Cerebral Cortex January 2013;23:210– 209
doi:10.1093/cercor/bhs008
Advance Access publication January 31, 2012
Analysis of Time and Space Invariance of BOLD Responses in the Rat Visual System
Christopher J. Bailey1,2,3,4, Basavaraju G. Sanganahalli1,2,5, Peter Herman1,2,5, Hal Blumenfeld2,6,7, Albert Gjedde3,4 and
Fahmeed Hyder1,2,5,8
1
Magnetic Resonance Research Center (MRRC) and 2Core Center for Quantitative Neuroscience with Magnetic Resonance
(QNMR), Yale University, New Haven, CT 06520, USA, 3Center of Functionally Integrative Neuroscience, Aarhus University,
DK-8000 Aarhus, Denmark, 4Pathophysiology and Experimental Tomography Center, Aarhus University Hospitals, DK-8000 Aarhus,
Denmark, 5Department of Diagnostic Radiology and 6Department of Neurology and 7Department of Neurobiology and 8Department
of Biomedical Engineering, Yale University, New Haven, CT 06520, USA
Address correspondence to D. S. Fahmeed Hyder, N143 TAC (MRRC), 300 Cedar Street, Yale University, New Haven, CT 06520, USA. Email:
[email protected].
Neuroimaging studies of functional magnetic resonance imaging
(fMRI) and electrophysiology provide the linkage between neural
activity and the blood oxygenation level--dependent (BOLD) response.
Here, BOLD responses to light flashes were imaged at 11.7T and
compared with neural recordings from superior colliculus (SC) and
primary visual cortex (V1) in rat brain—regions with different basal
blood flow and energy demand. Our goal was to assess neurovascular coupling in V1 and SC as reflected by temporal/spatial
variances of impulse response functions (IRFs) and assess, if any,
implications for general linear modeling (GLM) of BOLD responses.
Light flashes induced high magnitude neural/BOLD responses
reproducibly from both regions. However, neural/BOLD responses
from SC and V1 were markedly different. SC signals followed the
boxcar shape of the stimulation paradigm at all flash rates, whereas
V1 signals were characterized by onset/offset transients that
exhibited different flash rate dependencies. We find that IRFSC is
generally time-invariant across wider flash rate range compared with
IRFV1, whereas IRFSC and IRFV1 are both space invariant. These
results illustrate the importance of measured neural signals for
interpretation of fMRI by showing that GLM of BOLD responses may
lead to misinterpretation of neural activity in some cases.
Keywords: calibrated fMRI, local field potential, multiunit activity,
neuroenergetics, neurometabolic coupling, transfer function
Introduction
Functional magnetic resonance imaging (fMRI) is widely used
to map brain activity in humans and animals because of its high
spatiotemporal resolution and extensive volumetric coverage.
The popular use of fMRI relies on the fact that the blood
oxygenation level--dependent (BOLD) signal is a noninvasive,
albeit indirect, indicator of neural activity (Ogawa et al. 1990).
The BOLD signal is actually an index of the hyperemic
response, which has both hemodynamic (blood flow and
volume) and metabolic (oxidative energy metabolism) contributions (Hyder et al. 2001). Hence the interpretation of fMRI
results depends on the connection between the hyperemic
response and neural activity (for a recent review, see Hyder
et al. 2010), as indicated by neural spiking rate of multiunit
activity (MUA) and/or integrative processes reflected by local
field potentials (LFPs).
In experimental settings where neural activity cannot be
readily measured in conjunction with fMRI, general linear
modeling (GLM) of the BOLD response is used to decipher the
underlying, albeit unmeasured, neural activity (Friston 1998).
Today, GLM is the most prevalent method to examine fMRI
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time series from human experiments, both with and without
task (Frackowiak 2004; Huettel et al. 2004). When applied in
the most common context of activation detection, the GLM
consists of an assumed underlying ‘‘neural activity function’’
(typically where the stimulus paradigm itself is used as the
neural time course) that is convolved with a hemodynamic
response function (HRF) representing neurovascular coupling.
Coupling linearity is explicitly assumed, and hence, in its most
commonly applied form, GLM is undefined for nonlinear
effects, whether they are temporal or spatial in nature.
Studies exploring the neurophysiological basis of fMRI—now
being conducted in many laboratories for various systems and
species (Logothetis et al. 2001; Smith et al. 2002; Kim et al.
2004; Maandag et al. 2007; van der Linden et al. 2007; Goense
and Logothetis 2008; Huttunen et al. 2008; Pawela et al. 2008;
Liu et al. 2009)—aim to describe the link between neural
activity and the BOLD response. When both electrical and
vascular signals are measured in identical stimulation conditions, one may quantify this link in the form of an impulse
response function (IRF). An IRF, generated by deconvolution of
the measured neural activity from the measured BOLD
response, characterizes the neurovascular coupling for a given
region (Iadecola 2004) and can even be used to calibrate the
BOLD response (Herman et al. 2009; Sanganahalli et al. 2009b).
Another important IRF research direction for fMRI, however, is
to determine how widely applicable is the suggested link
between changes in neural activity and the BOLD response
across experimental conditions (e.g., across regions or variable
stimuli), because IRF estimation is an identification method
applicable to linear systems (Hespanha 2009). To accurately
interpret fMRI data, it is vital to know whether the timeinvariance assumption holds for a wide range of stimulus
parameters and how space-invariant IRFs are across regions
with divergent basal hemodynamics and metabolic demand
(Boynton et al. 1996; Engel et al. 1997).
Based on the hypotheses that neurovascular couplings in the
rat visual system are similar 1) across brain regions and 2) for
varying flash rates, we sought to evaluate temporal and spatial
variances of IRFs and their implications for GLM of BOLD
responses. We measured BOLD responses to light flashes at
11.7T in rat brain and compared these signals with extracellular
recordings from superior colliculus (SC) and primary visual
cortex (V1), two regions which have different basal blood flow
and energy demand (Iadecola et al. 1983; Klein et al. 1986;
Borowsky and Collins 1989; Maeda et al. 1998). A binocular
stimulus delivery system allowed variations of light color and
flash rate to evoke reproducible BOLD and neural responses at
a single-trial level. Although neural and BOLD responses to
blue/green light generally agreed with each other, responses
from V1 and SC were noticeably different. We find that timeinvariance holds for a wide range of flash rates in SC but not in
V1, whereas IRFSC and IRFV1 are both space invariant. These
results suggest caution in using GLM of BOLD responses
because of the potential to misconstrue underlying neural
activity for varying stimulus rates.
Materials and Methods
Animal Preparation
All procedures were performed in accordance with protocols approved
by the Yale University Institutional Animal Care and Use Committee, in
agreement with the National Institutes of Health Guide for the Care and
Use of Laboratory Animals. Experiments were conducted on artificially
ventilated (70% N2O/30% O2) adult male rats (Long Evans; 220--350 g;
Charles River, Wilmington, MA). A femoral artery was cannulated (PE-50)
for monitoring physiological parameters (pCO2, pO2, pH, and blood
pressure), and a femoral vein was cannulated (PE-10) to administer Dtubocurarine chloride (initial 0.5 mg/kg; supplemental 0.25 mg/kg/h)
and other substances. The rats were initially anesthetized with isoflurane
(3--4%) to minimize stress caused by injection of urethane (1.3 g/kg,
intraperitoneal), which was used to maintain anesthesia throughout the
experiment. Additional doses of urethane (0.13 g/kg, intravenous) were
administered if necessary depending on the duration of the experiment.
Ventilation parameters were adjusted to maintain normal physiology.
The animal core temperature was measured by a rectal probe and
controlled by a heated water blanket maintained at ~37 C. Adequate
analgesia was ensured by monitoring the pain response to an automated
electrical (5 mA, 0.3 ms, 3 Hz, 1--5 s) tail pinch every 15 min in general,
but not during the visual stimulation protocol.
Stimulus Presentation and Paradigms
Details of the stimulus delivery system are given elsewhere (Sanganahalli,
Bailey, et al. 2009), but briefly summarized here and illustrated in
Supplementary Figure 1. A computer-controlled CED l1401 analog-todigital converter unit (CED unit) and Spike2 software (Cambridge
Electronic Design, Cambridge, UK) were used to control stimulator
output and record measured data for off-line analysis. The design of the
setup allows control of light intensity and duration of flashes
continuously, whereas wavelength (color) could be varied between
trials by selecting a different light source amongst the chosen light
emitting diodes (LEDs; Luxeon Star III, Lumileds Lighting, LLC, San Jose,
CA; wavelengths blue = 455 nm, green = 530 nm, and red = 627 nm). We
used acrylic collimator lenses to target the wide-angle LED light into
optical cables (Fiber Optic Products, Clearlake Oaks, CA), which
attached to cradles in front of the LEDs. Two thin (inner/outer diameters
of 1.0/2.3 mm) polyethylene-coated fibers for independent stimulation of
each eye were led into the scanner room (Faraday cage) through small
access holes in the sidewall (back wall). A fiberglass platform in front of
the animal held in place and allowed the positioning of the thin cables by
means of cylindrical anchoring constructions, which also slightly
dispersed the light thus increasing the viewing angle of the stimuli.
We thus estimated the portion of the visual field subtended by each
stimulus to be approximately 35--50 azimuth and 10--40 elevation
relative to the horizontal meridian. However, as each emitted beam of
light illuminated the entire eyeball, the stimuli essentially cover the full
visual field. The illuminance of each color stimulus was measured before
each experiment, in order to ensure equal intensities for left and right
visual fields. The calibration was performed in Lux units using a standard
light meter (Extech Instruments, Waltham, MA). We emphasize that we
did not strive to attain equal illuminances between colors, as the Lux is
a measure dependent on human subjective intensity ratings, and thereby
ultimately on the properties of the human retina. The dim ambient
lighting conditions, that is, only reflections from distant halogen ceiling
lights, in the MR as well as electrophysiology settings, were not
considered to bias the detection of the stimuli toward any particular
wavelength. Beyond these low-light settings, the rats were not dark
adapted for the measurements. A standard block stimulation protocol was
used in all experiments with at least 300 s between consecutive trials.
Electrophysiology Experiments
Rats were mounted on a stereotaxic frame (David Kopf Instruments,
Tujunga, CA) placed on a vibration-free table inside a Faraday cage. The
scalp and the ‘‘galea aponeurotica’’ were removed and small burr holes
were drilled for insertion of high-impedance tungsten microelectrodes
(2--4 MX; FHC, Bowdoinham, ME) that measured neural electrical
signals. The coordinates for electrode placement were guided by our
fMRI data and the atlas of Paxinos and Watson (1998). With reference
to bregma and the sagittal midline plane, the electrodes were placed in
the following coordinates: V1 (–6.5 mm posterior, 3.5 mm lateral, ~1
mm from dura) and SC (–7.0 mm posterior, 0.8 mm lateral, 2.4--2.6 mm
from dura). Electrical signals were digitized at 20 kHz with CED l1401
using Spike2. LFP and MUA were obtained by splitting the electrical
signal into low ( <300 Hz) and high (400 Hz--10 kHz) frequency bands
using an online analogue Butterworth filter (24 dB/oct attenuation).
Off-line data analysis was performed using custom scripts in Matlab
(The MathWorks, Inc., USA). The MUA signal was squared and resampled
to a sampling rate of 8 Hz using the Matlab function decimate. The
resampling procedure was recursive in several steps, each decimation
stage being at maximum 10. The function decimate was applied using
a 30th order FIR lowpass filter and forward and backward filtering passes
to avoid distorting the phase of the signals (i.e, because the timing of
peaks would otherwise be affected). Then finally, the signals were
smoothed using a 1.25-s zero-phase moving average FIR filter, and square
rooted to obtain a root-mean-square (RMS) representation of the signal
power similar to Stark and Abeles (2007).
fMRI Experiments
The fMRI data were obtained on a modified 11.7T Bruker horizontal-bore
spectrometer (Bruker AVANCE, Billerica, MA) using a 1H surface coil
(diameter 1.4 cm). Details of fMRI measurements are discussed
elsewhere (Sanganahalli et al. 2008). Briefly, BOLD contrast images were
acquired using echo-planar imaging with sequential sampling (Hyder
et al. 1995) and the following parameters: repetition time = 1000 ms;
echo time = 15 ms; field of view = 2.56 3 2.56 cm2; image matrix = 64 3
64; number of slices = 5; slice thickness = 1 mm; and flip angle = 60. The
neuroanatomy was imaged with the rapid acquisition relaxation
enhanced (Hennig et al. 1986) or the fast low-angle single shot (Frahm
et al. 1986) contrast sequences. In the anesthetized rat, different gradient
amplitude and pulsing rates do not change the blood pressure and
electrical recordings outside the magnet (on the bench) and inside the
magnet (during an fMRI scan) are similar (Englot et al. 2008).
Analysis of fMRI data was performed on a trial-by-trial basis using
custom-written routines in Matlab. Trials with excessive motion
artifacts, defined by translational movement in excess of a quarter of
the voxel size and estimated using center-of-mass analysis, were
rejected. Each voxel’s BOLD data were subjected to a Student’s t-test
comparing the mean of the 30 s baseline to that of the stimulation
period. A significance threshold of P < 0.01 (uncorrected for multiple
comparisons) was used to create maps showing the activated tissue
area. Thresholded t-maps were overlaid on corresponding structural
images for visualization and used to define a region-of-interest (ROI) for
extraction of the BOLD signal time course. For responses lacking
sustained stimulus-induced signal increases, signal time courses were
extracted using an ROI defined by other stimuli. Before averaging
across activated voxels, the data were normalized to the baseline
period, thus yielding plots of DS/S.
Estimation of IRF
We modeled the 1-Hz BOLD signal as the output with MUA signal as the
input.
ð1Þ
BOLDiR ðt Þ[h R ðt Þ5MUAjR ðt Þ;
where BOLDiR MUAjR is the ith (jth) BOLD (MUA) records in region
R:{V1, SC}, the transfer function hR(t) is independent of i and j, and 5
denotes convolution. Since the general deconvolution problem of
Cerebral Cortex January 2013, V 23 N 1 211
estimating h(t) from BOLD-MUA pairs is ill-conditioned, we used the
gamma variate function (Madsen 1992) as the IRF
t 1ttp a
hðt Þ=A
e
;
ð2Þ
tp
where A is a scaling constant, tp is the peak time, and a is related to the
width of the function. We used standard nonlinear optimization (Matlab
function lsqcurvefit with trust region reflective algorithm) to find the
minimize the squared
difference between
parameters {A,tp,a} that
measured BOLDiR ðt Þ and modeled BOLD h R ðt Þ5MUAjR ðt Þ for i,j =
{1,. . . ,11} (121 pairs). The final parameter estimates were obtained by
averaging over all fits after regularizing against outliers by removing the
5% of the largest and smallest tp 3 a-products (corresponding to late
sharp and early broad peaks, respectively).
GLM of BOLD Response
A model-based analysis was performed on a subset of the data to
examine frequency-dependent effects. A single gamma variate was
chosen as the canonical HRF with tp =3.23 s and a = 11.33. The boxcar
regressors of the GLM were defined as follows and subsequently
convolved with the canonical HRF: initial onset response (0--2 s),
sustained response (0--30 s), offset response (31--33 s), and poststimulus signal elevation (31--90 s). Parameter estimates for ROI time
courses were obtained using ordinary least squares in Matlab. Statistical
parametric maps were calculated voxel-by-voxel using NeuroLens
(www.neurolens.org) after smoothing with a 0.8 mm full-width at halfmaximum Gaussian spatial filter.
Results
Color Sensitive Responses at a Single-Trial Level
Strong BOLD responses were observed in V1 and SC. Figure 1A
illustrates the activation maps above the selected threshold (30
s stimulation vs. 30 s baseline; P < 0.01) for 2 consecutive trials
of 1-Hz visual flash stimulation in one animal. Cortical
responses extended into surrounding secondary visual processing areas (V2), but peaked in slices approximately 6--7 mm
posterior to bregma, ~3.5 mm lateral to midline, and at a depth
of 1--1.2 mm relative to dura, which corresponds approximately
to layers IV--V in the V1 area. Retinal ganglion cells project
directly to the most dorsal layers of the SC, where maximal
BOLD responses were observed, approximately 7--8 mm
posterior to bregma, 0--1 mm lateral to midline, and at a depth
of 2.2--2.8 mm relative to dura. These coordinates were used for
subsequent microelectrode examinations of neural responses
to identical stimulation conditions. We limited our focus on V1
and SC responses because the surface transceiver coil was
positioned optimally to detect BOLD signals from these
regions. Thus low signal-to-noise ratio was observed in the
more anterior dorsal lateral geniculate (DLG) nucleus of the
thalamus (~4--5 mm posterior to bregma).
We anticipated, based on known retinal morphology of the rat
(see Discussion), that responses to red light flashes would be
poorer in eliciting neural and BOLD responses compared with
green and/or blue light flashes. Indeed, Figure 1B illustrates that
our paradigm is sufficiently sensitive to detect color-dependent
neural and BOLD responses at a single-trial level. Figure 1B
shows the effect of varying stimulus color (wavelength) for 2
individual animals (one for BOLD, another for MUA). Blue and
green light consistently produced responses of similar magnitude and temporal evolution in both V1 and SC. Cortical
responses to red light tend to be slightly weaker and less robust
compared with other colors, particularly in the SC (Figure 1B,
left). The spatial overlap of the BOLD responses to different
212 Dynamic and Regional BOLD Impulse Response Functions in Rat Visual System
d
colors is practically complete, with fewer significantly modulated voxels during red than blue/green stimulation, particularly
in the SC (Supplementary Fig. 2). We, therefore, analyzed trials
with green and blue light, whereas red light trials are not
included in subsequent analysis.
Differential V1 and SC Response Characteristics
Because V1 and SC signals were measured simultaneously,
whether they are in fMRI studies with the rat inside the magnet
or electrophysiology recordings with the rat on the bench, we
quantified BOLD and neural response reproducibility over trials
and animals by calculating the pairwise cross correlations of V1
and SC time courses in 11 representative trials in 6 animals and
plotted the squared correlation coefficient (Pearson R2) value
for each V1 3 V1, SC 3 SC, and V1 3 SC trial pair (gray scale
coded 11 3 11 matrix). We used the 1-Hz flash rate data for this
analysis. The darker shade in the correlation matrices in
Figure 2A indicate that stronger correlations are observed
within than across regions, more so for BOLD data than MUA
data (presumably because the initial onset response of the
former occupies a larger portion of the 30-s stimulation period)
used in the cross correlations. The mean (±1 standard deviation
[SD]) R2 between individual trials is 0.65 (±0.11) for V1 BOLD,
0.65 (±0.12) for SC BOLD, 0.76 (±0.09) for V1 MUA and 0.87
(±0.07) for SC MUA. In comparison, the cross regional (V1 3
SC) trial-by-trial correlations are smaller for BOLD (0.37 ± 0.15)
and MUA (0.68 ± 0.08) data (see bar graph insets in Fig. 2A).
The average V1 and SC response time courses to the 1-Hz
flash rate are shown for both BOLD (Fig. 2B) and MUA (Fig. 2C).
The V1 neural recordings exhibit a sharp onset transient (tpeak =
327 ± 79 ms), an initial rapid decay (peak-to-plateau = 791 ±
158 ms), followed by a plateau of more gradual decline in
response amplitude until cessation of the stimulus. The V1
mean plateau-to-peak ratio is 38.0 ± 12.0%. In contrast, the SC
shows a rapid rise to peak (382 ± 275 ms) but only moderate
decline during sustained stimulation. Similar dynamics were
obtained for the 80--200 Hz band of the LFP signal (for a full
time-frequency decomposition, see Supplementary Fig. 3 and
for details on the wavelet filtering applied, see Supplementary
Methods). The BOLD data are in excellent agreement with the
neural signals, indicating similar neurovascular coupling mechanisms in the 2 regions during 1 Hz stimulation. The V1 and SC
BOLD signal peaks occur at 5.2 ± 0.7 s and 5.8 ± 1.4 s,
respectively. The V1 plateau-to-peak ratio is 34.0 ± 11.0%. Note
that the V1 MUA signal, and correspondingly the V1 BOLD,
exhibits a transient event to stimulus train offset (30--32 s for
MUA; see arrows in Fig. 2B,C).
The averaged BOLD and neural temporal response profiles in
response to higher flash rates (5 and 10 Hz, respectively) are
shown in Figure 3A,B. Several features of the response
dynamics remain similar to the 1 Hz flash rate data (Fig. 2),
but differences are also evident at both 5- and 10-Hz flash rates
for SC and V1. A remarkable feature is that the plateau of the
BOLD response in V1 (but not its neural response) is strongly
attenuated at the 10 Hz flash rate, revealing neurovascular
uncoupling (i.e., MUA > BOLD during sustained response in
V1). Likewise in SC, the prominent offset BOLD response (but
not in its neural response) is augmented at the 10-Hz flash rate,
revealing neurovascular uncoupling but in the opposite direction from that observed in V1 (i.e., BOLD > MUA during
offset response in SC). The regional neurovascular uncouplings
for onset, sustained, and offset parts of the responses at 10-Hz
Bailey et al.
Figure 1. BOLD and neural responses to light stimulation in the rat visual system. (A) BOLD activation maps from 2 trials of green light 1 Hz flash stimulation executed on the
same animal (two-sample Student’s t-test between 30 s baseline and 30 s stimulation periods, thresholded at P 5 0.01, i.e., log(P) 5 4.6). Significant signal increases were
observed in the middle cortical layers of the primary (V1) and secondary (V2) visual areas, and in the dorsal layers of the superior colliculus (SC). The z-coordinates between slices
are relative to bregma (Paxinos and Watson 1998). (B) Single trial time courses of BOLD (top) and neural (bottom) responses to red, green, and blue light (1-Hz stimulation
blocks). BOLD and MUA data from V1 (right) and SC (left) show color dependence, where close resemblance of BOLD and neural responses are observed with green and blue
light. In comparison, red light induces weaker responses in both V1 and SC. The black horizontal bar below each plot marks the stimulation period (30 s). For illustration of the
custom-made nondark adapted binocular stimulus delivery system and regional overlap of BOLD activation maps with different light colors, see Supplementary Figures 1 and 2,
respectively.
flash rate are summarized in Table 1. For both of these features
observed in SC and V1, it can be argued that the neurovascular
uncoupling is maximum at 10-Hz flash rate, but the trend is
partly detectable at 5 Hz (but absent at 1 Hz) flash rate.
Supplementary Figures 4 and 5 represent the time-frequency
decompositions of the 5- and 10-Hz LFP data and illustrate the
good agreement between the MUA data shown in Figure 3 and
the 80--200 Hz band LFP signals.
IRFV1 and IRFSC for 1-Hz Flash Rate
To quantify the extent of neurovascular coupling in V1 and SC,
we estimated the parameters of the IRF (i.e., h (t) in equations
(1) and (2)) that lead to optimal fits between the measured and
modeled BOLD responses based on the convolution between
MUA and the IRF. We used the 1 Hz data shown in Figure 2 for
the estimation of h (t), leading to 121 pairs of MUA and BOLD
signals in both V1 and SC. For numerical tractability, we limited
the optimization to the 3 parameters (amplitude, peak, and
width) of the gamma variate family of functions. Furthermore,
the fitting time of each data set was limited to [–5, 40] s (i.e., to
mainly the stimulation period; for details on the estimation
procedure, see Materials and Methods).
The estimated IRFs for V1 and SC data at 1-Hz flash rate are
shown in Figure 4. The peak and width parameters of the IRFs
are of similar magnitude and estimates statistically indistinguishable (overlapping SDs): IRFV1 and IRFSC peak at 2.5 ± 0.5 s
Cerebral Cortex January 2013, V 23 N 1 213
Figure 2. BOLD and neural temporal response profiles in V1 and SC differ significantly. (A) Trial-by-trial reproducibility analysis of 11 examples of BOLD and neural responses to 1Hz flash stimulation (data from 6 animals). Each matrix, BOLD signal left, and MUA right, illustrates the R2-values for pairwise cross correlations between single trial time courses
from the same region (V1 3 V1 and SC 3 SC, i.e., intraregional) as well as those between time courses from different regions (V1 3 SC, i.e., interregional). The adjacent bar
graphs summarize these results, indicating higher correlations within a given region than between regions, due to different signal time courses in V1 and SC. (B and C) Average
time courses (±SD) of BOLD signal and MUA measured from V1 (black) and SC (gray) for 1-Hz flash stimulation. The time courses of BOLD and MUA from V1 show a prominent
onset peak, and a weaker but noticeable offset transient (arrows). The gray horizontal bar represents the stimulation period (30 s). For illustration of the corresponding LFP data,
see Supplementary Figure 3.
and 2.0 ± 1.1 s, respectively, with widths at half height of 1.5 ±
0.4 s and 1.4 ± 0.3 s. These large variations of the peaks and
widths of the IRFs are due to intersubject variations. Thus, we
conclude that there is no evidence supporting different
neurovascular (BOLD-MUA) couplings in V1 and SC during 1Hz flash stimulation. We repeated the estimation procedure
using the power in the 80--200 Hz band of the LFP signal as the
neural input function (for equations (1) and (2)). The IRFs
generated for the ‘‘high-gamma’’ LFP and BOLD responses are in
close agreement to those obtained for BOLD and MUA
responses (data not shown). We also calculated IRFs for SC
and V1 at 5-Hz flash rate and found negligible differences from
IRFs with 1-Hz flash rate (data not shown). However (linear)
IRFs at 10-Hz flash rate are not defined due to the inherent
neurovascular uncouplings observed in V1 during the sustained
response (MUA > BOLD) and in SC during the offset response
(BOLD > MUA) (see Table 1 and Fig. 3).
214 Dynamic and Regional BOLD Impulse Response Functions in Rat Visual System
d
Temporal Invariance of the IRF
We tested the temporal invariance of the IRFs estimated for the
1-Hz flash rate (Fig. 4) by applying them to data collected
during 5-Hz and 10-Hz flash rates. Thus, we convolved the MUA
signals recorded during stimulation at these higher flash rates
with the region-specific IRFs shown in Figure 4 (i.e., IRFV1 for
V1 data and IRFSC for SC data) to provide comparisons of
modeled and measured BOLD responses (Fig. 5). Assumption of
linearity (and temporal invariance) holds if the modeled
BOLD responses can be scaled to match the measured BOLD
responses at all flash rates. Comparisons of MUA and BOLD
responses (modeled and measured single trials) are shown for
1-, 5-, and 10-Hz flash rates in Figures 5A,B,C, respectively. The
predictions for SC are accurate within experimental noise for
all flash rates, whereas those for V1 concur with measurements
only for 1- and 5-Hz flash rates, but not for flash rate of 10 Hz.
Bailey et al.
Figure 3. Higher flash rates induce variable BOLD and neural temporal response profiles in V1 and SC. Average time courses (±SD) of BOLD signal (top) and MUA (bottom)
measured from V1 (black) and SC (gray) for (A) 5- and (B) 10-Hz flash rate stimulation (data from 6 animals). Data obtained at the higher flash rates of 5 Hz and 10 Hz
demonstrate different dynamics from data obtained at 1 Hz. First, there are prominent offset responses from V1 in the BOLD and MUA data. Second, the plateau BOLD response
from V1 is significantly attenuated at the10-Hz flash rate. Third, the BOLD and MUA data from SC do not show significant onset responses, but there are some offset responses at
higher flash rates. For summary of neurovascular couplings and uncouplings for different flash rates in V1 and SC, see Table 1. The gray horizontal bar represents the stimulation
period (30 s). For illustration of the corresponding LFP data, see Supplementary Figures 4 and 5.
Table 1
Summary of neurovascular coupling and uncoupling observed during 10-Hz flash rate
Onset (~3 s in duration)
Sustained ([25 s in duration)
Offset (~3 s in duration)
V1
SC
Coupling observed
Coupling NOT observed
Coupling observed
Coupling observed
Coupling observed
Coupling NOT observed
Therefore, the IRFSC (in Fig. 4) is time invariant at all applied
flash rates, whereas the IRFV1 (Fig. 4) is time invariant except at
the 10-Hz flash rate. We repeated the analysis shown in Figure 5
for single trials on the whole data set, and plotted the modeled
versus measured BOLD responses in the period from –5 s to
+40 s. Consistent with the above observations, the data points
for both SC and V1 comparisons lie close to the line of identity,
except for the case of 10-Hz flash rate stimulus in V1, where
the prediction consistently overestimates the measured BOLD
signal (Supplementary Fig. 6A,B).
Spatial Invariance of the IRF
The demonstration of space-invariant neurovascular coupling is
shown in Figure 6, in which IRFV1 is applied on the data
obtained form the SC and IRFSC on the data obtained from V1.
Assumption of linearity (and spatial invariance) holds if the
modeled BOLD responses can be scaled to match the measured
BOLD responses from both regions. As can be seen in Figure
6A,B,C, respectively, for 1-, 5-, and 10-Hz flash rates, the effect
of interchanging the IRF of one region with that of the other is
minimal and within experimental error at all flash rates
(compare Fig. 5 with Fig. 6). We repeated the analysis on all
trials and plotted modeled BOLD responses against measured
BOLD responses (Supplementary Fig. 6C,D). We conclude that
IRFSC and IRFV1 (Fig. 4) are space invariant within experimental
error.
GLM of the BOLD Response
We constructed a GLM for the rat visual system that embodies
the main features observed in V1 and SC BOLD responses: onset
(0--2 s) and offset (31--33 s) transients, a sustained component
during stimulation (0--30 s), and a poststimulus baseline shift
(31--90 s). Each of these 4 components of the model was
convolved with a gamma variate-based canonical HRF using
parameters set to the average of IRFV1 and IRFSC (tp = 3.23 s, a =
11.33). Results for a single representative animal are shown in
Figure 7. An identical analysis was performed for 5 other data
sets, and the group results are summarized in Table 2.
The left column of Figure 7 illustrates thresholded statistical
parametric maps (left panel) for each of the 4 model
components for 1- (Fig.7A), 5- (Fig. 7B), and 10-Hz (Fig. 7C)
flash rates, respectively. The first observation is that the V1
transient and the 2 sustained components (when present) are
colocalized, that is, all 3 response components are generated by
the same region of V1 and presumably in the same neuronal
population from which the electrical signals (i.e., MUA and LFP)
were recorded. Compared with the sustained SC response, the
poststimulus signal level elevation observed in SC is more
restricted to midline structures. The right column of Figure 7
demonstrates the GLM fits for each of the 4 model components
for 1- (Fig. 7A), 5- (Fig. 7B), and 10-Hz (Fig. 7C) flash rates. Good
model fits (dark solid lines) are observed in both SC and V1 at all
stimulus rates. Table 2 lists the estimated component amplitudes
for both regions and all flash rates (data from 6 animals).
Each phase of the V1 response shows strong dependence on
flash rate, whereas the SC response is generally less frequency
dependent. In V1, the onset and sustained response components diminish as a function of increasing frequency, whereas
the opposite is true for the offset transient. The sustained
response attenuates to the extreme when the flash rate reaches
10 Hz leading to potential misinterpretation of the underlying
neural responses. By contrast, the SC responses are dominated
by sustained signal at all frequencies, with smaller contributions from the transients. A small onset transient that decreases
in amplitude with higher flash rates is observed in some SC
traces. The offset transient in SC seems to be moderately
increasing with flash rate, but unlike in V1, it does not reach in
amplitude the signal level reached during sustained stimulation.
Cerebral Cortex January 2013, V 23 N 1 215
Figure 4. Average IRFs for V1 and SC (i.e., IRFV1 and IRFSC represented by solid and dashed lines, respectively) obtained by deconvolution between single-trial BOLD and MUA
data measured during 1 Hz stimulation (data from 6 animals). See text for details on the gamma variate function. IRFV1 and IRFSC peak at 2.5 ± 0.5 s and 2.0 ± 1.1 s,
respectively, with widths at half height of 1.5 ± 0.4 s and 1.4 ± 0.3 s. The gray shading represents the SD of the estimated IRFs.
Figure 5. Comparison between measured and modeled BOLD responses to test the temporal invariance of modeled SC and V1 signals (i.e., IRFSC and IRFV1). Data for V1 and SC
are shown in the right and left columns, respectively. Time courses of measured BOLD responses (lower panel, gray shade) for (A) 1-, (B) 5-, and (C) 10-Hz flash rates are
juxtaposed against the time courses of modeled BOLD responses (lower panel, black trace), which were generated by convolution between the respective MUA responses (upper
panel, black trace) and corresponding IRFs for 1 Hz stimulation for that region (Fig. 4). In other words, the modeled BOLD responses from V1 were obtained using IRFV1 and the
modeled BOLD responses from SC were obtained using IRFSC. Good agreement between modeled and measured BOLD responses is found in SC at all flash rates examined,
whereas only the 1 and 5 Hz responses are adequately modeled by IRFV1. See Supplementary Figure 6A,B for illustration of correspondence of measured and modeled signals
from all animals. The black horizontal bar represents the stimulation period (30 s). Data from a single representative animal.
The poststimulus signal level elevation is only observed in SC at
the higher flash rates.
Discussion
Neurovascular coupling is commonly modeled as a linear timeinvariant system that is fully characterized by its IRF (Boynton
216 Dynamic and Regional BOLD Impulse Response Functions in Rat Visual System
d
et al. 1996; Engel et al. 1997). GLM of the BOLD response relies
on this assumption and can only accommodate certain special
types of nonlinearities with uncertain physiological relevance
(Friston et al. 1998). Because interpreting fMRI data in an
acceptable manner requires that we know how stable neurovascular coupling is for varying stimuli and across brain regions,
using the rat visual system as a model, we evaluated temporal
Bailey et al.
Figure 6. Comparison between measured and modeled BOLD responses to test the spatial invariance of IRFSC and IRFV1. Data for V1 and SC are shown in the right and left
columns, respectively. Time courses of measured BOLD responses (lower panel, gray shade) for (A) 1-, (B) 5-, and (C) 10-Hz flash rates are juxtaposed against the time courses
of modeled BOLD responses (lower panel, black trace), which were generated by convolution between the respective MUA responses (upper panel, black trace) and
corresponding IRFs for 1 Hz stimulation for that region (Fig. 4). In other words, the modeled BOLD responses from V1 were obtained using IRFSC and the modeled BOLD responses
from SC were obtained using IRFV1. See Supplementary Figure 6C,D for illustration of space-invariant IRF analysis from all animals. The black horizontal bar represents the
stimulation period (30 s). Data from a different representative animal from that in Figure 5.
and spatial variances of IRFs and assessed their implications, if
any, on GLM of BOLD responses.
Summary of Present Findings
We built a visual stimulus system to allow change of light color
and/or flash rate of full-field binocular stimuli. Our recording
setups for fMRI (with multiple slices) and electrophysiology
(with multiple electrodes) enabled reproducible measurements of evoked responses from multiple loci (i.e., V1 and
SC). Both in SC and V1, reliable and reproducible single-trial
responses were obtained with green and blue colors, whereas
red color induced only weaker responses. SC time courses
showed a rapid rise to peak and moderate decrease during
sustained stimulation, whereas V1 exhibited onset/offset
transients in addition to the sustained signal during the
stimulus. These salient features were depicted in both neural
and BOLD responses, albeit at different time scales. Overall, we
found that BOLD and neural responses of V1 and SC, which are
color sensitive, differ greatly in their temporal evolutions and
dependencies on flash rates (Figs 1--3). While IRFV1 and IRFSC
were found to be similar at the 1-Hz flash rate, we determined
that in the SC temporal invariance generally holds for the flash
rate range examined (1--10 Hz), whereas this assumption
breaks down significantly in V1 at 10 Hz mainly due to strong
attenuation of the sustained BOLD component (i.e., where
MUA > BOLD). However, there is a small uncoupling in SC at
10-Hz flash rate for the offset response (i.e., where BOLD >
MUA). Both IRFV1 and IRFSC are space invariant within
experimental accuracy (Figs 4--6). We illustrate how the use
of a suitably designed GLM will accurately represent the
hemodynamics at all stimulus rates in both regions, but will
lead to the wrong conclusion regarding the underlying neural
activity (Fig. 7).
Comparison with Previous Imaging Studies of the Rat
Visual System
Neuroimaging of the rat visual system has recently been
performed by optical imaging and fMRI techniques. Gias et al.
(2005) demonstrated retinotopic organization in upper layers
of rat V1 with optical imaging. To reach deeper cortical layers
in the rat, van Camp et al. (2006) used 7.0T fMRI to image
functional responses in V1/V2, SC, and parts of the accessory
optic system of pigmented Long-Evans rats under medetomidine anesthesia. Although the relatively weak BOLD responses
necessitated long stimulus blocks (2 min) and low temporal
resolution (25 s), the most salient feature of their results was
the opposite frequency dependence of the sustained V1 versus
SC responses, a finding which the present study confirms.
Furthermore, the authors point to the observation that at high
flash rates the SC responses exceed the stimulation period,
which is in line with our own observations.
Cerebral Cortex January 2013, V 23 N 1 217
Figure 7. Comparison between experimentally measured BOLD responses and modeled BOLD responses created from GLM. Time courses (right column) of measured BOLD
responses (pink shade) from V1 (top trace) and SC (bottom trace) for (A) 1-, (B) 5-, and (C) 10-Hz flash rates are juxtaposed with the BOLD activation maps (left column) for the 4
phases of the response: onset, sustained, offset, and poststimulation. The modeled BOLD responses were generated by summing the time courses generated from GLM of the 4
components, where the canonical HRF used for GLM was the average of IRFSC and IRFV1 (in Fig. 4), but very similar results are obtained if either of IRFSC and IRFV1 is used (data
not shown). The gray horizontal bar represents the stimulation period (30 s). Data from a single representative animal; for summary statistics for 6 animals, see Table 2.
poststimulation.
Table 2
Values of parameter estimates of the four phases GLM following 1-, 5-, and 10-Hz flash rate stimulation (n 5 6)
V1 (% ± SD)
1 Hz
Onset
Sustained
Offset
Poststimulation
2.01
0.79
0.69
0.16
SC (% ± SD)
5 Hz
(±0.59)
(±0.19)
(±0.29)
(±0.12)
0.95
0.43
1.78
0.01
10 Hz
(±0.33)
(±0.24)
(±0.44)
(±0.20)
0.76
0.05
2.25
0.19
At 9.4T, Pawela et al. (2008) were able to considerably
improve the temporal resolution (2 s) and, presumably using
a much larger RF coil, covered extensively the posterior brain
regions and thereby detected BOLD responses from DLG, V1/
V2, and SC in albino Sprague-Dawley rats under medetomidine
anesthesia. Signal averaging was necessary across trials to reveal
transient responses (i.e., at onset/offset of stimuli) in V1/V2
compared with SC/DLG, a finding which we are also able to
corroborate. We note that the modeling approach taken by
Pawela et al., which attempts to explain measured BOLD signals
as a function of assumed underlying neural dynamics (including
218 Dynamic and Regional BOLD Impulse Response Functions in Rat Visual System
d
1 Hz
(±0.46)
(±0.47)
(±0.78)
(±0.23)
0.59
1.66
0.51
0.07
5 Hz
(±0.70)
(±0.29)
(±0.60)
(±0.29)
0.46
1.80
0.77
0.70
10 Hz
(±0.64)
(±0.40)
(±0.52)
(±0.50)
0.18
1.79
0.99
1.06
(±0.42)
(±0.45)
(±0.66)
(±0.36)
refractory nonlinearities), exhibits poorest performance in
visual cortex at the higher (5 and 10 Hz) flash rates. We
extend this finding by showing that measured neural activity
becomes increasingly decoupled from the BOLD response as
a function of increasing flash rate, the greatest extent of which
was observed at 10-Hz flash rate.
In a recent paper, Lau et al. report on BOLD modulations by
short (1-s duration) blocks of 10-Hz flash rate stimulation in SC
and thalamus of albino Sprague-Dawley rats under isoflurane
anesthesia (Lau et al. 2011). The IRFSC estimated in the present
work for 30 s blocks of 1-Hz flash rate stimulation predicts well
Bailey et al.
the SC responses at 5- and 10-Hz flash rates as well. To compare
our results with those of Lau et al., we generated BOLD
responses by applying IRFSC to the SC MUA data during the first
second of 10 Hz stimulation (data not shown). The modeled
BOLD response reached half-maximum (‘‘t50’’) at 2.8 (±0.2) s
and peaked at 4.1 (±0.2) s, which are in excellent agreement
with the results obtained by Lau et al. (t50 = 2.6 ± 0.1 s, peak =
~4 s). The apparently weaker V1 BOLD responses in the Lau
et al. study is also in line with our own observations of reduced
initial V1 BOLD transients to 10 Hz flash rate stimulation.
The similarities between the works cited above and the
present results are extensive, despite the use of varying light
delivery strategies (stroboscopic and LED based), varying
experimental settings (dark adapted and nonadapted), varying
anesthetics (medetomidine, isoflurane, and urethane) and
different rat strains (Sprague-Dawley and Long-Evans). Pigmented rats, such as the Long-Evans strain, exhibit some
neuroanatomical and functional differences compared with
albino strains such as Sprague-Dawley. Albino rats have
impaired vision as compared with normally pigmented rats
(melanin prevents reflections within the eyeball), and a translucent iris, which leads to retinal degeneration. Albino rats take
much longer than pigmented rats to adapt to low-light
conditions, have much poorer visual acuity of (20/1200) than
pigmented rats (20/600), and are thus, more visually impaired
compared with pigmented rats (Lund et al. 1974; Dräger and
Olsen 1980; Lund et al. 1980; Prusky et al. 2002). We chose
urethane to provide a stable state (Kannurpatti and Biswal
2006) during which sensory-evoked signals are unaffected
(Maggi and Meli 1986; Sceniak and Maciver 2006), thus
pointing to the compound’s suitability in fMRI studies (Yang
et al. 1998; Huttunen et al. 2008; Huttunen et al. 2011).
Medetomidine, an a2-adrenoreceptor agonist, is thought to
produce a lighter state of sedation (Sanganahalli et al. 2009a,
2010). Thus slight dissimilarities in stimulus-evoked magnitudes could partly be due to differences in the baseline
excitability levels attained with the 2 anesthetics used, for
example, see Maandag et al. (2007).
Color Vision and Acuity in Rats
The flexible stimulus presentation system allowed us to
examine single-trial color dependence of BOLD and neural
responses in SC and V1. The rat retina contains 3 classes of
photoreceptors with differing sensitivities to light color: rod
sensitivity peaks at ~500 nm (green/cyan), short-wavelength
cones peak at ~360 nm (ultraviolet), and medium-wavelength
cones peak at ~510 nm (green) (Jacobs et al. 2001). Colors
used in the present study were blue (455 nm), green (530 nm),
and red (627 nm). The BOLD and neural responses to blue and
green stimuli were robust, whereas red elicited weaker
responses, presumably because the sensitivity peak of the rods
and cones are far from the applied red wavelength. Although it
remains unclear what functional advantage color vision might
impart on a nocturnal species such as the rat, it was shown
using behavioral tasks that after training rats were able to
discriminate stimuli solely on the basis of their wavelengths,
that is, without brightness cues (Jacobs et al. 2001). Recent
work by La Garza et al. demonstrate the use of fMRI in the
study of the retina, but further work is needed to characterize
the hemodynamic and electrophysiological consequences of
variations in stimulus properties on downstream processing
structures (La Garza et al. 2011).
Neurovascular Uncouplings in V1 and SC and
Implications for GLM
The metabolic and hemodynamic properties of V1 and SC differ
(Iadecola et al. 1983; Klein et al. 1986; Maeda et al. 1998).
Although the capillary density is lower in SC than in V1, blood
flow and energy metabolism in SC are both higher. Studies of
cortical single-cell receptive field properties in both rat
(Girman et al. 1999; Girman and Lund 2007) and mouse (Niell
and Stryker 2008) have shown that—although less organized
than those of highly visual mammals (Ohki et al. 2005)—rodent
V1 and SC cells are well tuned to orientation and hence offer
a well-characterized test bed for neuroscientific inquiry (Binns
1999; Sefton et al. 2004). Afferent signals to V1 are relayed by
the thalamus (DLG), whereas SC receives direct retinal
innervations. The cortex and thalamus form a reciprocally
connected network in which each structure affects the other
(Castro-Alamancos 2004; Sherman 2005). Rapid adaptation in
V1 after a short initial transient may reflect relatively stronger
inhibitory feedback mechanisms (Iadecola 2004), whether they
are local or distant, in the cortical networks than in SC.
The majority of the dynamic phases observed in the fMRI data
from SC and V1 were confirmed by similar temporal features
in the electrophysiology data. Generally, these complimentary
observations of BOLD and neural responses indicate linear and
time-invariant neurovascular coupling in SC and V1 for most
stimuli examined. Furthermore, our results indicate that the
couplings in the 2 regions are similar. The sustained V1 and
offset SC BOLD responses, however, were uncoupled from the
neural activity at the 10-Hz flash rate (i.e., MUA > BOLD in V1 vs.
BOLD > MUA in SC). This mismatch between BOLD and neural
responses reveals the possibility of neurovascular uncoupling
at high flash rates (more so in V1 than in SC), the underlying
mechanisms for which could be metabolic, hemodynamic,
and/or neurophysiologic in nature. Because we do not fully
understand the mechanism for the absence of sustained BOLD
signal in V1 despite strong underlying elevated neural activity
(and perhaps also the presence of the offset BOLD signal in SC
despite small neuronal activity), and both observations which
have not yet been observed in humans, future fMRI and
electrophysiology studies in conjunction with localized pharmacological intervention in V1, DLG, and/or SC should address
these issues.
The use of piecewise linear models in the framework of GLM
have been advocated for the study of auditory steady-state
responses in humans to account for observed nonlinear
responses (Harms and Melcher 2003). To date, there are less
clear accounts of similar approaches for the visual modality.
Based on the initial observations of the data, we aimed to
ascertain whether a GLM consisting of 4 components was able
to accurately explain observed dynamics using a single HRF.
Our findings indicate that although the GLM provides the
desired fit to the data, the results do not represent the
underlying neural activity. The spatial distributions of the
onset/offset/sustained response components of the cortex
strongly overlap, thereby suggesting that most probably the
same V1 (and V2) neural networks gives rise to all of these
BOLD response components.
A recent human auditory fMRI study showed that highfrequency trains of click sounds produced weaker BOLD signals
than predicted by magnetic measurements of the sustained
electrical events in primary auditory cortex (Gutschalk et al.
Cerebral Cortex January 2013, V 23 N 1 219
2010). It is important to consider that neither intracortical
measures of electrical network activity (in present study) nor
extracranial recordings (in the Gutschalk study) can unambiguously distinguish between membrane fluctuations of excitatory
versus inhibitory cells. Rather, the power recorded by a microelectrode (in present study) or magnetic sensor (in the
Gutschalk study) is a weighted sum of many subpopulations of
neurons and possibly even glia. Thus, it remains to be shown
whether the weaker BOLD response in V1 at high flash rates is
due to a large metabolic demand or a small blood flow response.
Preliminary results using surface laser-Doppler flowmetry probes
over V1 indicate that blood flow time courses closely mimic the
BOLD response at all flash rates examined (data now shown),
thereby suggesting that it might be blood flow that is uncoupled
from neural activity during the sustained response at high flash
rates. While these preliminary results are not as comprehensive
as our BOLD and electrophysiological data, we believe that with
future improvements in fMRI sensitivity, we can conduct reliable
‘‘calibrated fMRI’’ studies (Herman et al. 2009; Sanganahalli et al.
2009b) of the visual system even though the typical BOLD
responses in this sensory system is several times smaller than
typical BOLD responses in other sensory systems (Sanganahalli
et al. 2008; Sanganahalli, Bailey, et al. 2009).
Heterogeneity of BOLD Transfer Functions
Several studies have used system identification techniques on
human fMRI data to characterize temporal and spatial
variability of HRFs (Boynton et al. 1996; Engel et al. 1997;
Vazquez and Noll 1998; Birn et al. 2001). Though insightful on
stimulus-BOLD coupling, they should be augmented by direct
neurovascular coupling analysis using IRFs, which relates local
changes in neural activity and dilation (or constriction) of
blood vessels to increase (or decrease) blood flow (or volume)
to a region. Many animal studies have measured both the neural
and vascular responses and show linear neurovascular coupling
within some range of stimuli (Logothetis et al. 2001; Matsuura
and Kanno 2001; Nemoto et al. 2004; Sheth et al. 2004; Ureshi
et al. 2004; Martin et al. 2006; Herman et al. 2009; Sanganahalli
et al. 2009b). For example, time invariance of the BOLD
transfer function in the somatosensory cortex has been
demonstrated (Herman et al. 2009; Sanganahalli et al. 2009b;
Hirano et al. 2011) by a procedure based on stimuli of the same
amplitude but varying frequencies, as done in the present.
While a detailed discussion of each transfer function is not
within the present scope, the general observation is that the
BOLD transfer function of the somatosensory cortex is
generally similar to those obtained here for V1 and SC (Herman
et al. 2009; Sanganahalli et al. 2009b).
Much less examined in fMRI is the spatial relationship
between neural activity and BOLD signal, which has been
measured mainly in the V1 and whisker barrel field of small
animals (Kim et al. 2004; Berwick et al. 2008). While these
animal studies generally show reasonable neurovascular coupling across small distances in homologous cortical regions,
other human studies (which usually do not have measured
neural activity) show subtle variations of neurovascular
coupling across larger distances in nonhomologous cortical
regions (Engel et al. 1997; Birn et al. 2001; Janz et al. 2001; Liu
and He 2008; Zhang et al. 2008; Liu et al. 2010; Ostwald et al.
2010; Carlson et al. 2011). However, it remains unclear if these
variations have practical consequences for BOLD signal
220 Dynamic and Regional BOLD Impulse Response Functions in Rat Visual System
d
modeling, as differences in experimental noise across the
regions have not been fully assessed. In the present study, we
found that BOLD transfer functions for SC and V1 are
interchangeable. The implication for GLM of BOLD responses
is that the use of a single canonical HRF for whole-brain
evaluations is likely to be accurate within experimental error,
once temporal dynamics of the responses are sufficiently
accounted for by the model structure.
Conclusions
Interpretation of fMRI data mandates that we know how stable
neurovascular coupling is for varying stimuli and across brain
regions (Boynton et al. 1996; Engel et al. 1997). This is achieved
by experimentally measuring IRFs that are calculated from
measured neural and BOLD responses. The underlying assumption of linearity and time invariance should not be taken for
granted, especially in human studies without neural recordings,
though our results suggest that the use of a space-invariant HRF
may be sufficient in GLM. Future efforts using dynamic
calibrated fMRI (Herman et al. 2009; Sanganahalli et al.
2009b) should be directed to specifically assess neurovascular
as well as neurometabolic couplings in a layer-specific manner
so that the neurophysiological basis of fMRI may be improved
to relate to classical metabolic-flow coupling studies with
autoradiographic techniques (Ueki et al. 1988, 1992).
Supplementary Material
Supplementary material
oxfordjournals.org/
can
be
found
at:
http://www.cercor.
Funding
The work was supported by grants from National Institutes of
Health (R01 MH067528 and P30 NS52519 to F.H.; R01 NS049307 and R01 NS-066974 to H.B.). C.J.B. is grateful to Aarhus
University for his graduate program scholarship and to Dagmar
Marshall’s Fond, Oticon Fonden, Brorsons Rejselegat, and
Torben and Alice Frimodts Fond for financial support.
Notes
The authors thank colleagues (Peter Brown, Scott McIntyre, Bei Wang,
and Alyssa Siefert) at MRRC (mrrc.yale.edu) and Core Center for QNMR
(qnmr.yale.edu) for assistance, materials, and help with building the
experimental setup. Conflict of Interest : None declared.
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