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1 From the Centre for Visual Sciences, Research School of Biological Sciences, Australian National University, Canberra; and the 2 Prince of Wales Hospital, Sydney, Australia.
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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METHODS. The nine stimulus regions were temporally modulated at incommensurate frequencies typically producing an FD percept. Two other spatial scales of the stimuli were also investigated. The sensitivity and specificity of MFP were examined using linear and quadratic discriminant methods.
RESULTS. Even with the simpler linear discriminant classification, sensitivities and specificities of 100% were obtained in eyes with moderate to severe glaucoma. Of eyes with glaucoma strongly suspected, 67% were classified as being glaucomatous. Stimulus patterns having differing spatial scales produced different PERG visual field dependencies.
CONCLUSIONS. The differing results for the 16-fold change in spatial scale may reflect the accessing of different mechanisms. The MFP method appears to have significant value for the diagnosis of glaucoma.
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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Long-term studies provide evidence that the PERG has predictive value in glaucoma,12 13 14 but what might be the best stimulus arrangement for glaucoma diagnosis? Trick15 showed that increasing the temporal frequency of contrast modulation from 1 to 8 Hz improved discrimination of normal subjects and patients with primary open-angle glaucoma (POAG) when using check sizes that have fundamental spatial frequencies in the range 0.18 to 1.41 cyc/deg (see also Reference 16). Marx et al.17 found that decreasing spatial frequency from 3.5 to 0.5 cyc/deg improved sensitivity in experimental glaucoma for stimulation at 6 Hz. Johnson et al.18 showed that spatial frequencies of approximately 0.18 cyc/deg (i.e., 2° checks) modulated at 10 Hz discriminated glaucomatous primate eyes well. The reader is further referred to an excellent review on the use of evoked potentials in assessing glaucoma.19
These studies share one factor: The visual stimulus is presented at the same scale to all parts of the retina, thus ignoring the 50-fold decline in ganglion cell density between 2° and 10° eccentricity.20 21 There is increasing evidence that there is diffuse as well as local ganglion cell loss in glaucoma.22 23 24 25 Anatomical25 and PERG studies12 13 26 indicate macular as well as peripheral retinal damage in early glaucoma, and the potential for central retinal involvement therefore should not be ignored. At the same time, peripheral scotomas are a diagnostic feature of glaucoma.27 Ideally, several image regions should be tested, and the size of these regions and the scale of any textures contained in them should be tailored to retinal ganglion cell density and characterization of both diffuse and sectoral losses. Some attempts have been made in this area, such as use of appropriately scaled dot patterns28 or separate recordings for different check sizes.26 29 In multifocal visual evoked potential (VEP) studies of glaucoma,30 the check sizes used were M-scaled.
The issue of spatial scale is separate from whether there is a component of the PERG that is suited to glaucoma diagnosis. There is considerable evidence, both from experimental glaucoma25 31 and human POAG,32 33 34 35 that large retinal ganglion cells are disproportionately damaged. In primates the parasol cells36 project to the magnocellular layers of the dorsal lateral geniculate nucleus (dLGN)6 37 and so are frequently referred to as M cells. The M pathway contains (at least) two functional classes that are similar to cat X and Y cells.6 39 Between 5% and 20% of dLGN M cells respond with a nonlinear Y-type response39 40 41 42 thus, the term My cells. The responses of LGN units largely reflect the characteristics of their retinal ganglion cell inputs.43 44 45 46 47 Subpopulations of parasol cells that are either coupled or not coupled to amacrine cells,48 a feature that discriminates cat X and Y cells,49 may have some relation to the primate X and Y types. At least three studies indicate that My-cell receptive fields39 50 and axons39 40 (based on conduction velocities) are larger than those of Mx cells. Therefore, it seems that My cells may be larger than Mx cells.
From the perspective of glaucoma diagnosis it is perhaps more important that My cells appear to have a very low retinal coverage factor,51 52 53 so that loss of a single cell perhaps leads to a complete local loss of visual sensitivity at a given retinal location. These findings, in conjunction with some selective loss of larger ganglion cells in glaucoma, suggest that the My-cell subsystem should be accessed to monitor glaucoma.
How then should the My-cell class be accessed? One possibility is that the spatial frequency-doubling (FD) illusion54 55 56 may be related to My-cell function.52 53 57 58 The FD illusion is seen when subjects view spatially coarse sinusoidal gratings with a contrast that is modulated at 15 to 30 Hz54 55 56 or that are presented briefly.59 60 The nonlinearity describing the characteristic response component of Y cells has the same rectifying form as that governing the FD illusion (cf. References 61 and 54). Some investigators57 58 62 have shown that when FD is seen, the PERG signal becomes dominated by components with phase shifts characteristic of the retinal gain control signal operating on the nonlinear response component of Y cells.63 This retinal gain control mechanism greatly increases the nonlinear responses of Y cells to stimuli combining low spatial frequencies and high temporal frequencies61 63 64 65 66 67 The nonlinear response component of Y cells is more amplified by retinal gain control than either the Y cells’ own linear response or that of X cells,61 64 68 69 which might explain the appearance of the illusion. Also, we53 have shown that the spatial density of the units subserving the FD illusion is very similar to the anatomic expectation for My cells. The ability of subjects with glaucoma to see the FD illusion is severely reduced.52 70 71 72 73 74 75 76 77 78 79 80 Evidence has been provided that FD stimuli are superior to wide-field flicker in detecting glaucoma.81 So, as might be predicted if the FD illusion corresponded to My-cell function, it appears that the strength of the FD illusion is highly correlated with glaucomatous damage.
Taking all the evidence into account, we created a visual stimulus that was correctly scaled with respect to My-cell density,53 that exploited the FD illusion, and that had multiple, relatively large stimulus zones.70 In a companion study82 we compared the MFP results with results from Humphrey Field Analyser (Humphrey, San Leandro, CA) examinations and a contrast threshold method using FD stimuli.73
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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F 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 (f1,
f2, and
f9) 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
(fi +
fj ) should equal any of the nine second
harmonic frequencies. If summed frequencies
fi + fj
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: F · (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
(fi +
fi =
2fi), the regional interaction
frequencies (fi +
fj, i 
j), and all the remaining noise frequencies in the
band f1 to
f9. 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 (fi +
fj, i
j) lie inside the circle representing the 95%
significance level. The derivation of that significance level is given
in the next paragraph.
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2. The squared modulus of the coefficient
|A(f)|2
is then 2 times a 
2
variate on 2 degrees of freedom. An estimate
s2 of 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)/(s2/n),
with (2, n) degrees of freedom. For large n the
F-test is closely approximated by a 2 test,
the test statistic being
|A(f)|2/s2,
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.
Subjects
Right eyes of 77 subjects were tested. We used the 24-2 program of
the Humphrey Field Analyzer (HFA; Humphrey, San Leandro, CA) to obtain
standard perimetric visual field threshold data from the 77 subjects in
the study group. By those and other previously described
criteria73
subjects were classified (initially by IG, and
confirmed by SW and JD) into four groups: normal subjects, persons with
glaucoma weakly suspected (weakly suspect group), persons with glaucoma
strongly suspected (strongly suspect group), and persons with known
glaucoma (glaucoma group). Of the glaucoma group, 12 of 14 met the
strict HFA criteria of Capriolli83
for glaucoma
diagnosis; all met the moderate Capriolli criteria. Strongly suspect
eyes did not meet either of these visual field criteria but had a
highest ever recorded elevated intraocular pressure (IOP), determined
by applanation tonometry, of more than 20 mm Hg and a glaucomatous
change in the optic disc verified by repeated fundus camera photography
of the optic disc over several years (by IG). For a more complete
description of the clinical evaluation of these subjects see Maddess et
al.73
Six of the glaucoma group had a blockage-mechanism form of glaucoma, and the remainder had POAG. The group was part of a larger study on 330 subjects in which no effect of these differing glaucoma types was found for visual field thresholds obtained for FD stimuli.73 Weakly suspect eyes had elevated IOP or suspect discs but had no observed change in the disc over several years. Disc condition was assessed by fundus photography, and vertical cup-to-disc ratios were evaluated by color and contour (see Table 1 of Reference 73 ). Further details of the diagnostic criteria are given elsewhere.73 Because of the long-term nature of the parent study,73 the glaucoma group were medicated, 10 exclusively with ß-blockers and 7 also with miotics. The miotics led to a significant reduction in pupil diameter of approximately 27% compared with that in normal subjects (P < 0.005; Table 1 ).
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Discriminant Analysis
The objective of this analysis was to determine whether the
structure of the data permitted a method that was able to discriminate
normal subjects from those with glaucoma. Note that the differing
covariance of each group suggested the use of quadratic discriminant
analysis (QDA).84
Linear discriminant analysis
(LDA)84
was also conducted for comparison. The Appendix
illustrates the two methods. Although the LDA models are simpler, LDA
was less appropriate than QDA, given the different covariance
structures of the data of normal subjects and those with
glaucoma.84
Sensitivities and specificities were estimated
from receiver operator curves (ROCs), for which in LDA the risk factors
were based on Fisher’s linear discriminant function , and
the QDA classifier was the likelihood ratio assuming separate variance
matrices.84
Extensive details of LDA, QDA, and the use of
ROCs have been given previously.73
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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Absolute phase was of little use. This was not unexpected, because at these frequencies small delays translate into phase shifts exceeding 1 cycle. Instead, we examined relative phase. We used the phase of region 9 as the reference phase for each data set, because it provided the most reliable signal (Figs. 2A 3 4B) , being significant at P < 0.001 in 76% of all subjects and in all normal subjects at P < 0.05 or better. To construct the relative phase, we subtracted the phase of region 9 for a given subject from each of the nine regional phases. In this way, the phase of region 9 for all subjects was brought to 0°, and the phase lags and leads of the other regional responses relative to that of region 9 were preserved.
For both the sorted and rotated data sets, we examined amplitude and relative phase and amplitude relative to the geometric means across normal subjects. Both decibel and linear amplitude measures were considered. In a further analysis, we subtracted the (geometric) mean model for normal subjects from the amplitude data, and in other cases we divided by the mean model (equivalent to subtracting the decibel version from data transformed to decibels). This weighting operation was a conservative operation, because it scaled large, reliable signals downward and small, less reliable, MFP signals upward. For all the cases we examined linear (LDA) and quadratic (QDA) discriminant analysis models (see the Methods section and Appendix) in which the models were constructed from the data from our normal and glaucoma groups. These discriminant functions were then used to classify the subjects in the weakly and strongly suspect groups. Further details are supplied later for specific cases.
One of the simplest measures, regional amplitudes divided by the geometric mean for normal subjects, so-called scaled amplitudes, was the most reliable diagnostically, providing a sensitivity of 92.9% at 91.7% specificity for the linear discriminant model, and sensitivities and specificities of 100% for the quadratic case. Note that means and covariances for the normal and glaucoma groups were used to form the discriminant functions () and then the vectors, xi, of nine scaled amplitudes from each subject were used as the inputs for classification (x0 in ). Sorted amplitude differences from normal performance gave poor performance at 71.4% sensitivity for 75% specificity (simultaneously highest values, 85.7% specificity at 83.3% sensitivity for the quadratic case). Relative phase alone was as good as sorted amplitudes at 71.4% sensitivity for 75% specificity for LDA. There was no general pattern of relative phase changes with respect to visual field location. Including both amplitude and relative phase gave 100% sensitivity and specificity even in the LDA case. This was true for both scaled and unscaled amplitudes. In these models the vectors, xi, of nine amplitudes and nine relative phases from each subject were used as the inputs for classification (x0 in ). The scaled amplitude LDA model diagnosed 52.7% of weakly suspect eyes and 66.7% of strongly suspect eyes as glaucomatous. Performance for the QDA model was 50.0% and 60.0% for weakly and strongly suspect eyes, respectively.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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Inspection of Table 1 shows that the mean defect (MD) and pattern standard deviations (PSDs) of our normal subjects were slightly high. Although this may at first seem at odds with our high reported sensitivities and specificities for the MFP method, it may also be related to earlier findings that HFA MD is not well correlated with glaucomatous damage.73 In any case, improved diagnosis in our normal subjects would only improve our sensitivities and specificities.
The large MFP regions used in this study mean the detected loss was relatively diffusely distributed. This apparent diffuse loss is in accord with a study in which 330 subjects performed an FD-based contrast threshold test up to seven times over 2 years.73 In that study the thresholds were obtained with large (FD) patterns similar to the MFP stimuli used in the this study, and the tests provided median sensitivities of 90.8% at specificities of 94%. These two studies indicate that tests based on the FD illusion can pick up diffuse early glaucomatous loss, as in the strongly suspect group in this study.82 Such a result is consistent with anatomical22 23 24 25 87 and conventional PERG studies,12 13 26 indicating diffuse cell loss in glaucoma.
An interesting feature of the MFP data was the differing responses by the different visual field quadrants over a 16-fold range of spatial frequencies (Fig. 4) . Visual field dependencies similar to those found for our usual stimulus condition (Figs. 3 4B) have been reported before in which the four quadrants were tested sequentially with an 8.33-Hz, 0.5-cyc/deg pattern.88 A study examining the density of the units subserving the FD illusion has shown similar differences53 that were found to be related to known anatomic retinal ganglion cell densities. Thus, it seems with these spatially coarse fast stimuli, we may be accessing a different retinal pathway. A study comparing the diagnostic utility for glaucoma of a range of low spatial frequencies, modulated at 27 Hz and presented in the periphery, showed that the usual spatial frequencies used in this study are approximately optimal for glaucoma diagnosis.81
Virtues of Using the My Pathway for the Early Detection
of Retinal Damage
Examining the My-cell system may provide
greater sensitivity to glaucomatous damage than examining other more
populous systems.52
53
Improved sensitivity to damage
would arise from two sources: cell size and retinal coverage factor.
Early suggestions that in humans larger retinal ganglion cells were
more susceptible to glaucomatous damage22
32
33
34
have been
supported by many studies31
32
33
34
indicating that primate
retinal ganglion cell loss in glaucoma is proportional to ganglion cell
size. The size dependence extends even to the fovea.25
At
least three studies indicate that My cells are
larger than Mx cells.39
40
42
As mentioned, perhaps the primary reason for My-cell sensitivity to glaucomatous damage may reside in retinal coverage factors.51 52 53 Anatomical89 90 and electrophysiological44 estimates of the ganglion cell coverage factors (or number of receptive fields/image point) range between 2 and 7 for M cells (cf. 24 for P cells44 ; for review see Reference 91). Evidence from studies on humans53 and macaques39 40 41 42 indicates that the My cells make up 20% or less of the M pathway, and as a result their coverage factor could be less than 1. It follows that the performance of the My system would be particularly susceptible to any diffuse cell loss across the retina, because there would be little redundancy to hide the loss. Such low coverage factors would lead to spatial aliasing effects, which have been reported.51 53
Problems
Perhaps the major problem with the present method is that in a few
eyes we could not obtain significant amplitudes from all nine regions,
even after 12 repeats. Some nonsignificant amplitudes can be expected
in glaucoma; however, at 40 seconds per repeat this would make the
method uncompetitive with frequency doubling technology (FDT; Zeiss
Humphrey Systems, Dublin, CA) perimetry.71
72
74
ERG recording itself has its problems19
and advances in
VEP recording methods for glaucoma30
may make that avenue
more attractive.
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Summary |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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Appendix 1 |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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1, and n observations of the same
format from population 2. From these data sets
the correct classification is assumed to be known. The technique of
discriminant analysis derives a classification rule for any new data
point, which seeks to minimize the cost of a misclassification. Let us assume that:
1 or 2 is
p1 and
p2 = 1 -
p1 respectively (the prior
probabilities). 1 as being from the other population is
C1, and the cost of misclassifying a
point that is really from population 2 as
being from the other population is C2.
Note that the probability density function
f1(x) is the conditional
probability density for observing the value x, given that
the point came from population 1. The joint
probability density of observing the value x and that the
point came from 1 is thus
f1(x)p1,
and the marginal probability of observing the value x
irrespective of the class is f(x) =
f1(x)p1
+
f2(x)p2.
Bayes’ rule can be used to invert the conditional probabilities: The
probability that an observed value x came from population
1 is
p(1|x) =
f1(x)p1/f(x),
and the probability that it came from population
2 is
p(2|x) =
f2(x)p2/f(x).
For a given new observation x, the expected cost if we assign to class 2 is the probability that it was really from population 1 multiplied by that cost: C1f1(x)p1/f(x). The expected cost if we assign to class 1 is likewise C2f2(x)p2/f(x).
The optimal rule is now clear: We should assign to class 1 if that
expected cost is less—that is, if
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The further assumption may be made that each of the two populations follows a multivariate normal distribution, for which we estimate the population mean vectors by the sample means u1 and u2 (p x 1), and we estimate the population covariance matrices by the sample covariance matrices, S1 and S2 (p x p).
If the covariances are assumed to be equal, they are both estimated by
the pooled covariance, Spooled =
[(m - 1)S1 +
(n -
1)S2]/(m +
n - 2). The multivariate normal probability density
for population 1 is then estimated as
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2. The
condition for assigning to class 1 using the logarithm of the ratio is
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 | (A1) |
If the covariance matrices are not equal, i.e.,
S1
S2, then the resultant rule is to
classify an observation x0 as being from
population 1 (1) if the following quadratic
condition holds.
 | (A2) |
Geometrically, the linear discriminant function defines a decision boundary, or separatrix, that is a (possibly diagonal) straight line across the plane in the case of a bivariate observation and in general is a hyperplane in the multivariate case. The quadratic discriminant rule defines a decision boundary that is (possibly rotated) a parabola in the bivariate case and is a paraboloidal surface in the general multivariate case (for examples see73 ).
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Acknowledgements |
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Footnotes |
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Commercial relationships policy: P (TM, ACJ); N (all others).
Corresponding author: Teddy Maddess, Centre for Visual Sciences, Research School of Biological Sciences, Australian National University, Canberra ACT 0200, Australia. ted.maddess{at}anu.edu.au
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References |
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TopAbstractIntroductionMethodsResultsDiscussionSummaryAppendix 1References |
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This article has been cited by other articles:
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  T. Maddess, A. C. James, I. Goldberg, S. Wine, and J. Dobinson Comparing a Parallel PERG, Automated Perimetry, and Frequency-Doubling Thresholds Invest. Ophthalmol. Vis. Sci., November 1, 2000; 41(12): 3827 - 3832. [Abstract] [Full Text]
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) nine fundamentals, (
)
second, (
) third, and (
) fourth harmonics. There is a component
from the frame rate (101.50 Hz; right). (B) An
Argand diagram showing the nine second harmonics in the complex plane
(numbered vector trajectories). The four segments of each
trajectory represent the gain and phase for each of the four trial
responses, with gain scaled by [1/4], so that that each
trajectory is the vector mean, and its distance from the origin denotes
the mean response amplitude. Regional interaction frequencies
fi + fj
and noise frequencies (gray lines terminated with
small dots) have random phase and therefore form random
walks around the origin. The dashed circle is the 95%
confidence limit computed from the noise frequencies. Thus, vectors
escaping from the dashed circle with increasing trial number
are significantly different from noise.