Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

Nonlinearity in all-night sleep EEG recorded with foramen ovale electrodes in a patient with temporal lobe epilepsy

Objective: It is investigated to which extent measures of nonlinearity derived from surrogate data analysis are capable to quantify the changes of epileptic activity related to varying vigilance levels. Methods: Surface and intracranial EEG from foramen ovale (FO-)electrodes was recorded from a patient with temporal lobe epilepsy under presurgical evaluation over one night. Different measures of nonlinearity were estimated for non-overlapping 30-s segments for selected channels from surface and intracranial EEG. Additionally spectral measures were calculated. Sleep stages were scored according to Rechtschaffen/Kales and epileptic transients were counted and classified by visual inspection. Results: In the intracranial recordings stronger nonlinearity was found ipsilateral to the epileptogenic focus, more pronounced in NREM sleep, weaker in REM sleep. The dynamics within the NREM episodes varied with the different nonlinearity measures. Some nonlinearity measures showed variations with the sleep cycle also in the intracranial recordings contralateral to the epileptic focus and in the surface EEG. It is shown that the nonlinearity is correlated with short-term fluctuations of the delta power. The higher frequency of occurrence of clinical relevant epileptic spikes in the first NREM episode was not clearly reflected in the nonlinearity measures. Conclusions: It was confirmed that epileptic activity renders the EEG nonlinear. However, it was shown that the sleep dynamics itself also effects the nonlinearity measures. Therefore, at the present stage it is not possible to establish a unique connection between the studied nonlinearity measures and specific types of epileptic activity in sleep EEG recordings.

The value of magnetoencephalography to guide electrode implantation in epilepsy

To investigate if Magnetoencephalography (MEG) can add non-redundant information to guide implantation sites for intracranial recordings (IR). The contribution of MEG to intracranial recording planning was evaluated in 12 consecutive patients assessed pre-surgically with MEG followed by IR. Primary outcome measures were the identification of focal seizure onset in IR and favorable surgical outcome. Outcome measures were compared to those of 12 patients matched for implantation type in whom non-invasive pre-surgical assessment suggested clear hypotheses for implantation (non-MEG group). In the MEG group, non-invasive assessment without MEG was inconclusive, and MEG was then used to further help identify implantation sites. In all MEG patients, at least one virtual MEG electrode generated suitable hypotheses for the location of implantations. No differences in outcome measures were found between non-MEG and MEG groups. Although the MEG group included more complex patients, it showed similar percentage of successful implantations as the non-MEG group. This suggests that MEG can contribute to identify implantation sites where standard methods failed. © 2013 Springer Science+Business Media New York.

Bayesian neural network approach for determining the risk of re-intervention after endovascular aortic aneurysm repair

This article proposes a Bayesian neural network approach to determine the risk of re-intervention after endovascular aortic aneurysm repair surgery. The target of proposed technique is to determine which patients have high chance to re-intervention (high-risk patients) and which are not (low-risk patients) after 5 years of the surgery. Two censored datasets relating to the clinical conditions of aortic aneurysms have been collected from two different vascular centers in the United Kingdom. A Bayesian network was first employed to solve the censoring issue in the datasets. Then, a back propagation neural network model was built using the uncensored data of the first center to predict re-intervention on the second center and classify the patients into high-risk and low-risk groups. Kaplan-Meier curves were plotted for each group of patients separately to show whether there is a significant difference between the two risk groups. Finally, the logrank test was applied to determine whether the neural network model was capable of predicting and distinguishing between the two risk groups. The results show that the Bayesian network used for uncensoring the data has improved the performance of the neural networks that were built for the two centers separately. More importantly, the neural network that was trained with uncensored data of the first center was able to predict and discriminate between groups of low risk and high risk of re-intervention after 5 years of endovascular aortic aneurysm surgery at center 2 (p = 0.0037 in the logrank test).

An artificial neural network stratifies the risks of reintervention and mortality after endovascular aneurysm repair:a retrospective observational study

Background Lifelong surveillance after endovascular repair (EVAR) of abdominal aortic aneurysms (AAA) is considered mandatory to detect potentially life-threatening endograft complications. A minority of patients require reintervention but cannot be predictively identified by existing methods. This study aimed to improve the prediction of endograft complications and mortality, through the application of machine-learning techniques. Methods Patients undergoing EVAR at 2 centres were studied from 2004-2010. Pre-operative aneurysm morphology was quantified and endograft complications were recorded up to 5 years following surgery. An artificial neural networks (ANN) approach was used to predict whether patients would be at low- or high-risk of endograft complications (aortic/limb) or mortality. Centre 1 data were used for training and centre 2 data for validation. ANN performance was assessed by Kaplan-Meier analysis to compare the incidence of aortic complications, limb complications, and mortality; in patients predicted to be low-risk, versus those predicted to be high-risk. Results 761 patients aged 75 +/- 7 years underwent EVAR. Mean follow-up was 36+/- 20 months. An ANN was created from morphological features including angulation/length/areas/diameters/ volume/tortuosity of the aneurysm neck/sac/iliac segments. ANN models predicted endograft complications and mortality with excellent discrimination between a low-risk and high-risk group. In external validation, the 5-year rates of freedom from aortic complications, limb complications and mortality were 95.9% vs 67.9%; 99.3% vs 92.0%; and 87.9% vs 79.3% respectively (p0.001) Conclusion This study presents ANN models that stratify the 5-year risk of endograft complications or mortality using routinely available pre-operative data.

Magnetoencephalography in epilepsy

Magnetoencephalographic (MEG) signals, like electroencephalographic (EEG) measures, are the direct extracranial manifestations of neuronal activation. The two techniques can detect time-varying changes in electromagnetic activity with a sub-millisecond time resolution. Extra-cranial electromagnetic measures are the cornerstone of the non-invasive diagnostic armamentarium in patients with epilepsy. Their extremely high temporal resolution – comparable to intracranial recordings – is the basis for a precise definition of onset and propagation of ictal and interictal abnormalities. Given the cost of the infrastructure and equipment, MEG has yet to develop into a routinely applicable diagnostic tool in clinical settings. However, in recent years, an increasing number of patients with epilepsy have been investigated – usually in the context of presurgical evaluation of refractory epilepsies – and initial encouraging results have been reported. We will briefly review the principles and the technology behind MEG and its contribution in the diagnostic work-up of patients with epilepsy.

Source localization methods

One of the most pressing demands on electrophysiology applied to the diagnosis of epilepsy is the non-invasive localization of the neuronal generators responsible for brain electrical and magnetic fields (the so-called inverse problem). These neuronal generators produce primary currents in the brain, which together with passive currents give rise to the EEG signal. Unfortunately, the signal we measure on the scalp surface doesn't directly indicate the location of the active neuronal assemblies. This is the expression of the ambiguity of the underlying static electromagnetic inverse problem, partly due to the relatively limited number of independent measures available. A given electric potential distribution recorded at the scalp can be explained by the activity of infinite different configurations of intracranial sources. In contrast, the forward problem, which consists of computing the potential field at the scalp from known source locations and strengths with known geometry and conductivity properties of the brain and its layers (CSF/meninges, skin and skull), i.e. the head model, has a unique solution. The head models vary from the computationally simpler spherical models (three or four concentric spheres) to the realistic models based on the segmentation of anatomical images obtained using magnetic resonance imaging (MRI). Realistic models – computationally intensive and difficult to implement – can separate different tissues of the head and account for the convoluted geometry of the brain and the significant inter-individual variability. In real-life applications, if the assumptions of the statistical, anatomical or functional properties of the signal and the volume in which it is generated are meaningful, a true three-dimensional tomographic representation of sources of brain electrical activity is possible in spite of the ‘ill-posed’ nature of the inverse problem (Michel et al., 2004). The techniques used to achieve this are now referred to as electrical source imaging (ESI) or magnetic source imaging (MSI). The first issue to influence reconstruction accuracy is spatial sampling, i.e. the number of EEG electrodes. It has been shown that this relationship is not linear, reaching a plateau at about 128 electrodes, provided spatial distribution is uniform. The second factor is related to the different properties of the source localization strategies used with respect to the hypothesized source configuration.

The value of magnetoencephalography to guide electrode implantation in epilepsy

Purpose: To investigate if magnetoencephalography (MEG) can identify implantation sites for intracranial recordings (IR). Method: Two groups of 12 patients assessed for surgery with IR with and without MEG were compared (MEG and control groups). In the control group, non-invasive presurgical assessment without MEG suggested clear hypotheses for implantation. In the MEG group, non-invasive assessment was inconclusive, and MEG was used to identify implantation sites. Both groups were matched for implantation type. The success of implantation was defined by findings in IR: a) Focal seizure onset; b)Unilateral focal abnormal responses to single pulse electrical stimulation(SPES); and c) Concordance between a) and b). Results: In all MEG patients, at least one virtual MEG electrode generated suitable hypotheses for the location of implantations. The proportion of patients showing focal seizure onset restricted to one hemisphere was similar in control and MEG groups (6/12 vs. 11/12, Fisher’s exact test,p = 0.0686). The proportion of patients showing unilateral responses to SPES was lower in the control than in the MEG group (7/12 vs. 12/12,p = 0.0373). Conclusion: The MEG group showed similar or higher incidence of successful implantations than controls.

The functional neuroanatomy of auditory sensory gating and its behavioural implications

Auditory sensory gating (ASG) is the ability in individuals to suppress incoming irrelevant sensory input, indexed by evoked response to paired auditory stimuli. ASG is impaired in psychopathology such as schizophrenia, in which it has been proposed as putative endophenotype. This study aims to characterise electrophysiological properties of the phenomenon using MEG in time and frequency domains as well as to localise putative networks involved in the process at both sensor and source level. We also investigated the relationship between ASG measures and personality profiles in healthy participants in the light of its candidate endophenotype role in psychiatric disorders. Auditory evoked magnetic fields were recorded in twenty seven healthy participants by P50 ‘paired-click’ paradigm presented in pairs (conditioning stimulus S1- testing stimulus S2) at 80dB, separated by 250msec with inter trial interval of 7-10 seconds. Gating ratio in healthy adults ranged from 0.5 to 0.8 suggesting dimensional nature of P50 ASG. The brain regions active during this process were bilateral superior temporal gyrus (STG) and bilateral inferior frontal gyrus (IFG); activation was significantly stronger in IFG during S2 as compared to S1 (at p<0.05). Measures of effective connectivity between these regions using DCM modelling revealed the role of frontal cortex in modulating ASG as suggested by intracranial studies, indicating major role of inhibitory interneuron connections. Findings from this study identified a unique event-related oscillatory pattern for P50 ASG with alpha (STG)-beta (IFG) desynchronization and increase in cortical oscillatory gamma power (IFG) during S2 condition as compared to S1. These findings show that the main generator for P50 response is within temporal lobe and that inhibitory interneurons and gamma oscillations in the frontal cortex contributes substantially towards sensory gating. Our findings also show that ASG is a predictor of personality profiles (introvert vs extrovert dimension).