Axel Hutt - Academia.edu (original) (raw)

Papers by Axel Hutt

Physik studiert - und dann?

Frontiers in Applied Mathematics and Statistics

Neuroinformatics

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally ... more Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ − (0 − 4 Hz) and α − (8 − 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

Frontiers in neuroscience, 2018

In the past decade, there has been a surge of interest in using patterned brain stimulation to ma... more In the past decade, there has been a surge of interest in using patterned brain stimulation to manipulate cortical oscillations, in both experimental and clinical settings. But the relationship between stimulation waveform and its impact on ongoing oscillations remains poorly understood and severely restrains the development of new paradigms. To address some aspects of this intricate problem, we combine computational and mathematical approaches, providing new insights into the influence of waveform of both low and high-frequency stimuli on synchronous neural activity. Using a cellular-based cortical microcircuit network model, we performed numerical simulations to test the influence of different waveforms on ongoing alpha oscillations, and derived a mean-field description of stimulation-driven dynamics to better understand the observed responses. Our analysis shows that high-frequency periodic stimulation translates into an effective transformation of the neurons' response funct...

Journal of mathematical neuroscience, Jan 5, 2018

Understanding the neural field activity for realistic living systems is a challenging task in con... more Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues.In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for t...

PLOS Computational Biology

ABSTRACTBrain stimulation can be used to engage and modulate rhythmic activity in cortical networ... more ABSTRACTBrain stimulation can be used to engage and modulate rhythmic activity in cortical networks. However, the outcomes have been shown to be impacted by behavioral states and endogenous brain fluctuations. To better understand how this intrinsic oscillatory activity controls the brain’s susceptibility to stimulation, we analyzed a computational model of the thalamocortical system in both the rest and task states, to identify the mechanisms by which endogenous alpha oscillations (8Hz-12Hz) are impacted by periodic stimulation. Our analysis shows that the differences between different brain states can be explained by a passage through a bifurcation combined to stochastic resonance - a mechanism whereby irregular fluctuations amplify the response of a nonlinear system to weak signals. Indeed, our findings suggest that modulating brain oscillations is best achieved in states of low endogenous rhythmic activity, and that irregular state-dependent fluctuations in thalamic inputs shape...