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Relation of olfactory bulb and cortex. II. Model for driving of cortex by bulb
Brain Research, 409 (1987) 294-301 Elsevier
294 BRE 12513
Relation of olfactory bulb and cortex. II. Model for driving of cortex by bulb Steven L. Bressler Department of Physiology-Anatomy, University of California, Berkeley, CA 94720 (U.S.A.) (Accepted 9 September 1986)
Key words: Central nervous system (CNS); Electrophysioiogy; Cortex; Olfaction; Field potential; Modelling; Transmission
The major projection pathway of the olfactory bulb is by way of the lateral olfactory tract (LOT) to the olfactory cortex. Oscillatory bursts of extracellular potential appear during inspiration in both bulb and cortex. Based on anatomical and physiological considerations, a model was proposed, consisting of a bulbar transmitter, a conduction line representing axons in the LOT, and a cortical receiver. The model predicted the relation between phase and frequency of bulbar and cortical burst pairs, based on the expectation that the bulb drives the cortex. Experimental phase-frequency plots were computed from bursts of 9 bulbocortical electrode site pairs from each of 10 rabbits. For each site pair, the model predicted the expected range of the joint variation of phase and frequency, using the known distance between the bulbar and cortical sites. The m o d e l was highly successful (greater than 95% prediction accuracy) for one quarter of the total number of site pairs examined. The wide range of variation for the rest of the data suggested that higher order interactions are responsible for the phase relation between bulb and cortex. Convergence of input, independence of the cortical generator, cortical feedback to the bulb and synchronization by an outside source are all discussed as possible contributors to this variation.
INTRODUCTION During normal respiration, the characteristic pattern of extracellular electrical activity in both the olfactory bulb and cortex is a sequence of sinusoidal bursts of potential. Each burst is initiated by inspiration and terminates during expiration. O d o r in the inspired air is not necessary to induce bursts in either bulb or cortex. The burst frequency lies in the 35-85 cps ),-range. The bulbar and cortical burst frequencies are approximately the same, with the cortical frequency statistically d e p e n d e n t on that of the bulb 4. The goal of this study was to learn about the relation between the bulb and cortex by measuring how well bulbocortical burst pairs conform to a simple model in which the bulb drives the cortex. There is considerable evidence that the cortical burst is generated, at least partially, in response to driving input which originates in the olfactory bulb. First is the arrangement of synaptic connections. The axons of mitral and tufted cells, whose cell bodies are
located in the bulb, form the lateral olfactory tract ( L O T ) and terminate on the apical dendrites of pyramidal cells in the olfactory cortex. The L O T is the principal pathway by which olfactory information arrives at the olfactory cortex. Second, single-shock stimulation of the L O T between the bulb and cortex produces an oscillatory e v o k e d potential in the cortex, with frequency in the y-range 9 (as well as an antidromically activated oscillatory e v o k e d potential in the bulb at a p p r o x i m a t e l y the same frequency). Thus, excitation of buibar cell axons causes an oscillatory event in the cortex. Third, the pulse probability density of mitrai and tufted cells, as observed by the bulbar post-stimulus time histogram (PSTH), is oscillatory at the same frequency as the buibar evoked potential 1°. This implies that the bulbar oscillatory state is transmitted as pulse probability density over the L O T and delivered to the cortex at mitral and tufted cell axon terminals. Fourth, bursts are commonly observed in the bulb and not in the cortex, but are rarely seen in cortex without also being in the
Correspondence: S.L. Bressler. Present address: EEG Systems Laboratory, 1855 Folsom Street, San Francisco, CA 94103, U.S.A. 0006-8993/87/$03.50 t~) 1987 Elsevier Science Publishers B.V. (Biomedical Division)
295 bulb 3. Finally, when the bulb is surgically isolated from the cortex, it still manifests sinusoidal bursts, but activity in the cortex disappears 1L16. Yet, when bulb and cortex are together isolated from the forebrain, bursts persist in both 1. The oscillatory mechanisms of both bulb and cortex have been shown to be negative feedback loops between excitatory projection neurons and inhibitory interneurons 1L21, the loop of each structure being confined entirely to that structure. Receptor input to the bulb during inspiration is not itself oscillatory, but rather causes the bulb to enter a self-generated oscillatory state H. Centrifugal inputs may affect the interaction of bulb and cortex, but the lesion studies mentioned above indicate that they are not responsible for triggering each cycle of a burst. The anatomical and physiological evidence implies that the olfactory bulb contains populations of neurons that serve as generators of ),-activity, that this activity is transmitted from the bulb over the LOT, and that the cortex contains populations which are thereby driven at the same frequency. A local population in which y-activity arises can be called a 'transmitter' at a certain frequency, and those populations to which it gives significant numbers of axons can be called 'receivers'. In these terms, an act of transmission from one population to another requires that a burst in the transmitter be accompanied by a burst at the same frequency in the receiver. It is expected that the cortical receiver has its own 'characteristic' frequency which may differ from the driving transmitter frequency 11. This conceptual model of unidirectional transmission is the basis for the present study. In light of the feedback pathway from the cortex to the bulb and the connections of both bulb and cortex with the anterior olfactory nucleus 5-7,25 olfactory processing obviously involves many more interactions than simple forward driving. Yet the forward projection from bulb to cortex in the LOT is the primary olfactory pathway, whereas feedback pathways are in some way modulatory. As a first approximation, consideration is given to transmission from bulb to cortex, with more complex interactions left for future analysis. Thus the aim of this study was to test whether the olfactory bulb drives the olfactory cortex. A model was derived that incorporated the relevant anatomical and physiological features of these two structures,
treating the bulb as transmitter and cortex as receiver. Given the known distance between specific bulbar and cortical recording sites, the model predicted the expected range of the phase-frequency relation between their electrical activities, taking into account the known sources of variation. Experimental phase-frequency plots, described in the first part of this report, were compared to the ranges predicted by the model. For unidirectional transmission (driving) to be in effect, the experimental phase-frequency plot was expected to lie within the predicted range. MATERIALS AND METHODS The data set used in this study has previously been described 3. Sample sets of 50 bulbocortical burst pairs were collected from each of 9-channel pairs (every pairwise combination of 3 bulbar and 3 cortical electrode sites). Phase and cofrequency were computed for each pair in the set. Plots of phase vs cofrequency were made for each of 283 sample sets collected from 37 recording sessions for 10 rabbits. A model was constructed to predict the expected range of the relation between bulbocortical phase and cofrequency, based on the known anatomical and physiological features of the bulb and cortex, with the hypothesis that the bulb drives the cortex. The details of this model are presented in the Results. A key component of the model was the transfer function established by the extensive evoked potential studies of Freeman, which describes the olfactory cortex as a linear system with negative feedback II (Fig. 1). The transfer function for this negative feedback system is given by
C(s) = A(s)/(1 + KnA(s) B(s)) where C(s) is the cortical transfer function, A(s) is the transfer function of the superficial pyramidal cell (A) population, B(s) is the transfer function of the deep, short-axon, granule cell (B) population, and Kn is the negative feedback gain. The dynamics of populations A and B are both approximated by the second-order differential equation for which the transfer function is
A(s) = B(s) = ab/(s + a) (s + b)
296 RESULTS
The model
Fig. 1. Lumped linear circuit representing the olfactory cortex as a single negative feedback loop. Input (I) at the left represents pulse activity on the axons of the lateral olfactory tract, which terminate on the apical dendrites of the superficial pyramidal cell (A) population. A(s) represents the transfer function of this population. Output (O) at the right represents the observable field potential of the superficial pyramidal cell population. This population is excitatory onto the deep short-axon granule cell (B) population whose transfer function is B(s). Kn represents the negative feedback gain of this population which is inhibitory back onto the superficial pyramidal cell population.
where a = 220 S-1 and b = 720 S -1 a r e empirically determined rate constants. Then, the cortical transfer function becomes:
C(s) = ab(s + a) (s + b)/[(s + a)2(s + b) 2 + KnaZb2] This transfer function describes the response of the system to a given input. During the burst event, the input to the cortex is the sinusoidal pulse probability wave on mitral-tufted cell axons in the LOT. The system output, the cortical burst, has the same frequency as its input but is phase shifted. The poles of the transfer function are solutions for the terms in the denominator and represent the natural frequencies and decay rates of the system. The zeros are solutions for the terms in the numerator and represent frequencies and decay rates at which activity cannot occur. To determine the phase angle of the cortical burst in response to driving sinusoidal input from the bulb, a technique was taken from control theory which uses the graphic representation of the system transfer function in coordinates of decay rate and frequency 8. The steady-state response of a linear system to sinusoidal inputs is derived from the pole-zero map of the transfer function. Vectors are drawn from the poles and zeros to the point on the frequency axis representing the input frequency. The sum of the angles between the zero vectors and the decay rate axis, less the sum of the angles between the pole vectors and the decay rate axis, gives the phase angle of the system output at this frequency.
A model was proposed to predict the phase between bursts of extracellular potential from the olfactory bulb and cortex dependent on their cofrequency. The model consisted of a transmitter (bulb), a transmission line (axons of the LOT), and a receiver (cortex). The cortical burst was considered to be a manifestation of the response of excitatory pyramidal cells, involved in a negative feedback loop with inhibitory interneurons, to driving input from the transmitter. The 'characteristic frequency' of this negative feedback loop has been defined as the frequency at which oscillations occur on impulse input 11. Variation in phase was incorporated into the model from the following 4 sources: (1) conduction delay due to transmission from the transmitter over the transmission pathway to the receiver; (2) the cortical frequency response, due to the difference between the driving transmitter frequency and the characteristic frequency of the receiver; (3) variation of the characteristic frequency of the receiver; and (4) variation in phase between the bulbar field potential and the pulse density transmitted over the LOT. Conduction delay. Conduction delay was determined by the distance between bulbar and cortical electrode sites, and by the mean L O T conduction velocity between those sites. Postmortem measurements indicated a range of possible interelectrode distances from 4 to 19 mm, depending on electrode location in bulb and cortex. Kerr and Dennis 17 reported that conduction velocity in the L O T of the cat is 6 m/s, dropping to 0.8 m/s in collaterals. Haberly 13 similarly found the opossum L O T conduction velocity to be 7 m/s, falling to 1.6 m/s in the cortex lateral to the tract. Assuming similar velocities for the rabbit, the range of possible values for conduction delay is from 0.5 to 25 ms. Considering only conduction delay, a fixed time delay for conduction would represent a smaller fraction of a cycle (and therefore a smaller phase) at lower frequencies than at higher ones. The rate of change of phase with frequency would depend on the time delay, longer delays increasing the rate. The relation of phase as a function of driving frequency is plotted in Fig. 2A for two different values of conduction delay (2 and 6 ms). Cortical frequency response. As mentioned in the
297 Introduction, the pulse probability density of mitral cells has been observed to oscillate at the same frequency as the bulbar evoked potential. For this reason, it was assumed that, during each burst, pulses, whose probability oscillated at the burst frequency, were transmitted over L O T axons to the cortex. The feedback loop in the cortex between excitatory pyramidal cells and inhibitory interneurons was assumed to be driven at the same frequency. The graphic method described in the Methods was used to determine the phase shift of the cortical response for a range of driving frequencies. Given a fixed cortical characteristic frequency, cortical phase lag increased with increasing driving frequency. Variation of characteristic frequency. The model
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Fig. 2. A: receiver phase as a function of driving frequency, based solely on conduction delay. Negative phase corresponds to receiver lag. The top curve represents a 2-ms delay; the bottom, 6 ms. B: receiver phase as a function of driving frequency, based solely on the cortical frequency response. The points on each curve represent a different driving frequency from 35 to 85 cps. The top curve represents a receiver characteristic frequency of 85 cps; the bottom, 35 cps. Negative phase corresponds to receiver lag.
assumed that, like the bulbar driving frequency, the characteristic frequency of the cortex could vary over the ), frequency range, and that it would take different values from one burst to the next. Because cortical characteristic frequency was not directly measurable for each burst, the model predicted a range of possible phase values, depending on cortical characteristic frequency. Therefore, the output of the model was a family of curves, one for each value of cortical characteristic frequency in the ~ range. The characteristic frequencies were 85 and 35 cps, respectively, for the top and bottom curves in Fig. 2B, representing the experimentally observed limits for the range of burst frequencies. Variation of mitral-granule phase in bulb. Another source of variation was the variability of the phase difference between the granule cell population and the mitral cell population. Many previous studies have established the inhibitory granule cell population as the dominant generator of bulbar field potentials, and the excitatory mitral cell population (including tufted cells) as generator of the pulse activity which is transmitted over the L O T to the cortex lt'2t. Freeman 11 measured the phase between bulbar averaged evoked potentials and post-stimulus time histograms (measuring granule and mitral population output, respectively). He also accurately predicted this phase from system analysis of the olfactory bulb. Granule output lagged mitral output by 82 + 10°. The effect of including this factor in the model is demonstrated in Fig. 3A. The solid curves show the predicted relation of phase to driving frequency for 2ms conduction delay (85 cps characteristic frequency, top; 35 cps, bottom). The dashed curves show the same relation except that phase was relative to the granule rather than mitral output. Since granule output lagged mitral output, the cortical phase relation was shifted in the direction of greater cortical lead. In order to determine the maximal range of predicted variation of bulbocortical phase, the greatest value of granule lag (92 °) was added to the upper curve (85 cps) and the least (72 °) was added to the lower curve (35 cps). Fig. 3B shows a family of curves for a conduction delay of 2.50 ms, representing the complete model (i.e. sources (a)-(d)). The family contains 11 curves representing characteristic cortical frequencies from 35 to 85 cps in steps of 5 cps.
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Fig. 3. A: receiver phase as a function of driving frequency. The solid curves represent the relation based on sources (a) to (c) (time delay = 2,5 ms; 85 cps characteristic frequency, top; 35 cps, bottom). The dashed curves represent the result of adding source (d), the phase lag of the granule population. Thus, while the solid curves represent phase with respect to the transmitter neurons (mitral cells), the dashed curves show phase with respect to the cells which generate the observable bulbar EEG (granule cells). B: receiver phase as a function of driving frequency: the complete model with phase equal to the resultant phase from sources (a) to (d). The family contains 11 curves representing characteristic frequencies from 35 (bottom) to 85 (top) cps, in steps of 5 cps, each with conduction delay ot"2.5 ms. Negative phase corresponds to receiver lag.
Fitting the model to the data For each of the 283 sample sets, a scatter diagram of bulbocortical phase vs cofrequency was displayed graphically. The distance between the bulbar and cortical recording sites was estimated from postmortem measurements, and from the dimensions Of the cortical electrode array. Distance was divided by velocity to give conduction delay. Families of curves predicted from the model for different values of conduction delay were overlaid on the scatter diagram. The fraction of data points falling within the domain of each family was a simple expression of the degree
of conformance of the experimentally determined distribution of points to the predicted range. The optimal family of curves was that which had the lowest fraction ~ . The values of f ranged from 0.44 to 1.00 over all 283 sample sets (mean = 0.82 + 0.14). For 25% of the 283 sample sets examined in this study, f was at 0.95 or above. For 50%, f w a s from 0.71 to 0.94, and for 25% it was below 0.71. Considering the average value of f for each site pair, the values ranged from 0.61 to 1.00 (mean = 0.83 + 0.15) over the 90 site pairs (9 pairs from each of 10 rabbits). Twenty-six percent of the site pairs had values of f exceeding 0.95, 47% were from 0.73 to 0.95, and 27% were below 0.73. The values of velocity for the optimal family of curves ranged from 0.7 to 6.5 m/s over all sample sets (mean = 2.3 + 1.4 m/s). Since conduction from a bulbar site to most cortical locations in the array most likely involved some passage over collaterals, this range of values for velocity was compatible with that reported in the literature 13.17. An inverse relation was expected between f and the dispersion of phase from its mean since increased dispersion would tend to reduce the number of data points falling within the predicted range. A mean value o f f and of the standard deviation of phase were calculated for each of the 9 site pairs from each rabbit. The Pearson r was -0.86 for the relation between f and standard deviation of phase. This r was significantly different from zero at P < < 0.001. The 95% confidence interval on r was f r o m - 0 . 9 0 t o - 0 . 7 9 . Approximately 0.74 of the variation in f c o u l d be attributed to a linear relation with phase dispersion. It was previously reported that phase dispersion was inversely related to mean bulbocortical correlation 3. To determine whether the sample sets with high values o f f also had high mean bulbocortical correlation , the Student's t-test was performed, comparing mean bulbocorticai correlation between the class of 71 sets with highest f ( > 0.94) and the class of 70 sets with lowest f ( < 0.71). The buibocortical correlation of the first class was significantly higher than than that of the second (t -- 7.86, df = 139) at P < < 0.0005. It has also been shown that the interdependence between bulbar and cortical recording sites varies with location in bulb and cortex 3. To test the spatial
299 variation off, a value o f f was determined for each of the 90 bulbocortical pairs (9 pairs for 10 rabbits) by averaging over recording sessions. The 90 values were then put through a logarithmic transformation to form a normal distribution. To compare the effect of bulbar location on f, the data were organized as a 30 x 3 matrix, each row containing the ordered values of f for the 3 bulbar sites relating to a single cortical site. Then analysis of variance was employed to test for an effect due to bulbar location. The F ratio (F2,58 = 10.1) for this effect was significant at P << 0,005. The effect of cortical location on f was analyzed in the same manner. The Fratio (F2.58 = 6.3) for the effect of cortical location was significant at P < 0.005. However, no spatial regularities were observed in either structure from the f values between site pairs. DISCUSSION A model was proposed based on the hypothesis that the olfactory bulb drives the olfactory cortex. It was used to predict the expected range of relation between phase and cofrequency of bulbocortical burst pairs. Site pairs were found with phase-frequency plots within the range predicted by the model (high values off). These site pairs had low phase dispersion and physiologically consistent phase differences. However, there was wide variation among the site pairs studied, the values o f f ranging from 1.0 down to as low as 0.61. There was significant variation in f among bulbar sites in relation to any one cortical site, and significant variation among cortical sites in relation to any one bulbar site. An inverse relation existed between f and phase dispersion. The distribution of phase for site pairs with low phase dispersion fell within the range predicted by the model. As phase dispersion increased, the model was less able to account for the phase distribution. An inverse relation was previously found between mean bulbocortical correlation and phase dispersion 3. This implied that sample sets which conformed to the model also had a high mean level of bulbocortical correlation. This was confirmed in the present study by the finding that mean bulbocortical correlation for the class of sample sets which conformed to the model (highest f) was significantly higher than the class with the lowest f.
The major findings of this report, therefore, are that: (1) a substantial proportion of site pairs (26%), with high bulbocortical correlation, conformed highly ( f > 0.95) to the simple model of bulbar driving of cortex; (2) there was a large range of variation over site pairs in the degree of conformance; (3) there were significant differences among bulbar sites in their relation with a cortical site; and (4) there were significant differences among cortical sites in their relation with a bulbar site. What possible mechanisms are there to account for these findings? For site pairs which conform to the model, the cortical burst is expected to be highly dependent on the bulbar burst. For this to take place, the dominant effect is expected to be a strong influence, in terms of number, position and/or strength of synapses on apical dendrites of pyramidal cells at the cortical site from axons of mitral cells at the bulbar site. There are at least 4 explanations, consistent with the anatomical evidence, which could account for the variation in conformance to the model among site pairs. One likely possibility is that, due to convergence of input, the cortical response is a summation of activity transmitted from different parts of the bulb. The anatomical projection of the bulb to cortex is generally thought to be diffuse rather than point-to-point (although there is at least one report of some anatomical precision in the bulbocortical projection2°). Most anatomical studies have suggested that each location in the cortex receives LOT projections from mitral cells in a large fraction of the bulb, and similarly, that each region of the bulb sends axons to a large area of cortex 12'14'18'19. Thus, there might be a strong synaptic input from the bulbar site in a site pair, but the receiver at the cortical site would not necessarily be driven by the transmitter at that one bulbar site alone. Rather it might integrate effective inputs from transmitters at other bulbar sites as well. For any given site pair, the degree of dependence of the cortical on the bulbar burst would be determined by the strength of influence of the bulbar input relative to competing inputs. A second possibility is that variation in the bulbocortical relation is due to variation in the degree to which the cortical site is a passive receiver. According to this hypothesis, even if a cortical site receives driving input from a transmitter in just one local bulbar region, the degree to which its burst depends on
300 bulbar input may vary. It is likely that the cortex, just as the bulb, has the ability to enter an independent self-generated oscillatory state H. The degree to which a cortical site acted as a receiver with respect to a bulbar transmitter would depend on the relative strengths of the bulbar driving input vs its own internal tendency to self-generated oscillation. A third possible explanation is that of feedback from the cortex to the bulb in response to driving input. There are several reports of centrifugal fibers from cortex to bulb 5-7'15. Evidence has previously been presented for cortical feedback in the 15-35 cps frequency range 2. Feedback might also occur in the 35-85 cps ),-range. Even if the cortical receiver acted passively rather than generating its own oscillatory state, feeding back with delay to the bulbar transmitter the activity imposed upon it, the effect of feedback would be to alter the phase relation between bulbar and cortical bursts. Variation in the efficacy of the feedback pathway might be responsible for the varied relations among site pairs. This explanation could account for the substantial number of sample sets (47%) found to have a positive correlation of bulbocortical phase and cofrequency (increasing cortical lead with increasing frequency) 3. For the model of unidirectional driving, the correlation was always found to be negative (increasing cortical lag with increasing frequency). When a term was added to the other terms in the model, to represent feedback onto granule cells at their deep ends, phase-frequency relations with positive correlation were found. A fourth alternative is that synchronization of bulbar and cortical bursts depends on a c o m m o n outside source such as the anterior olfactory nucleus or the nucleus of the horizontal limb of the diagonal band, REFERENCES 1 Becket, C.J. and Freeman, W.J., Prepyriform electrical activity after loss of peripheral or central input, or both, Physiol. Behav., 3 (1968) 597-599. 2 Bressler, S.L., Spatial organization of EEGs from olfactory bulb and cortex, Electroencephalogr. Clin. Neurophysiol., 57 (1984) 270-276. 3 Bressler, S.L., Relation of olfactory bulb and cortex. I. Spatial variation of bulbocortical interdependence, Brain Research, 409 (1987) 285-293. 4 Bressler, S.L. and Freeman, W.J., Frequency analysis of olfactory EEG in cat, rabbit and rat, Electroencephalogr. Clin. Neurophysiol., 50 (1980) 19-24.
which are both known to project to both structures. Convergence of bulbar inputs could be uniform rather than patterned as in the first hypothesis. In this hypothesis, the cortical site would not show a fixed time relation to the bulbar site unless both sites received input from the c o m m o n outside source. The effect of the outside source might be to selectively entrain pairs of bulbocortical sites out of a field of randomly active transmitters and receivers. The degree of entrainment of a particular bulbocortical site pair would determine its apparent conformance to the driving model, although, strictly speaking, the model would not be satisfied. At present, it is not possible to distinguish among these alternatives. Since they are not all mutually exclusive, it is possible that some combination of these mechanisms is at play. For future studies, it would be useful to repeat these experiments with lesioning of the centrifugal fiber pathways to the bulb, to remove centrifugal and feedback input. Since these findings were based on a small sample of electrode sites, future studies should examine a larger number of site pairs. Whatever the mechanism, the present findings imply that, functionally, the relation between bulb and cortex is not as spatially diffuse as indicated by most anatomical studies.
ACKNOWLEDGEMENTS The author thanks Dr. Walter J. Freeman for guidance throughout the course of this work and Dr. Alan S. Gevins for critical review of the manuscript. This research was supported by Grant MH06686 from the National Institute of Mental Health to Walter J. Freeman. 5 Broadwell, R.D. and Jacobowitz, D.M., Olfactory relationships of the telencephalon and diencephalon in the rabbit. III. The ipsilateral centrifugal fibers to the olfactory bulbar and retrobulbar formations, J. Comp. Neurol., 170 (1976) 321-346. 6 Dennis, B.J. and Kerr, D.I., Origins of olfactory bulb centrifugal fibres in the cat, Brain Research, 110 (1976) 593-600. 7 De Olmos, J., Hardy, H. and Heimer, L., The afferent connections of the main and the accessory olfactory bulb formations in the rat: an experimental HRP study, J. Comp. Neurol., 181 (1978) 213-244. 8 Di Stefano, J., Stubberud, A. and Williams, I., Feedback and Control Systems, McGraw-Hill, New York, 1967.
301 9 Freeman, W.J., Patterns of variation in waveform of averaged evoked potentials from prepyriform cortex of cats, J. Neurophysiol., 31 (1968) 1-13. 10 Freeman, W.J., Measurement of oscillatory responses to electrical stimulation in olfactory bulb of cat, J. Neurophysiol., 35 (1972) 762-779. 11 Freeman, W.J., Mass Action in the Nervous System, Academic. New York, 1975. 12 Haberly, L.B., Unitary analysis of opossum prepyriform cortex, J. Neurophysio/., 36 (1973)762-774. 13 Haberly, L.B., Summed potentials evoked in opossum prepyriform cortex, J. Neurophysiol., 36 (1973) 775-788. 14 Haberly, L.B. and Price, J.L., The axonal projection patterns of the mitral and tufted cells of the olfactory bulb in the rat, Brain Research, 129 (1977) 152-157. 15 Haberly, L.B. and Price, J.L., Association and commissural fiber systems of the olfactory cortex of the rat. 1. Systems originating in the piriform cortex and adjacent areas, J. Comp. Neurol., 178 (1978) 711-740.
16 Kerr, D., Olfactory centrifugal pathways. In P. LeMagnen and P. MacLeod (Eds.), Olfaction and Taste, Vol. 6, Information Retrieval, London, 1977. 17 Kerr, D. and Dennis, B., Collateral projection of the lateral olfactory tract to entorhinal cortical areas in the cat, Brain Research, 36 (1972) 399-403. 18 Price, J.L., An autoradiographic study of complementary laminar patterns of termination of afferent fibers to the olfactory cortex, J. Cornp. Neurol., 150 (1973) 87-108. 19 Price, J.L. and Sprich, W.W., Observations on the lateral olfactory tract of the rat, J. Comp. Neurol., 162 (1975) 321-336. 20 Scott, J.W., McBride, R.L. and Schneider, S.P., The organization of projections from the olfactory bulb to the piriform cortex and olfactory tubercle in the rat, J. Comp. Neurol., 194 (1980) 519-534. 21 Shepherd, G.M., Synaptic organization of the mammalian olfactory bulb, Physiol. Rev., 52 (1972) 864-917.
294 BRE 12513
Relation of olfactory bulb and cortex. II. Model for driving of cortex by bulb Steven L. Bressler Department of Physiology-Anatomy, University of California, Berkeley, CA 94720 (U.S.A.) (Accepted 9 September 1986)
Key words: Central nervous system (CNS); Electrophysioiogy; Cortex; Olfaction; Field potential; Modelling; Transmission
The major projection pathway of the olfactory bulb is by way of the lateral olfactory tract (LOT) to the olfactory cortex. Oscillatory bursts of extracellular potential appear during inspiration in both bulb and cortex. Based on anatomical and physiological considerations, a model was proposed, consisting of a bulbar transmitter, a conduction line representing axons in the LOT, and a cortical receiver. The model predicted the relation between phase and frequency of bulbar and cortical burst pairs, based on the expectation that the bulb drives the cortex. Experimental phase-frequency plots were computed from bursts of 9 bulbocortical electrode site pairs from each of 10 rabbits. For each site pair, the model predicted the expected range of the joint variation of phase and frequency, using the known distance between the bulbar and cortical sites. The m o d e l was highly successful (greater than 95% prediction accuracy) for one quarter of the total number of site pairs examined. The wide range of variation for the rest of the data suggested that higher order interactions are responsible for the phase relation between bulb and cortex. Convergence of input, independence of the cortical generator, cortical feedback to the bulb and synchronization by an outside source are all discussed as possible contributors to this variation.
INTRODUCTION During normal respiration, the characteristic pattern of extracellular electrical activity in both the olfactory bulb and cortex is a sequence of sinusoidal bursts of potential. Each burst is initiated by inspiration and terminates during expiration. O d o r in the inspired air is not necessary to induce bursts in either bulb or cortex. The burst frequency lies in the 35-85 cps ),-range. The bulbar and cortical burst frequencies are approximately the same, with the cortical frequency statistically d e p e n d e n t on that of the bulb 4. The goal of this study was to learn about the relation between the bulb and cortex by measuring how well bulbocortical burst pairs conform to a simple model in which the bulb drives the cortex. There is considerable evidence that the cortical burst is generated, at least partially, in response to driving input which originates in the olfactory bulb. First is the arrangement of synaptic connections. The axons of mitral and tufted cells, whose cell bodies are
located in the bulb, form the lateral olfactory tract ( L O T ) and terminate on the apical dendrites of pyramidal cells in the olfactory cortex. The L O T is the principal pathway by which olfactory information arrives at the olfactory cortex. Second, single-shock stimulation of the L O T between the bulb and cortex produces an oscillatory e v o k e d potential in the cortex, with frequency in the y-range 9 (as well as an antidromically activated oscillatory e v o k e d potential in the bulb at a p p r o x i m a t e l y the same frequency). Thus, excitation of buibar cell axons causes an oscillatory event in the cortex. Third, the pulse probability density of mitrai and tufted cells, as observed by the bulbar post-stimulus time histogram (PSTH), is oscillatory at the same frequency as the buibar evoked potential 1°. This implies that the bulbar oscillatory state is transmitted as pulse probability density over the L O T and delivered to the cortex at mitral and tufted cell axon terminals. Fourth, bursts are commonly observed in the bulb and not in the cortex, but are rarely seen in cortex without also being in the
Correspondence: S.L. Bressler. Present address: EEG Systems Laboratory, 1855 Folsom Street, San Francisco, CA 94103, U.S.A. 0006-8993/87/$03.50 t~) 1987 Elsevier Science Publishers B.V. (Biomedical Division)
295 bulb 3. Finally, when the bulb is surgically isolated from the cortex, it still manifests sinusoidal bursts, but activity in the cortex disappears 1L16. Yet, when bulb and cortex are together isolated from the forebrain, bursts persist in both 1. The oscillatory mechanisms of both bulb and cortex have been shown to be negative feedback loops between excitatory projection neurons and inhibitory interneurons 1L21, the loop of each structure being confined entirely to that structure. Receptor input to the bulb during inspiration is not itself oscillatory, but rather causes the bulb to enter a self-generated oscillatory state H. Centrifugal inputs may affect the interaction of bulb and cortex, but the lesion studies mentioned above indicate that they are not responsible for triggering each cycle of a burst. The anatomical and physiological evidence implies that the olfactory bulb contains populations of neurons that serve as generators of ),-activity, that this activity is transmitted from the bulb over the LOT, and that the cortex contains populations which are thereby driven at the same frequency. A local population in which y-activity arises can be called a 'transmitter' at a certain frequency, and those populations to which it gives significant numbers of axons can be called 'receivers'. In these terms, an act of transmission from one population to another requires that a burst in the transmitter be accompanied by a burst at the same frequency in the receiver. It is expected that the cortical receiver has its own 'characteristic' frequency which may differ from the driving transmitter frequency 11. This conceptual model of unidirectional transmission is the basis for the present study. In light of the feedback pathway from the cortex to the bulb and the connections of both bulb and cortex with the anterior olfactory nucleus 5-7,25 olfactory processing obviously involves many more interactions than simple forward driving. Yet the forward projection from bulb to cortex in the LOT is the primary olfactory pathway, whereas feedback pathways are in some way modulatory. As a first approximation, consideration is given to transmission from bulb to cortex, with more complex interactions left for future analysis. Thus the aim of this study was to test whether the olfactory bulb drives the olfactory cortex. A model was derived that incorporated the relevant anatomical and physiological features of these two structures,
treating the bulb as transmitter and cortex as receiver. Given the known distance between specific bulbar and cortical recording sites, the model predicted the expected range of the phase-frequency relation between their electrical activities, taking into account the known sources of variation. Experimental phase-frequency plots, described in the first part of this report, were compared to the ranges predicted by the model. For unidirectional transmission (driving) to be in effect, the experimental phase-frequency plot was expected to lie within the predicted range. MATERIALS AND METHODS The data set used in this study has previously been described 3. Sample sets of 50 bulbocortical burst pairs were collected from each of 9-channel pairs (every pairwise combination of 3 bulbar and 3 cortical electrode sites). Phase and cofrequency were computed for each pair in the set. Plots of phase vs cofrequency were made for each of 283 sample sets collected from 37 recording sessions for 10 rabbits. A model was constructed to predict the expected range of the relation between bulbocortical phase and cofrequency, based on the known anatomical and physiological features of the bulb and cortex, with the hypothesis that the bulb drives the cortex. The details of this model are presented in the Results. A key component of the model was the transfer function established by the extensive evoked potential studies of Freeman, which describes the olfactory cortex as a linear system with negative feedback II (Fig. 1). The transfer function for this negative feedback system is given by
C(s) = A(s)/(1 + KnA(s) B(s)) where C(s) is the cortical transfer function, A(s) is the transfer function of the superficial pyramidal cell (A) population, B(s) is the transfer function of the deep, short-axon, granule cell (B) population, and Kn is the negative feedback gain. The dynamics of populations A and B are both approximated by the second-order differential equation for which the transfer function is
A(s) = B(s) = ab/(s + a) (s + b)
296 RESULTS
The model
Fig. 1. Lumped linear circuit representing the olfactory cortex as a single negative feedback loop. Input (I) at the left represents pulse activity on the axons of the lateral olfactory tract, which terminate on the apical dendrites of the superficial pyramidal cell (A) population. A(s) represents the transfer function of this population. Output (O) at the right represents the observable field potential of the superficial pyramidal cell population. This population is excitatory onto the deep short-axon granule cell (B) population whose transfer function is B(s). Kn represents the negative feedback gain of this population which is inhibitory back onto the superficial pyramidal cell population.
where a = 220 S-1 and b = 720 S -1 a r e empirically determined rate constants. Then, the cortical transfer function becomes:
C(s) = ab(s + a) (s + b)/[(s + a)2(s + b) 2 + KnaZb2] This transfer function describes the response of the system to a given input. During the burst event, the input to the cortex is the sinusoidal pulse probability wave on mitral-tufted cell axons in the LOT. The system output, the cortical burst, has the same frequency as its input but is phase shifted. The poles of the transfer function are solutions for the terms in the denominator and represent the natural frequencies and decay rates of the system. The zeros are solutions for the terms in the numerator and represent frequencies and decay rates at which activity cannot occur. To determine the phase angle of the cortical burst in response to driving sinusoidal input from the bulb, a technique was taken from control theory which uses the graphic representation of the system transfer function in coordinates of decay rate and frequency 8. The steady-state response of a linear system to sinusoidal inputs is derived from the pole-zero map of the transfer function. Vectors are drawn from the poles and zeros to the point on the frequency axis representing the input frequency. The sum of the angles between the zero vectors and the decay rate axis, less the sum of the angles between the pole vectors and the decay rate axis, gives the phase angle of the system output at this frequency.
A model was proposed to predict the phase between bursts of extracellular potential from the olfactory bulb and cortex dependent on their cofrequency. The model consisted of a transmitter (bulb), a transmission line (axons of the LOT), and a receiver (cortex). The cortical burst was considered to be a manifestation of the response of excitatory pyramidal cells, involved in a negative feedback loop with inhibitory interneurons, to driving input from the transmitter. The 'characteristic frequency' of this negative feedback loop has been defined as the frequency at which oscillations occur on impulse input 11. Variation in phase was incorporated into the model from the following 4 sources: (1) conduction delay due to transmission from the transmitter over the transmission pathway to the receiver; (2) the cortical frequency response, due to the difference between the driving transmitter frequency and the characteristic frequency of the receiver; (3) variation of the characteristic frequency of the receiver; and (4) variation in phase between the bulbar field potential and the pulse density transmitted over the LOT. Conduction delay. Conduction delay was determined by the distance between bulbar and cortical electrode sites, and by the mean L O T conduction velocity between those sites. Postmortem measurements indicated a range of possible interelectrode distances from 4 to 19 mm, depending on electrode location in bulb and cortex. Kerr and Dennis 17 reported that conduction velocity in the L O T of the cat is 6 m/s, dropping to 0.8 m/s in collaterals. Haberly 13 similarly found the opossum L O T conduction velocity to be 7 m/s, falling to 1.6 m/s in the cortex lateral to the tract. Assuming similar velocities for the rabbit, the range of possible values for conduction delay is from 0.5 to 25 ms. Considering only conduction delay, a fixed time delay for conduction would represent a smaller fraction of a cycle (and therefore a smaller phase) at lower frequencies than at higher ones. The rate of change of phase with frequency would depend on the time delay, longer delays increasing the rate. The relation of phase as a function of driving frequency is plotted in Fig. 2A for two different values of conduction delay (2 and 6 ms). Cortical frequency response. As mentioned in the
297 Introduction, the pulse probability density of mitral cells has been observed to oscillate at the same frequency as the bulbar evoked potential. For this reason, it was assumed that, during each burst, pulses, whose probability oscillated at the burst frequency, were transmitted over L O T axons to the cortex. The feedback loop in the cortex between excitatory pyramidal cells and inhibitory interneurons was assumed to be driven at the same frequency. The graphic method described in the Methods was used to determine the phase shift of the cortical response for a range of driving frequencies. Given a fixed cortical characteristic frequency, cortical phase lag increased with increasing driving frequency. Variation of characteristic frequency. The model
260
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Fig. 2. A: receiver phase as a function of driving frequency, based solely on conduction delay. Negative phase corresponds to receiver lag. The top curve represents a 2-ms delay; the bottom, 6 ms. B: receiver phase as a function of driving frequency, based solely on the cortical frequency response. The points on each curve represent a different driving frequency from 35 to 85 cps. The top curve represents a receiver characteristic frequency of 85 cps; the bottom, 35 cps. Negative phase corresponds to receiver lag.
assumed that, like the bulbar driving frequency, the characteristic frequency of the cortex could vary over the ), frequency range, and that it would take different values from one burst to the next. Because cortical characteristic frequency was not directly measurable for each burst, the model predicted a range of possible phase values, depending on cortical characteristic frequency. Therefore, the output of the model was a family of curves, one for each value of cortical characteristic frequency in the ~ range. The characteristic frequencies were 85 and 35 cps, respectively, for the top and bottom curves in Fig. 2B, representing the experimentally observed limits for the range of burst frequencies. Variation of mitral-granule phase in bulb. Another source of variation was the variability of the phase difference between the granule cell population and the mitral cell population. Many previous studies have established the inhibitory granule cell population as the dominant generator of bulbar field potentials, and the excitatory mitral cell population (including tufted cells) as generator of the pulse activity which is transmitted over the L O T to the cortex lt'2t. Freeman 11 measured the phase between bulbar averaged evoked potentials and post-stimulus time histograms (measuring granule and mitral population output, respectively). He also accurately predicted this phase from system analysis of the olfactory bulb. Granule output lagged mitral output by 82 + 10°. The effect of including this factor in the model is demonstrated in Fig. 3A. The solid curves show the predicted relation of phase to driving frequency for 2ms conduction delay (85 cps characteristic frequency, top; 35 cps, bottom). The dashed curves show the same relation except that phase was relative to the granule rather than mitral output. Since granule output lagged mitral output, the cortical phase relation was shifted in the direction of greater cortical lead. In order to determine the maximal range of predicted variation of bulbocortical phase, the greatest value of granule lag (92 °) was added to the upper curve (85 cps) and the least (72 °) was added to the lower curve (35 cps). Fig. 3B shows a family of curves for a conduction delay of 2.50 ms, representing the complete model (i.e. sources (a)-(d)). The family contains 11 curves representing characteristic cortical frequencies from 35 to 85 cps in steps of 5 cps.
298 260 f A
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Fig. 3. A: receiver phase as a function of driving frequency. The solid curves represent the relation based on sources (a) to (c) (time delay = 2,5 ms; 85 cps characteristic frequency, top; 35 cps, bottom). The dashed curves represent the result of adding source (d), the phase lag of the granule population. Thus, while the solid curves represent phase with respect to the transmitter neurons (mitral cells), the dashed curves show phase with respect to the cells which generate the observable bulbar EEG (granule cells). B: receiver phase as a function of driving frequency: the complete model with phase equal to the resultant phase from sources (a) to (d). The family contains 11 curves representing characteristic frequencies from 35 (bottom) to 85 (top) cps, in steps of 5 cps, each with conduction delay ot"2.5 ms. Negative phase corresponds to receiver lag.
Fitting the model to the data For each of the 283 sample sets, a scatter diagram of bulbocortical phase vs cofrequency was displayed graphically. The distance between the bulbar and cortical recording sites was estimated from postmortem measurements, and from the dimensions Of the cortical electrode array. Distance was divided by velocity to give conduction delay. Families of curves predicted from the model for different values of conduction delay were overlaid on the scatter diagram. The fraction of data points falling within the domain of each family was a simple expression of the degree
of conformance of the experimentally determined distribution of points to the predicted range. The optimal family of curves was that which had the lowest fraction ~ . The values of f ranged from 0.44 to 1.00 over all 283 sample sets (mean = 0.82 + 0.14). For 25% of the 283 sample sets examined in this study, f was at 0.95 or above. For 50%, f w a s from 0.71 to 0.94, and for 25% it was below 0.71. Considering the average value of f for each site pair, the values ranged from 0.61 to 1.00 (mean = 0.83 + 0.15) over the 90 site pairs (9 pairs from each of 10 rabbits). Twenty-six percent of the site pairs had values of f exceeding 0.95, 47% were from 0.73 to 0.95, and 27% were below 0.73. The values of velocity for the optimal family of curves ranged from 0.7 to 6.5 m/s over all sample sets (mean = 2.3 + 1.4 m/s). Since conduction from a bulbar site to most cortical locations in the array most likely involved some passage over collaterals, this range of values for velocity was compatible with that reported in the literature 13.17. An inverse relation was expected between f and the dispersion of phase from its mean since increased dispersion would tend to reduce the number of data points falling within the predicted range. A mean value o f f and of the standard deviation of phase were calculated for each of the 9 site pairs from each rabbit. The Pearson r was -0.86 for the relation between f and standard deviation of phase. This r was significantly different from zero at P < < 0.001. The 95% confidence interval on r was f r o m - 0 . 9 0 t o - 0 . 7 9 . Approximately 0.74 of the variation in f c o u l d be attributed to a linear relation with phase dispersion. It was previously reported that phase dispersion was inversely related to mean bulbocortical correlation 3. To determine whether the sample sets with high values o f f also had high mean bulbocortical correlation , the Student's t-test was performed, comparing mean bulbocorticai correlation between the class of 71 sets with highest f ( > 0.94) and the class of 70 sets with lowest f ( < 0.71). The buibocortical correlation of the first class was significantly higher than than that of the second (t -- 7.86, df = 139) at P < < 0.0005. It has also been shown that the interdependence between bulbar and cortical recording sites varies with location in bulb and cortex 3. To test the spatial
299 variation off, a value o f f was determined for each of the 90 bulbocortical pairs (9 pairs for 10 rabbits) by averaging over recording sessions. The 90 values were then put through a logarithmic transformation to form a normal distribution. To compare the effect of bulbar location on f, the data were organized as a 30 x 3 matrix, each row containing the ordered values of f for the 3 bulbar sites relating to a single cortical site. Then analysis of variance was employed to test for an effect due to bulbar location. The F ratio (F2,58 = 10.1) for this effect was significant at P << 0,005. The effect of cortical location on f was analyzed in the same manner. The Fratio (F2.58 = 6.3) for the effect of cortical location was significant at P < 0.005. However, no spatial regularities were observed in either structure from the f values between site pairs. DISCUSSION A model was proposed based on the hypothesis that the olfactory bulb drives the olfactory cortex. It was used to predict the expected range of relation between phase and cofrequency of bulbocortical burst pairs. Site pairs were found with phase-frequency plots within the range predicted by the model (high values off). These site pairs had low phase dispersion and physiologically consistent phase differences. However, there was wide variation among the site pairs studied, the values o f f ranging from 1.0 down to as low as 0.61. There was significant variation in f among bulbar sites in relation to any one cortical site, and significant variation among cortical sites in relation to any one bulbar site. An inverse relation existed between f and phase dispersion. The distribution of phase for site pairs with low phase dispersion fell within the range predicted by the model. As phase dispersion increased, the model was less able to account for the phase distribution. An inverse relation was previously found between mean bulbocortical correlation and phase dispersion 3. This implied that sample sets which conformed to the model also had a high mean level of bulbocortical correlation. This was confirmed in the present study by the finding that mean bulbocortical correlation for the class of sample sets which conformed to the model (highest f) was significantly higher than the class with the lowest f.
The major findings of this report, therefore, are that: (1) a substantial proportion of site pairs (26%), with high bulbocortical correlation, conformed highly ( f > 0.95) to the simple model of bulbar driving of cortex; (2) there was a large range of variation over site pairs in the degree of conformance; (3) there were significant differences among bulbar sites in their relation with a cortical site; and (4) there were significant differences among cortical sites in their relation with a bulbar site. What possible mechanisms are there to account for these findings? For site pairs which conform to the model, the cortical burst is expected to be highly dependent on the bulbar burst. For this to take place, the dominant effect is expected to be a strong influence, in terms of number, position and/or strength of synapses on apical dendrites of pyramidal cells at the cortical site from axons of mitral cells at the bulbar site. There are at least 4 explanations, consistent with the anatomical evidence, which could account for the variation in conformance to the model among site pairs. One likely possibility is that, due to convergence of input, the cortical response is a summation of activity transmitted from different parts of the bulb. The anatomical projection of the bulb to cortex is generally thought to be diffuse rather than point-to-point (although there is at least one report of some anatomical precision in the bulbocortical projection2°). Most anatomical studies have suggested that each location in the cortex receives LOT projections from mitral cells in a large fraction of the bulb, and similarly, that each region of the bulb sends axons to a large area of cortex 12'14'18'19. Thus, there might be a strong synaptic input from the bulbar site in a site pair, but the receiver at the cortical site would not necessarily be driven by the transmitter at that one bulbar site alone. Rather it might integrate effective inputs from transmitters at other bulbar sites as well. For any given site pair, the degree of dependence of the cortical on the bulbar burst would be determined by the strength of influence of the bulbar input relative to competing inputs. A second possibility is that variation in the bulbocortical relation is due to variation in the degree to which the cortical site is a passive receiver. According to this hypothesis, even if a cortical site receives driving input from a transmitter in just one local bulbar region, the degree to which its burst depends on
300 bulbar input may vary. It is likely that the cortex, just as the bulb, has the ability to enter an independent self-generated oscillatory state H. The degree to which a cortical site acted as a receiver with respect to a bulbar transmitter would depend on the relative strengths of the bulbar driving input vs its own internal tendency to self-generated oscillation. A third possible explanation is that of feedback from the cortex to the bulb in response to driving input. There are several reports of centrifugal fibers from cortex to bulb 5-7'15. Evidence has previously been presented for cortical feedback in the 15-35 cps frequency range 2. Feedback might also occur in the 35-85 cps ),-range. Even if the cortical receiver acted passively rather than generating its own oscillatory state, feeding back with delay to the bulbar transmitter the activity imposed upon it, the effect of feedback would be to alter the phase relation between bulbar and cortical bursts. Variation in the efficacy of the feedback pathway might be responsible for the varied relations among site pairs. This explanation could account for the substantial number of sample sets (47%) found to have a positive correlation of bulbocortical phase and cofrequency (increasing cortical lead with increasing frequency) 3. For the model of unidirectional driving, the correlation was always found to be negative (increasing cortical lag with increasing frequency). When a term was added to the other terms in the model, to represent feedback onto granule cells at their deep ends, phase-frequency relations with positive correlation were found. A fourth alternative is that synchronization of bulbar and cortical bursts depends on a c o m m o n outside source such as the anterior olfactory nucleus or the nucleus of the horizontal limb of the diagonal band, REFERENCES 1 Becket, C.J. and Freeman, W.J., Prepyriform electrical activity after loss of peripheral or central input, or both, Physiol. Behav., 3 (1968) 597-599. 2 Bressler, S.L., Spatial organization of EEGs from olfactory bulb and cortex, Electroencephalogr. Clin. Neurophysiol., 57 (1984) 270-276. 3 Bressler, S.L., Relation of olfactory bulb and cortex. I. Spatial variation of bulbocortical interdependence, Brain Research, 409 (1987) 285-293. 4 Bressler, S.L. and Freeman, W.J., Frequency analysis of olfactory EEG in cat, rabbit and rat, Electroencephalogr. Clin. Neurophysiol., 50 (1980) 19-24.
which are both known to project to both structures. Convergence of bulbar inputs could be uniform rather than patterned as in the first hypothesis. In this hypothesis, the cortical site would not show a fixed time relation to the bulbar site unless both sites received input from the c o m m o n outside source. The effect of the outside source might be to selectively entrain pairs of bulbocortical sites out of a field of randomly active transmitters and receivers. The degree of entrainment of a particular bulbocortical site pair would determine its apparent conformance to the driving model, although, strictly speaking, the model would not be satisfied. At present, it is not possible to distinguish among these alternatives. Since they are not all mutually exclusive, it is possible that some combination of these mechanisms is at play. For future studies, it would be useful to repeat these experiments with lesioning of the centrifugal fiber pathways to the bulb, to remove centrifugal and feedback input. Since these findings were based on a small sample of electrode sites, future studies should examine a larger number of site pairs. Whatever the mechanism, the present findings imply that, functionally, the relation between bulb and cortex is not as spatially diffuse as indicated by most anatomical studies.
ACKNOWLEDGEMENTS The author thanks Dr. Walter J. Freeman for guidance throughout the course of this work and Dr. Alan S. Gevins for critical review of the manuscript. This research was supported by Grant MH06686 from the National Institute of Mental Health to Walter J. Freeman. 5 Broadwell, R.D. and Jacobowitz, D.M., Olfactory relationships of the telencephalon and diencephalon in the rabbit. III. The ipsilateral centrifugal fibers to the olfactory bulbar and retrobulbar formations, J. Comp. Neurol., 170 (1976) 321-346. 6 Dennis, B.J. and Kerr, D.I., Origins of olfactory bulb centrifugal fibres in the cat, Brain Research, 110 (1976) 593-600. 7 De Olmos, J., Hardy, H. and Heimer, L., The afferent connections of the main and the accessory olfactory bulb formations in the rat: an experimental HRP study, J. Comp. Neurol., 181 (1978) 213-244. 8 Di Stefano, J., Stubberud, A. and Williams, I., Feedback and Control Systems, McGraw-Hill, New York, 1967.
301 9 Freeman, W.J., Patterns of variation in waveform of averaged evoked potentials from prepyriform cortex of cats, J. Neurophysiol., 31 (1968) 1-13. 10 Freeman, W.J., Measurement of oscillatory responses to electrical stimulation in olfactory bulb of cat, J. Neurophysiol., 35 (1972) 762-779. 11 Freeman, W.J., Mass Action in the Nervous System, Academic. New York, 1975. 12 Haberly, L.B., Unitary analysis of opossum prepyriform cortex, J. Neurophysio/., 36 (1973)762-774. 13 Haberly, L.B., Summed potentials evoked in opossum prepyriform cortex, J. Neurophysiol., 36 (1973) 775-788. 14 Haberly, L.B. and Price, J.L., The axonal projection patterns of the mitral and tufted cells of the olfactory bulb in the rat, Brain Research, 129 (1977) 152-157. 15 Haberly, L.B. and Price, J.L., Association and commissural fiber systems of the olfactory cortex of the rat. 1. Systems originating in the piriform cortex and adjacent areas, J. Comp. Neurol., 178 (1978) 711-740.
16 Kerr, D., Olfactory centrifugal pathways. In P. LeMagnen and P. MacLeod (Eds.), Olfaction and Taste, Vol. 6, Information Retrieval, London, 1977. 17 Kerr, D. and Dennis, B., Collateral projection of the lateral olfactory tract to entorhinal cortical areas in the cat, Brain Research, 36 (1972) 399-403. 18 Price, J.L., An autoradiographic study of complementary laminar patterns of termination of afferent fibers to the olfactory cortex, J. Cornp. Neurol., 150 (1973) 87-108. 19 Price, J.L. and Sprich, W.W., Observations on the lateral olfactory tract of the rat, J. Comp. Neurol., 162 (1975) 321-336. 20 Scott, J.W., McBride, R.L. and Schneider, S.P., The organization of projections from the olfactory bulb to the piriform cortex and olfactory tubercle in the rat, J. Comp. Neurol., 194 (1980) 519-534. 21 Shepherd, G.M., Synaptic organization of the mammalian olfactory bulb, Physiol. Rev., 52 (1972) 864-917.