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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

Ensemble dynamics in the hybrid model. After an initial period of initialization, a synchronous phenomenon within each population arises and the network activity shows oscillations with a frequency of 13 Hz. After a few cycles (t > 350 ms) a traveling wave phenomenon arises. The oscillatory frequency is unaffected by the spontaneous emergence of the waves. The waves of network activity diffuse along the sagittal axis. GrCs are represented with the colored continuous graph; GoCs are described with bars showing potentials multiplied by a factor 3 for graphical reasons. The bottom panels describe the dynamics of a sample GoC cell and GrC node up to 5 s. Both of them show a quasi-periodic dynamics.
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Figure 3: Ensemble dynamics in the hybrid model. After an initial period of initialization, a synchronous phenomenon within each population arises and the network activity shows oscillations with a frequency of 13 Hz. After a few cycles (t > 350 ms) a traveling wave phenomenon arises. The oscillatory frequency is unaffected by the spontaneous emergence of the waves. The waves of network activity diffuse along the sagittal axis. GrCs are represented with the colored continuous graph; GoCs are described with bars showing potentials multiplied by a factor 3 for graphical reasons. The bottom panels describe the dynamics of a sample GoC cell and GrC node up to 5 s. Both of them show a quasi-periodic dynamics.

Mentions: Frames extracted from a video (see Supplementary Material: Video 1) of the GoC-GrC dynamics are shown in Figure 3. This dynamics was obtained by exploiting (5)–(11) and (8)–(12), assuming the topology described by (13). The excitatory input delivered by MFs to GrCs drives their activity above threshold and induces an increase in GoC potentials. The subsequent inhibition elicited in GrCs by the GoC inhibitory feedback loop (MFs-GrCs-PFs-GoCs-GrCs, see Figure 1) suppresses the GrC activity and the cycle restarts. In the early stages of the dynamics local microcircuit synchronous phenomena arise. The same phenomena arise in the biologically realistic model of reference (Solinas et al., 2010b) and this is a characteristic dynamics observed in the GLN in vivo (Vos et al., 1999) and computational models (Maex and DeSchutter, 1998). Furthermore, at a later time in the simulation, t > 350 ms, the synchronous dynamics spontaneously converts to an interesting dynamics where excitatory waves travel in the whole domain involving both GoCs and GrCs. In particular, these oscillations exhibit a quasi-periodic behavior at the level of both the network and the single node dynamics. The amplitude of the MF input can modulate the frequency of oscillations driving it into the θ or to higher β ranges. Moreover, the waves traveling along the sagittal axis show the high degree of synchrony of the GoCs aligned along the transversal axis that was shown in Vos et al. (1999), see Section 4.


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

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

Ensemble dynamics in the hybrid model. After an initial period of initialization, a synchronous phenomenon within each population arises and the network activity shows oscillations with a frequency of 13 Hz. After a few cycles (t > 350 ms) a traveling wave phenomenon arises. The oscillatory frequency is unaffected by the spontaneous emergence of the waves. The waves of network activity diffuse along the sagittal axis. GrCs are represented with the colored continuous graph; GoCs are described with bars showing potentials multiplied by a factor 3 for graphical reasons. The bottom panels describe the dynamics of a sample GoC cell and GrC node up to 5 s. Both of them show a quasi-periodic dynamics.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 3: Ensemble dynamics in the hybrid model. After an initial period of initialization, a synchronous phenomenon within each population arises and the network activity shows oscillations with a frequency of 13 Hz. After a few cycles (t > 350 ms) a traveling wave phenomenon arises. The oscillatory frequency is unaffected by the spontaneous emergence of the waves. The waves of network activity diffuse along the sagittal axis. GrCs are represented with the colored continuous graph; GoCs are described with bars showing potentials multiplied by a factor 3 for graphical reasons. The bottom panels describe the dynamics of a sample GoC cell and GrC node up to 5 s. Both of them show a quasi-periodic dynamics.
Mentions: Frames extracted from a video (see Supplementary Material: Video 1) of the GoC-GrC dynamics are shown in Figure 3. This dynamics was obtained by exploiting (5)–(11) and (8)–(12), assuming the topology described by (13). The excitatory input delivered by MFs to GrCs drives their activity above threshold and induces an increase in GoC potentials. The subsequent inhibition elicited in GrCs by the GoC inhibitory feedback loop (MFs-GrCs-PFs-GoCs-GrCs, see Figure 1) suppresses the GrC activity and the cycle restarts. In the early stages of the dynamics local microcircuit synchronous phenomena arise. The same phenomena arise in the biologically realistic model of reference (Solinas et al., 2010b) and this is a characteristic dynamics observed in the GLN in vivo (Vos et al., 1999) and computational models (Maex and DeSchutter, 1998). Furthermore, at a later time in the simulation, t > 350 ms, the synchronous dynamics spontaneously converts to an interesting dynamics where excitatory waves travel in the whole domain involving both GoCs and GrCs. In particular, these oscillations exhibit a quasi-periodic behavior at the level of both the network and the single node dynamics. The amplitude of the MF input can modulate the frequency of oscillations driving it into the θ or to higher β ranges. Moreover, the waves traveling along the sagittal axis show the high degree of synchrony of the GoCs aligned along the transversal axis that was shown in Vos et al. (1999), see Section 4.

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