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Efficient Integration of Coupled Electrical-Chemical Systems in Multiscale Neuronal Simulations
Stockholm University, Science for Life Laboratory (SciLifeLab). Stockholm University, Faculty of Science, Numerical Analysis and Computer Science (NADA). KTH Royal Institute of Technology, Sweden; Karolinska Institute, Sweden.
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Number of Authors: 52016 (English)In: Frontiers in Computational Neuroscience, ISSN 1662-5188, E-ISSN 1662-5188, Vol. 10, article id 97Article in journal (Refereed) Published
Abstract [en]

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience.

Place, publisher, year, edition, pages
2016. Vol. 10, article id 97
Keywords [en]
multiscale modeling, multiscale simulation, co-simulation, coupled system, adaptive time step integration, backward differentiation formula, parallel numerical integration, coupled integration
National Category
Mathematics Neurosciences
Identifiers
URN: urn:nbn:se:su:diva-174687DOI: 10.3389/fncom.2016.00097ISI: 000383015600001PubMedID: 27672364OAI: oai:DiVA.org:su-174687DiVA, id: diva2:1367558
Available from: 2019-11-04 Created: 2019-11-04 Last updated: 2019-11-04Bibliographically approved

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