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. 2015 Apr 15;244:136-53.
doi: 10.1016/j.jneumeth.2014.07.013. Epub 2014 Jul 30.

Multifractal Analysis of Information Processing in Hippocampal Neural Ensembles During Working Memory Under δ⁹-Tetrahydrocannabinol Administration

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Multifractal Analysis of Information Processing in Hippocampal Neural Ensembles During Working Memory Under δ⁹-Tetrahydrocannabinol Administration

Dustin Fetterhoff et al. J Neurosci Methods. .
Free PMC article

Abstract

Background: Multifractal analysis quantifies the time-scale-invariant properties in data by describing the structure of variability over time. By applying this analysis to hippocampal interspike interval sequences recorded during performance of a working memory task, a measure of long-range temporal correlations and multifractal dynamics can reveal single neuron correlates of information processing.

New method: Wavelet leaders-based multifractal analysis (WLMA) was applied to hippocampal interspike intervals recorded during a working memory task. WLMA can be used to identify neurons likely to exhibit information processing relevant to operation of brain-computer interfaces and nonlinear neuronal models.

Results: Neurons involved in memory processing ("Functional Cell Types" or FCTs) showed a greater degree of multifractal firing properties than neurons without task-relevant firing characteristics. In addition, previously unidentified FCTs were revealed because multifractal analysis suggested further functional classification. The cannabinoid type-1 receptor (CB1R) partial agonist, tetrahydrocannabinol (THC), selectively reduced multifractal dynamics in FCT neurons compared to non-FCT neurons.

Comparison with existing methods: WLMA is an objective tool for quantifying the memory-correlated complexity represented by FCTs that reveals additional information compared to classification of FCTs using traditional z-scores to identify neuronal correlates of behavioral events.

Conclusion: z-Score-based FCT classification provides limited information about the dynamical range of neuronal activity characterized by WLMA. Increased complexity, as measured with multifractal analysis, may be a marker of functional involvement in memory processing. The level of multifractal attributes can be used to differentially emphasize neural signals to improve computational models and algorithms underlying brain-computer interfaces.

Keywords: Cannabinoid; Cognition; Delayed non-match to sample; Electrophysiology; Wavelet leaders; Working memory.

Figures

Fig. 1
Fig. 1
Comparison of singularity spectra for multiple types of time series. (Top) Three example interspike interval time sequences recorded from the hippocampus (Section 2.4.5). (Bottom) The respective singularity spectra computed for each signal: uncorrelated signal (red), monofractal (green), and multifractal (blue). The singularity spectrum quantifies the distribution of variability in time series. The fractal (Hausdorff) dimension D(h) on the vertical axis is plotted against the range of Hölder exponents h on the horizontal axis (Sections 2.4.3 and 2.4.4). The global Hurst exponent and consequently the peak position on the horizontal axis is 0.5 of the uncorrelated signal. The monofractal and multifractal signals have global Hurst exponents greater than 0.5 indicating long-range temporal correlations in the signal. The multifractal spectrum (blue) is much wider than the others because a larger range of Hölder exponents is needed to accurately describe the heterogenous distribution of variability. The uncorrelated was selected based on results obtained using multifractal analysis because it has a global Hurst exponent of 0.5. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 2
Fig. 2
Delayed non-match to sample (DNMS) task and hippocampal functional cell types. (A) Diagram of different phases of DNMS task: (1) Sample lever presentation (SP) in one of two positions (left or right) and Sample lever response (SR) followed by (2) delay interval of random durations during which delay timeout was contingent on a nosepoke (last nosepoke, LNP) into photocell mounted on opposite wall, followed by (3) simultaneous presentation of both levers (left and right) in Non-match phase in which (4) a Non-match Response (NR) on the lever opposite the spatial position to the prior SR produced, delivery of 0.2 ml of water to the trough between levers for the correct (Non-match) choice or (5) a response on the same lever as the SR shut off houselights for 5 s indicating an incorrect (Match) choice and no reward. Timeline shows sequence of task phases: ITI – intertrial interval; SP – sample lever presentation; SR – sample response; Delay – delay interval; NPs – nosepokes during Delay; LNP – last nosepoke; NR – nonmatch position response; Reinf. – delivery of water (0.2 ml) reward. (B) Examples of functional cell types of hippocampal neurons recorded on same bilateral arrays determined by correlated firing (±1.5 s) to Sample (SR) and Non-match (NR) task events (0.0 s). Raster and perievent histograms for 4 different types of FCTs, Left and Right Trial Types, Right Sample Conjunctive and Non-match Phase, are shown for each lever position (right or left) and each phase (sample or nonmatch) of the task (Hampson et al., 1999). (C) Hippocampal recording array consisted of eight pairs of stainless steel 20 μm wires positioned longitudinally within each hippocampus at 200 μm intervals. For each pair one electrode was positioned in CA3 and the other in CA1 cell field in a line tangent to the longitudinal axis of the hippocampus. Arrays were implanted bilaterally in each hippocampus providing a total of 32 electrodes per animal.
Fig. 3
Fig. 3
Illustration of Wavelet Leaders-based Multifractal Analysis. (A) (Bottom) The interspike interval time series of one neuron recorded during on DNMS session (Section 2.4.5). (Top) The continuous wavelet transform of this interspike interval sequence. A continuous wavelet transform is shown here for illustrational purposes only; a discrete wavelet transform was used for all data analysis presented in this paper. (B) The wavelet coefficients are selected on dyadic grid. The measurement scale (bin size) increases moving up the vertical axis, and time is increasing along the horizontal axis. At each point in the dyadic grid, the wavelet leader (circled) is the maximum wavelet coefficient among the wavelet coefficients to the immediate right and left and for all lower scales (the two gray boxes). (C) The wavelet leaders dL are calculated as a function of measurement scale j. Since wavelet leaders are averaged according to the scale (bin size), this results in the fewer wavelet leader data points at each scale. In order for the scale invariant structure of the wavelet leaders to be seen, the average wavelet leader is plotted according to its bin size. As measurement precision increases from top to bottom, the measurement scale (bin size) decreases. This is why the length of the ISI index does not change and the wavelet leaders appear to have higher resolution (Section 2.4.5). (D) The log-cumulants are derived from the slopes second characteristic functions derived from the natural log of the time averaged wavelet leaders. c1 is obtained from the slope of the red line, c2 from the blue line, and c3 from the green line. (E) The singularity spectrum can be estimated from the log-cumulants (red) or the scaling function (gray). Both methods yield very similar estimates. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 4
Fig. 4
Average DNMS task performance during control and THC sessions. Mean (±SEM) % correct non-match responses (NRs) summed across animals (n = 6) shows significant decline in accuracy (F(5,595) = 61.79, p < 0.001) as a function of delay duration in 5.0 s blocks. A main effect of drug condition (F(1,119) = 32.09, p < 0.001) and interaction between drug condition and delay interval (F(5,595) = 2.36, p < 0.05) were detected. Solid lines show THC significantly impaired performance at all six delay intervals (p < 0.05). The dashed lines illustrate correct performance according to lever preferences which demonstrate that stereotyped responding underlies reduction in performance during THC administration. Under THC, there was a larger difference between preferred and non-preferred choices at all delay intervals. Preferred responding begins in the control condition only when delays are greater than 20 s. A within subjects design with at least 2 non-drug days between THC administration was used. All animals were given THC (1.0 mg/kg) for no less than five sessions spaced over multiple weeks.
Fig. 5
Fig. 5
Multifractal differences of interspike intervals quantified by singularity spectra. The first four graphs each show the sequence of interspike intervals recorded during one daily DNMS behavioral session. The ISI amplitude is normalized to one for each session based on the largest ISI and the ISI index represents the temporal ISI pattern (Section 2.4.5). Above each graph, the bracketed numbers signify (in order): the measurement scale, the average firing rate in hertz, and the standard deviation of ISIs. On the right, the singularity spectra are plotted with Hausdorff dimension D(h) on the vertical axis and Hölder exponent h on the horizontal axis. (A) The interspike intervals (ISI) of one FCT (top) and one non-FCT (bottom) recorded over one control session. (B) The ISI of one FCT (top) and one non-FCT (bottom) recorded over one THC session; the same neurons as in (A) are shown in (B) when recorded under THC administration. (C) In the FCT control condition (top, blue), the central location of the spectrum exists at a larger Hölder exponent (signified by larger c1) and the spectrum is wider (signified by larger c2) than all other illustrated neurons. THC reduces both c1 and c2, designated by the leftward shift and decreased width, respectively. The fractal characteristics of the non-FCT are unchanged by THC. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 6
Fig. 6
Multifractal singularity spectra of Trial-Type Cells during THC administration. Right trial-type cells discharge for the right sample response and the left non-match response, while left trial-types respond during the left sample and right non-match. Together, these cell types provide the most essential information for DNMS performance. In the left graphics, each trace represents the results for that specific neuron obtained during one session. Control sessions are in blue and THC sessions are in green. We used a repeated measures design to collect data from the same neuron on a daily basis while interspersing control and THC days. Each of the two cells was recorded over multiple days from two different rats. The right figures represent the averaged spectrum by condition. The log-cumulant values in the table are averaged for each cumulant over all sessions the neuron was recorded. THC significantly reduces c1 in these functional cell types (p < 0.05). However, THC non-significantly reduces c2 (p = 0.12 for the left trial type and p = 0.14 for the right trial type). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 7
Fig. 7
Effects of THC by FCT-group designation. (A and B) THC did not significantly affect mean firing rate recorded throughout the entire behavior session using either FCT grouping scheme. (C) THC significantly reduced long-range temporal correlations, as measured with c1, in both classic and new FCTs. (D) THC significantly reduced c1 in Conjunctive, Trial-Type, Nosepoke-Nonmatch and 3 Peak FCT-groups. Recorded in the control condition, Trial-Type and 3 Peaks FCT-groups had significantly larger c1 values than control non-FCTs. (E) Both classic and new FCTs in the control condition have significantly larger c2 values compared to non-FCTs in the control condition. THC significantly reduced multifractal complexity in both classic and new FCTs. F. All FCT groups recorded in the control condition, except position cells, exhibited greater multifractal complexity than non-FCTs from the control condition. THC reduced multifractal properties of phase, conjunctive, NP-NM and 3 Peaks FCT-groups. In all graphs, * p < 0.05, ** p < 0.01, # p < 0.0001.
Fig. 8
Fig. 8
Scatter plots comparison of control versus THC condition. These scatter plots show the entire recorded neuronal population coded by color-symbol patterns based on FCT-group designation. The midline is plotted on all graphs to visually show deviations from equal dependent variables between control and THC conditions. (A) The mean firing rate of the neuronal population did not change due to THC administration, and data points cluster around the midline. (B) THC reduced c1 in many different neurons across FCT-groups, as noted by the rightward-shifted cluster below the midline. (C) THC reduced multifractal complexity as measured by c2 values closer to zero. This is visually seen by the clustering of neurons to the upper left of the midline. (D) The “dense” section of (C), designated by the black square, is enlarged with axes limits to −0.1 instead of −0.6. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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