone, Piotr J. Franaszczuk
Mechanisms of cortical high-gamma activity (60-200 Hz) investigated with computational modeling
Very fast oscillations in LFP and EEG, ranging in frequency between 80 Hz and 250 Hz, have been observed in spatial and temporal patterns corresponding to the epileptogenic zone in patients with epilepsy and in experimental models of epilepsy (Fisher et al., J Clin Neurophysiol, 1992; Traub et al., Epilepsia, 2001). On the other hand, high-gamma activity (HGA) in overlapping frequencies (~60-200 Hz) have been observed during task-related cortical activation in humans (Crone et al., Prog Brain Res, 2006) and in animals (Ray et al., J Neurosci, 2008), and have been used to map normal brain function and to decode commands in brain-computer interfaces. To understand the role that high-gamma activity (HGA) plays in both normal and pathological brain states, deeper insights into its generating mechanisms are essential. Because the neural populations recorded by LFPs and EEG cannot be comprehensively recorded at scales that are likely to be relevant, we used a biologically based computational model of a cortical network to investigate the mechanisms generating HGA.
The computational model included excitatory pyramidal regular-spiking (PY) and inhibitory fast-spiking (I) neurons described by Hodgkin – Huxley dynamics. We compared activity generated by this model with HGA that was observed in LFP recorded in monkey somatosensory cortex during vibrotactile stimulation. These animal data were used because simultaneously recorded LFP and single unit activity were available, in contrast to the human case. Sensory input was modeled as uncorrelated Poisson spike input arriving to subpopulation of excitatory and inhibitory neurons. Input rate was modeled as fast ON response followed by slowly decaying response simulating responses of fast adapting and slowly adapting receptors to step stimulation.
Increase of firing rate and broadband HGA responses in LFP signals generated by the model were in agreement with experimental results. Blocking the I→PY connections in the model abolishes the HGA while blocking PY→I, PY-PY or I-I does not. Thus, these HGA appear to be mediated mostly by an excited population of inhibitory fast-spiking interneurons firing at high-gamma frequencies and pacing excitatory regular-spiking pyramidal cells, which fire at lower rates but in phase with the population rhythm. HGA were generated for a broad range of model parameters and sensory input values and did not require setting the network close to pathological regime.
HGA reflects local cortical activation under normal conditions and as such is a good candidate for mapping cortical areas engaged by a specific task. Pathological conditions are not necessary to observe HGA in the model. There might be different mechanisms leading to activity in similarly high frequencies and frequency alone may not be sufficient to distinguish between normal and pathologic oscillatory activity. The mechanisms of HGA, in this model of local cortical circuits, appear to be similar to those proposed for hippocampal ripples generated by subset of interneurons that regulate discharge of principal cells.
Microcircuit motifs in health and disease
Recent neuroimaging experiments have shown not only structural network differences between patients suffering from psychiatric illnesses and control subjects, but also differences in their large scale network dynamics. The link between local circuit abnormalities due to psychiatric illnesses and corresponding behavioural symptoms has not yet been explored extensively, but the combination of theoretical and optogenetical approaches promises to make rapid progress in addressing this question. I will review the role of oscillatory dynamics generated by microcircuit motifs in cognitive processes and indicate how defects in these motifs caused by psychiatric illnesses could affect cognition. I will focus on the (1) I-I motif of mutually connected inhibitory cells, (2) E-I motif of reciprocally connected excitatory and inhibitory cells and (3) E-2I motif consisting of excitatory and two inhibitory cell types (soma- and dendrite-targeting).
Visualising the spatiotemporal neuronal effects of deep brain stimulation
Deep brain stimulation (DBS) is a surgical therapy widely used to treat the disabling motor symptoms of Parkinson’s disease, tremor and dystonia, and is being applied to an increasing number of neurological and psychiatric conditions. DBS involves the chronic implantation of electrodes into disorder specific sub-cortical nuclei through which a continuous oscillatory current is passed. While the treatment is successful, the mechanisms which lead to the observed clinical improvements remain unclear and debated, which in turn slows the optimisation of present day DBS and hinders future developments and applications. This is particularly difficult as it is not possible to directly image the electric field induced by DBS in the human brain. Recently, computational modelling has been used to visualise the current spread induced by DBS and, estimate the impact of this current on the surrounding neural structures. I present such a structural modelling approach which begins with the construction of a finite element model. Such structural models can be used to understand the differences of stimulation at different time stages post-implantation, between commonly used contact configurations, and the effect of the surrounding anatomy. The spatial spread of the electric field can then be applied to surrounding neural structures to estimate the stimulation induced changes in firing rate. Most work currently estimates this effect using compartmental models of unconnected myelinated axons. I discuss alternative methods of estimating this “volume of tissue activated”, specifically the use of target specific neuronal models. These results demonstrate a means through which to quantitatively assess the induced current spread in DBS, which will allow us to investigate the neuronal changes induced by DBS, as well as configure the shape and strength of the electric field to maximise therapeutic benefit and minimise unwanted side effects.