Conceived and designed the experiments: JMK WDP. Performed the experiments: JMK WDP. Analyzed the data: MJR WDP. Contributed reagents/materials/analysis tools: MJR JMK WDP. Wrote the paper: MJR JMK WDP.
The authors have declared that no competing interests exist.
Functional magnetic resonance imaging (fMRI), with blood oxygenation leveldependent (BOLD) contrast, is a widely used technique for studying the human brain. However, it is an indirect measure of underlying neuronal activity and the processes that link this activity to BOLD signals are still a topic of much debate. In order to relate findings from fMRI research to other measures of neuronal activity it is vital to understand the underlying neurovascular coupling mechanism. Currently, there is no consensus on the relative roles of synaptic and spiking activity in the generation of the BOLD response. Here we designed a modelling framework to investigate different neurovascular coupling mechanisms. We use Electroencephalographic (EEG) and fMRI data from a visual stimulation task together with biophysically informed mathematical models describing how neuronal activity generates the BOLD signals. These models allow us to noninvasively infer the degree of local synaptic and spiking activity in the healthy human brain. In addition, we use Bayesian model comparison to decide between neurovascular coupling mechanisms. We show that the BOLD signal is dependent upon both the synaptic and spiking activity but that the relative contributions of these two inputs are dependent upon the underlying neuronal firing rate. When the underlying neuronal firing is low then the BOLD response is best explained by synaptic activity. However, when the neuronal firing rate is high then both synaptic and spiking activity are required to explain the BOLD signal.
Functional magnetic resonance imaging (fMRI), with blood oxygenation leveldependent (BOLD) contrast, is a widely used technique for studying the human brain. However, the relationship between neuronal activity and blood flow, the basis of fMRI, is still under much debate. A growing body of evidence from animal studies suggests that fMRI signals are more closely coupled to synaptic input activity than to the spiking output of a neuronal population. However, data from neurosurgical patients does not seem to support this view and this hypothesis hasn't yet been tested in the healthy human brain. Here we design a powerful and efficient modelling framework that can be used to noninvasively compare different biologically plausible hypotheses of neurovascular coupling. We use this framework to explore the contribution of these two aspects of neuronal activity (synaptic and spiking) to the generation of hemodynamic signals in human visual cortex, with Electroencephalographic (EEG)fMRI data. Our results provide preliminary evidence that depending on the frequency of the visual stimulus and underlying firing rate, fMRI relates closer to synaptic activity (lowfrequencies) or to both synaptic and spiking activities (highfrequencies).
Functional magnetic resonance imaging (fMRI) is an extensively employed neuroimaging technique that allows the noninvasive recordings from human brain of neuronal activity with relatively high spatial resolution. However, the blood oxygenation leveldependent (BOLD) contrast on which fMRI is based is only an indirect measure of this activity. The processes that link the underlying neuronal activity to the BOLD signals are still a topic of much debate. In particular, there is no consensus on the relative roles of synaptic and spiking activity in the generation of BOLD signals. In order to relate findings from fMRI research to other measures of neuronal activity it is important to understand the underlying neurovascular coupling mechanism
Most of our present knowledge about neurovascular coupling comes from animal experiments. These studies have combined hemodynamic measures such as cerebral blood flow (CBF), with electrical measurements such as local field potentials (LFPs) and single/multiunit activity (S/MUA). LFPs correspond primarily to weighted averages of synchronised dendrosomatic components of synaptic signals in a neuronal population, whilst S/MUA measures the action potentials of a single cell or population of cells, respectively
In a pioneering study
This growing body of evidence (
Reference  Paradigm  Main findings  Brain regions  Species  Signals 

Visual (rotating checkerboard)  LFP (40–130 Hz) better predictor of BOLD than MUA (300–1.5 kHz)  V1  Monkey  BOLD, LFP, MUA 

Visual (rotating checkerboard)  BOLDÕs variance best explained by LFP (20–60 Hz)  V1  Monkey (awake)  BOLD, LFP, MUA, SUA 

Visual (moving dots; changing coherence)  BOLD contrast in human V5 isproportional to SUA in monkey V5  V5  Monkey/Human  BOLD, SUA 

Visual (changing contrast)  BOLD in human V1 is proportional to SUA in monkey V1  V1  Monkey/Human  BOLD, SUA 

Restingstate  Drug induced increase in Purkinje cell spike activity was not sufficient to raise blood flow above baseline  Cerebellum  Rat  CBF, SUA 

Visual (sinewave gratings, 1–20 Hz)  Correlation between BOLD and LFPs in the absence of spiking activity (suppressed by the stimulus)  V1  Cat  LFP, MUA, 

Visual (rotating checkerboard)  Injected neuromodulator BP554 induces hyperpolarization of efferent membrane, reducing MUA (800–3 k Hz) without affecting either LFP (24–90 Hz) or BOLD activity  V1  Monkey  BOLD, LFP, MUA 

Visual (sinewave gratings, natural movies and pink pixel noise)  Agreement between BOLD and LFP (in terms of 
Visual cortex (17,18,19 and 21a)  Cat  BOLD, LFP, MUA 

Visual  BOLD correlates better with gammaband LFP  Visual cortex  Cat  BOLD, LFP, MUA 

Perceptual suppresion  Only BOLD and lowHz LFP (not highHz LFP or spikes) significantly decreased during perceptual suppression  V1  Monkey (awake)  BOLD, LFP, Spikes 

Whisker pad stimulation  Deep layer negative BOLD, adjacent to layers of positive BOLD, associated with reductions in MUA  Somatosensory cortex  Rat  BOLD, LFP, MUA, OHb, dHb, CBV 

Optical stimulus  Negative BOLD signal caused by optically driving genetically modified inhibitory cells  Motor cortex  Rat  Optogenetics 
However, when it comes to the human brain the number of studies directly addressing the question of how BOLD relates to synaptic versus spiking activity is relatively smaller (
Reference  Paradigm  Main findings  Brain regions  Species  Signals 

Movie segment  Significant correlation between patients predicted BOLD signals from SUA and signals measure in healthy subjects  Auditory cortex  Human (patients)  BOLD, LFP, SUA 

Spatial navigation in virtual environment  Correlation between the BOLD signal andthetaband activity; no significant correlation with MUA/SUA  Hippocampal areas  Human (patients)  BOLD, LFP, MUA, SUA 
Restingstate  Reductions in alpha power correlate with increases in BOLD  Occipital cortex  Human (healthy)  BOLD, EEG  

Semantic decision task  Close spatial correspondence between BOLD activation regions and gammaECoG sites  Temporal and sulcal cortex and insula  Human (patients)  BOLD, ECoG 

Visual (flickering checkerboard 4–60 Hz)  Rootmean squared frequency explains more BOLD activity than the total spectral power or any linear combination of frequencybands  Visual cortex  Human (healthy)  BOLD, EEG 

Movie segments  GammaLFP coupled well to BOLD; coupling for SUA highly variable  Auditory cortex  Human (patients)  BOLD, LFP, SUA 

Wakefulness (AW), slowwave and rapideyemovement sleep (REM)  Stateinvariant significant structural correlation between BOLD and slow cortical potentials ( 
Sensorimotor cortex  Human (patients)  BOLD, ECoG 

Restingstate  BOLD response is negatively correlated with GABA concentration and gamma oscillation frequency  Visual cortex  Human (healthy)  MEG, GABA concentration 
The link between neuronal activity and the BOLD response has not only been investigated at a microscopic level, using invasive colocalised recordings, but also at a macroscopic scale using fMRI and Electroencephalography (EEG). EEG (and Magnetoencephalography (MEG)), are well established noninvasive techniques that are well suited to studying neuronal activity since they provide direct (not confounded by the hemodynamic response) measurement of postsynaptic potentials (magnetic fields) in cortical pyramidal cell populations with high temporal resolution
Here we design a powerful and efficient modelling framework to explicitly investigate competing hypotheses for the relationship between neuronal activity and the BOLD response in the healthy human brain. We use this framework to explore the relative contribution of synaptic and spiking activity to the generation of fMRI signals in visual cortex.
The participation of healthy subjects prohibits the use of invasive electrophysiological measures. Therefore we use a mathematical modelling framework that allows us to noninvasively infer the degree of local synaptic and spiking activity, together with EEGfMRI data, in which subjects were exposed to a reversing checkerboard of varying frequencies. This is similar in spirit to the use of ‘virtual electrodes’ in EEG analysis
Models linking neuronal activity to EEG/MEG signals have been proposed by
Models linking a common underlying neuronal substratum to both EEG and fMRI signals have also been developed
Biophysically motivated models include
Despite these theoretical efforts, the existing modelling frameworks have not yet been used in conjunction with real electrophysiological and hemodynamic data to compare different neurovascular coupling mechanisms, although important steps in this direction have been taken by
Here we use the forward model proposed by
However, inverting generative models using multimodality datasets, can be a technically demanding task, if the temporal characteristics of the datasets are very different, which is the case for EEGfMRI data. Here we develop a computationally efficient scheme for model inversion. Instead of inverting the model in a single (computationally demanding) step we adopt a ‘multistep inversion’ approach. This approach is based on partitioning model inversion into multiple, independent and computationally efficient steps that are motivated by the timescales of data involved. This is a general procedure that can be used with other datasets and in other multimodal studies, such as with MEGfMRI or LFPfMRI data.
Finally, once equiped with this mathematical and computational framework we posit models embodying different hypotheses about neurovascular coupling and adjudicate between them using Bayesian model evidence
We use a realistic biophysical model, proposed by
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,
A neural mass model (NMM) characterises the population dynamics of electrical states such as the membrane potentials in the somas of the neurons and electric currents flowing in the neuropil. This modelling framework is appropriate for data that reflect the behaviour of neuronal populations, such as EEG and fMRI data. The neural mass model can be viewed as a special case of ensemble density models, where the ensemble density is summarised with a single number representing mean activity
The time variations of membrane potential in the individual compartments of the pyramidal cell and single compartment interneurons,
In terms of synaptic connections within the cortical unit, the total inhibitory synaptic effect on the pyramidal cell is given by:
The parameters are set to
The equations for the membrane potential at the soma of the threecompartment pyramidal cell, as well as the extracellular potential along its apical dendrites can be determined from the potentials and currents at the individual compartments (given by Eq. 1). These equations can be found in
The state variables,
Electrical, vascular and coupling parameters  
Synthetic  Observed  
Type  Description  Symbol  Units  Prior  True  Estimated  Estimated 
Electrical ( 

Synaptic input 


1.00  0.80  0.85  0.94  
Synaptic input 


1.00  1.00  1.00  1.00  
Synaptic input 


1.00  0.50  0.60  0.60  
GABAergic IN synaptic factor 


0.30  0.50  0.49  0.53  
PC voltageampere function 


0.60  0.90  0.78  0.42  
V PC voltageampere function 


6.00  4.00  5.62  5.95  
Vascular ( 

Signal decay 


0.65  0.50  0.65  0.59  
Autoregulation 


0.41  0.28  0.41  0.40  
Transit time 


0.98  0.78  0.98  0.91  
Stiffness 

no dim.  0.32  0.25  0.32  0.32  
Resting O2 extraction fraction 

no dim.  0.34  0.30  0.34  0.34  
Coupling  
NO model ( 
NO concentration baseline 

no dim.  0.10  0.30  0.29  0.29 
NO synaptic current factor (IN) 


1.59e03  1.50e03  1.59e03  1.59e03  
FR model ( 
PC voltageampere function 


0.78  0.90  0.63  0.17 
PC voltageampere function 


5.62  4.00  5.70  7.98  
Mixture model ( 
NO coefficient 

no dim.  0.50  0.40  0.40  0.29 
FR coefficient 

no dim.  0.50  0.60  0.60  0.71 
The coupling between local neuronal activity, described by the neural mass model, and subsequent changes in vascular dynamics is our question of interest. These changes are expressed in the BOLD signal and have previously been modelled in an extended Balloon approach
The hemodynamic parameters,
The whole dynamic system is driven by the input
In the next section we specify the neurovascular coupling mechanisms we are interested in comparing.
The original electrovascular model proposed by
The observation equations for EEG,
The temporal variations of the EEG signal are well approximated by the extracellular electric current in the neuropil,
The observation function for fMRI is a static nonlinear function of the cerebral blood volume and the concentration of deoxyhemoglobin directly
The factors
To link the two main components of the biophysical model, the neural mass model and the Balloon model, we specified three different biologically plausible neurovascular coupling mechanisms based on previous empirical results. These mechanisms are described below:
The first model considered assumes that the input to the Balloon model,
NO is a potent vasoactive and rapidly diffusing gas
The total concentration of NO in the cortical unit is modelled as a nonlinear function,
The energetic factors
The amount of NO released in the cortical unit (Eq. 6) is then passed through a lowpass filter with gain
The baseline concentration of NO before stimulation,
Synaptic input model (blue),
For the second neurovascular coupling hypothesis we consider blood flow to be driven by the output spikes of the cortical unit, i.e the firing rate of the pyramidal cells. We refer to this model as the
The spiking activity of the layer V pyramidal cells is the outcome of the processing of information in the cortical unit and contains the information that is transmitted to other areas within and outside the cortex. Therefore this model looks at how BOLD signals are related to the output of local neuronal information processing as opposed to the synaptic input assessed by the previous model.
In this model the generalised logistic function (Eq. (2)) is employed to transform the average membrane potential of the pyramidal cell population,
This model has seven free parameters (the same number of parameters of the input model),
The third coupling model assumes that both synaptic and spiking activities can contribute to the generation of the hemodynamic signals. Therefore, the mixture model is a sum of the amount of NO released by synaptic activity in the cortical unit and the firing rate of its pyramidal cells:
We use EEG and fMRI data from a previous study
Images were acquired from a 1.5 T wholebody scanner (Magnetom Sonata, Siemens Medical, Erlangen, Germany) operated with its standard body transmit and circularly polarised head receive coil. The manufacturer's standard automatic 3Dshim procedure was performed at the beginning of each experiment. The scanner produced T2*weighted images with a singleshot gradientecho EPI sequence. Whole brain images consisting of 34 contiguous transverse slices, on a 64by64 grid, were acquired every 3.06 seconds resulting in a total of 320 functional scans for each of the three sessions of each subject (slice thickness = 2 mm, gap between slices = 1 mm, repetition time TR = 90 ms, flip angle =
The fMRI data were preprocessed with SPM8 software (
In previous work
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),
EEG was acquired with an MRcompatible BrainAmp amplifier and BrainCap EEG cap with ring Ag/AgCl electrodes (Brainproducts GmbH, Munich, Germany). Raw EEG was sampled at 5 kHz and a low pass filter (cut off frequency: 1 kHz) was used. This system provided 29 EEG channels, 2 EOG channels, and 1 ECG channel. The electrodes were distributed according to the 10/20 system, and the reference electrode was located between Fz and Cz. We additionally measured the pulse using a pulse oxymeter attached to the subject's finger and the locations of the EEG electrodes were recorded with a Polhemus digitiser.
The EEG data were preprocessed as described in
Here we use the scalp steady state visual evoked responses (SSVERs) to reconstruct the electrical activity at the source level. SSVERs were computed by first epoching the artefactcorrected 27electrode EEG data acquired inside the MRI scanner, for each session, in a 15second poststimulus window and then averaging (in the time domain) across trials. This procedure yielded 7 averaged 15second timeseries for each session corresponding to the 7 different flicker frequencies used. The source electrical activity was then obtained as follows. Given a source region with known anatomical location, we can form the
Using EEGfMRI data in combination with Bayesian inference allows us to estimate the underlying synaptic and spiking activities, along with other parameters of the biophysical framework. Additionally, we can compare the different neurovascular coupling hypotheses using Bayesian model evidence.
In Bayesian inference, prior beliefs about parameters,
The posterior density is an optimal combination of prior knowledge and new observations, weighted by their relative precision (i.e., inverse variance), and provides a complete description of uncertainty about the parameters. Generally, the choice of priors reflects either empirical knowledge (e.g., previous measurements) or formal considerations (e.g., biological or physical constraints). Here we use empirical knowledge for both the neural mass model parameters and the coupling/hemodynamic parameters, based on estimates obtained by
Under Gaussian assumptions, also known as a fixedform Laplace approximation
A nonlinear model, such as the local electrovascular (LEV) model used here, Eq. (3), can be linearised by expanding the observation equation about a working estimate
The linearised model, Eq. (13), can be used in a Variational Laplace (VL) optimisation scheme that iteratively updates the moments of the conditional density,
The maximisation of
The model evidence is the probability of obtaining observed data,
This approximation to the posterior density has been evaluated using Markov Chain Monte Carlo (MCMC)
The use of both EEG and fMRI data to estimate the electrovascular model is affected by the difficult problem of how to deal with the disparity between the two datasets' time scales. In our study, for each fMRI point (sampled every 3 secs) we have 300 EEG data points (sampled at 100 Hz). The large amount of EEG data renders the model inversion computationally intensive, as for each parameter update we must integrate the model equations at a fine temporal scale (1000 Hz).
To overcome this problem we developed a computationally efficient inversion scheme based on partitioning model inversion into separate steps depending on the timescales of the data involved. We refer to this scheme as a ‘multistep inversion’ approach. This procedure generalises to other datasets and can be used in other multimodal studies, such as MEGfMRI or LFPfMRI, where the amount of data and time scales are very different between modalities.
This ‘multistep inversion’ approach works as follows (
First we selected 2 secs of the source SSVERs (Eq. 11) for each frequency (4 to 30 Hz) and session to identify the electrical states,
After estimating the electrical parameters (previous step), we used these estimates to integrate the full LEV model. Importantly, this integration takes place only once (as opposed to a ‘singlestep’ approach, where it would have to be integrated at every iteration). The integration is implemented as above but instead of 2 secs, the input to the model is now 15 secs of stimulation and 15 secs of rest for each frequency. We integrate the full models with the three different coupling mechanisms described above and produced the following timeseries as our input to the BOLD response (next step). For the synaptic input model the output timeseries is the total NO concentration, Eq. (8). For the spiking output model the output timeseries is the firing rate of pyramidal cells, Eq. (9), whilst for the mixture model both of these output timeseries were produced, Eq. (10). These output timeseries were downsampled to 10 Hz to reduce the estimation time of the next step and used as inputs to the Balloon model.
Finally, with the timeseries for all coupling models obtained in the previous step we estimated the extended Balloon model using the epoched BOLD data for all frequencies. The estimation was again performed iteratively as described above (
Here we adopted a ‘multistep’ approach as opposed to inverting the model in a single step. a) Singlestep approach: the EEG and fMRI data are used to estimate the neuronal and hemodynamic parameters (
Again through Bayes' rule we can relate the model evidence to the model posterior probability,
Given two models,
Bayes factors have been stratified into different ranges deemed to correspond to different strengths of evidence. ‘Strong’ evidence, for example, corresponds to a BF of over 20 (logBF over 3)
In this section, simulations are used to explore the behaviour of the model and its ability to reproduce EEG and BOLD data under the experimental conditions described in the previous section. The response of the three neurovascular coupling models to changes in stimulus frequency is also shown. These synthetic signals are used to test the model inversion routines and to verify that Bayesian model comparison can be used to infer the correct coupling model.
The LEV model was numerically integrated using the multistep AdamsBashforthMoulton predictorcorrector algorithm implemented in the MATLAB (The MathWorks, Inc.) function
The input to the LEV model was generated by creating a series of single events with the same frequency as the reversing checkerboard (4.0, 7.5, 10.0 … Hz). These events are modelled as Gaussian functions of
We first generated data from the LEV model separately for the different stimulus frequencies (4 to 30 Hz). We used the three neurovascular coupling mechanisms described above. The data were simulated using the parameter values summarised in
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.
We then looked at the behaviour of the fMRI signal predicted by the different coupling models for all frequencies.
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).
a) Measured BOLD response versus reversing frequency. The values on the yaxis correspond to per cent changes of the global mean signal. b) Frequencyresponse curve for EEG data. Each point corresponds to the amplitude of the evoked response (divided by the maximum response) at that frequency (
The frequencyresponse curve for the measured SSVERs is plotted in
When using the observed EEG and fMRI signals, the priors on the parameters corresponded to the parameter estimates obtained by
We then tested if Bayesian model comparison could be used to correctly decide upon which coupling model was used to generate the data, and if despite the small number of samples of fMRI compared to EEG we could still infer the right model.
We again generated data using the three coupling models as described above. We generated data for all the frequencies concatenated, with additive Gaussian observation noise:
We verified that Bayesian model comparison inferred the correct model in all cases, with a minimum Bayes factor of approximately 20 (logBayes factor of 3) (
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 logevidences relative to worst model. b) Corresponding model posterior probabilities.
As an aside, we note that, as with any gradientascent based optimisation algorithms, our inversion scheme is subjected to the possibility of running into local minima. However, one way to tackle this problem can be to initialise the inversion in different parameter regimes. In this work we have only observed once a clear case of local minimum, where the fit of one of the models to one session was extremely poor. We have then initialised the parameters with the estimates from other sessions and the inversion scheme was able to find new parameter estimates that provided a good fit to the data, similar to what was obtained for the other sessions.
Finally we fit the electrovascular model with the three different coupling mechanisms to the EEG and fMRI data. We used the same ‘multistep’ inversion procedure described in the previous section.
a) EEG timeseries (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.
Our analysis focused on the relevant contributions of synaptic and spiking activity models as a function of stimulation frequency. To this end we divided the stimuli into ‘lowfrequencies’ (4 to 15 Hz), ‘highfrequencies’ (10 to 30 Hz) and ‘allfrequencies’ (4 to 30 Hz) and the analysis was repeated for these three regimes. A summary of the model comparison results for all subjects can be found in
(MIX: mixture model; IN: synaptic input model; OUT: spiking output model): logmodel evidence relative to worst model (for low, high and all frequencies). These are group results for all subjects and sessions analysed (the logevidences are summed over subjects).
As can be seen in
However, when we analysed the high frequencies, the mixture model was found to be the best model with probability
For both regimes, the inferred neuronal firing rates were found to be commensurate with the stimulation frequency. Finally, an additional analysis across all frequencies revealed that the mixture model was the best model, again with probability
We note here that it has come as no surprise the fact that when we analyse all frequencies the mixture model was found to explain the data better than the input and output models alone. As we observe in
These results were robust to the choice of partition into low/high frequencies. Similar results (not shown) were obtained with partitions such as: lowfrequencies (4, 8, 10, 12 Hz) and highfrequencies (15, 20, 30 Hz).
In this paper we used EEGfMRI data and a biophysically informed mathematical model to investigate the relationship between neuronal activity and the BOLD signal in human visual cortex. In particular, we explored the contributions of synaptic input and spiking output activities to the generation of the BOLD response.
We have provided preliminary evidence that the BOLD signal is dependent upon both synaptic and spiking activity but that the relative contribution of these two factors are dependent upon the underlying neuronal firing rate. When the underlying neuronal firing is low then BOLD signals are best explained by synaptic input, in agreement with previous animal studies, such as
However, when the neuronal firing rate is high then both synaptic and spiking activity are required to explain the BOLD signal, as observed in, for example
One possible explanation for the increased performance of the output model with higher frequencies comes from neuroenergetic studies such as e.g.
Our results also support the conclusion that the relationship between synaptic activity, spikes and BOLD signals depends on the specific neuronal circuitry engaged in task processing. Moreover, one can speculate that different coupling mechanisms involving different types of cells and molecules could come into play depending on the task in question.
Despite our initial concern about the small number of fMRI samples compared to EEG, our initial results with synthetic data showed that it is possible to make inferences on different hypotheses for the neurovascular coupling using a generative modelling framework and Bayesian model comparison. The issue of different timescales was addressed by partitioning the estimation of electrical and vascular states into a multistep approach. In this approach we first estimated the electrical states and parameters from the EEG data and then integrated the full electrovascular model using these estimates. From the integrated model we extracted the input timeseries to the Balloon model, which we then inverted using BOLD data. The last two steps were repeated for each coupling model.
This method significantly increases the computational efficiency of the model inversion. However, this multistep approach is only possible with a deterministic model. In this work we used a deterministic version of the stochastic electrovascular model proposed by
It is also worth noting that despite the fact that the mixture model had more parameters than the input and output models, this extra complexity did not provide a significantly better fit to the data in the lowfrequency analysis than the input model. This complexity is correctly penalised using Bayesian methods, such as the one used here.
One concern about the coupling models defined here regards the definition of NO concentration. As mentioned in the
A natural extension to this work is the inclusion of multiple cortical units in the model representing multiple brain areas. For instance, subcortical areas such as the thalamus and other cortical areas activated by the experimental task could be included. Having more than one area would facilitate the differentiation between input and local processing synaptic activity, such as in
Another extension would be to probe the contribution of excitatory and inhibitory neuronal populations to the generation of BOLD signals, such as in
To our knowledge this paper presents the first quantitative model comparison of different biologically plausible mechanisms for neurovascular coupling in human cortex using EEGfMRI data and a realistic biophysical model.
However, even though our results were consistent across the three subjects and the majority of sessions, the case study approach adopted here has its limitations. Namely, it does not quantitatively address the issue of intersubject variability and it therefore precludes inferences at the population level. With a larger sample of subjects, intersubject variability can be accommodated using the RandomEffects (RFX) model selection approach developed by
Understanding the underlying biophysical mechanisms behind the coupling between neuronal activity and the BOLD response is vital not only for improving the interpretability of the BOLD response, but also for relating findings from fMRI research with results from other neuroscientific disciplines.
We present the full biophysical model (i.e. all the equations that comprise the neural mass model and Balloon model used in this work, as well as their parameter values). We also provide detailed results of model comparisons for all subjects and sessions.
(PDF)
We thank Oliver Josephs and Felix Blankenburg for acquiring the data and the FIL Methods group for helpful discussions.