Limits...
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 biologically realistic model (Solinas et al., 2010b) to the activation of 13 MF terminals located within 20 μm from the network center. As in the 2010 publication, at the end of each simulation the voltage trace of GrCs aligned along the vertical axis are pooled together to represent their ensemble activity. The resulting 2D surface represents the activity of this 3D GLN network (vertical axes show the mean membrane potential in mV). The simulations in control and partial inhibition block configuration are repeated 10 times, using each time a different network structure. The 2D surfaces belonging to each configuration class are used to build an average response for that class of GLN to the stimulus. The arrangement of data plots replicates the organization of Figure 5. The activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The stimulus consists in a sequence of 3 spikes with an inter-spike interval of 333 ms. The first peak of GLN activation is reached within 4.5 ms from stimulus onset (E peak; upper left panel). The GLN shows a second peak of activity E2 with latency 8.2 ms from stimulus onset (upper right panel). Blocking inhibitory synapses induces a generalized increase of the GLN activity from this time on, note the E2 peak amplitude and its spatial extension (E2ib; upper right panel). The spatial effect of inhibition is calculated as the point difference of the E2 and E2ib surfaces (−I; lower left panel). The center-surround is represented as the difference the surfaces E and the I (lower right panel). The CPU time required to run one of the 20 simulations was 20 min on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz) plus 30 min to process the recorded data.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4837690&req=5

Figure 6: Response of the biologically realistic model (Solinas et al., 2010b) to the activation of 13 MF terminals located within 20 μm from the network center. As in the 2010 publication, at the end of each simulation the voltage trace of GrCs aligned along the vertical axis are pooled together to represent their ensemble activity. The resulting 2D surface represents the activity of this 3D GLN network (vertical axes show the mean membrane potential in mV). The simulations in control and partial inhibition block configuration are repeated 10 times, using each time a different network structure. The 2D surfaces belonging to each configuration class are used to build an average response for that class of GLN to the stimulus. The arrangement of data plots replicates the organization of Figure 5. The activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The stimulus consists in a sequence of 3 spikes with an inter-spike interval of 333 ms. The first peak of GLN activation is reached within 4.5 ms from stimulus onset (E peak; upper left panel). The GLN shows a second peak of activity E2 with latency 8.2 ms from stimulus onset (upper right panel). Blocking inhibitory synapses induces a generalized increase of the GLN activity from this time on, note the E2 peak amplitude and its spatial extension (E2ib; upper right panel). The spatial effect of inhibition is calculated as the point difference of the E2 and E2ib surfaces (−I; lower left panel). The center-surround is represented as the difference the surfaces E and the I (lower right panel). The CPU time required to run one of the 20 simulations was 20 min on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz) plus 30 min to process the recorded data.

Mentions: To compare our hybrid model with the biologically realistic model, we re-ran the simulations of Solinas et al. (2010b), using the code published in Solinas et al. (2010a). We changed the stimulus protocol to activate 13 MF terminals, instead of the original 8 terminals, to enlarge the stimulated area. This change brought an increase of the spot size to 33 μm at 70% of the maximum peak amplitude, consistent with the published experimental evidence (Mapelli et al., 2010b). The network size was left at 100 μm by 100 μm as increasing it to the 200 μm by 200 μm size of our hybrid network model would imply a prohibitive computational cost. The recorded data were processed using the same procedure applied to the hybrid model. Figure 6 shows the stimulus effect 4.5 ms after onset, E peak, and at 8 ms, E2 peak. Like in the hybrid model the block of inhibition induces an increase of the network activity clearly visible at the time of the second peak. In the lower right panel of Figure 6 the spatial organization of the inhibitory feedback generates deeper spots in proximity of the central area, shaping the center-surround.


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 biologically realistic model (Solinas et al., 2010b) to the activation of 13 MF terminals located within 20 μm from the network center. As in the 2010 publication, at the end of each simulation the voltage trace of GrCs aligned along the vertical axis are pooled together to represent their ensemble activity. The resulting 2D surface represents the activity of this 3D GLN network (vertical axes show the mean membrane potential in mV). The simulations in control and partial inhibition block configuration are repeated 10 times, using each time a different network structure. The 2D surfaces belonging to each configuration class are used to build an average response for that class of GLN to the stimulus. The arrangement of data plots replicates the organization of Figure 5. The activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The stimulus consists in a sequence of 3 spikes with an inter-spike interval of 333 ms. The first peak of GLN activation is reached within 4.5 ms from stimulus onset (E peak; upper left panel). The GLN shows a second peak of activity E2 with latency 8.2 ms from stimulus onset (upper right panel). Blocking inhibitory synapses induces a generalized increase of the GLN activity from this time on, note the E2 peak amplitude and its spatial extension (E2ib; upper right panel). The spatial effect of inhibition is calculated as the point difference of the E2 and E2ib surfaces (−I; lower left panel). The center-surround is represented as the difference the surfaces E and the I (lower right panel). The CPU time required to run one of the 20 simulations was 20 min on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz) plus 30 min to process the recorded data.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 6: Response of the biologically realistic model (Solinas et al., 2010b) to the activation of 13 MF terminals located within 20 μm from the network center. As in the 2010 publication, at the end of each simulation the voltage trace of GrCs aligned along the vertical axis are pooled together to represent their ensemble activity. The resulting 2D surface represents the activity of this 3D GLN network (vertical axes show the mean membrane potential in mV). The simulations in control and partial inhibition block configuration are repeated 10 times, using each time a different network structure. The 2D surfaces belonging to each configuration class are used to build an average response for that class of GLN to the stimulus. The arrangement of data plots replicates the organization of Figure 5. The activated spot (upper left panel) has a diameter of 36μm if measured at 70% of its peak amplitude (Mapelli et al., 2010b). The stimulus consists in a sequence of 3 spikes with an inter-spike interval of 333 ms. The first peak of GLN activation is reached within 4.5 ms from stimulus onset (E peak; upper left panel). The GLN shows a second peak of activity E2 with latency 8.2 ms from stimulus onset (upper right panel). Blocking inhibitory synapses induces a generalized increase of the GLN activity from this time on, note the E2 peak amplitude and its spatial extension (E2ib; upper right panel). The spatial effect of inhibition is calculated as the point difference of the E2 and E2ib surfaces (−I; lower left panel). The center-surround is represented as the difference the surfaces E and the I (lower right panel). The CPU time required to run one of the 20 simulations was 20 min on a Apple® MacBook Pro (Intel Core 2 Duo 2.93 GHz) plus 30 min to process the recorded data.
Mentions: To compare our hybrid model with the biologically realistic model, we re-ran the simulations of Solinas et al. (2010b), using the code published in Solinas et al. (2010a). We changed the stimulus protocol to activate 13 MF terminals, instead of the original 8 terminals, to enlarge the stimulated area. This change brought an increase of the spot size to 33 μm at 70% of the maximum peak amplitude, consistent with the published experimental evidence (Mapelli et al., 2010b). The network size was left at 100 μm by 100 μm as increasing it to the 200 μm by 200 μm size of our hybrid network model would imply a prohibitive computational cost. The recorded data were processed using the same procedure applied to the hybrid model. Figure 6 shows the stimulus effect 4.5 ms after onset, E peak, and at 8 ms, E2 peak. Like in the hybrid model the block of inhibition induces an increase of the network activity clearly visible at the time of the second peak. In the lower right panel of Figure 6 the spatial organization of the inhibitory feedback generates deeper spots in proximity of the central area, shaping the center-surround.

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