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Article ; Online: Modelling the effect of ephaptic coupling on spike propagation in peripheral nerve fibres.

Schmidt, Helmut / R Knösche, Thomas

2022 Volume 116, Issue 4, Page(s) 461–473

Abstract: Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of ... ...

Abstract	Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of identical axons, whereas realistic peripheral nerve bundles contain numerous axons with different diameters. Here, we present a computationally efficient spike propagation model, which captures the essential features of propagating spikes and their ephaptic interaction, and facilitates the theoretical investigation of spike volleys in large, heterogeneous fibre bundles. We first lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model based on Hodgkin-Huxley dynamics. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that a higher level of heterogeneity requires stronger ephaptic coupling to achieve full synchronisation between spikes.
MeSH term(s)	Action Potentials/physiology ; Axons/physiology ; Membrane Potentials ; Nerve Fibers ; Peripheral Nerves
Language	English
Publishing date	2022-05-10
Publishing country	Germany
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	220699-7
ISSN	1432-0770 ; 0340-1200
ISSN (online)	1432-0770
ISSN	0340-1200
DOI	10.1007/s00422-022-00934-9
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Article ; Online: PyRates-A code-generation tool for modeling dynamical systems in biology and beyond.

Gast, Richard / Knösche, Thomas R / Kennedy, Ann

PLoS computational biology

2023 Volume 19, Issue 12, Page(s) e1011761

Abstract: The mathematical study of real-world dynamical systems relies on models composed of differential equations. Numerical methods for solving and analyzing differential equation systems are essential when complex biological problems have to be studied, such ... ...

Abstract	The mathematical study of real-world dynamical systems relies on models composed of differential equations. Numerical methods for solving and analyzing differential equation systems are essential when complex biological problems have to be studied, such as the spreading of a virus, the evolution of competing species in an ecosystem, or the dynamics of neurons in the brain. Here we present PyRates, a Python-based software for modeling and analyzing differential equation systems via numerical methods. PyRates is specifically designed to account for the inherent complexity of biological systems. It provides a new language for defining models that mirrors the modular organization of real-world dynamical systems and thus simplifies the implementation of complex networks of interacting dynamic entities. Furthermore, PyRates provides extensive support for the various forms of interaction delays that can be observed in biological systems. The core of PyRates is a versatile code-generation system that translates user-defined models into "backend" implementations in various languages, including Python, Fortran, Matlab, and Julia. This allows users to apply a wide range of analysis methods for dynamical systems, eliminating the need for manual translation between code bases. PyRates may also be used as a model definition interface for the creation of custom dynamical systems tools. To demonstrate this, we developed two extensions of PyRates for common analyses of dynamic models of biological systems: PyCoBi for bifurcation analysis and RectiPy for parameter fitting. We demonstrate in a series of example models how PyRates can be used in combination with PyCoBi and RectiPy for model analysis and fitting. Together, these tools offer a versatile framework for applying computational modeling and numerical analysis methods to dynamical systems in biology and beyond.
MeSH term(s)	Ecosystem ; Systems Biology/methods ; Software ; Computer Simulation ; Brain ; Models, Biological
Language	English
Publishing date	2023-12-27
Publishing country	United States
Document type	Journal Article
ZDB-ID	2193340-6
ISSN	1553-7358 ; 1553-734X
ISSN (online)	1553-7358
ISSN	1553-734X
DOI	10.1371/journal.pcbi.1011761
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Article ; Online: PyRates-A code-generation tool for modeling dynamical systems in biology and beyond.

Richard Gast / Thomas R Knösche / Ann Kennedy

PLoS Computational Biology, Vol 19, Iss 12, p e

2023 Volume 1011761

Abstract	The mathematical study of real-world dynamical systems relies on models composed of differential equations. Numerical methods for solving and analyzing differential equation systems are essential when complex biological problems have to be studied, such as the spreading of a virus, the evolution of competing species in an ecosystem, or the dynamics of neurons in the brain. Here we present PyRates, a Python-based software for modeling and analyzing differential equation systems via numerical methods. PyRates is specifically designed to account for the inherent complexity of biological systems. It provides a new language for defining models that mirrors the modular organization of real-world dynamical systems and thus simplifies the implementation of complex networks of interacting dynamic entities. Furthermore, PyRates provides extensive support for the various forms of interaction delays that can be observed in biological systems. The core of PyRates is a versatile code-generation system that translates user-defined models into "backend" implementations in various languages, including Python, Fortran, Matlab, and Julia. This allows users to apply a wide range of analysis methods for dynamical systems, eliminating the need for manual translation between code bases. PyRates may also be used as a model definition interface for the creation of custom dynamical systems tools. To demonstrate this, we developed two extensions of PyRates for common analyses of dynamic models of biological systems: PyCoBi for bifurcation analysis and RectiPy for parameter fitting. We demonstrate in a series of example models how PyRates can be used in combination with PyCoBi and RectiPy for model analysis and fitting. Together, these tools offer a versatile framework for applying computational modeling and numerical analysis methods to dynamical systems in biology and beyond.
Keywords	Biology (General) ; QH301-705.5
Subject code	005
Language	English
Publishing date	2023-12-01T00:00:00Z
Publisher	Public Library of Science (PLoS)
Document type	Article ; Online
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Book ; Online: PyRates -- A Code-Generation Tool for Dynamical Systems Modeling

Gast, Richard / Knösche, Thomas R. / Kennedy, Ann

2023

Abstract: Mathematical models allow us to gain a deeper understanding of real-world dynamical systems. One of the most powerful mathematical frameworks for modeling real-world phenomena are systems of differential equations. In the majority of fields that use ... ...

Abstract	Mathematical models allow us to gain a deeper understanding of real-world dynamical systems. One of the most powerful mathematical frameworks for modeling real-world phenomena are systems of differential equations. In the majority of fields that use differential equations, numerical methods are essential for conducting model-based research. Although many software solutions are available for the numerical study of differential equation systems, a common framework for implementing differential equation systems is lacking. This hinders progress in dynamical systems research and limits the shareability and reproducibility of results. PyRates is a Python-based software for modeling and analyzing dynamical systems. It provides a user-friendly interface for defining models, which is based on a graph-based, hierarchical structure that mirrors the modular organization of real-world dynamical systems. This design allows users to leverage the hierarchical structure of their systems and create their models with minimal effort. Importantly, the core of PyRates is a versatile code-generation system, which can translate user-defined models into "backend" implementations in various languages, including Python, Fortran, and Julia. This allows users to access a wide range of analysis methods for dynamical systems, eliminating the need for manual translation between code bases. We demonstrate PyRates's capabilities in three use cases, where it generates NumPy code for numerical simulations, Fortran code for bifurcation analysis, and PyTorch code for neural network optimization. Finally, PyRates can be used as a model definition interface for the creation of new dynamical systems tools. We developed two such software packages, PyCoBi and RectiPy, as extensions of PyRates for specific dynamical systems modeling applications. Comment: 20 pages, 4 figures, 1 table
Keywords	Condensed Matter - Disordered Systems and Neural Networks ; Physics - Computational Physics ; Quantitative Biology - Neurons and Cognition
Subject code	000
Publishing date	2023-02-07
Publishing country	us
Document type	Book ; Online
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Article ; Online: Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity.

Gast, Richard / Knösche, Thomas R / Schmidt, Helmut

Physical review. E

2021 Volume 104, Issue 4-1, Page(s) 44310

Abstract: Low-dimensional descriptions of spiking neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled oscillators ... ...

Abstract	Low-dimensional descriptions of spiking neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled oscillators have sparked the development of a new generation of neural mass models. Of notable interest are mean-field descriptions of all-to-all coupled quadratic integrate-and-fire (QIF) neurons, which have already seen numerous extensions and applications. These extensions include different forms of short-term adaptation considered to play an important role in generating and sustaining dynamic regimes of interest in the brain. It is an open question, however, whether the incorporation of presynaptic forms of synaptic plasticity driven by single neuron activity would still permit the derivation of mean-field equations using the same method. Here we discuss this problem using an established model of short-term synaptic plasticity at the single neuron level, for which we present two different approaches for the derivation of the mean-field equations. We compare these models with a recently proposed mean-field approximation that assumes stochastic spike timings. In general, the latter fails to accurately reproduce the macroscopic activity in networks of deterministic QIF neurons with distributed parameters. We show that the mean-field models we propose provide a more accurate description of the network dynamics, although they are mathematically more involved. Using bifurcation analysis, we find that QIF networks with presynaptic short-term plasticity can express regimes of periodic bursting activity as well as bistable regimes. Together, we provide novel insight into the macroscopic effects of short-term synaptic plasticity in spiking neural networks, as well as two different mean-field descriptions for future investigations of such networks.
MeSH term(s)	Action Potentials ; Computer Simulation ; Models, Neurological ; Neural Networks, Computer ; Neuronal Plasticity ; Neurons
Language	English
Publishing date	2021-11-30
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.104.044310
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Article: Spatiotemporal phase slip patterns for visual evoked potentials, covert object naming tasks, and insight moments extracted from 256 channel EEG recordings.

Ramon, Ceon / Graichen, Uwe / Gargiulo, Paolo / Zanow, Frank / Knösche, Thomas R / Haueisen, Jens

Frontiers in integrative neuroscience

2023 Volume 17, Page(s) 1087976

Abstract: Phase slips arise from state transitions of the coordinated activity of cortical neurons which can be extracted from the EEG data. The phase slip rates (PSRs) were studied from the high-density (256 channel) EEG data, sampled at 16.384 kHz, of five adult ...

Abstract	Phase slips arise from state transitions of the coordinated activity of cortical neurons which can be extracted from the EEG data. The phase slip rates (PSRs) were studied from the high-density (256 channel) EEG data, sampled at 16.384 kHz, of five adult subjects during covert visual object naming tasks. Artifact-free data from 29 trials were averaged for each subject. The analysis was performed to look for phase slips in the theta (4-7 Hz), alpha (7-12 Hz), beta (12-30 Hz), and low gamma (30-49 Hz) bands. The phase was calculated with the Hilbert transform, then unwrapped and detrended to look for phase slip rates in a 1.0 ms wide stepping window with a step size of 0.06 ms. The spatiotemporal plots of the PSRs were made by using a montage layout of 256 equidistant electrode positions. The spatiotemporal profiles of EEG and PSRs during the stimulus and the first second of the post-stimulus period were examined in detail to study the visual evoked potentials and different stages of visual object recognition in the visual, language, and memory areas. It was found that the activity areas of PSRs were different as compared with EEG activity areas during the stimulus and post-stimulus periods. Different stages of the insight moments during the covert object naming tasks were examined from PSRs and it was found to be about 512 ± 21 ms for the 'Eureka' moment. Overall, these results indicate that information about the cortical phase transitions can be derived from the measured EEG data and can be used in a complementary fashion to study the cognitive behavior of the brain.
Language	English
Publishing date	2023-06-13
Publishing country	Switzerland
Document type	Journal Article
ZDB-ID	2452962-X
ISSN	1662-5145
ISSN	1662-5145
DOI	10.3389/fnint.2023.1087976
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Article ; Online: Laminar neural dynamics of auditory evoked responses: Computational modeling of local field potentials in auditory cortex of non-human primates.

Chien, Vincent S C / Wang, Peng / Maess, Burkhard / Fishman, Yonatan / Knösche, Thomas R

NeuroImage

2023 Volume 281, Page(s) 120364

Abstract: Evoked neural responses to sensory stimuli have been extensively investigated in humans and animal models both to enhance our understanding of brain function and to aid in clinical diagnosis of neurological and neuropsychiatric conditions. Recording and ... ...

Abstract	Evoked neural responses to sensory stimuli have been extensively investigated in humans and animal models both to enhance our understanding of brain function and to aid in clinical diagnosis of neurological and neuropsychiatric conditions. Recording and imaging techniques such as electroencephalography (EEG), magnetoencephalography (MEG), local field potentials (LFPs), and calcium imaging provide complementary information about different aspects of brain activity at different spatial and temporal scales. Modeling and simulations provide a way to integrate these different types of information to clarify underlying neural mechanisms. In this study, we aimed to shed light on the neural dynamics underlying auditory evoked responses by fitting a rate-based model to LFPs recorded via multi-contact electrodes which simultaneously sampled neural activity across cortical laminae. Recordings included neural population responses to best-frequency (BF) and non-BF tones at four representative sites in primary auditory cortex (A1) of awake monkeys. The model considered major neural populations of excitatory, parvalbumin-expressing (PV), and somatostatin-expressing (SOM) neurons across layers 2/3, 4, and 5/6. Unknown parameters, including the connection strength between the populations, were fitted to the data. Our results revealed similar population dynamics, fitted model parameters, predicted equivalent current dipoles (ECD), tuning curves, and lateral inhibition profiles across recording sites and animals, in spite of quite different extracellular current distributions. We found that PV firing rates were higher in BF than in non-BF responses, mainly due to different strengths of tonotopic thalamic input, whereas SOM firing rates were higher in non-BF than in BF responses due to lateral inhibition. In conclusion, we demonstrate the feasibility of the model-fitting approach in identifying the contributions of cell-type specific population activity to stimulus-evoked LFPs across cortical laminae, providing a foundation for further investigations into the dynamics of neural circuits underlying cortical sensory processing.
MeSH term(s)	Animals ; Humans ; Auditory Cortex/physiology ; Evoked Potentials, Auditory/physiology ; Electroencephalography/methods ; Haplorhini ; Computer Simulation ; Acoustic Stimulation/methods
Language	English
Publishing date	2023-09-07
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	1147767-2
ISSN	1095-9572 ; 1053-8119
ISSN (online)	1095-9572
ISSN	1053-8119
DOI	10.1016/j.neuroimage.2023.120364
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Zs.A 3664: Show issues			Location: Je nach Verfügbarkeit (siehe Angabe bei Bestand) bis Jg. 1994: Bestellungen von Artikeln über das Online-Bestellformular Jg. 1995 - 2021: Lesesall (2.OG) ab Jg. 2022: Lesesaal (EG)
Zs.MO 7: Show issues

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Article ; Online: Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion.

Weise, Konstantin / Müller, Erik / Poßner, Lucas / Knösche, Thomas R

Mathematical biosciences and engineering : MBE

2022 Volume 19, Issue 8, Page(s) 7425–7480

Abstract: As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and ... ...

Abstract	As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of <0.1%, <1%, and <10%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions.
MeSH term(s)	Algorithms ; Reproducibility of Results ; Uncertainty
Language	English
Publishing date	2022-07-14
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2265126-3
ISSN	1551-0018 ; 1551-0018
ISSN (online)	1551-0018
ISSN	1551-0018
DOI	10.3934/mbe.2022351
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Article ; Online: Action potential propagation and synchronisation in myelinated axons.

Schmidt, Helmut / Knösche, Thomas R

PLoS computational biology

2019 Volume 15, Issue 10, Page(s) e1007004

Abstract: With the advent of advanced MRI techniques it has become possible to study axonal white matter non-invasively and in great detail. Measuring the various parameters of the long-range connections of the brain opens up the possibility to build and refine ... ...

Abstract	With the advent of advanced MRI techniques it has become possible to study axonal white matter non-invasively and in great detail. Measuring the various parameters of the long-range connections of the brain opens up the possibility to build and refine detailed models of large-scale neuronal activity. One particular challenge is to find a mathematical description of action potential propagation that is sufficiently simple, yet still biologically plausible to model signal transmission across entire axonal fibre bundles. We develop a mathematical framework in which we replace the Hodgkin-Huxley dynamics by a spike-diffuse-spike model with passive sub-threshold dynamics and explicit, threshold-activated ion channel currents. This allows us to study in detail the influence of the various model parameters on the action potential velocity and on the entrainment of action potentials between ephaptically coupled fibres without having to recur to numerical simulations. Specifically, we recover known results regarding the influence of axon diameter, node of Ranvier length and internode length on the velocity of action potentials. Additionally, we find that the velocity depends more strongly on the thickness of the myelin sheath than was suggested by previous theoretical studies. We further explain the slowing down and synchronisation of action potentials in ephaptically coupled fibres by their dynamic interaction. In summary, this study presents a solution to incorporate detailed axonal parameters into a whole-brain modelling framework.
MeSH term(s)	Action Potentials/physiology ; Algorithms ; Animals ; Axons/physiology ; Brain Diseases, Metabolic ; Brain Mapping/methods ; Computer Simulation ; Cortical Synchronization/physiology ; Humans ; Models, Neurological ; Myelin Sheath/physiology ; Nerve Fibers, Myelinated/physiology ; Neural Conduction/physiology ; White Matter
Language	English
Publishing date	2019-10-17
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2193340-6
ISSN	1553-7358 ; 1553-734X
ISSN (online)	1553-7358
ISSN	1553-734X
DOI	10.1371/journal.pcbi.1007004
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Article ; Online: A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation.

Gast, Richard / Schmidt, Helmut / Knösche, Thomas R

Neural computation

2020 Volume 32, Issue 9, Page(s) 1615–1634

Abstract: Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between ... ...

Abstract	Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.
MeSH term(s)	Action Potentials/physiology ; Computer Simulation ; Humans ; Nerve Net/physiology ; Neural Networks, Computer ; Neurons/physiology ; Synaptic Transmission/physiology
Language	English
Publishing date	2020-07-20
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	1025692-1
ISSN	1530-888X ; 0899-7667
ISSN (online)	1530-888X
ISSN	0899-7667
DOI	10.1162/neco_a_01300
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