the significant interactions at couples of frequen- cies f
1
and f
2
, we tested the hypothesis that the bispectrum was equal to zero Huber et al., 1971;
Brillinger and Irizarry, 1998 at the 99 confi- dence limit. Phase-coupled frequencies f
3
= f
1
+ f
2
were determined for corresponding significant bis- pectral analysis at couples of frequencies f
1
and f
2
.
3. Results
Radioenzymatic ChAT assays were performed to assess the effect of the treatments. Samples of
medial septal area of equal weight 17.9 mg on average were analyzed and the ChAT activity in
controls was equal to 21.1 9 1.3 mmolh aver- age 9 S.E.M. per 100 mg of protein. In agree-
ment with previous reports Fusco et al., 1990; Rylett et al., 1993; Villa et al., 1996, the NGF
administration elicited a significant increase of ChAT activity + 48, Fig. 1. On the opposite,
the level of ChAT activity in the septum was decreased significantly by the injection of 192
IgG-saporin − 40, Fig. 1. ChAT activity de- creased also by the same proportion in the
neocortex samples 79.0 mg on average of the SAP-treated rats compared with controls 4.5 9
0.9 vs. 6.9 9 0.3 mmolh per 100 mg of protein, two-tailed t-test 2 P B 0.05. The decreased corti-
cal ChAT activity is in line with data reported elsewhere in the literature related to the use of the
same type of commercial 192 IgG-saporin in simi- lar doses Rossner et al., 1995. The radiochemical
detection of ChAT activity indicates that both NGF- and SAP-protocols used in the present
study were highly effective in altering the function of BFCN.
We recorded four LFPs simultaneously from 24, 20 to 28 different sites in controls, NGF- and
SAP-treated animals, respectively. The recordings analyzed here were obtained under steady-state
anesthetized condition in the absence of external sensory stimulation, a condition often referred to
as spontaneous or background activity. At each location, the recorded time analyzed here varied
between 6 and 8 min, which represents a total time corresponding to more than eight consecu-
tive hours for all groups of animals. The power spectrum was computed in the range 7 – 100 Hz
for each LFP over the duration of the recording at one location. The number of spectra computed
in each group was n = 112, 72, 117 for controls, NGF- and SAP-treated animals, respectively. All
power spectra of brain signals recorded in one group of animals were grouped together and then
normalized in order to have 100 density in the range 7 – 100 Hz Fig. 2. All power spectra densi-
ties were characterized by the effect of notch filtering centered on 50 Hz.
NGF treatment provoked a decrease in 15 – 20 Hz power whereas the injection of 192 IgG-sa-
porin provoked an increase of lower frequencies with a peak at 13 Hz. Interstingly, both treat-
ments increased the relative power in the 20 – 50 Hz frequency range and decreased at higher fre-
quencies, but with a very distinct pattern. An increase between 29 and 35 Hz was observed in
the cortical activity of NGF-treated animals, whereas SAP-treated were characterized by an
increase in power in the 38 – 42 Hz range. The main changes observed at high frequencies \ 50
Hz were not related to the change in relative power, but rather by the quasi-sinusoidally modu-
Fig. 1. ChAT activity expressed as percent of control n = 6 in homogenates of medial septal area of animals that received
intraventricular injections of either rhNGF or 192 IgG-saporin and were allowed to survive 14 – 20 days following injections.
Each value represents the mean and error bars the S.E.M. The asterisks denote significant differences by two-tailed t-test
from control rats 2P B 0.05 and 2P B 0.01.
Fig. 2. Averaged power spectrum densities for each group of animals. The bin size of the histogram is 1 Hz. The vertical
scale is in arbitrary units normalized to the highest bin in the distributions. The dotted lines in the uppermost and lower-
most panels correspond to the averaged power spectrum of the control group.
representative data from all recording sites and to avoid that a limited number of recordings, charac-
terized by a larger number of very significant bicoherencies, would bias the grand average anal-
ysis. The values of the bicoherence for single- channel calculations, where f
1
and f
2
are observed in the same signal, were larger in controls than in
treated rats median values equal to 8.1 versus 4.5 and 3.7 in NGF- and SAP-treated, respectively.
The 2-D plot of the bicoherences for cross-chan- nel calculations Fig. 3 has a complex shape due
to the symmetry properties of bispectral analysis Brillinger, 1965; Nikias and Raghuveer, 1987.
Values of cross-bicoherence tended to be 40 lower than in single-channel bicoherence, but the
same difference in magnitude remained between controls and treated rats. The data for single- and
cross-bicoherence were pooled together and the distribution of f
3
in the three groups of animals is illustrated in Fig. 4. The effect of the treatment
was higly significant Kruskal – Wallis nonpara- metric test, P B 0.001. The high frequencies val-
ues \ 70
Hz were
increased after
NGF treatment and accounted for 46 of the distribu-
tion. Conversely, the effect of 192 IgG-saporin was clear-cut towards the opposite direction, with
predominant low frequencies 61 were less than 50 Hz and few high frequencies.
Fig. 3. Bicoherence analysis across two channels. The bicoher- ence peaks represented by circle of phase coupled frequencies
f
1
and f
2
are plotted for frequency ranges 7 – 100 Hz at a resolution of 1 Hz. If pairs of frequences corresponding to
significant non-linear interactions observed at distinct record- ing sites, coincided exactly the overlap, is graphically shown by
bigger circles, whose radius is proportional to the number of overlapping points.
lated spectral envelopes ripples observed in this band. The ripple frequency in the controls was
equal to 11 cycles per octave. NGF treatment slowed the ripple frequency down to nine cycles
per octave but did not alter its amplitude near 1 dB. Conversely, in the SAP-treated animals the
amplitude of the ripples was reduced to 0.1 dB but its frequency remained the same as in
controls.
For each recording site we selected up to ten phase-coupled frequencies f
3
= f
1
+ f
2
correspond- ing to the bifrequencies with the most significant
bicoherence. This procedure allowed us to obtain
Fig. 4. Relative distribution of the non-linearly coupled fre- quencies f
3
= f
1
+ f
2
in the three groups of animals during spontaneous activity. Bispectral and cross-bispectral results
were pooled together. The bin size of the histogram is 10 Hz. Note the majority of frequencies higher than 70 Hz in NGF-
treated animals compared with the frequencies lower than 50 Hz in SAP-treated rats.
fore, we assume that our manipulations allowed us to modify the acticity of BFCN and to study
the effect of these projections on functional con- nectivity at the cortical level.
Some degree of synchronization between the activity of cortical units must exist in order to
generate the relatively slow up to 100 Hz electric brain activity typical of LFPs Elul, 1972. Each
cortical neuron can be viewed as a generator contributing its fraction to the UP, hence this
electric potential is the summed activity of all generators around the electrode tip. Different sites
within the same cortical area can show various degrees of synchronous activity in the time do-
main and of coupling of frequency components in the power spectra depending on the way, how
information is processed. Far-away structures are expected to contribute some common pattern of
waveform to all the recording sites. Such patterns could be generated by deep nuclei e.g. the thala-
mus, the basal forebrain that spread their effect over large cortical areas. In addition, the summed
activity of many seemingly uncorrelated local pro- cesses contributes to the LFP Abeles, 1982. The
detection
of synchronous
activity becomes
difficult if the activity is organized in groups of neurons synchronized among each other, but with
the activity of anyone such group that is uncorre- lated with that of any other group.
Signal analysis functions are subdivided into classes derived from their relationship with the
statistical moments and cumulant series. Second order cumulant class includes correlation, power
spectrum density and coherence. As second order cumulant statistics decompose the signal into a
linear combination of mutually uncorrelated fre- quency components Huber et al., 1971, they can
be applied only to stationary Gaussian signals and are not used to detect signal components
which are in non-linear, phase dependent, rela- tionships Nikias and Raghuveer, 1987. Recent
studies about the effect of NGF and 192 IgG-sa- porin on rat EEG Holschneider et al., 1997,
1999 used these techniques and showed that de- creased ChAT activity was associated with in-
crease in low frequency power, whereas increased ChAT activity was positively correlated with b
2
power. Our results show the same tendency but
4. Discussion
