Phase-dependent stimulation effects on bursting activity in a neural network cortical simulation

Abstract

Purpose: A neural network simulation with realistic cortical architecture has been used to study synchronized bursting as a seizure representation. This model has the property that bursting epochs arise and cease spontaneously, and bursting epochs can be induced by external stimulation. We have used this simulation to study the time-frequency properties of the evolving bursting activity, as well as effects due to network stimulation.

Methods: The model represents a cortical region of 1.6 mm x 1.6mm, and includes seven neuron classes organized by cortical layer, inhibitory or excitatory properties, and electrophysiological characteristics. There are a total of 65,536 modeled single compartment neurons that operate according to a version of Hodgkin-Huxley dynamics. The intercellular wiring is based on histological studies and our previous modeling efforts.

Results: The bursting phase is characterized by a flat frequency spectrum. Stimulation pulses are applied to this modeled network, with an electric field provided by a 1mm radius circular electrode represented mathematically in the simulation. A phase dependence to the post-stimulation quiescence is demonstrated, with local relative maxima in efficacy occurring before or during the network depolarization phase in the underlying activity. Brief periods of network insensitivity to stimulation are also demonstrated. The phase dependence was irregular and did not reach statistical significance when averaged over the full 2.5s of simulated bursting investigated. This result provides comparison with previous in vivo studies which have also demonstrated increased efficacy of stimulation when pulses are applied at the peak of the local field potential during cortical after discharges. The network bursting is synchronous when comparing the different neuron classes represented up to an uncertainty of 10 ms. Studies performed with an excitatory chandelier cell component demonstrated increased synchronous bursting in the model, as predicted from experimental work.

Conclusions: This large-scale multi-neuron neural network simulation reproduces many aspects of evolving cortical bursting behavior as well as the timing-dependent effects of electrical stimulation on that bursting.

Figure 1

Plot of cellular membrane potentials relative to the resting potential for all 16 cells contained within one minicolumn in the simulation during a period of active bursting for a one second recording. Rows 1−4 are the Layer II/III pyramidal cells, row 5 is the stellate cell, rows 6−9 are the Layer V pyramidal cells, row 10−13 are the Layer VI pyramidal cells, row 14 is the basket cell, row 15 is the double bouquet cell, and row 16 is the chandelier cell.

Figure 2

(A-C) Model with no stimulation applied, same connection pattern as used in stimulation studies. (A) Summed Layer II/III pyramidal cell action potentials in 10 msec bins. (B) Filtered mean field potential. (C) MP analysis. (D) Filtered mean field potential of the same simulation with a stimulation pulse applied at 3.00 sec stopping the ongoing bursting activity. A second stimulation pulse at 3.8 sec is used to restart a stable long bursting period. Red arrows above the plot demonstrate the stimulation points. (E) Filtered mean field potential of the same pulse sequence, now with a further 3^rd stimulation pulse (stop pulse) used to investigate the phase dependence of stimulation-induced activity alteration. Red arrows above the plot demonstrate the stimulation points.

Figure 3

(A) Summed Layer II/III pyramidal cell action potentials in 10 msec bins, with superimposed stimulation-induced quiescent periods. The time interval between the second and third pulses of the three-pulse paradigm is demonstrated by the position of the quiescent period value. These quiescent periods induced by the stop pulse demonstrate a phase dependence with respect to the underlying activity. Also shown are the details of network activity occurring during the three periods of loss of stimulation efficacy at 0.12, 0.98−1.0, and 2.29−2.31 seconds into the constant bursting period (Layer II/III pyramidal cell activity). At 0.12 sec, 0.98 sec, and 2.29 sec, the activity does exhibit a period of quiescence, albeit delayed, with the presence of a single pulse of activity in the normally quiet post-stimulation window. The “sawtooth” region described in the text is demonstrated by the quiescence time peaks in red primarily between 1.0−3.0 seconds. (B) Similar plot demonstrating quiescent periods shown with the underlying network MFP.

Figure 3

(A) Summed Layer II/III pyramidal cell action potentials in 10 msec bins, with superimposed stimulation-induced quiescent periods. The time interval between the second and third pulses of the three-pulse paradigm is demonstrated by the position of the quiescent period value. These quiescent periods induced by the stop pulse demonstrate a phase dependence with respect to the underlying activity. Also shown are the details of network activity occurring during the three periods of loss of stimulation efficacy at 0.12, 0.98−1.0, and 2.29−2.31 seconds into the constant bursting period (Layer II/III pyramidal cell activity). At 0.12 sec, 0.98 sec, and 2.29 sec, the activity does exhibit a period of quiescence, albeit delayed, with the presence of a single pulse of activity in the normally quiet post-stimulation window. The “sawtooth” region described in the text is demonstrated by the quiescence time peaks in red primarily between 1.0−3.0 seconds. (B) Similar plot demonstrating quiescent periods shown with the underlying network MFP.

Figure 4

Plot of the five sampled quiescence times before and after each of the MFP peaks examined. Times are relative to the peak in the MFP. The vertical red line additionally indicates the peak location. The average of these 11 peri-peak measurements (± sem) is shown in red. There were no statistical differences in these values based on matched t-testing.

Figure 5

Network activity with no stimulation, 10 second simulation. Red line indicates summed action potentials in 10 msec bins for the Layer II/III pyramidal cells as a function of time. Blue line indicates the same for the Layer V pyramidal cells. Inset is the data presented in more detail from the 6.0 to 8.0 second region.

Figure 6

(A) Network activity utilizing a model with excitatory chandelier cells. The synaptic weights used were the same as Layer II/III pyramidal cell excitatory connections. Note the more synchronous bursting pattern produced with a distributed background source, compared to the previous simulations. (B,C) Single stimulation pulses were applied at 4.308 sec (B) and 4.313 sec (C) on the underlying activity presented in (A). Stimulation times marked by the red arrow. Note the disruption of the bursting period between 4 and 5 seconds and the alteration of the subsequent bursting behavior compared to (A).