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A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer.

Cattani A, Solinas S, Canuto C - Front Comput Neurosci (2016)

Bottom Line: Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables.By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics.Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia Rovereto, Italy.

ABSTRACT
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

No MeSH data available.


Connection topology between GrCs and GoCs from a postsynaptic neuron perspective: GrCs linked to the i-th GoC (left) and GoCs which are connected to the GrC at the point ξ (right). The domain decomposition of the GoC layer is obtained by exploiting the triangular mesh generator leading to a sparse mesh. Instead, a regular grid discretizes the GrC layer (not shown). The long and short edges of the rectangular map are 1500 and 500 μm, respectively.
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Figure 2: Connection topology between GrCs and GoCs from a postsynaptic neuron perspective: GrCs linked to the i-th GoC (left) and GoCs which are connected to the GrC at the point ξ (right). The domain decomposition of the GoC layer is obtained by exploiting the triangular mesh generator leading to a sparse mesh. Instead, a regular grid discretizes the GrC layer (not shown). The long and short edges of the rectangular map are 1500 and 500 μm, respectively.

Mentions: Only a few cellular populations in the cerebellar cortex compose this geometrically regular network and are localized in three well distinct layers called molecular, Purkinje, and granular. The latter is densely populated by GrCs (density 4, 000, 000∕mm3) and sparsely by GoCs. The key point supporting the application of our new modeling method is that the number of GoCs significantly differs from that of GrCs: GoCs are very few compared to GrCs (Korbo et al., 1993; Solinas et al., 2010b; Billings et al., 2014) in the ratio of about 1 : 400. Thus, by virtue of this considerable density difference, there is clear motivation to study combined discrete and continuum models of the cerebellar granular layers. In particular, the variables (vi, ri, si) describe each GoC through (5), while (ω, ρ, σ) portray the GrC species as a whole by means of (8). Inspired by assumptions in Simões de Souza and De Schutter (2011) and for modeling purposes, we consider the two populations belonging to two-dimensional parallel layers, as described in Figure 2. The bottom one consists of the GrC continuum and the upper one contains GoCs. A third layer, above them, consists of PFs.


A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer.

Cattani A, Solinas S, Canuto C - Front Comput Neurosci (2016)

Connection topology between GrCs and GoCs from a postsynaptic neuron perspective: GrCs linked to the i-th GoC (left) and GoCs which are connected to the GrC at the point ξ (right). The domain decomposition of the GoC layer is obtained by exploiting the triangular mesh generator leading to a sparse mesh. Instead, a regular grid discretizes the GrC layer (not shown). The long and short edges of the rectangular map are 1500 and 500 μm, respectively.
© Copyright Policy
Related In: Results  -  Collection

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Figure 2: Connection topology between GrCs and GoCs from a postsynaptic neuron perspective: GrCs linked to the i-th GoC (left) and GoCs which are connected to the GrC at the point ξ (right). The domain decomposition of the GoC layer is obtained by exploiting the triangular mesh generator leading to a sparse mesh. Instead, a regular grid discretizes the GrC layer (not shown). The long and short edges of the rectangular map are 1500 and 500 μm, respectively.
Mentions: Only a few cellular populations in the cerebellar cortex compose this geometrically regular network and are localized in three well distinct layers called molecular, Purkinje, and granular. The latter is densely populated by GrCs (density 4, 000, 000∕mm3) and sparsely by GoCs. The key point supporting the application of our new modeling method is that the number of GoCs significantly differs from that of GrCs: GoCs are very few compared to GrCs (Korbo et al., 1993; Solinas et al., 2010b; Billings et al., 2014) in the ratio of about 1 : 400. Thus, by virtue of this considerable density difference, there is clear motivation to study combined discrete and continuum models of the cerebellar granular layers. In particular, the variables (vi, ri, si) describe each GoC through (5), while (ω, ρ, σ) portray the GrC species as a whole by means of (8). Inspired by assumptions in Simões de Souza and De Schutter (2011) and for modeling purposes, we consider the two populations belonging to two-dimensional parallel layers, as described in Figure 2. The bottom one consists of the GrC continuum and the upper one contains GoCs. A third layer, above them, consists of PFs.

Bottom Line: Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables.By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics.Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia Rovereto, Italy.

ABSTRACT
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

No MeSH data available.