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With approximately 100 billion neurons and 1014 synaptic connections, the human brain is among the most complex structures in nature. Complex systems are often characterized by an intrinsic nonlinearity leading to seemingly random behavior. This means that the input to the system does not relate to its output in a simple linear or proportional way. This nonlinearity can be observed on every scale of observation beginning from the generation of single cell action potentials according to the all-or-nothing principle up to the organization of functional related brain areas to hubs. Despite the brain’s high complexity, humans are normally able to respond to internal and external cues in a reproducible and adequate manner. In the pathological state however, many neurological diseases, like the idiopathic Parkinson’s disease lead to an inability to adequately respond to internal cues, which might lead to a wide array of symptoms like e. g. slowing of movements.
Given their broad distribution, most commonly linear methods are chosen in order to study pathological neurophysiological changes. Among classic linear methods are simple (auto)correlations, Fourier-based frequency analyses or model-based causality analyses. However, these linear methods only capture a small proportion of the brain’s temporal dynamics as they are insensitive to nonlinear behavior. Despite their great potential, nonlinear methods are just slowly adopted in the neuroscientific community. Possible reasons for this are their high computational demands, a low availability of easy to use analysis tools and few studies on caveats, stability of results and interactions with typical neurobiological preprocessing routines.
The present dissertation is based on three studies, which overall aim was to establish a broad array of nonlinear methods in neuroscientific research.
With the first study, I developed NoLiTiA, a free, easy to use Matlab-toolbox with a wide array of nonlinear methods and routines to analyze neuroscientific datasets. The approximately 50 nonlinear methods and routines originate mostly from three distinct topics: nonlinear dynamics, information theory and recurrence analysis. Beside classical approaches from chaos theory like correlation dimension for complexity analysis or estimation of Lyapunov exponents for stability analysis, I also implemented very recent methods like active information storage from information theory and even developed new methods like the time resolved recurrence period spectrum with neurobiological research questions in mind. A big challenge in establishing new complex methods is making them easy and intuitive to use for programming unexperienced researchers. In order to be accessible for programming experienced and unexperienced researchers, the toolbox offers three analysis pathways: an intuitive graphical user interface, a batch-editor for large datasets and the option to develop individualized custom-made scripts. An additional interface offers the possibility to plot analysis results and even supports topographical representations of electroencephalographic data. All basic functions are validated using simulated data with known ground truths and exemplified using electromyographic data of a single Parkinson’s disease patient. The toolbox and all its functions were completely designed and implemented by me. The example dataset of one Parkinson’s disease patient was kindly provided by Prof. Dr. Esther Florin.
As recent studies could demonstrate, typical electrophysiological preprocessing routines can have tremendous effects on the estimation of certain linear, model-based, directional coupling methods based on Wiener-Granger causality. Transfer entropy is a model-free generalization of classic Wiener-Granger causality derived from information theory. Due to its nonparametric character, it can make inferences on linear as well as on nonlinear systems and is thus especially suited to study directional information flow between brain regions. The aim of the second study was to analyze the influence of different electrophysiological preprocessing routines, including different digital filter and downsampling option, on the estimation of Transfer entropy. We tested the different preprocessing options in a simulation framework using one established linear and two self-designed nonlinear coupling models. For successively lower low-pass filter frequencies we observed up to 72 % false negative direct connections and up to 26 % false positive connections when analyzing the nonlinear models. When conducting the same analysis using the linear model, only up to 86 % false negative indirect connections could be detected. Using a high-pass filter had no influence on the estimation of transfer entropy. Downsampling should be avoided if the sampling factor is greater than the assumed interaction delay of the information transmission. In our simulations we observed 67 % up to 100 % false negative direct connections. In conclusion, preprocessing should be avoided when estimating Transfer entropy or should at least be performed with great care as it may lead to a high number of spurious or missed connections. The study was designed in cooperation with Prof. Dr. Esther Florin, Prof. Dr. Lars Timmermann and Dr. Michael von Papen. All analyses and implementations of established and new models were done by me.
Incorporating the results from study 1 and 2, the aim of the third study was to characterize information processing in the basal ganglia of Parkinson’s disease patients. The idiopathic Parkinson’s disease is among the most common neurodegenerative diseases. Besides medical treatment, deep brain stimulation is an efficient and well-established treatment option. Despite its wide-spread application not much is known regarding its mechanism of action. A recent theory suggests that the electrical stimulation overrides pathological brain activity with a more physiological signal. A direct implication of this informational lesion hypothesis is a possible correlation of pathological neural information content of the basal ganglia with clinical symptoms, which has already been validated for the globus pallidus internus in animal studies. Thus, for the third study the aim was to correlate information content of intraoperatively recorded electrophysiological activity from the subthalamic area of Parkinson’s disease patients, during a rest and a hold condition, with their clinical symptoms. In accordance with animal studies I could demonstrate a significant positive correlation between information content and clinical symptoms at rest, both in the zona incerta as well as in the subthalamic nucleus. In a second analysis I studied the information storage capabilities of the subthalamic area, using active information storage implemented in NoLiTiA. I could demonstrate a significant larger processing memory in the zona incerta than in the subthalamic nucleus, which might explain the need of clinical effective stimulation being high frequency. Finally, I analysed the information transfer between the subthalamic area and three forearm muscles during the rest and hold condition. I detected more bidirectional couplings between the subthalamic nucleus and muscles than between the zona incerta and muscles. However, in contrast to the subthalamic nucleus, I observed a movement dependent increase of couplings from the zona incerta to muscles. These results are subsequently discussed with respect to recent studies claiming that the zona incerta might be a better target for deep brain stimulation than the subthalamic nucleus. The study was designed in cooperation with Prof. Dr. Esther Florin, Prof. Dr. Lars Timmermann and Dr. Michael von Papen. All analyses and implementations of established and new methods were done by me. Intraoperative data was recorded by Prof. Dr. Esther Florin at the university hospitals Düsseldorf and Cologne.
In conclusion, I developed an intuitive, open-source toolbox for nonlinear time series analysis with the aim of increasing the visibility, availability and accessibility of nonlinear methods in the neuroscientific community. With the second study I demonstrated the effects of using classic electrophysiological preprocessing routines on nonlinear coupling techniques, thus providing guidance on how to use these techniques. Finally, with the third study exemplified usage of nonlinear methods by validating a recent relevant hypothesis on the relation of pathological information processing in the basal ganglia and clinical symptoms of Parkinson’s disease patients.