Neuronal synchrony and the relation between the blood-oxygen-level dependent response and the local field potential

<div><p>The most widespread measures of human brain activity are the blood-oxygen-level dependent (BOLD) signal and surface field potential. Prior studies report a variety of relationships between these signals. To develop an understanding of how to interpret these signals and the relationship between them, we developed a model of (a) neuronal population responses and (b) transformations from neuronal responses into the functional magnetic resonance imaging (fMRI) BOLD signal and electrocorticographic (ECoG) field potential. Rather than seeking a transformation between the two measures directly, this approach interprets each measure with respect to the underlying neuronal population responses. This model accounts for the relationship between BOLD and ECoG data from human visual cortex in V1, V2, and V3, with the model predictions and data matching in three ways: across stimuli, the BOLD amplitude and ECoG broadband power were positively correlated, the BOLD amplitude and alpha power (8–13 Hz) were negatively correlated, and the BOLD amplitude and narrowband gamma power (30–80 Hz) were uncorrelated. The two measures provide complementary information about human brain activity, and we infer that features of the field potential that are uncorrelated with BOLD arise largely from changes in synchrony, rather than level, of neuronal activity.</p></div

Decomposing electrocorticographic (ECoG) data into three summary components.

<p>(A) A schematic to show the summary metrics derived from ECoG spectra: broadband power elevation (bb), narrowband gamma (ϒ), and alpha (α). Broadband was calculated by the increase in a 1/fⁿ signal, gamma was calculated by fitting a Gaussian on top of the 1/fⁿ line, and alpha was calculated as the difference from baseline in the alpha-frequency range. (B) Power spectrum for one example electrode during a blank stimulus (black), gratings (red), and noise patterns (blue). (C) From the power spectrum, changes in broadband, gamma, and alpha were calculated. These values were bootstrapped 100 times across trials. Error bars represent 68% confidence intervals. (code to download data and reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script03_Fig3.m).</p

Pooling with different orders of operations can have a large effect on measured brain signals.

<p>(A) The approach to directly correlate local field potential (LFP) and blood-oxygen-level dependent (BOLD) data. (B) The current approach to relate the LFP and BOLD from the same neuronal population activity. (C) In this illustration, the currents of two neurons (x₁ and x₂) has the shape of a sinusoid with noise, and the sinusoid is in phase between the two neurons. In the simulated electrode measurement, the signals are summed and the power is calculated (POWER[SUM] = 2.00). In the simulated measurement of metabolic demand, the power of each of these neurons is first calculated and then summed across the neurons (SUM[POWER] = 1.01). Here, the LFP and BOLD are both large. (D) In this illustration, the membrane currents of two neurons (x₁ and x₂) are the same as in panel (C) except that the two time series are in counterphase. Here, unlike (C), the LFP is nearly 0 and the BOLD signal is large (code to reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script01_Fig1.m).</p

The effect of varying simulated neural inputs on output spectra.

<p>The effect of manipulating one of the three neural inputs used in the simulations produced different effects in the spectral power of the local field potential (LFP) of 200 neurons. (A) For <i>C</i>^<i>1</i> (broadband), a high amplitude results in a broadband power elevation, with no narrow peaks in the spectrum. (B) For <i>C</i>^<i>2</i> (gamma), a high correlation results in a narrowband gamma power elevation, with no broadband elevation or change in alpha power. (C) For <i>C</i>^<i>3</i> (alpha), a high amplitude input results in a narrowband power elevation in the alpha band, with no change in broadband power or narrowband gamma power. For each spectrum in each plot, 10 simulated trials were run. The plotted spectra are averaged across the 10 trials and are computed from <i>I(t)</i>, the time series after leaky integration of the inputs. (Code to reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script05_Fig5.m).</p

The correlation between blood-oxygen-level dependent (BOLD) and local field potential (LFP) as a function of frequency.

<p>(A) The correlation between electrocorticographic (ECoG) and BOLD for the V1 data shows a positive correlation between ECoG and BOLD for a broad range of frequencies, except those including the alpha changes. Gray lines represent the 9 individual V1 electrodes, the black line is the average, and the red line corresponds to the example sites shown also in <b><a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001461#pbio.2001461.g007" target="_blank">Fig 7</a></b>. (B) In the V2/V3 data, there was a strong negative correlation between ECoG and BOLD in the alpha range around 10 Hz and a positive correlation between ECoG and BOLD for a broad range of frequencies. Gray lines represent the 13 individual V2/V3 electrodes, the black line is the average, and the red line corresponds to the example electrode shown also in <b><a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001461#pbio.2001461.g007" target="_blank">Fig 7</a></b>. Note that neither the V1 electrodes nor the V2/V3 electrodes show a peak at the gamma frequency. (C) The correlation between LFP and BOLD for simulations fit to V1 shows that there is a positive correlation across most frequencies, except those including the alpha and gamma changes. (D) The correlation between LFP and BOLD for the simulations fit to V2/V3 shows that there is a strong negative correlation around 10 Hz and a positive correlation across a broad range of frequencies. (Code to download data and reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script10_Fig10.m).</p

Accuracy of predicted blood-oxygen-level dependent (BOLD) signals from simulated neuronal activity.

<p>(A) Simulated BOLD (<i>x</i>-axis) versus measured BOLD (<i>y</i>-axis) for a V1 site. Each color corresponds to one stimulus condition (red dots, grating patterns; blue dots, noise patterns; black dot, uniform stimulus, or blank). Error bars indicate 68% confidence intervals, bootstrapped 100 times over 30 trials per stimulus for simulation and over repeated scans for BOLD data. (B) The same as A but for a V2 site. (C) The accuracy of BOLD predictions for all V1 and V2/V3 sites. Each site is indicated by a yellow dot. The orange lines show the medians and the red boxes the 0.25 and 0.75 quantiles. The thin, gray, solid lines show the BOLD data-to-data reliability, and the gray dashed lines show the accuracy when the BOLD data and trial conditions are shuffled in the training dataset. Accuracy is quantified as the coefficient of determination after subtracting the mean from the data and the predictions, and dividing each variable by its vector length. Because the simulations were fit to electrocorticographic (ECoG) data and tested on BOLD data, the predictions are cross-validated, and the coefficient of determination spans (−∞,1]. A value of −1 is expected when the data and predictions are unrelated and have equal variance, as in the case of the shuffled control analysis. (Code to reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script07.m).</p

The accuracy of predicted blood-oxygen-level dependent (BOLD) signals from electrocorticographic (ECoG) components.

<p>The correlation between ECoG and BOLD was calculated for a V1 site and a V2 site. The locations of one sample electrode in V1 and one in V2 are indicated by the enlarged white discs on the cortical surface for subject 1. (A) In a foveal V1 site, the broadband ECoG amplitude accurately predicted the BOLD signal (left). Error bars show 68% confidence intervals across bootstraps. Narrowband gamma power (center) and alpha power (right) were uncorrelated with BOLD. (B) In a V2 site, the broadband ECoG was weakly correlated with BOLD (left). Narrowband gamma did not predict BOLD (middle). Alpha was negatively correlated with BOLD (right). Scatter plots for all other V1 and V2/V3 sites are shown in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001461#pbio.2001461.s005" target="_blank">S5 Fig</a>. (C-D) The same as A and B but for simulated neuronal population data fit to the V1 and V2 ECoG data. For all panels: data points are the bootstrapped median across 30 trials per stimulus (ECoG) and across scans (BOLD). The trend lines are least square fits to the 8 data points plotted. The <i>R</i>^<i>2</i> values are the coefficient of determination computed by cross-validation, with a regression fit to half the data and evaluated on the other half. The black outlines indicate the regressions that show reliable predictors of the BOLD signal—broadband in V1, broadband and alpha in V2/V3. (Code to download data and reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology function" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology function</a> ns_script09A_Fig8AB_Fig9AB.m and function ns_script07B_Fig7AB_Fig8CD.m).</p

Simulated local field potential (LFP) and blood-oxygen-level dependent (BOLD).

<p>(A) Three different inputs to each neuron were simulated: a broadband, random input with a small positive offset (<i>C</i>^<i>1</i>), an oscillatory input with a time scale of 40 Hz to 60 Hz (<i>C</i>^<i>2</i>), and a negative input with a time scale of 10 Hz (<i>C</i>^<i>3</i>). (B) The 3 inputs (<i>C</i>^<i>1</i>, <i>C</i>^<i>2</i>, <i>C</i>^<i>3</i>) were summed in each neuron to produce the total input to the neuron. (C) The total input was passed through a leaky integrator to produce the dendritic dipole current (<i>I</i>_<i>i</i>). The LFP was simulated by summing the dendritic currents. (D) The BOLD signal was simulated by taking the power of the dendritic current for each neuron and then summing across neurons. (Code to simulate data reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script07D_Fig4.m).</p

Explained variance in the blood-oxygen-level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal in the simulations and in data.

<p>(A) Variance in the measured BOLD signal explained by broadband, gamma, and alpha changes in the electrocorticographic (ECoG) data. The colored box plots show the variance explained by each of the 7 model types: black bar = median, upper and lower boxes = quartiles, and error bars = data range excluding outliers (outliers plotted as red plusses). The <i>R</i>^<i>2</i> was cross-validated (split between subjects for BOLD and stimulus repetitions for ECoG) to ensure that the <i>R</i>^<i>2</i> can be compared between models with different numbers of explanatory variables. Gray dashed lines indicate the noise floor (<i>R</i>^<i>2</i> when shuffling the BOLD labels in the training data), and the solid gray lines indicate the data-to-data reliability for the BOLD signal. Bottom: the regression coefficients show whether the broadband, gamma, and alpha signals were positive or negative predictors of the BOLD signal. A red * in the lower plot indicates whether regression coefficients differed significantly from 0 by a bootstrap test (<i>p</i> < 0.05). (B) The same as A but for the 13 V2/V3 electrodes. (C) The same as A but for the 9 simulations fitted to V1 data. The <i>R</i>^<i>2</i> was cross-validated (split between even and odd stimulus repetitions). D) Same as C, except for the 13 simulations fitted to the V2/V3 data. (Code to download data and reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a>).</p

The influence of time series parameters on the power of the sum, the sum of the power, and the cross-power.

<p>(A) LFP power, computed as the power of the sum of 5 time series from a multivariate Gaussian distribution (<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001461#pbio.2001461.e007" target="_blank">Eq 6</a>). The LFP power is shown as a function of the correlation (ρ), variance (σ), and mean (μ) of the time series (<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001461#pbio.2001461.e008" target="_blank">Eq 7</a>). (B) The same as A, except plotting the sum of the power rather than the power of the sum, in order to model the BOLD signal. (C) The same as B but for cross-power. The power of the sum—Panel A—is the sum of the terms in Panels B & C. (Code to reproduce this figure can be found on <a href="https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology" target="_blank">https://github.com/dorahermes/Paper_Hermes_2017_PLOSBiology</a> function ns_script02_Fig2.m).</p