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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

Transfer functions associated with a convolution mass model when changing the excitatory time constant and the connection driving the pyramidal cells over a log-scaling range of (−2, 1) x (−2, −1) (from top to bottom and left to right). The image format summarizes the transfer function in terms of its peak frequency. Transfer functions can be regarded as the spectral response that would be seen if the model was driven by independent (white) fluctuations. They are also the Fourier transform of the impulse response functions of the previous figures.
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Figure 4: Transfer functions associated with a convolution mass model when changing the excitatory time constant and the connection driving the pyramidal cells over a log-scaling range of (−2, 1) x (−2, −1) (from top to bottom and left to right). The image format summarizes the transfer function in terms of its peak frequency. Transfer functions can be regarded as the spectral response that would be seen if the model was driven by independent (white) fluctuations. They are also the Fourier transform of the impulse response functions of the previous figures.

Mentions: We varied the inhibitory intrinsic connectivity, a32 and excitatory time constant, 1/λ, of the inhibitory populations between 10 and 36% and between 10 and 270%, respectively, of the values in Tables 1, 2 (this corresponds to a log-scaling of between minus two and minus one and minus one and plus one, respectively). We denote these new values by ā32 and 1/λ, respectively. The transfer functions for the neural mass variants of the convolution and conductance models are shown in Figures 4, 5, respectively. The images in subsequent figures report the peak frequency of the spectral and response as a function of the two model parameters (the peak frequency corresponds to maximum system response). Exemplar transfer functions for selected parameter value pairs are shown as functions of frequency. We focus on spectral responses produced by fixed point perturbations; where lack of convergence to a fixed point is encoded by dark blue regions in the images.


On conductance-based neural field models.

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

Transfer functions associated with a convolution mass model when changing the excitatory time constant and the connection driving the pyramidal cells over a log-scaling range of (−2, 1) x (−2, −1) (from top to bottom and left to right). The image format summarizes the transfer function in terms of its peak frequency. Transfer functions can be regarded as the spectral response that would be seen if the model was driven by independent (white) fluctuations. They are also the Fourier transform of the impulse response functions of the previous figures.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Transfer functions associated with a convolution mass model when changing the excitatory time constant and the connection driving the pyramidal cells over a log-scaling range of (−2, 1) x (−2, −1) (from top to bottom and left to right). The image format summarizes the transfer function in terms of its peak frequency. Transfer functions can be regarded as the spectral response that would be seen if the model was driven by independent (white) fluctuations. They are also the Fourier transform of the impulse response functions of the previous figures.
Mentions: We varied the inhibitory intrinsic connectivity, a32 and excitatory time constant, 1/λ, of the inhibitory populations between 10 and 36% and between 10 and 270%, respectively, of the values in Tables 1, 2 (this corresponds to a log-scaling of between minus two and minus one and minus one and plus one, respectively). We denote these new values by ā32 and 1/λ, respectively. The transfer functions for the neural mass variants of the convolution and conductance models are shown in Figures 4, 5, respectively. The images in subsequent figures report the peak frequency of the spectral and response as a function of the two model parameters (the peak frequency corresponds to maximum system response). Exemplar transfer functions for selected parameter value pairs are shown as functions of frequency. We focus on spectral responses produced by fixed point perturbations; where lack of convergence to a fixed point is encoded by dark blue regions in the images.

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