Investigations of effective connectivity in small and large scale neural networks

The correct signal processing of neuronal signals requires coordination of different groups of neurons. To achieve this there has to be a connection between those neurons. This connection and especially the strength of the connection is not known a priori and can only be measured directly in rare cases. In this thesis I present three publications (Rosjat et al., 2014; Tóth et al., 2015; Popovych et al., under review) and the results from two additional studies focussing on the analysis of couplings in experimental measured neuronal activities. The publications can be divided into investigations of intrinsic, as well as extrinsic intra- and intersegmental connections in the stick insect Carausius morosus and into analysis and mathematical modeling of couplings from EEG-measurements of the human brain while subjects were performing different tasks. In both parts I made use of mathematical models to build hypotheses about so far unknown coupling mechanisms. The first study deals with connectivity changes in the thalamo-cortical loop caused by schizophrenia (Rosjat et al., 2014). To build a mathematical model consisting of neural populations representing the thalamus and the auditory cortex we made use of published EEG-data, which were collected while subjects performed a double-click paradigm. The individual populations comprised a large number of phase oscillators with continuously distributed natural frequencies. Applying reduction methods by Pikovsky and Rosenblum, Ott and Antonsen together with the reduction method by Watanabe and Strogatz we investigated the influences of the bidirectional connections between the brain areas on the synchronization of the neuronal populations. The model was able to replicate the experimental data adequately. We observed that the coupling strength from the thalamic region to the cortical region mainly affected the duration of synchrony while the feedback to the thalamic region had a bigger effect on the strength of synchrony. This led to the hypothesis that the back coupling to the thalamic region might be reduced in schizophrenia patients. The second study will show an analysis of intersegmental couplings in the protractorretractor system of the pro- and mesothoracic ganglion of the stick insect Carausius morosus using mathematical models based on experimental data (Tóth et al., 2015). We made use of phase-response curves that were calculated experimentally on the one hand and simulated by mathematical models on the other hand to determine the nature and the strength of their connection. We showed that connections on both sides from the prothoracic to the mesothoracic network were necessary to achieve a good agreement with the experimental phase-response curves. Additionally, it was found that the strength of the excitatory connection played a key role, while the strength of the inhibitory connection did not have a big influence on the shape of the phase-response curves. The third study deals with the identification of a neuronal marker of movement execution (Popovych et al., under review). In this work we investigated the influence of internally and externally triggered movement on the phase synchronization in the motor system. We tested the signals, that were recorded from electrodes lying above the motor cortex, in the phase space including the major frequency bands (delta-, theta-, alpha-, beta- and low gamma-frequencies) for inter-trial phase synchrony. The study revealed a strong lateralized phase synchronization in the lower frequency bands (delta and theta) in the electrodes above the contralateral primary motor cortex independent of the hand performing and the cue triggering the movement. The results suggest that this phase synchronization could serve as an electrophysiological marker of movement execution additionally to the well established event-related desynchronization and event-related synchronization that are based on the amplitude changes in alpha- and beta- frequency bands

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

DST (Dynamic Synchronization Toolbox): A MATLAB Implementation of the Dynamic Phase-Locking Pipeline from Stimulus Transformation into Motor Action: Dynamic Graph Analysis Reveals a Posterior-to-Anterior Shift in Brain Network Communication of Older Subjects

The Dynamic Synchronization Toolbox allows the calculation of dynamic graphs based on phase synchronization in experimental data. This enables an analysis of the time-development of network connectivity between multiple recording sites (e.g. in electroencephalography (EEG) or magnetoencephalography (MEG) data) with a high temporal resolution. Optionally, the toolbox offers the possibility to compute several graph metrics (such as cluster dynamics, node degree, HUB nodes) via the Brain Connectivity toolbox

Movement related synchronization affected by aging:A dynamic graph study

P60 Movement related synchronization affected by aging: A dynamic graph studyNils Rosjat, Gereon Fink, Silvia DaunResearch Centre Jülich, Institute of Neuroscience and Medicine (INM-3), Jülich, GermanyCorrespondence: Nils Rosjat ([email protected])BMC Neuroscience 2019, 20(Suppl 1):P60The vast majority of motor actions, including their preparation and execution, is the result of a complex interplay of various brain regions. Novel methods in computational neuroscience allow us to assess interregional interactions from time series acquired with in-vivo techniques like electro-encephalography (EEG). However, our knowledge of the functional changes in neural networks during non-pathological aging is relatively poor.To advance our knowledge on this topic, we recorded EEG (64 channels) from 18 right-handed healthy younger subjects (YS, 22–35 years) and 24 right-handed healthy older subjects (OS, 60–79 years) during a simple motor task. The participants had to execute visually-cued low frequency left or right index finger tapping movements. Here, we used the relative phase-locking value (rPLV) [1] to examine whether there is an increase in functional coupling of brain regions during this simple motor task. We analyzed the connectivity for 42 electrodes focusing on connections between electrodes lying above the ipsi- and contralateral premotor and sensorimotor areas and the supplementary motor area.Widely used approaches for network definition are based on certain functional connectivity measures (e.g. similarity in BOLD time series, phase locking, coherence). These methods typically focus on constructing a single network representation over a fixed time period. However, this approach cannot make use of the high temporal resolution of EEG data and is not able to shed light on the understanding of temporal network dynamics. Here we used graph theory-based metrics that were developed in the last several years that can deal with the analysis of temporally evolving network structures [2].Our rPLV network analysis revealed four major results: An underlying coupling structure around movement onset in the low frequencies (2–7 Hz) that is present in YS and OS. The network in OS involved several additional connections and showed an overall increased coupling structure (Fig. 1). While the motor related networks of YS mainly involved ipsilateral frontal, contralateral frontal and central electrodes and interhemispheric pairs of electrodes connecting frontal ipsilateral with central contralateral ones, the networks of OS showed especially an increased interhemispheric connectivity. The analysis of hub nodes and communities showed a strong involvement of occipital, parietal, sensorimotor and central regions in YS. While the networks of OS involved similar hub nodes, the first occurrence of sensorimotor regions was clearly delayed and central electrodes played a more important role in the network (Fig. 1). Moreover, the motor related node degrees were significantly increased in OS.Fig. 1figure26Aggregated networks for younger (left) and older subjects (right) summarizing the network connectivity over the whole time interval. Edges lying above the motor cortex are highlighted in blue (ipsilateral), green (contralateral) and orange (interhemispheric). Hub nodes are marked in the order of first appearance scaled by their frequencyFull size imageIn addition to previously published results [3, 4], we were able to unravel the time-development of specific age-related dynamic network structures that seem to be a necessary prerequisite for the execution of a motor act. The increased interhemispheric connectivity of frontal electrodes fits very well to previous fMRI literature reporting an overactivation in frontal regions in older subjects. Our results also hint at a loss of lateralization via increased connectivity in both hemispheres as well as interhemispheric connections.References 1. Lachaux JP, Rodriguez E, Martinerie J, Varela FJ. Measuring phase synchrony in brain signals. Human brain mapping 1999, 8(4), 194–208. 2. Sizemore AE, Bassett DS. Dynamic graph metrics: Tutorial, toolbox, and tale. NeuroImage 2018, 180, 417-427. 3. Dennis NA, Cabeza R. Neuroimaging of healthy cognitive aging. The handbook of aging and cognition 2008, 3, 1-54. 4. Cabeza R. Hemispheric asymmetry reduction in older adults: the HAROLD model. Psychology and aging 2002, 17(1), 85

A mathematical model of dysfunction of the thalamo-cortical loop in schizophrenia

Background: Recent experimental results suggest that impairment of auditory information processing in the thalamo-cortical loop is crucially related to schizophrenia. Large differences between schizophrenia patients and healthy controls were found in the cortical EEG signals. Methods: We derive a phenomenological mathematical model, based on coupled phase oscillators with continuously distributed frequencies to describe the neural activity of the thalamo-cortical loop. We examine the influence of the bidirectional coupling strengths between the thalamic and the cortical area with regard to the phase-locking effects observed in the experiments. We extend this approach to a model consisting of a thalamic area coupled to two cortical areas, each comprising a set of nonidentical phase oscillators. In the investigations of our model, we applied the Ott-Antonsen theory and the Pikovsky-Rosenblum reduction methods to the original system. Results: The results derived from our mathematical model satisfactorily reproduce the experimental data obtained by EEG measurements. Furthermore, they show that modifying the coupling strength from the thalamic region to a cortical region affects the duration of phase synchronization, while a change in the feedback to the thalamus affects the strength of synchronization in the cortex. In addition, our model provides an explanation in terms of nonlinear dynamics as to why brain waves desynchronize after a given phase reset. Conclusion: Our model can explain functional differences seen between EEG records of healthy subjects and schizophrenia patients on a system theoretic basis. Because of this and its predictive character, the model may be considered to pave the way towards an early and reliable clinical detection of schizophrenia that is dependent on the interconnections between the thalamic and cortical regions. In particular, the model parameter that describes the strength of this connection can be used for a diagnostic classification of schizophrenia patients

Unravelling intra- and intersegmental neuronal connectivity between central pattern generating networks in a multi-legged locomotor system

Animal walking results from a complex interplay of central pattern generating networks (CPGs), local sensory signals expressing position, velocity and forces generated in the legs, and coordinating signals between neighboring legs. In particular, the CPGs control the activity of motoneuron (MN) pools which drive the muscles of the individual legs and are thereby responsible for the generation of rhythmic leg movements. The rhythmic activity of the CPGs as well as their connectivity can be modified by the aforementioned sensory signals. However, the precise nature of the interaction between the CPGs and these sensory signals has remained generally largely unknown. Experimental methods aiming at finding out details of these interactions often apply cholinergic agonists such as pilocarpine in order to induce rhythmic activity in the CPGs. Using this general approach, we removed the influence of sensory signals and investigated the putative connections between CPGs controlling the upward/downward movement in the different legs of the stick insect. The experimental data, i.e. the measured MN activities, underwent connectivity analysis using Dynamic Causal Modelling (DCM). This method can uncover the underlying coupling structure and strength between pairs of segmental CPGs. For the analysis we set up different coupling schemes (models) for DCM and compared them using Bayesian Model Selection (BMS). Models with contralateral connections in each segment and ipsilateral connections on both sides, as well as the coupling from the meta-to the ipsilateral prothoracic ganglion were preferred by BMS to all other types of models tested. Moreover, the intrasegmental coupling strength in the mesothoracic ganglion was the strongest and most stable in all three ganglia