Ion dynamics at the energy-deprived tripartite synapse.

The anatomical and functional organization of neurons and astrocytes at 'tripartite synapses' is essential for reliable neurotransmission, which critically depends on ATP. In low energy conditions, synaptic transmission fails, accompanied by a breakdown of ion gradients, changes in membrane potentials and cell swelling. The resulting cellular damage and cell death are causal to the often devastating consequences of an ischemic stroke. The severity of ischemic damage depends on the age and the brain region in which a stroke occurs, but the reasons for this differential vulnerability are far from understood. In the present study, we address this question by developing a comprehensive biophysical model of a glutamatergic synapse to identify key determinants of synaptic failure during energy deprivation. Our model is based on fundamental biophysical principles, includes dynamics of the most relevant ions, i.e., Na+, K+, Ca2+, Cl- and glutamate, and is calibrated with experimental data. It confirms the critical role of the Na+/K+-ATPase in maintaining ion gradients, membrane potentials and cell volumes. Our simulations demonstrate that the system exhibits two stable states, one physiological and one pathological. During energy deprivation, the physiological state may disappear, forcing a transit to the pathological state, which can be reverted when blocking voltage-gated Na+ and K+ channels. Our model predicts that the transition to the pathological state is favoured if the extracellular space fraction is small. A reduction in the extracellular space volume fraction, as, e.g. observed with ageing, will thus promote the brain's susceptibility to ischemic damage. Our work provides new insights into the brain's ability to recover from energy deprivation, with translational relevance for diagnosis and treatment of ischemic strokes.

Neural field models with transmission delays and diffusion.

A neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models by including a diffusion term into the neural field, which models direct, electrical connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of connectivity functions in the neural field model, we are able to compute its spectral properties and the first Lyapunov coefficient of a Hopf bifurcation. By examining a numerical example, we find that the addition of diffusion suppresses non-synchronised steady-states while favouring synchronised oscillatory modes.

Pathological responses to single-pulse electrical stimuli in epilepsy: The role of feedforward inhibition.

Delineation of epileptogenic cortex in focal epilepsy patients may profit from single-pulse electrical stimulation during intracranial EEG recordings. Single-pulse electrical stimulation evokes early and delayed responses. Early responses represent connectivity. Delayed responses are a biomarker for epileptogenic cortex, but up till now, the precise mechanism generating delayed responses remains elusive. We used a data-driven modelling approach to study early and delayed responses. We hypothesized that delayed responses represent indirect responses triggered by early response activity and investigated this for 11 patients. Using two coupled neural masses, we modelled early and delayed responses by combining simulations and bifurcation analysis. An important feature of the model is the inclusion of feedforward inhibitory connections. The waveform of early responses can be explained by feedforward inhibition. Delayed responses can be viewed as second-order responses in the early response network which appear when input to a neural mass falls below a threshold forcing it temporarily to a spiking state. The combination of the threshold with noisy background input explains the typical stochastic appearance of delayed responses. The intrinsic excitability of a neural mass and the strength of its input influence the probability at which delayed responses to occur. Our work gives a theoretical basis for the use of delayed responses as a biomarker for the epileptogenic zone, confirming earlier clinical observations. The combination of early responses revealing effective connectivity, and delayed responses showing intrinsic excitability, makes single-pulse electrical stimulation an interesting tool to obtain data for computational models of epilepsy surgery.

A Comparison of Evoked and Non-evoked Functional Networks.

The growing interest in brain networks to study the brain's function in cognition and diseases has produced an increase in methods to extract these networks. Typically, each method yields a different network. Therefore, one may ask what the resulting networks represent. To address this issue we consider electrocorticography (ECoG) data where we compare three methods. We derive networks from on-going ECoG data using two traditional methods: cross-correlation (CC) and Granger causality (GC). Next, connectivity is probed actively using single pulse electrical stimulation (SPES). We compare the overlap in connectivity between these three methods as well as their ability to reveal well-known anatomical connections in the language circuit. We find that strong connections in the CC network form more or less a subset of the SPES network. GC and SPES are related more weakly, although GC connections coincide more frequently with SPES connections compared to non-existing SPES connections. Connectivity between the two major hubs in the language circuit, Broca's and Wernicke's area, is only found in SPES networks. Our results are of interest for the use of patient-specific networks obtained from ECoG. In epilepsy research, such networks form the basis for methods that predict the effect of epilepsy surgery. For this application SPES networks are interesting as they disclose more physiological connections compared to CC and GC networks.

A framework for directional and higher-order reconstruction in photoacoustic tomography.

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered back-projection, time reversal and least squares suffer from curved line artefacts and blurring, especially in the case of limited angles or strong noise. In recent years, there has been great interest in regularised iterative methods. These methods employ prior knowledge of the image to provide higher quality reconstructions. However, easy comparisons between regularisers and their properties are limited, since many tomography implementations heavily rely on the specific regulariser chosen. To overcome this bottleneck, we present a modular reconstruction framework for photoacoustic tomography, which enables easy comparisons between regularisers with different properties, e.g. nonlinear, higher-order or directional. We solve the underlying minimisation problem with an efficient first-order primal-dual algorithm. Convergence rates are optimised by choosing an operator-dependent preconditioning strategy. A variety of reconstruction methods are tested on challenging 2D synthetic and experimental data sets. They outperform direct reconstruction approaches for strong noise levels and limited angle measurements, offering immediate benefits in terms of acquisition time and quality. This work provides a basic platform for the investigation of future advanced regularisation methods in photoacoustic tomography.

A Rate-Reduced Neuron Model for Complex Spiking Behavior.

We present a simple rate-reduced neuron model that captures a wide range of complex, biologically plausible, and physiologically relevant spiking behavior. This includes spike-frequency adaptation, postinhibitory rebound, phasic spiking and accommodation, first-spike latency, and inhibition-induced spiking. Furthermore, the model can mimic different neuronal filter properties. It can be used to extend existing neural field models, adding more biological realism and yielding a richer dynamical structure. The model is based on a slight variation of the Rulkov map.

Quantifying HER-2 expression on circulating tumor cells by ACCEPT.

Circulating tumor cells (CTCs) isolated from blood can be probed for the expression of treatment targets. Immunofluorescence is often used for both the enumeration of CTC and the determination of protein expression levels related to treatment targets. Accurate and reproducible assessment of such treatment target expression levels is essential for their use in the clinic. To enable this, an open source image analysis program named ACCEPT was developed in the EU-FP7 CTCTrap and CANCER-ID programs. Here its application is shown on a retrospective cohort of 132 metastatic breast cancer patients from which blood samples were processed by CellSearch® and stained for HER-2 expression as additional marker. Images were digitally stored and reviewers identified a total of 4084 CTCs. CTC's HER-2 expression was determined in the thumbnail images by ACCEPT. 150 of these images were selected and sent to six independent investigators to score the HER-2 expression with and without ACCEPT. Concordance rate of the operators' scoring results for HER-2 on CTCs was 30% and could be increased using the ACCEPT tool to 51%. Automated assessment of HER-2 expression by ACCEPT on 4084 CTCs of 132 patients showed 8 (6.1%) patients with all CTCs expressing HER-2, 14 (10.6%) patients with no CTC expressing HER-2 and 110 (83.3%) patients with CTCs showing a varying HER-2 expression level. In total 1576 CTCs were determined HER-2 positive. We conclude that the use of image analysis enables a more reproducible quantification of treatment targets on CTCs and leads the way to fully automated and reproducible approaches.

Cross-scale effects of neural interactions during human neocortical seizure activity.

Small-scale neuronal networks may impose widespread effects on large network dynamics. To unravel this relationship, we analyzed eight multiscale recordings of spontaneous seizures from four patients with epilepsy. During seizures, multiunit spike activity organizes into a submillimeter-sized wavefront, and this activity correlates significantly with low-frequency rhythms from electrocorticographic recordings across a 10-cm-sized neocortical network. Notably, this correlation effect is specific to the ictal wavefront and is absent interictally or from action potential activity outside the wavefront territory. To examine the multiscale interactions, we created a model using a multiscale, nonlinear system and found evidence for a dual role for feedforward inhibition in seizures: while inhibition at the wavefront fails, allowing seizure propagation, feedforward inhibition of the surrounding centimeter-scale networks is activated via long-range excitatory connections. Bifurcation analysis revealed that distinct dynamical pathways for seizure termination depend on the surrounding inhibition strength. Using our model, we found that the mesoscopic, local wavefront acts as the forcing term of the ictal process, while the macroscopic, centimeter-sized network modulates the oscillatory seizure activity.

Sparse pallidal connections shape synchrony in a network model of the basal ganglia.

Neural synchrony in the basal ganglia, especially in the beta frequency band (13-30 Hz), is a hallmark of Parkinson's disease and considered as antikinetic. In contrast, the healthy basal ganglia show low levels of synchrony. It is currently unknown where synchrony and oscillations arise in the parkinsonian brain and how they are transmitted through the basal ganglia, as well as what makes them dependent on dopamine. The external part of the globus pallidus has recently been identified as a hub nucleus in the basal ganglia, possessing intrinsic inhibitory connections and possibly also gap junctions. In this study, we show that in a conductance-based network model of the basal ganglia, the combination of sparse, high-conductance inhibitory synapses and sparse, low-conductance gap junctions in the external part of the globus pallidus could effectively desynchronize the whole network. However, when gap junction coupling became strong enough, the effect was impeded and activity synchronized. In particular, sustained periods of beta coherence occurred between some neuron pairs. As gap junctions can change their conductance with the dopamine level, we suggest pallidal gap junction coupling as a mechanism contributing to the development of beta synchrony in the parkinsonian basal ganglia.

Estimation and Identifiability of Model Parameters in Human Nociceptive Processing Using Yes-No Detection Responses to Electrocutaneous Stimulation.

Healthy or pathological states of nociceptive subsystems determine different stimulus-response relations measured from quantitative sensory testing. In turn, stimulus-response measurements may be used to assess these states. In a recently developed computational model, six model parameters characterize activation of nerve endings and spinal neurons. However, both model nonlinearity and limited information in yes-no detection responses to electrocutaneous stimuli challenge to estimate model parameters. Here, we address the question whether and how one can overcome these difficulties for reliable parameter estimation. First, we fit the computational model to experimental stimulus-response pairs by maximizing the likelihood. To evaluate the balance between model fit and complexity, i.e., the number of model parameters, we evaluate the Bayesian Information Criterion. We find that the computational model is better than a conventional logistic model regarding the balance. Second, our theoretical analysis suggests to vary the pulse width among applied stimuli as a necessary condition to prevent structural non-identifiability. In addition, the numerically implemented profile likelihood approach reveals structural and practical non-identifiability. Our model-based approach with integration of psychophysical measurements can be useful for a reliable assessment of states of the nociceptive system.

A Biophysical Model for Cytotoxic Cell Swelling.

We present a dynamic biophysical model to explain neuronal swelling underlying cytotoxic edema in conditions of low energy supply, as observed in cerebral ischemia. Our model contains Hodgkin-Huxley-type ion currents, a recently discovered voltage-gated chloride flux through the ion exchanger SLC26A11, active KCC2-mediated chloride extrusion, and ATP-dependent pumps. The model predicts changes in ion gradients and cell swelling during ischemia of various severity or channel blockage with realistic timescales. We theoretically substantiate experimental observations of chloride influx generating cytotoxic edema, while sodium entry alone does not. We show a tipping point of Na+/K+-ATPase functioning, where below cell volume rapidly increases as a function of the remaining pump activity, and a Gibbs-Donnan-like equilibrium state is reached. This precludes a return to physiological conditions even when pump strength returns to baseline. However, when voltage-gated sodium channels are temporarily blocked, cell volume and membrane potential normalize, yielding a potential therapeutic strategy. SIGNIFICANCE STATEMENT: Cytotoxic edema most commonly results from energy shortage, such as in cerebral ischemia, and refers to the swelling of brain cells due to the entry of water from the extracellular space. We show that the principle of electroneutrality explains why chloride influx is essential for the development of cytotoxic edema. With the help of a biophysical model of a single neuron, we show that a tipping point of the energy supply exists, below which the cell volume rapidly increases. We simulate realistic time courses to and reveal critical components of neuronal swelling in conditions of low energy supply. Furthermore, we show that, after transient blockade of the energy supply, cytotoxic edema may be reversed by temporary blockade of Na+ channels.

Dependence of Nociceptive Detection Thresholds on Physiological Parameters and Capsaicin-Induced Neuroplasticity: A Computational Study.

Physiological properties of peripheral and central nociceptive subsystems can be altered over time due to medical interventions. The effective change for the whole nociceptive system can be reflected in changes of psychophysical characteristics, e.g., detection thresholds. However, it is challenging to separate contributions of distinct altered mechanisms with measurements of thresholds only. Here, we aim to understand how these alterations affect Aδ-fiber-mediated nociceptive detection of electrocutaneous stimuli. First, with a neurophysiology-based model, we study the effects of single-model parameters on detection thresholds. Second, we derive an expression of model parameters determining the functional relationship between detection thresholds and the interpulse interval for double-pulse stimuli. Third, in a case study with topical capsaicin treatment, we translate neuroplasticity into plausible changes of model parameters. Model simulations qualitatively agree with changes in experimental detection thresholds. The simulations with individual forms of neuroplasticity confirm that nerve degeneration is the dominant mechanism for capsaicin-induced increases in detection thresholds. In addition, our study suggests that capsaicin-induced central plasticity may last at least 1 month.

Computational modeling of Adelta-fiber-mediated nociceptive detection of electrocutaneous stimulation.

Sensitization is an example of malfunctioning of the nociceptive pathway in either the peripheral or central nervous system. Using quantitative sensory testing, one can only infer sensitization, but not determine the defective subsystem. The states of the subsystems may be characterized using computational modeling together with experimental data. Here, we develop a neurophysiologically plausible model replicating experimental observations from a psychophysical human subject study. We study the effects of single temporal stimulus parameters on detection thresholds corresponding to a 0.5 detection probability. To model peripheral activation and central processing, we adapt a stochastic drift-diffusion model and a probabilistic hazard model to our experimental setting without reaction times. We retain six lumped parameters in both models characterizing peripheral and central mechanisms. Both models have similar psychophysical functions, but the hazard model is computationally more efficient. The model-based effects of temporal stimulus parameters on detection thresholds are consistent with those from human subject data.

Modeling focal epileptic activity in the Wilson-cowan model with depolarization block.

UNLABELLED: Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson-Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson-Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

Exploiting pallidal plasticity for stimulation in Parkinson's disease.

OBJECTIVE: Continuous application of high-frequency deep brain stimulation (DBS) often effectively reduces motor symptoms of Parkinson's disease patients. While there is a growing need for more effective and less traumatic stimulation, the exact mechanism of DBS is still unknown. Here, we present a methodology to exploit the plasticity of GABAergic synapses inside the external globus pallidus (GPe) for the optimization of DBS. APPROACH: Assuming the existence of spike-timing-dependent plasticity (STDP) at GABAergic GPe-GPe synapses, we simulate neural activity in a network model of the subthalamic nucleus and GPe. In particular, we test different DBS protocols in our model and quantify their influence on neural synchrony. MAIN RESULTS: In an exemplary set of biologically plausible model parameters, we show that STDP in the GPe has a direct influence on neural activity and especially the stability of firing patterns. STDP stabilizes both uncorrelated firing in the healthy state and correlated firing in the parkinsonian state. Alternative stimulation protocols such as coordinated reset stimulation can clearly profit from the stabilizing effect of STDP. These results are widely independent of the STDP learning rule. SIGNIFICANCE: Once the model settings, e.g., connection architectures, have been described experimentally, our model can be adjusted and directly applied in the development of novel stimulation protocols. More efficient stimulation leads to both minimization of side effects and savings in battery power.

Pallidal gap junctions-triggers of synchrony in Parkinson's disease?

Although increased synchrony of the neural activity in the basal ganglia may underlie the motor deficiencies exhibited in Parkinson's disease (PD), how this synchrony arises, propagates through the basal ganglia, and changes under dopamine replacement remains unknown. Gap junctions could play a major role in modifying this synchrony, because they show functional plasticity under the influence of dopamine and after neural injury. In this study, confocal imaging was used to detect connexin-36, the major neural gap junction protein, in postmortem tissues of PD patients and control subjects in the putamen, subthalamic nucleus (STN), and external and internal globus pallidus (GPe and GPi, respectively). Moreover, we quantified how gap junctions affect synchrony in an existing computational model of the basal ganglia. We detected connexin-36 in the human putamen, GPe, and GPi, but not in the STN. Furthermore, we found that the number of connexin-36 spots in PD tissues increased by 50% in the putamen, 43% in the GPe, and 109% in the GPi compared with controls. In the computational model, gap junctions in the GPe and GPi strongly influenced synchrony. The basal ganglia became especially susceptible to synchronize with input from the cortex when gap junctions were numerous and high in conductance. In conclusion, connexin-36 expression in the human GPe and GPi suggests that gap junctional coupling exists within these nuclei. In PD, neural injury and dopamine depletion could increase this coupling. Therefore, we propose that gap junctions act as a powerful modulator of synchrony in the basal ganglia.

Synchrony in Parkinson's disease: importance of intrinsic properties of the external globus pallidus.

The mechanisms for the emergence and transmission of synchronized oscillations in Parkinson's disease, which are potentially causal to motor deficits, remain debated. Aside from the motor cortex and the subthalamic nucleus, the external globus pallidus (GPe) has been shown to be essential for the maintenance of these oscillations and plays a major role in sculpting neural network activity in the basal ganglia (BG). While neural activity of the healthy GPe shows almost no correlations between pairs of neurons, prominent synchronization in the ß frequency band arises after dopamine depletion. Several studies have proposed that this shift is due to network interactions between the different BG nuclei, including the GPe. However, recent studies demonstrate an important role for the properties of neurons within the GPe. In this review, we will discuss these intrinsic GPe properties and review proposed mechanisms for activity decorrelation within the dopamine-intact GPe. Failure of the GPe to desynchronize correlated inputs can be a possible explanation for synchronization in the whole BG. Potential triggers of synchronization involve the enhancement of GPe-GPe inhibition and changes in ion channel function in GPe neurons.

Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus.

The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays.

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis.

Efficacy, nephrotoxicity and ototoxicity of aminoglycosides, mathematically modelled for modelling-supported therapeutic drug monitoring.

Therapeutic drug monitoring (TDM) of aminoglycosides has been a topic during the last thirty years. There is a tendency that - because of the once-daily regimen - TDM is considered not necessary anymore. Although once daily dosing has the potential for decreased toxicity, long-term usage can cause severe nephro- and ototoxicity. Furthermore, inadequate plasma concentrations can lead to treatment failure. This work is devoted to the development and application of the first mathematical model of aminoglycosides, which simulates in relation to the pharmacokinetics both their effects on bacteria as well as their nephrotoxicity and cochleotoxicity. Our software system is suitable for TDM. Based on theoretical considerations, a multi-compartment mathematical model in a numerical program in Matlab is derived that incorporates the antimicrobial effects of aminoglycosides, the saturable and active uptake into kidney cells, the reversible nephrotoxicity and the irreversible cochleotoxicity. Using fictitious person data, and an assumed pharmacokinetic and dynamic parameter set obtained from the literature, we simulated the drug concentrations, antibacterial effects, and toxicity over time in virtual patients to illustrate the benefits of optimized, efficacious dosage regimens that minimize (acceptable) nephro- and auditory ototoxicity. Our model confirms that extended-interval dosing seems the most appropriate to achieve this goal. By this manner, the present mathematical model contributes to an increase in our knowledge of how to obtain an optimized dosing strategy for individual patients. With the developed program, we are able to demonstrate that optimal aminoglycoside dosing still needs a sophisticated system of TDM.