To permit extraction of responses to the different regions while
recording with one electrode, the contrast of each stimulus region was
sinusoidally modulated in time, each region at a slightly different
temporal frequency (described later). The MFP signals were amplified
125,000 times and sampled in synchrony with the video frames displayed
on the monitor. Electrodes (ERG-Jet; Universo SA, La Chaux-de-Fonds,
Switzerland) were used for the eye contact, and AgCl button
electrodes were used for the indifferent and earth electrodes.
The indifferent electrode was placed on the temple, and the ground on
the cheekbone half way between the midline of the eye and the temple.
Control experiments revealed no contamination by cortical potentials.
The time base for the analogue-to-digital converter (ADC)
sampling (Labmaster MDA, Scientific Solutions, Solon, OH; 16 bit) was
the horizontal line-scan clock (45,473 Hz) supplied by the graphics
board. The video frame rate was 101.50 Hz (noninterlaced), and there
were 448 cycles of the horizontal line-scan clock per frame. A single
stimulus sequence contained 4096 frames of video providing an overall
stimulus duration of 40.4 seconds. Response components were extracted
by the fast Fourier transform (FFT), the run length providing a
temporal frequency resolution ΔF of 0.0248 Hz.
For the FFT signal extraction process to work, an orthogonal design was
needed. That is to say, it was necessary for all nine stimulus
frequencies (f 1, f 2, and f 9) to contain an integral number of
cycles over the 4096 video frames. Because we were interested in the
second harmonics, it was also necessary that no two summed frequencies
(f i + f j ) should equal any of the nine second
harmonic frequencies. If summed frequencies f i + f j appeared in the record, they would represent interaction or light
scattering between the stimulus zones, and these frequencies were
therefore also monitored. The actual stimulus frequencies were the
multiples: ΔF · (889, 898, 904, 911, 921, 935, 947, and 955). The
resultant second harmonic signals thus ranged from 44.06 to 47.33 Hz
(contrast reversals/sec).
We recorded several repeats of the 40.4-second stimulus sequence. An
FFT of each record was computed, and the resultant complex Fourier
transfer coefficients were averaged.
Figure 2 demonstrates graphically the output of the data acquisition program and
the initial analysis.
Figure 2A shows the amplitude spectrum
highlighting the fundamental, second, third, and fourth harmonics.
Figure 2B shows the second harmonics, numbered 1 through 9 and some
other frequencies in the complex plane in an Argand diagram. For this
part of the analysis, we extracted the second harmonics
(
f i +
f i =
2
f i ), the regional interaction
frequencies (
f i +
f j ,
i ≠
j), and all the remaining noise frequencies in the
band
f 1 to
f 9. In the Argand diagram, frequencies
are represented as vectors for which the length from the origin
represents signal amplitude and the orientation represents phase lag.
Note in this case that because the stimulus frequencies were bunched
(range, 1.8 Hz) differences in phase corresponded closely to
differences in conduction delays. In the Argand representation if
response vectors were concatenated from repeated runs and scaled by the
number of repeats (i.e., take the vector average in the complex plane),
then only responses with relatively constant phase would grow in
amplitude. Noise frequencies would have random phase and so would
stagger in a random walk around the origin. The coefficients from the
noise frequencies thus form a bivariate normal distribution that can be
used to measure the significance of the measured harmonics. In
Figure 2B the noise frequency coefficients and regional interaction
frequencies (
f i +
f j ,
i ≠
j) lie inside the circle representing the 95%
significance level. The derivation of that significance level is given
in the next paragraph.
The actual significance of a frequency component is related to its
amplitude, which is the modulus of the Fourier transform coefficient at
that frequency,
A(
f). A test of
significance for a particular frequency can be performed as follows.
Under a null hypothesis of no signal, the real and imaginary parts
of the Fourier transform coefficients,
Real[
A(
f)] and
Imag[
A(
f)], are independent
normal variates with zero mean and some varianceς
2. The squared modulus of the coefficient|
A(
f)|
2 is then ς
2 times a χ
2 variate on 2 degrees of freedom. An estimate
s 2 of ς
2 is
obtained from frequencies not in the set of second-order stimulus
frequencies, say with
n degrees of freedom. An F-test is
then performed on the quotient
(|
A(
f)|
2/2)/(
s 2/
n),
with (2,
n) degrees of freedom. For large
n the
F-test is closely approximated by a χ
2 test,
the test statistic being|
A(
f)|
2/
s 2,
with 2 degrees of freedom. This method was used to draw the circle
denoting 95% confidence in
Figure 2 . Thus, a given frequency component
is significant if, and only if, it lies outside the circle.
As can be seen
(Fig. 2B) , unlike the noise frequencies, the nine signal
components had relatively constant phase and so over four runs had
grown outside the significance level. In practice, the operator viewed
the Argand diagram
(Fig. 2B) and judged whether sufficient repeats had
been obtained to ensure that most or all the signals from the nine
regions exceeded the significance level. Preliminary experiments
determined that all nine responses could be significant in as few as
four repeats (as shown in
Fig. 2B ). Therefore, the operator was
instructed to perform at least 4 repeats, but not more than 12, so that
recording time did not exceed 10 minutes. The operator was instructed
to stop after fewer than 12 repeats if all nine regional signals had
reached 95% significance. These averaged responses were used for
subsequent off-line analysis.