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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.


Related in: MedlinePlus

Response of the hybrid model to 5 ms pulse delivered by MFs to GrCs and GoCs. The GLN activation at time 4.2 ms from the initiation of the stimulus shows the maximal activation yielded by the excitatory input (E peak; upper left panel). After 4 ms the GLN activation fades off due to the emergence of the inhibitory feedback (E2 peak; upper right panel). The time of the E2 peak is chosen at 4.2 ms after the peak response to reproduce a data analysis following the methods used in Solinas et al. (2010b). Partial block of inhibitory synapses increases the E2 peak amplitude and spatial extension (E2ib; upper right panel). The amount of inhibition is calculated as the change in GLN activation amplitude due to the partial block of inhibition at 8.2 ms from the stimulus initiation (−I; lower left panel). The center-surround is represented as in Solinas et al. (2010b) as the difference from the E peak and the inhibition I (lower right panel). The stimulus is carried by all the MFs included in a circle located in the network center (250, 250)μm and with radius equal to 70μm. The intensity of stimulation is decreased from center to periphery of the circle following an exponential profile (intensity from 0.4 to 0 with space constant 0.6). The input intensity is randomized using an additive random noise with range [0, 0.05]. The so activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The CPU time required to run this simulation was 2 s on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz).
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Figure 5: Response of the hybrid model to 5 ms pulse delivered by MFs to GrCs and GoCs. The GLN activation at time 4.2 ms from the initiation of the stimulus shows the maximal activation yielded by the excitatory input (E peak; upper left panel). After 4 ms the GLN activation fades off due to the emergence of the inhibitory feedback (E2 peak; upper right panel). The time of the E2 peak is chosen at 4.2 ms after the peak response to reproduce a data analysis following the methods used in Solinas et al. (2010b). Partial block of inhibitory synapses increases the E2 peak amplitude and spatial extension (E2ib; upper right panel). The amount of inhibition is calculated as the change in GLN activation amplitude due to the partial block of inhibition at 8.2 ms from the stimulus initiation (−I; lower left panel). The center-surround is represented as in Solinas et al. (2010b) as the difference from the E peak and the inhibition I (lower right panel). The stimulus is carried by all the MFs included in a circle located in the network center (250, 250)μm and with radius equal to 70μm. The intensity of stimulation is decreased from center to periphery of the circle following an exponential profile (intensity from 0.4 to 0 with space constant 0.6). The input intensity is randomized using an additive random noise with range [0, 0.05]. The so activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The CPU time required to run this simulation was 2 s on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz).

Mentions: Figure 5 shows the GLN response to a stimulus set on at t = 0 ms and set off at t = 5 ms. The spot size increases over time also after the end of the stimulus. According to Solinas et al. (2010b), the center-surround organization of the inhibitory projections shapes the GLN response in space and in time. In order to highlight the effect of inhibition, Figure 5 compares the spot of Figure 4 with the spot achieved after partial block of the inhibitory GoC to GrC synapses and synaptic strength reduced from 0.1 to 0.03. More precisely, we reproduce in Figure 5 the same computational steps taken in Solinas et al. (2010b). After the onset of the MF input the GLN initiates its response with 1 ms of delay, reaching its maximal activation after 4 ms indicated as E peak in Figure 5. After 8 ms the GLN activation fades off due to the emergence of the inhibitory feedback and we chose this time to measure the E2 peak. After partial block of the inhibitory synapses, the E2 peak increases in amplitude and extension (inhibition partially blocked: E2ib). As in Solinas et al. (2010b), the amount of inhibition I is calculated as the change in GLN activity amplitude due to the partial block of inhibition. Like in Solinas et al. (2010b), the difference between the E peak and the inhibition I reveals, in the lower right panel of Figure 5, the center-surround organization of inhibition as the central peak surrounded by a deeper crown.


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

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

Response of the hybrid model to 5 ms pulse delivered by MFs to GrCs and GoCs. The GLN activation at time 4.2 ms from the initiation of the stimulus shows the maximal activation yielded by the excitatory input (E peak; upper left panel). After 4 ms the GLN activation fades off due to the emergence of the inhibitory feedback (E2 peak; upper right panel). The time of the E2 peak is chosen at 4.2 ms after the peak response to reproduce a data analysis following the methods used in Solinas et al. (2010b). Partial block of inhibitory synapses increases the E2 peak amplitude and spatial extension (E2ib; upper right panel). The amount of inhibition is calculated as the change in GLN activation amplitude due to the partial block of inhibition at 8.2 ms from the stimulus initiation (−I; lower left panel). The center-surround is represented as in Solinas et al. (2010b) as the difference from the E peak and the inhibition I (lower right panel). The stimulus is carried by all the MFs included in a circle located in the network center (250, 250)μm and with radius equal to 70μm. The intensity of stimulation is decreased from center to periphery of the circle following an exponential profile (intensity from 0.4 to 0 with space constant 0.6). The input intensity is randomized using an additive random noise with range [0, 0.05]. The so activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The CPU time required to run this simulation was 2 s on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz).
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Related In: Results  -  Collection

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Show All Figures
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Figure 5: Response of the hybrid model to 5 ms pulse delivered by MFs to GrCs and GoCs. The GLN activation at time 4.2 ms from the initiation of the stimulus shows the maximal activation yielded by the excitatory input (E peak; upper left panel). After 4 ms the GLN activation fades off due to the emergence of the inhibitory feedback (E2 peak; upper right panel). The time of the E2 peak is chosen at 4.2 ms after the peak response to reproduce a data analysis following the methods used in Solinas et al. (2010b). Partial block of inhibitory synapses increases the E2 peak amplitude and spatial extension (E2ib; upper right panel). The amount of inhibition is calculated as the change in GLN activation amplitude due to the partial block of inhibition at 8.2 ms from the stimulus initiation (−I; lower left panel). The center-surround is represented as in Solinas et al. (2010b) as the difference from the E peak and the inhibition I (lower right panel). The stimulus is carried by all the MFs included in a circle located in the network center (250, 250)μm and with radius equal to 70μm. The intensity of stimulation is decreased from center to periphery of the circle following an exponential profile (intensity from 0.4 to 0 with space constant 0.6). The input intensity is randomized using an additive random noise with range [0, 0.05]. The so activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The CPU time required to run this simulation was 2 s on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz).
Mentions: Figure 5 shows the GLN response to a stimulus set on at t = 0 ms and set off at t = 5 ms. The spot size increases over time also after the end of the stimulus. According to Solinas et al. (2010b), the center-surround organization of the inhibitory projections shapes the GLN response in space and in time. In order to highlight the effect of inhibition, Figure 5 compares the spot of Figure 4 with the spot achieved after partial block of the inhibitory GoC to GrC synapses and synaptic strength reduced from 0.1 to 0.03. More precisely, we reproduce in Figure 5 the same computational steps taken in Solinas et al. (2010b). After the onset of the MF input the GLN initiates its response with 1 ms of delay, reaching its maximal activation after 4 ms indicated as E peak in Figure 5. After 8 ms the GLN activation fades off due to the emergence of the inhibitory feedback and we chose this time to measure the E2 peak. After partial block of the inhibitory synapses, the E2 peak increases in amplitude and extension (inhibition partially blocked: E2ib). As in Solinas et al. (2010b), the amount of inhibition I is calculated as the change in GLN activity amplitude due to the partial block of inhibition. Like in Solinas et al. (2010b), the difference between the E peak and the inhibition I reveals, in the lower right panel of Figure 5, the center-surround organization of inhibition as the central peak surrounded by a deeper crown.

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.


Related in: MedlinePlus