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Multiscale modeling via split-step methods in neural firing
(English)In: Mathematical and Computer Modelling of Dynamical Systems, ISSN 1387-3954, E-ISSN 1744-5051Article in journal (Refereed) Accepted
Abstract [en]

Neuronal models based on the Hodgkin-Huxley equation form a  fundamental framework in the field of computational  neuroscience. While the neuronal state is often modeled  deterministically, experimental recordings show stochastic  fluctuations, presumably driven by molecular noise from the  underlying microphysical conditions. In turn, the firing of  individual neurons gives rise to an electric field in extracellular  space, also thought to affect the firing pattern of nearby neurons.  We develop a multiscale model which combines a stochastic ion  channel gating process taking place on the neuronal membrane,  together with the propagation of an action potential along the  neuronal structure. We also devise a numerical method relying on a  split-step strategy which effectively couples these two processes  and we experimentally test the feasibility of this approach. We  finally also explain how the approach can be extended with Maxwell's  equations to allow the potential to be propagated in extracellular  space.

National Category
Biophysics Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-332008OAI: oai:DiVA.org:uu-332008DiVA, id: diva2:1151107
Available from: 2017-10-22 Created: 2017-10-22 Last updated: 2017-10-22
In thesis
1. Parallelism in Event-Based Computations with Applications in Biology
Open this publication in new window or tab >>Parallelism in Event-Based Computations with Applications in Biology
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Event-based models find frequent usage in fields such as computational physics and biology as they may contain both continuous and discrete state variables and may incorporate both deterministic and stochastic state transitions. If the state transitions are stochastic, computer-generated random numbers are used to obtain the model solution. This type of event-based computations is also known as Monte-Carlo simulation.

In this thesis, I study different approaches to execute event-based computations on parallel computers. This ultimately allows users to retrieve their simulation results in a fraction of the original computation time. As system sizes grow continuously or models have to be simulated at longer time scales, this is a necessary approach for current computational tasks.

More specifically, I propose several ways to asynchronously simulate such models on parallel shared-memory computers, for example using parallel discrete-event simulation or task-based computing. The particular event-based models studied herein find applications in systems biology, computational epidemiology and computational neuroscience.

In the presented studies, the proposed methods allow for high efficiency of the parallel simulation, typically scaling well with the number of used computer cores. As the scaling typically depends on individual model properties, the studies also investigate which quantities have the greatest impact on the simulation performance.

Finally, the presented studies include other insights into event-based computations, such as methods how to estimate parameter sensitivity in stochastic models and how to simulate models that include both deterministic and stochastic state transitions.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. p. 48
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1586
Keywords
Event-based computations, Parallel algorithms, Discrete-event simulation, Monte-Carlo methods, Systems biology.
National Category
Other Computer and Information Science Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-332009 (URN)978-91-513-0125-9 (ISBN)
Public defence
2017-12-11, 2347, ITC, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Projects
UPMARC
Available from: 2017-11-30 Created: 2017-10-22 Last updated: 2018-03-07

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