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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

Evolution in time of the GrC membrane potential shown in the upper left panels of Figures 5, 6 (thin black and thin red trace, respectively). The thick red and black traces show the time evolution of the same integrals after total block of inhibition in the 2010 model and partial block of inhibition in the hybrid model, respectively. Note that the thick traces generated by models with reduced inhibitory feedback have the tendency to stay above the thinner traces of model with control configuration as a result of more intense ensemble network activity in absence of inhibitory feedback. Furthermore, our hybrid model can follow the biologically realistic model up to the first peak E and conserve a qualitatively similar behavior at the time of the E2 peak.
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Figure 7: Evolution in time of the GrC membrane potential shown in the upper left panels of Figures 5, 6 (thin black and thin red trace, respectively). The thick red and black traces show the time evolution of the same integrals after total block of inhibition in the 2010 model and partial block of inhibition in the hybrid model, respectively. Note that the thick traces generated by models with reduced inhibitory feedback have the tendency to stay above the thinner traces of model with control configuration as a result of more intense ensemble network activity in absence of inhibitory feedback. Furthermore, our hybrid model can follow the biologically realistic model up to the first peak E and conserve a qualitatively similar behavior at the time of the E2 peak.

Mentions: To further highlight the similarities and discrepancies between the two GLN models we calculated the spatial integral of the activity surface for each time step of both models. The plot in Figure 7 shows how the time evolution of the hybrid model follows the traces of the biologically realistic model until the first peak is reached. From there on the discrepancy between the two models progressively increases but, in both models, the reduction of the inhibitory feedback leads to an increase of the overall model activity with the specific spatial distribution shown in Figures 5, 6.


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

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

Evolution in time of the GrC membrane potential shown in the upper left panels of Figures 5, 6 (thin black and thin red trace, respectively). The thick red and black traces show the time evolution of the same integrals after total block of inhibition in the 2010 model and partial block of inhibition in the hybrid model, respectively. Note that the thick traces generated by models with reduced inhibitory feedback have the tendency to stay above the thinner traces of model with control configuration as a result of more intense ensemble network activity in absence of inhibitory feedback. Furthermore, our hybrid model can follow the biologically realistic model up to the first peak E and conserve a qualitatively similar behavior at the time of the E2 peak.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4837690&req=5

Figure 7: Evolution in time of the GrC membrane potential shown in the upper left panels of Figures 5, 6 (thin black and thin red trace, respectively). The thick red and black traces show the time evolution of the same integrals after total block of inhibition in the 2010 model and partial block of inhibition in the hybrid model, respectively. Note that the thick traces generated by models with reduced inhibitory feedback have the tendency to stay above the thinner traces of model with control configuration as a result of more intense ensemble network activity in absence of inhibitory feedback. Furthermore, our hybrid model can follow the biologically realistic model up to the first peak E and conserve a qualitatively similar behavior at the time of the E2 peak.
Mentions: To further highlight the similarities and discrepancies between the two GLN models we calculated the spatial integral of the activity surface for each time step of both models. The plot in Figure 7 shows how the time evolution of the hybrid model follows the traces of the biologically realistic model until the first peak is reached. From there on the discrepancy between the two models progressively increases but, in both models, the reduction of the inhibitory feedback leads to an increase of the overall model activity with the specific spatial distribution shown in Figures 5, 6.

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