Walter J. Freeman
Journal Article e–Reprint
Correlation of Goal–Directed Work With Sensory Cortical Excitability
By
Walter J. Freeman, M. D.
Supported by grants (MH–06686 and NB–05035) from the National Institute of Health, U.S.P.H.S., and by the Berkeley Computer Center. This paper was awarded first prize in the Annual A. E. Bennett Award in Biological Psychiatry.
INTRODUCTION
Cats generally do not work for food in
proportion to the strength of a stimulus (e.g., concentration of an odor), but
in proportion to an internal excitability state having multiple determinants
(e.g., hunger or duration of food deprivation, attentiveness to relevant
stimuli, etc.). These determining factors may operate on primary sensory
cortex. If so, the rate of behavioral response to any given external stimulus
might be varied by changes in the excitability level of that neuronal relay.
The cortical neuronal response to any fixed level of afferent stimulation
should then co–vary with cortical excitability and with an ongoing
behavioral measure.
In this study on cats, a repetitive
constant–current electrical pulse was delivered, with implanted
electrodes, to the lateral olfactory tract, evoking sequential single–shock
electrical responses in the primary olfactory (prepyriform) cortex. These
evoked potentials were averaged over a 12–sec period, during which each
cat was induced to pull on a rope to get food in an ergometer. Each averaged
evoked potential was measured in terms of eight parameters. These eight values
were then compared (by means of multivariate statistics) with the rate of work
for food that was measured during the period when the evoked potentials were
averaged.
Three questions were asked: What was the
level of covariance between cortical excitability and goal–directed work?
How many factors could be identified? And which of the eight measurements on
the evoked potentials best represented each of these factors?
METHODS
At least two pairs of bipolar electrodes
were implanted in the prepyriform cortex of each of seven adult cats, one pair
in the lateral olfactory tract for electrical stimulation and the other pair
across the prepyriform cortical dipole for recording [1]. On recovery, the cats
were trained to work in an ergometer [2] for food.
Stimulus intensities were optimized for
obtaining electrical responses in the linear dynamic range of cortical function
[3], and were kept well below levels required for orienting [4]. Stimulus rate
(7.5 sec) was adjusted to minimize averaging of spontaneous activity
("noise") into the records, to avoid overlap of the tail of one
evoked response with the initial portion of the succeeding one, and to give as
large a number of evoked potentials (90) as possible in the 12–sec period
of work. Averaging was by use of the Mnemotron 400A computer, with on–line
conversion of its analog output to 100 digital values at 1.25 msec intervals by
means of a digital voltmeter. The digitized signals were stored on magnetic
tape and later punched on cards for processing on the IBM 7090.
The data reported here constitute a set of 25–38 runs
made on each cat during a single day, after several weeks of training. The
entire set of averaged evoked potentials (AEP) on each cat was then averaged,
and the mean data were fitted with a generated curve by means of nonlinear
regression. The equation for this curve was derived from a transfer function
previously developed for this cortex [5], consisting of the sum of two damped
sinusoids, each specified by its frequency (2πf = OMEGA), initial
amplitude (V), decay rate (1/Q), and phase of onset (P); with V in microvolts,
OMEGA in radians/sec, P in radians, and t in seconds. The optimized parameters
then constituted the coefficients of a matched filter for the response of each
cat to electrical stimulation. They were treated as a centroid in the eight –dimensional
parameter space for each cat, about which the values for each AEP in the set of
25–38 runs lay scattered in a hyperellipsoid. Identification of the
coefficients for each AEP was then done by means of adaptive digital filters
[6].
The criterion for optimal fit between
the data and the fitted curves was the least squares deviation, expressed as
signal–to–noise ratio, and obtained by dividing the sums of squares
of the generated curve ("signal") by the sums of squares of the
residuals ("noise") after subtraction of the signal from the
digitized AEP. Computations were iterated as often as the signal–to–noise
ratio continued to improve; the level–off values differed between cats,
implying inherent variability for the ratio of amplitudes for evoked and
spontaneous potentials. A ratio persisting below 8:1 was regarded as cause for
rejection of a case. The rejection rate was not more than two cases per cat per
day.
The question arose next, what
transformations might be required on these data in preparation for the use of a
linear regression model? No simple or obvious procedures suggested themselves
during preliminary analysis, so the approach taken was the formulation of a
hypothetical neuronal mechanism generating the evoked potential, and this model
then supplied equations for the transformation of data from measured quantities
to estimates of state variables in the mechanism. Specifically [6], the cortex
was viewed as consisting of a sheet of pyramidal cells interacting by recurrent
inhibition. The evoked potential was treated as a succession of alternating
excitatory and inhibitory postsynaptic potentials, which was smoothed to a
sinusoidal shape because of distributed conduction delay in the recurrent
feedback path. The frequency and Q of oscillation in the evoked potential (in
this model) gave the basis for estimating, respectively, peak feedback delay
and loop gain, representing (again respectively) the volume extent and the
density of pyramidal cell interaction in the cortex.
The values for frequency (OMEGA) and (Q) were converted to
estimates of peak feedback delay (T) and loop gain (G) using the following
transformations:
These transformations proved useful as a
means for normalizing the variance of some of the coefficients and for
simplifying factor analysis. The meaning and methods for estimation of the
constants (B1 = 220; B2 = 720) are not important here and
will be discussed in a later report.
The
statistical procedures used will be stated with the results.
RESULTS
I. Level of Covariance
Mean values ±SD for the
parameters after conversion are shown in Table 1. Also given for each cat is
the over–all signal–to–noise ratio.
Two characteristics of these data
require special attention. The first is that the signal from each cat could be
represented by the sum of two and only two sinusoids. These took the form of a
"dominant" component having a high–amplitude, initially negative
peak of duration equal to about one quarter of a cycle (P1 SIGN
π/2 radians), and a subsidiary or "shaping" component, usually
of low amplitude and initial positivity (P2<0). The latter was
highly variable between cats, the apparent reasons being not immediately
relevant. The former was more easily and precisely determined, was less
variable between cats, and provided the major source of covariance between the
prepyriform AEP and rate of work.
The second characteristic was that
values for parameters were often intercorrelated, i.e., nonorthogonal. Whereas
the independently measured values for frequency (OMEGA) and Q were uncorrelated
in the data from each cat (r(OMEGA • Q) = –0.062), the transformed
parameters T and G were highly correlated (r(T1 • G1)
– 0.841, r (T2 • G2) = 0.959). The mean
ordinary correlation coefficient for (T1 • P1) was
0.591 and that for (T2•P2) was 0.552. These and
other smaller intercorrelations enjoined the use of multiple and partial
correlation techniques.
Multiple
correlation on the data from each cat was done on the IBM 7090, using rate of
work as the dependent variable (Table II). The coefficient of multiple
determination (R2), which is the ratio of the variance in rate of
work that is correlated with changes in the evoked potential to the total
variance in rate of work [7,8], ranged between 0.189 and 0.539. That is,
between 20% to 50% of the variance in rate of work was correlated with variance
in prepyriform excitability.
A multiple correlation coefficient (R)
was calculated for each cat. The distribution of these from the seven cats
following z–transformation [7] showed that the set could be treated as a
random sample from a common population, with a 99% confidence interval for the
mean multiple correlation coefficient (R) of from 0.46 to 0.70 and for R2
of 0.22 to 0.48.
An F–ratio was calculated for each
cat to estimate the significance of R. For three cats, values of R lay at or
near chance levels, and for each of four other cats the probability was between
0.10 and 0.05 that those values of R were obtained by chance.
The data were then normalized by
subtracting the eight means of each set of eight parameters from all values in
that set and dividing by the eight standard deviations for each set. Thus, for
each cat the values for each of the eight parameters had zero mean and unit
standard deviation. Multiple regression was then performed on the pooled data,
yielding a coefficient of multiple determination of 0.139 and an F–ratio
of 4.31, d.f. = 8,23, which lay well outside the chance range. This result gave
a pooled likelihood estimate for the validity of the multiple correlation, but
not for the level of covariance for each cat, because of the differences in
wave forms between cats.
II. Factor Analysis
A factor matrix was calculated from the
data for each cat, which showed that on the average among cats 88.1
±4.4% of the cumulative variance was inherent in the largest four
factors and 94.4 + 2.6% in the largest five factors. In all cats, the first two
factors were aligned on the T1 • G1 axis or the T2
• G2 axis. P1 and V1 were always
included among the remaining three factors, but the order was variable.
An attempt was made to submerge
individual differences between cats in order to reach for a more general
picture. The combined covariance matrix for the seven sets of data was
partitioned into an interset covariance matrix and an intraset covariance
matrix. The latter was converted to a correlation matrix on which factor
analysis was performed.
The results (Table III) showed that the
first five factors in the pooled intracat variance included 83.5% of the
cumulative variance. Detailed analysis is beyond the scope of this report.
Attention is called to the fact that the major factors in part loading on the W–axis
were I (T1 • G1), III (V1 • P2),
and IV and V (P1), but specifically not II (T2 • G2).
The number of factors operating in the covariance of cortical excitability with
rate of work therefore appeared to be three and possibly four.
III. Partial Correlation
Because eight parameters were required
to describe each evoked potential with a signal–to–noise ratio of
8:1 or better, and because fewer than 40 runs were obtainable on any one day,
the regression coefficients between the parameters and W were not reliably
determined for any cat, and the variability was too great to allow pooling of
their estimates. In any case, the patterns of evoked potentials differed among
cats, particularly in regard to the subsidiary or "shaping" component.
The best that could be done was to determine for the group which parameters
were correlated with W, with what sign, and with what level of significance.
For this the partial correlation
coefficents were used in two ways. First, an rp for each parameter
with W was calculated for each cat (holding the other seven parameters
constant) and the set was combined by z–transformation to give a set of–mean
values, <?>(Table IV). Only V1 and P1 were
uniformly similar in sign for the group of cats. Overall, V1 showed
a significant positive correlation with W1 and P1 a
negative correlation with W.
Second, the multiple regression done one the entire
normalized set of data yielded both ordinary (r) and partial (rp)
correlation coefficients, and (for rp) t–values indicating the
levels of significance. These data showed positive correlations between V1•W
(cf factor III), T1 • W, (cf factor I), and P2 • W, and
a negative correlation between P1 • W (cf factors IV and V). This was
quite similar to the pattern revealed by factor analysis, with the notable
exception that G1 appeared correlated with W(r =0.167) only by
virtue of its high correlation with T1, and in fact was not by
itself covariant with W (rP= –0. 002). Neither T2
nor G2 was correlated with W (cf factor II).
DISCUSSION
These findings established that there
was covariance beyond chance levels between sensory cortical excitability (as
measured by evoked potential techniques) and the rate of concomitant goal–directed
work; that from 20% to 50% of variance in whole–body work output was
correlated with changes in prepyriform excitability; and that the bulk of this
covariance lay between W and four measurements on the evoked potential: V1,
T1, P1, and P2. That is, the amplitude of the
dominant sinusoid, the phases of onset of the two sinusoids, and the peak
feedback delay time computed from measurements of the frequency and decay rate
of the dominant sinusoid were the best predictors of rate of work.
It is probable that the estimate of
level of covariance was inflated by virtue of certain characteristics of the
adaptive filters used here, and also because of trends in the data from three
of the cats. On the other hand, certain inadequacies in the measurement processes
(e.g., use of discrete interval approximations) probably reduced the attainable
level of covariance. Space does not permit discussion of the technical details.
Validation of these results was based mainly on comparisons with previous, less
sophisticated observations on the prepyriform evoked potential [5]. The
magnitudes and directions of correlations between V1 • W, T1
• W, and P1 • W were observed as predicted. The positive
ordinary correlation and the lack of partial correlation between G1
• W (as well as Q1 • W) was in contrast to a negative
correlation previously found between Q1• W. It is not clear
whether this difference arose because of the differing techniques of
measurement and calculation, or because the present set of measurements was
made on cats not oriented to the electrical stimulus, whereas previous
estimates of r(Q1 • W) came from cats attentive to the evoking
stimulus. This is now being checked.
The
existence of three factors was expected on the basis of previous studies of
this cortex [5]. The new data implied that T1 was the best predictor
for factor I, V1 for factor III, and P1 for factor IV or
V. Further behavioral manipulation will be required to establish the behavioral
correlates of these factors beyond the present tentative levels.
Three
main lines of study lead from these results. One is the exploration of the
uncorrelated variance in W, especially in terms of the excitabilities of motor
and other sensory cortexes. The second is the search for three or four subsidiary
inputs to the prepyriform cortex that regulate its excitability. It might be
possible, for example, to reproduce the patterns of change seen in the AEP
accompanying changes in behavior by stimulation of midbrain, thalamic, or other
limbic structures, and thus to determine the locations of controlling neurons.
The third is analysis of the cellular mechanism of this cortex in terms of the
signals that it generates during the performance of its normal operations on
sensory input data. The use of the transformation from OMEGA and Q to T and G
in this report is a reflection of that line of study, indicating that the three
lines are really interlocking and inseparable aspects of the same problem.
SUMMARY
Cats
with implanted electrodes were trained to work for food in an ergometer.
Measurements were made on averaged prepyriform evoked potentials of eight
parameters (two each for amplitude, frequency, decay rate, and phase of onset)
by means of digital adaptive filters on the IBM 7090. Multiple correlation was carried
out between these parameters and concomitantly measured rate of work. Between
20% to 50% of the variance in rate of work was correlated with changes in
levels of prepyriform excitability. Factor analysis showed the presence of
three and possibly four dominant factors in the covariance, and partial
correlation showed that four of the eight parameters of the evoked potential
were useful predictors of rate of work.
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