Measuring Instantaneous Frequency of Local Field Potential Oscillations using the Kalman Smoother

Rhythmic local field potentials (LFPs) arise from coordinated neural activity. Inference of neural function based on the properties of brain rhythms remains a challenging data analysis problem. Algorithms that characterize non-stationary rhythms with high temporal and spectral resolution may be useful for interpreting LFP activity on the timescales in which they are generated. We propose a Kalman smoother based dynamic autoregressive model for tracking the instantaneous frequency (iFreq) and frequency modulation (FM) of noisy and non-stationary sinusoids such as those found in LFP data. We verify the performance of our algorithm using simulated data with broad spectral content, and demonstrate its application using real data recorded from behavioral learning experiments. In analyses of ripple oscillations (100–250 Hz) recorded from the rodent hippocampus, our algorithm identified novel repetitive, short timescale frequency dynamics. Our results suggest that iFreq and FM may be useful measures for the quantification of small timescale LFP dynamics.National Institutes of Health (U.S.) (NIH/NIMH R01 MH59733)National Institutes of Health (U.S.) (NIH/NIHLB R01 HL084502)Massachusetts Institute of Technology (Henry E. Singleton Presidential Graduate Fellowship Award

Potential cost savings with terrestrial rabies control

BACKGROUND: The cost-benefit of raccoon rabies control strategies such as oral rabies vaccination (ORV) are under evaluation. As an initial quantification of the potential cost savings for a control program, the collection of selected rabies cost data was pilot tested for five counties in New York State (NYS) in a three-year period. METHODS: Rabies costs reported to NYS from the study counties were computerized and linked to a human rabies exposure database. Consolidated costs by county and year were averaged and compared. RESULTS: Reported rabies-associated costs for all rabies variants totalled $2.1 million, for human rabies postexposure prophylaxes (PEP) (90.9$784,529). Average costs associated with the raccoon variant varied across counties from $440 to$1,885 per PEP, $14 to$44 per specimen, and $0.33 to$15 per pet vaccinated. CONCLUSION: Rabies costs vary widely by county in New York State, and were associated with human population size and methods used by counties to estimate costs. Rabies cost variability must be considered in developing estimates of possible ORV-related cost savings. Costs of PEPs and specimen preparation/shipments, as well as the costs of pet vaccination provided by this study may be valuable for development of more realistic scenarios in economic modelling of ORV costs versus benefits

Oral Rabies Vaccination in North America: Opportunities, Complexities, and Challenges

Steps to facilitate inter-jurisdictional collaboration nationally and continentally have been critical for implementing and conducting coordinated wildlife rabies management programs that rely heavily on oral rabies vaccination (ORV). Formation of a national rabies management team has been pivotal for coordinated ORV programs in the United States of America. The signing of the North American Rabies Management Plan extended a collaborative framework for coordination of surveillance, control, and research in border areas among Canada, Mexico, and the US. Advances in enhanced surveillance have facilitated sampling of greater scope and intensity near ORV zones for improved rabies management decision-making in real time. The value of enhanced surveillance as a complement to public health surveillance was best illustrated in Ohio during 2007, where 19 rabies cases were detected that were critical for the formulation of focused contingency actions for controlling rabies in this strategically key area. Diverse complexities and challenges are commonplace when applying ORV to control rabies in wild meso-carnivores. Nevertheless, intervention has resulted in notable successes, including the elimination of an arctic fox (Vulpes lagopus) rabies virus variant in most of southern Ontario, Canada, with ancillary benefits of elimination extending into Quebec and the northeastern US. Progress continues with ORV toward preventing the spread and working toward elimination of a unique variant of gray fox (Urocyon cinereoargenteus) rabies in west central Texas. Elimination of rabies in coyotes (Canis latrans) through ORV contributed to the US being declared free of canine rabies in 2007. Raccoon (Procyon lotor) rabies control continues to present the greatest challenges among meso-carnivore rabies reservoirs, yet to date intervention has prevented this variant from gaining a broad geographic foothold beyond ORV zones designed to prevent its spread from the eastern US. Progress continues toward the development and testing of new bait-vaccine combinations that increase the chance for improved delivery and performance in the diverse meso-carnivore rabies reservoir complex in the US

Ripple oscillations and CA1 spiking during ripples reflects the dynamics of CA3 input to CA1.

<p><b>a,</b> Normalized ripple power (measured from threshold for detecting ripples) vs. speed. For clarity, normalized ripple power is displayed both as binned averages (binned means and standard error using logarithmically spaced bin centers) and regression to the underlying data (slope with 95% confidence range by bootstrap). <b>b,</b> Changes in speed modulation over exposures to the environment. Points represent means +/−95% confidence bounds by bootstrap. <b>c,</b> On days in which a second novel environment was experienced immediately following the first, more familiar environment (n = 4; see methods), the effect of novelty on ripple power could be directly measured. Shown are the mean binned ripple power in the novel (dark gray) and familiar (light gray) environments. Ripple power is significantly increased in the novel as compared to the familiar environment for all speeds (rank sum test between novel and familiar session, p<10⁻⁵ for all speed bins). <b>d,</b> The depth of ripple power modulation by speed is larger in a novel as compared to a familiar environment. For all animals where it was possible to measure within day changes, we find that there was a significant increase in the depth of modulation (more negative slope) in the novel as compared to more familiar environment. Bars show grouped data, means with 95% confidence intervals, thin lines show change in slope for individual animals (bootstrap estimate of slope, novel slope vs. familiar slope, p<0.05 for group, p<0.05 for individual animals). *p<0.05; ***p<10⁻⁵. <b>e,</b> Activation probability during each ripple for CA1 and CA3 cells during the first exposure to the environment. For clarity, activation probability is displayed both as binned averages (binned mean and standard error using logarithmically spaced speed bins) and best fit line (linear regression of the underlying data with 95% confidence intervals). <b>f,</b> Mean activation probability for CA1 and CA3 neurons across exposures to the environment. Points show mean probability with 95% confidence bounds by bootstrap.</p

The spectrum of rhythmic local field potential activity in area CA1 is smoothly modulated by behavior.

<p>Example spectrograms across speeds. Power in each frequency is shown as a z-score relative to the mean power across speeds. <b>(left)</b> Spectrogram calculated in the first exposure to a novel environment. <b>(middle)</b> Spectrogram calculated after the environment has become familiar (epoch 12). <b>(right)</b> Three known and physiologically relevant rhythms, the ripple oscillation (150–250 Hz), fast gamma (65–100 Hz), and slow gamma (25–55 Hz).</p

Rapid modulation of the Schaffer collateral pathway as a function of movement speed.

<p><b>a,</b> In this study we combined measurements of fPSPs recorded in 4 animals and a total of 31 behavioral epochs. <b>a,</b> There is considerable variation in measured fPSP slopes as the rat behaves. In an example epoch (same animal, and one of the two epochs aggregated in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0073114#pone-0073114-g005" target="_blank">Figure 5</a>), the inverse relationship between the slopes of evoked fPSPs (blue dots) and movement speed (green with measurement times denoted with dots) can be observed. Note that the speed axis is logarithmic for similarity with our analyses and that the larger fPSP slopes are at the bottom of the axis. Furthermore, note the times when speeds went below 1/8 cm/s (marked in gray) are excluded from analyses. <b>b,</b> Modulation of EPSPs evoked in area CA1 by stimulation of the SC pathway as a function of speed. Colored points represent the measured slopes of the individual fPSP example shown at top. The regression of fPSP slope against log(speed) is shown with a 95% confidence interval estimated by bootstrap. <b>c,</b> The modulation of the SC pathway by speed is seen in fPSP measurements normalized and pooled across animals/recording sessions. Normalized measurements are displayed both as binned averages (binned mean and standard error using bin centers on horizontal axis) and a regression line with bootstrapped 95% confidence interval. <b>d,</b> The strength of evoked fPSPs is most strongly related to the speed measured at the time of stimulation. Depicted are mean and bootstrapped 95% confidence interval of the R² for regressions of normalized fPSP size to log(offset speed). <b>e,</b> Speed is a better predictor of evoked fPSP size than theta_power. Compared are R² for log(speed) vs fPSP slope and for theta power vs fPSP slope. Error bars show 95% confidence interval estimated by bootstrap. **p<0.001.</p

Slow and fast gamma oscillations in CA1 are modulated by speed.

<p><b>a,</b> There are two distinct gamma bands in CA1. Shown is an example cross-frequency coherence plot from a novel run session showing that gamma power (y-axis) is modulated by the theta phase (x-axis). <b>b,</b> CA1 is more coherent with CA3 in slow gamma range and more coherent with layer 3 of the medial entorhinal cortex in fast gamma range. Coronal and sagittal sections show electrolytic lesions in recording sites from CA3-CA1 recordings (1) and CA1-MEC recordings (2 and 3). Coherence plots for a representative pair of CA3-CA1 (blue) and MEC-CA1 (red) recordings. There is a pronounced peak in the slow gamma range (25–55 Hz) of CA3-CA1 coherence, and a noticeable increase in the fast gamma range (∼70–130 Hz) of MEC-CA1 coherence. Slow gamma coherence was greater than fast gamma coherence for 80 out of 85 pairs of CA3-CA1 recordings (z-test for proportions, p<10⁻⁵; n = 5 animals), while fast gamma coherence was greater than slow gamma coherence for 19 out of 22 pairs of MEC-CA1 recordings (z-test for proportions, p<10⁻⁵; n = 3 animals). <b>c,</b> Population data showing normalized power of slow gamma vs. speed. Points represent binned means with standard error using logarithmically spaced bin centers; line represents linear regression of underlying data with 95% confidence intervals. <b>d,</b> Population data showing normalized power of fast gamma oscillations vs. speed. Points and line as in (<b>c</b>). <b>e,</b> There are very small changes in coherence as a function of behavioral state. <b>(top)</b> Average change in coherence between CA3 and CA1 in the slow gamma frequency band (n = 4 animals) as a function of speed (average slow gamma coherence between CA3 and CA1 = 0.51). Coherence was measured for all tetrode pairs. For each pair, the deviation from the mean value in each 500 ms time window was calculated. Each time window was associated with the appropriate speed. Shown are the regression of speed and change in coherence with 95% C.I. and binned histograms as in (<b>c</b>). Change in coherence vs. speed is not significantly different from zero (bootstrap test). <b>(bottom)</b> Average change in coherence between MEC and CA1 in the fast gamma frequency band (n = 3 animals, average mean fast gamma coherence between MEC and CA1 = 0.49). Change in coherence vs. speed is not significantly different from zero (bootstrap test).</p

Modulation of gamma oscillations by speed in CA1 is rapid.

<p><b>a, (top)</b> The autocorrelation of speed (shown with bootstrap 95% confidence interval) during the first exposure shows a rapid fall-off of on the timescale of ∼1 second. <b>(bottom)</b> Both fast and slow gamma power is most modulated by the animal’s speed measured within a second of the gamma power estimate, implying a rapid timescale of modulation. Shown are the Spearman correlation and bootstrap 95% confidence interval of fast (red) and slow (blue) gamma power with log(speed) for offsets in speed measurement ranging from −2.5 to 2.5 s relative to the 0.5 s window used to estimate gamma power. <b>b,</b> Rapid and opposing changes in the power of slow and fast gamma are apparent in 2 second windows over which rats’ speed increase from less than 2 cm/s to more than 10 cm/s. <b>(left)</b> Increasing mean speed (with standard errors) in 0.5 s windows corresponding to the isolated increasing speed incidents. <b>(right)</b> Mean slow gamma power (blue bars with standard errors) decreases significantly, while fast gamma simultaneously increases significantly (red bars) over the course of the two-second increasing speed events. <b>c,</b> Same analysis as (<b>b</b>) but for 2 s windows when speed decreased from more than 10 cm/s to less than 2 cm/s. Periods of decreasing speed are marked by an increase in slow gamma power (blue bars) and a concomitant decrease in fast gamma power (red bars). <b>d,</b> Correlation between theta power and log(speed). The graph shows population data of normalized power of theta oscillation (7–9 Hz) vs. speed, both measured over 0.5 s windows. Points represent binned means with standard error; line shows linear regression of underlying data with 95% confidence intervals. <b>e,</b> Speed is a better predictor of fast and slow gamma power than theta power. Comparison of Spearman correlation log(speed) or theta power with fast gamma power (red) and slow gamma power (blue). Depicted are correlations with bootstrap 95% confidence intervals. **p<0.01.</p