Hosting group: The research of the nonlinear time series analysis group is positioned at the interface between physics, applied mathematics, neuroscience, and engineering. One of our main targets is the development of innovative nonlinear time series analysis techniques. These techniques aim to characterize dynamical systems for which nonlinearities cause a complicated temporal evolution. A further main target of our work is the application of nonlinear time series techniques to electrophysiological recordings from the brain as well as to further types of experimental biomedical signals.
Research question / open problem: In patients with a certain type of epilepsy an optimal diagnostics requires to carry out electroencephalographic recordings directly from inside the patients’ skull (intracranial EEG). In the past few years, the intracranial EEG has been complemented by intracranial micro-EEG recordings, which allow one to monitor the neuronal activity with a much higher temporal and spatial resolution. The question we will study is: Are nonlinear signal analysis techniques, which have been shown to be very successful in the characterization of intracranial EEG, also suited to study intracranial micro-EEG recordings?
Scientific approach: Intracranial EEG recordings allow medical doctors to localize the areas in the patients’ brain in which epileptic seizures start (epileptic focus). Provided that a number of medical criteria are fulfilled, these brain areas can then be removed by neurosurgery rendering the patient completely seizure-free. For medical doctors the most important information remains to observe several acute seizure onsets. Recent work has shown that the application of signal analysis techniques to conventional intracranial EEG recordings allows one to localize the epileptic focus also from recordings from time periods where no seizure took place. We will apply these techniques to intracranial micro-EEG recordings to test whether this allows for an even more accurate localization of the epileptic focus.
Methodological approach: In a first phase the student will familiarize himself/herself with the signal analysis techniques studying signals from mathematical model systems. In the second step, the student will learn about conventional intracranial EEG recordings and intracranial micro-EEG recordings. In particular, this will be done in cooperation with medical hospitals and the student will have the opportunity to carry out internships in these hospitals to fully understand the context of these recordings. The final phase will consist of the application of the signal analysis techniques to the EEG recordings. All analysis will be carried out using the Matlab programming language. Large scale computations can be done on a High Performance Computing Cluster.
Requirements: As a starting point, the student should have a good knowledge in basics of dynamical systems theory as well as in linear signal techniques such as spectral and correlation analysis. Knowledge on nonlinear signals techniques is a plus. However, the essentials of this nonlinear analysis framework will also be taught in one of the elective courses. The student should certainly know how to program in Matlab or some other higher programming language. On the other hand, the student will be instructed how to use the High Performance Computing Cluster for distributed computing. Basic knowledge in electrophysiology and epileptology is a plus but not a prerequisite.
Previous work of our group in this context includes the references below. You can find pdf-files linked from here.
- Andrzejak RG, Olivier D, Gnatkovsky V, Wendling F, Bartlomei F, Francione S, Kahane P, Schindler K, de Curtis M. 2015. Localization of epileptogenic zone on pre-surgical intracranial EEG recordings: toward a validation of quantitative signal analysis approaches. Brain Topography. 28(6)
- Rummel C, Abela E, Andrzejak RG, Hauf M, Pollo C, Müller M, Weisstanner C, Wiest R, Schindler K. 2015. Resected Brain Tissue, Seizure Onset Zone and Quantitative EEG Measures: Towards Prediction of Post-Surgical Seizure Control. PLOS ONE. 10(10): e0141023.
- Andrzejak RG, Schindler K, Rummel C. 2012. Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients. PHYSICAL REVIEW E. 86:046206.
- Andrzejak RG, Chicharro D, Lehnertz K, Mormann F. 2011. Using bivariate signal analysis to characterize the epileptic focus: The benefit of surrogates. PHYSICAL REVIEW E. 83:046203.
- Andrzejak RG, Mormann F, Widman G, Kreuz T, Elger CE, Lehnertz K. 2006. Improved spatial characterization of the epileptic brain by focusing on nonlinearity. EPILEPSY RESEARCH. 69:30-44
- Leguia MG, Martínez CGB, Malvestio I, Campo AT, Rocamora R, Levnajic Z, Andrzejak RG (2019) Inferring directed networks using a rank-based connectivity measure. Physical Review E. 99, 012319
- Andrzejak RG, Rummel C, Mormann F, Schindler K (2016) All together now: Analogies between chimera state collapses and epileptic seizures. Scientific Reports. 6. 23000