## Mean-field methods for multiscale models in neuroscience

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**Mean-field methods for multiscale models in neuroscience.** / Seppälä, Ippa; Lehtimäki, Mikko; Paunonen, Lassi; Linne, Marja-Leena.

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*Mean-field methods for multiscale models in neuroscience*. Julkaisun esittämispaikka: 3RD Nordic Neuroscience Meeting 2019, Helsinki, Suomi.

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TY - CONF

T1 - Mean-field methods for multiscale models in neuroscience

AU - Seppälä, Ippa

AU - Lehtimäki, Mikko

AU - Paunonen, Lassi

AU - Linne, Marja-Leena

PY - 2019/6/12

Y1 - 2019/6/12

N2 - Multiscale modelling of the brain is necessary in order to understand howinteractions on the molecular and cellular levels can give rise to higher-levelbrain functions. As microscale processes tie into mesoscopic populations thatfacilitate whole-brain behaviour, being able to describe the full-scaleinterconnectivity of the brain is clearly imperative. In order to interpret allof the different mechanisms, we need comprehensive models with accurate system dynamics. However, incorporating multiple levels into mathematical models often results in large networks of interlinked neural cells that are analytically intractable. Additionally, their numerical simulation is resource intensive. Useful ways of mitigating the computational burden include using a mean-field approach, as well as mathematical model order reduction (MOR).Using mean-field approximation, random fluctuations of variables can beaccounted for by replacing them by their averages. Cells are grouped togetherinto populations based on their statistical similarities, in order to representthe dynamics of the system in terms of the mean ensemble behaviour. Thesepopulations can then be described by a probability density function expressingthe distribution of neuronal states at a given time. We use the Fokker-Planckformalism, which results in a nonlinear system of partial differentialequations (PDEs).With mathematical MOR methods the dimensions of a PDE model can be reduced with minimal information loss. The simulation time of the model is radicallyshortened, albeit not without dimension-dependent approximation error. Thetolerated amount of inaccuracy depends on the final application of the model.Due to being well-suited for depicting mesoscopic behaviour, the mean-fieldapproach in combination with the MOR methods allows us to describe thebehaviour of any large multiscale brain model with a relatively low computational burden. This can be particularly useful when attempting to model whole-brain connectivity, for which there is an immediate demand in clinical and robotic applications.

AB - Multiscale modelling of the brain is necessary in order to understand howinteractions on the molecular and cellular levels can give rise to higher-levelbrain functions. As microscale processes tie into mesoscopic populations thatfacilitate whole-brain behaviour, being able to describe the full-scaleinterconnectivity of the brain is clearly imperative. In order to interpret allof the different mechanisms, we need comprehensive models with accurate system dynamics. However, incorporating multiple levels into mathematical models often results in large networks of interlinked neural cells that are analytically intractable. Additionally, their numerical simulation is resource intensive. Useful ways of mitigating the computational burden include using a mean-field approach, as well as mathematical model order reduction (MOR).Using mean-field approximation, random fluctuations of variables can beaccounted for by replacing them by their averages. Cells are grouped togetherinto populations based on their statistical similarities, in order to representthe dynamics of the system in terms of the mean ensemble behaviour. Thesepopulations can then be described by a probability density function expressingthe distribution of neuronal states at a given time. We use the Fokker-Planckformalism, which results in a nonlinear system of partial differentialequations (PDEs).With mathematical MOR methods the dimensions of a PDE model can be reduced with minimal information loss. The simulation time of the model is radicallyshortened, albeit not without dimension-dependent approximation error. Thetolerated amount of inaccuracy depends on the final application of the model.Due to being well-suited for depicting mesoscopic behaviour, the mean-fieldapproach in combination with the MOR methods allows us to describe thebehaviour of any large multiscale brain model with a relatively low computational burden. This can be particularly useful when attempting to model whole-brain connectivity, for which there is an immediate demand in clinical and robotic applications.

M3 - Paper, poster or abstract

ER -