Xiaodi Zhang^{1}, Wen-Ju Pan^{1}, and Shella Keilholz^{1}

^{1}Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, United States

### Synopsis

Many studies that involve simultaneous local field
potential (LFP) and blood-oxygenation-level dependent (BOLD) signal
measurements use correlation analysis, which assumes a linear relationship
between the two. To experimentally determine whether the relationship is linear,
we obtained a LFP vs BOLD response curve from simultaneous LFP and BOLD measurements.
The relationship between the two was nonlinear under isoflurane but not under
dexmedetomidine, which suggests that correlation may not always correctly
capture the relationship between LFPs and BOLD.

**Purpose**

Recent studies have shown the blood-oxygenation-level
dependent (BOLD) signal in resting-state fMRI is correlated with the power
modulations of the local field potential (LFP) under various conditions^{1-5}.
However, these analysis involving Pearson correlation automatically assume a
linear relationship between LFP and BOLD, which is not necessarily true. From
the perspective of basic neuroscience, the type of relationship between LFPs
and BOLD can help in interpreting neuroimaging studies. Here we closely
examined the simultaneous LFP and BOLD recording data, and found that the
relationship between LFP and BOLD can be nonlinear, depending on the anesthetic
agent used. Subsequent analysis suggests that such nonlinearity solely comes
from the non-Gaussian distribution of LFP power.**Methods**

Experiments: Resting state-fMRI scans
and LFP recordings were acquired simultaneously on 22 Sprague-Dawley rats, with
32 sessions from 12 rats under Isoflurane (ISO) ranging from 1.2% to 2%, and 22
sessions from 10 rats under dexmedetomidine (DMED) anesthesia (subcutaneous
infusion stepping from 0.05 mg/kg/h to 0.15 mg/kg/h after 1.5 hours). Single
slice gradient echo EPI scans were obtained on a 9.4T small animal MRI system
(Bruker, Billerica, MA) with scan parameters: TR/TE = 500/15ms, voxel size =
0.3*0.3*2mm, matrix size=64*64, repetitions=1000. LFPs were recorded using
glass electrodes placed on the primary somatosensory cortex (S1) in both
hemispheres at a sampling rate of 12KHz. FMRI preprocessing:
Motion-correction, spatially smoothing (FWHM=0.84mm), bandpass filtering
(0.01~0.1Hz under ISO and 0.01~0.25Hz under DMED), global signal and linear
trend regression were performed sequentially. LFP preprocessing: the
gradient-induced artifacts was removed following established methods^{4}
and the LFP time courses were low pass filtered to 100Hz. The LFP band-limited
power time courses were calculated by integrating the power spectral density
(PSD) function estimated from a 1-second long sliding window, (which moves 0.5
second at each step to match the fMRI temporal resolution) and then band pass
filtered (0.01~0.1Hz under ISO and 0.01~0.25Hz under DMED). LFP vs BOLD response:
both LFP and BOLD time points were z-scored and pooled together, then the BOLD
time points were evenly divided into 10 groups based on the amplitude, and the
LFP power time points a certain lag before the corresponding BOLD time points
(4 seconds under ISO, 2.5 seconds under DMED) were averaged within each BOLD
group, producing the experimental LFP vs BOLD response.**Results and Discussions**

Figure 1 shows the
relationship between LFP and BOLD using a scatter plot. It can be seen that the
LFP vs BOLD response (line plot) appear nonlinear under ISO and linear under
DMED, across almost all LFP frequency bands. This nonlinearity can be modeled
rather well by adding a quadratic term (shown in Figure 2), however, the origin
of the nonlinearity is not identified, and the quadratic term is difficult to
interpret. We noticed that under ISO, the LFP power distribution is positively
skewed (right tailed). So we hypothesized that the nonlinearity in the LFP vs
BOLD response solely comes from the non-Gaussian distribution of the LFP power
under ISO. Following the hypothesis, we evenly divided the LFP broadband power
into 10 groups, and within each LFP group, assigned the mean LFP amplitude of
each LFP group to the mean BOLD amplitude of its corresponding BOLD group (the
process is illustrated in Figure 3). The obtained theoretical LFP vs BOLD
response was then validated by fitting with the LFP power in individual
frequency bands. It can be seen from Figure 4 that the derived theoretical LFP
vs BOLD responses match fairly well with the experimental ones, suggesting the
nonlinearity solely comes from the non-Gaussian distribution of LFP power under
ISO anesthesia, which might be attributed to the burst firing. Since the
Pearson correlation coefficient only reflects linear dependency, considering
the nonlinearity present between LFP and BOLD, in the future it is reasonable
to use more generalized methods that do not assume linear relationship (e.g.
mutual information) when analyzing simultaneous LFP and BOLD measurements,
although preliminary analysis shows that correcting the nonlinearity does not
influence Pearson correlation coefficient significantly (Figure 5).**Conclusion**

We examined the simultaneous LFP and BOLD recording
data and found that the relationship between LFP and BOLD can be nonlinear,
depending on the anesthetic agent used. Under ISO there is clear evidence not
only showing the relationship is nonlinear, but also suggesting such
nonlinearity solely comes from the non-Gaussian distribution of LFP power. This
implies that in the future, more generalized methods that do not assume linear
dependency might be preferred to correlation analysis, although in this
particular situation under ISO, the nonlinearity has little impact on the
Pearson correlation coefficient.### Acknowledgements

Funding sources: NIH 1 R01NS078095-01, BRAIN initiative and
NSF INSPIRE. The authors would like to thank Chinese Scholarship Council (CSC)
for financial support.### References

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