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On conductance-based neural field models.

Pinotsis DA, Leite M, Friston KJ - Front Comput Neurosci (2013)

Bottom Line: Our main finding is that both the evoked responses (impulse response functions) and induced responses (transfer functions) show qualitative differences depending upon whether one uses a neural mass or field model.Overall, all models reproduce a characteristic increase in frequency, when inhibition was increased by increasing the rate constants of inhibitory populations.However, convolution and conductance-based models showed qualitatively different changes in power, with convolution models showing decreases with increasing inhibition, while conductance models show the opposite effect.

View Article: PubMed Central - PubMed

Affiliation: The Wellcome Trust Centre for Neuroimaging, University College London London, UK.

ABSTRACT
This technical note introduces a conductance-based neural field model that combines biologically realistic synaptic dynamics-based on transmembrane currents-with neural field equations, describing the propagation of spikes over the cortical surface. This model allows for fairly realistic inter-and intra-laminar intrinsic connections that underlie spatiotemporal neuronal dynamics. We focus on the response functions of expected neuronal states (such as depolarization) that generate observed electrophysiological signals (like LFP recordings and EEG). These response functions characterize the model's transfer functions and implicit spectral responses to (uncorrelated) input. Our main finding is that both the evoked responses (impulse response functions) and induced responses (transfer functions) show qualitative differences depending upon whether one uses a neural mass or field model. Furthermore, there are differences between the equivalent convolution and conductance models. Overall, all models reproduce a characteristic increase in frequency, when inhibition was increased by increasing the rate constants of inhibitory populations. However, convolution and conductance-based models showed qualitatively different changes in power, with convolution models showing decreases with increasing inhibition, while conductance models show the opposite effect. These differences suggest that conductance based field models may be important in empirical studies of cortical gain control or pharmacological manipulations.

No MeSH data available.


Related in: MedlinePlus

This figure shows the changes in the transfer function of a conductance field model. This is the equivalent to the results for the mass model in Figure 5, where we now include spatial propagation effects.
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Figure 7: This figure shows the changes in the transfer function of a conductance field model. This is the equivalent to the results for the mass model in Figure 5, where we now include spatial propagation effects.

Mentions: We generated synthetic electrophysiological responses by integrating equations (3) or (4) from their fixed points and characterized the responses to external (excitatory) impulses to spiny stellate cells, in the time and frequency domain. The spectral responses correspond to the model's transfer function. Electrophysiological signals (LFP or M/EEG data) were simulated by passing neuronal responses through a lead field that varies with location on the cortical patch. The resulting responses in sensor space (see Figures 5–7) are given by a mixture of currents flowing in and out of pyramidal cells in Figure 1:(5)y(t,θ)=∫L(x,θ)Q·v˙(x,t)dxIn this equation, Q⊂ θ is a vector of coefficients that weight the relative contributions of different populations to the observed signal and L(x, θ) is the lead field. This depends upon parameters θ and we assume it is a Gaussian function of location—as in previous models of LFP or MEG recordings: see (Pinotsis et al., 2012). This equation is analogous to the usual (electromagnetic) gain matrix for equivalent current dipoles. We assume here that these dipoles are created by pyramidal cells whose current is the primary source of an LFP signal. With spatially extended sources (patches), this equation integrates out the dependence on the source locations within a patch and provides a time series for each sensor.


On conductance-based neural field models.

Pinotsis DA, Leite M, Friston KJ - Front Comput Neurosci (2013)

This figure shows the changes in the transfer function of a conductance field model. This is the equivalent to the results for the mass model in Figure 5, where we now include spatial propagation effects.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3824089&req=5

Figure 7: This figure shows the changes in the transfer function of a conductance field model. This is the equivalent to the results for the mass model in Figure 5, where we now include spatial propagation effects.
Mentions: We generated synthetic electrophysiological responses by integrating equations (3) or (4) from their fixed points and characterized the responses to external (excitatory) impulses to spiny stellate cells, in the time and frequency domain. The spectral responses correspond to the model's transfer function. Electrophysiological signals (LFP or M/EEG data) were simulated by passing neuronal responses through a lead field that varies with location on the cortical patch. The resulting responses in sensor space (see Figures 5–7) are given by a mixture of currents flowing in and out of pyramidal cells in Figure 1:(5)y(t,θ)=∫L(x,θ)Q·v˙(x,t)dxIn this equation, Q⊂ θ is a vector of coefficients that weight the relative contributions of different populations to the observed signal and L(x, θ) is the lead field. This depends upon parameters θ and we assume it is a Gaussian function of location—as in previous models of LFP or MEG recordings: see (Pinotsis et al., 2012). This equation is analogous to the usual (electromagnetic) gain matrix for equivalent current dipoles. We assume here that these dipoles are created by pyramidal cells whose current is the primary source of an LFP signal. With spatially extended sources (patches), this equation integrates out the dependence on the source locations within a patch and provides a time series for each sensor.

Bottom Line: Our main finding is that both the evoked responses (impulse response functions) and induced responses (transfer functions) show qualitative differences depending upon whether one uses a neural mass or field model.Overall, all models reproduce a characteristic increase in frequency, when inhibition was increased by increasing the rate constants of inhibitory populations.However, convolution and conductance-based models showed qualitatively different changes in power, with convolution models showing decreases with increasing inhibition, while conductance models show the opposite effect.

View Article: PubMed Central - PubMed

Affiliation: The Wellcome Trust Centre for Neuroimaging, University College London London, UK.

ABSTRACT
This technical note introduces a conductance-based neural field model that combines biologically realistic synaptic dynamics-based on transmembrane currents-with neural field equations, describing the propagation of spikes over the cortical surface. This model allows for fairly realistic inter-and intra-laminar intrinsic connections that underlie spatiotemporal neuronal dynamics. We focus on the response functions of expected neuronal states (such as depolarization) that generate observed electrophysiological signals (like LFP recordings and EEG). These response functions characterize the model's transfer functions and implicit spectral responses to (uncorrelated) input. Our main finding is that both the evoked responses (impulse response functions) and induced responses (transfer functions) show qualitative differences depending upon whether one uses a neural mass or field model. Furthermore, there are differences between the equivalent convolution and conductance models. Overall, all models reproduce a characteristic increase in frequency, when inhibition was increased by increasing the rate constants of inhibitory populations. However, convolution and conductance-based models showed qualitatively different changes in power, with convolution models showing decreases with increasing inhibition, while conductance models show the opposite effect. These differences suggest that conductance based field models may be important in empirical studies of cortical gain control or pharmacological manipulations.

No MeSH data available.


Related in: MedlinePlus