Table 1.
Main findings of previous animal studies on neurovascular coupling.
Table 2.
Main findings of previous human studies on neurovascular coupling.
Figure 1.
Local electro-vascular model: cortical unit.
a) The unit comprises three subpopulations of cells, two layer IV GABAergic interneurons and a layer V pyramidal cell. The unit receives input from cortical or thalamic connections, ,
and
, whilst its output is the firing rate of layer V pyramidal cells,
; b) Non-linear function of the transmembrane capacitive currents used to calculate the NO concentration. This function is symmetric because both positive and negative currents increase the amount of NO released. This function is used in the synaptic input coupling model. c) Sigmoid function from membrane potential to firing rate. This function is used as the input to the vascular equations in the spiking output model.
Table 3.
Estimated parameters: these are the parameters estimated from synthetic and measured EEG-fMRI data (one example session, all frequencies).
Figure 2.
Input to Balloon model for different frequencies.
Synaptic input model (blue), , spiking output model (black),
, and mixture model (red),
. The signals have been standardised (mean corrected and divided by the standard deviation of the signal).
Figure 3.
a) SPM results (3 sessions, example subject): effect of visual flicker stimulation on fMRI data. The voxel location corresponds to the most significant cluster maximum (Talairach space), (FWE). b) Epoched BOLD signal (eigenvariate) from the most significant cluster maximum - one example session. c) 2 second source SSVER,
, from the same cluster peak from 1 example session and frequency (10 Hz). Both signals have been standardised (mean corrected and divided by the standard deviation of the signal) as used in the optimisation scheme.
Figure 4.
Here we adopted a ‘multi-step’ approach as opposed to inverting the model in a single step. a) Single-step approach: the EEG and fMRI data are used to estimate the neuronal and hemodynamic parameters ( and
) simultaneously. At each iteration the model equations are integrated at a small time scale matching that of neuronal activity,
, for the entire time interval,
. b) Multi-step method: here the inversion is performed in three main steps. (1) First the neuronal parameters,
, are estimated (using
iterations) from the EEG data with a fine temporal resolution,
, but for a smaller period,
(2 seconds). (2) In the second step these parameter estimates are used to integrate the neuronal equations of the LEV model,
, with the same temporal resolution
but entire time interval
. (3) In the last step we use the BOLD data to estimate (using
iterations) only the hemodynamic parameters,
, with a lower time resolution of
over the full time interval,
. The total number of time steps,
, for each approach is displayed in each gray box.
Figure 5.
a) BOLD response for a stimulation block (15 seconds of stimulation and 15 second of rest) of 8 Hz reversing frequency; b) EEG signal for the same stimulus (2 seconds). Both signals have been standardised (mean corrected and divided by the standard deviation of the signal) as used for model inversion.
Figure 6.
Model frequency response curves -synthetic data.
a) Predicted BOLD response versus reversing frequency for the synaptic input and spiking output models. The curves show the BOLD response obtained for each stimulus frequency (divided by the maximum peak for each model).
Figure 7.
Measured frequency response curves - EEG-fMRI data.
a) Measured BOLD response versus reversing frequency. The values on the y-axis correspond to per cent changes of the global mean signal. b) Frequency-response curve for EEG data. Each point corresponds to the amplitude of the evoked response (divided by the maximum response) at that frequency (). The maximum value was
.
Figure 8.
Model comparison with synthetic data.
We generated data with the different coupling models (IN: synaptic input model; OUT: spiking output model; MIX: mixture model). We then fitted these datasets with the same three coupling models and obtained the results plotted in the figure. a) Difference in log-evidences relative to worst model. b) Corresponding model posterior probabilities.
Figure 9.
Model identification from EEG-fMRI data.
a) EEG time-series (dotted line) and model fit (solid line) for one example session and subject (2 seconds of data per frequency). b) Model predictions and BOLD data for the same example session and subject (all frequencies: 4 to 30 Hz). As can be seen in the figure, the input model (blue) provides the best fit to the BOLD data (black) for the lowest frequencies (e.g. 4.0 and 7.5 Hz), whilst for the highest frequency (30 Hz) it's clear that this model underestimates the BOLD response. The output model (green) provides a better fit for this frequency but predicts a higher response than the one observed. The signals have been standardised (mean centred and divided by the standard deviation of the signal) as used in the model inversion scheme.
Figure 10.
(MIX: mixture model; IN: synaptic input model; OUT: spiking output model): log-model evidence relative to worst model (for low, high and all frequencies). These are group results for all subjects and sessions analysed (the log-evidences are summed over subjects).