As mentioned earlier, we built point process models for STN neurons in seven Parkinson’s patients and one healthy primate, which captured dynamics across four different epochs within a directed hand-movement task. We summarize results for each species later. For the PD data, 28 STN neuron models passed the KS test and for the primate data, 35 models passed the KS test.

Recall from (2) that λ(*t|H*_{t})Δ is approximately the probability that the neuron will spike at time *t* given extrinsic and intrinsic dynamics up to time *t*, which is captured in *H*_{t}. By virtue of (6), we allow the probability that each STN neuron will spike at some time *t* to be modulated by movement direction, short-term history, and long-term history spiking dynamics. illustrates these three modulation factors on spiking activity for both PD and primate single neuron models by plotting the optimal parameters and their corresponding 95% confidence bounds before and after MV onset. We make the following observations.

*Refractoriness:* As illustrated in the second row of , both the PD and primate STN neuron exhibits refractory periods [9] as indicated by down modulation by a factor of ten or more due to a spike occurring 1 ms prior to a given time *t*. That is, if a spike occurs 1 ms prior to time *t*, then it is very unlikely that another spike will occur at time *t* (*e*^{β1} < 1 for all *e*^{β1} within its 95% confidence band).*Bursting:* As illustrated in the second row of , the PD STN neuron spikes in rapid succession before and after MV onset as indicated by one or more of the short-term history parameters (*e*^{βi} ‘s) corresponding to 2–10 ms in the past being larger than 1. That is, if a spike occurs 2–10 ms prior to time *t*, then it is more likely that another spike will occur at time *t*. Formally, a neuron bursts if its model parameters satisfy the following: for at least one *i* = 2,3,…, 10, LB_{i} ≥ 1 and UB_{i} ≥ 1.5, where LB_{i} ≤ *e*^{βi} ≤ UB_{i}, LB and UB are the 95% lower and upper confidence bounds, respectively.*10–30 Hz oscillations:* As illustrated in the third row of , the PD STN neuron exhibits 10–30 Hz oscillatory firing before movement. That is, the probability that the PD STN neuron will spike at a given time *t* is modulated up if a spike occurs 30–100 ms prior to *t*. Formally, a neuron has 10–30 Hz oscillations if its model parameters satisfy the following: for at least one *i* = 2, 3,…, 5, LB_{i} ≥ 1 and UBi ≥ 1.5, where LB_{i} ≤ *e*^{γi} ≤ UB_{i}.*Directional tuning:* As illustrated in the first row of , the PD STN neuron appears to exhibit more directional tuning after MV onset. That is, the PD neuron seems more likely to spike in one direction more than at least one other direction. To quantify directional tuning, we performed the following test for each neuron, each time relative to onset, and each epoch:
- For each direction
*d** = {*U, R, D, L*}, compute *P*_{d*d} = Pr(*e*^{αd*} >*e*^{αd}) = Pr(α_{d}. > α_{d}) for *d ≠ d**. Define *p*_{d*d*} = 0. Use the Gaussian approximation for α_{d}, which is one of the asymptotic properties of ML estimates to compute *p*_{d*d}. - If max
_{d}* = 1,2,3,4 *P*_{d*d} ≥ 0.975 then neuron exhibits directional tuning.

provides a population summary for each of these spiking characteristics for each epoch and subject group.

| **TABLE II**Population Summary for PD Patients and Primate |

plots the population summary for each subject group and also marks with a “+” sign when the population summary for a given characteristic is statistically significantly above or below (with a

*p*-value ≤ 0.05) the population summary baseline value, which is taken as right before the GA appears (GA–). Sign tests are used to test the null hypothesis that the median of a distribution (in our case, the median is baseline) is equal to some value [

39]. Under the null hypothesis, we expect half of the observations to be above the median and half to be below, therefore, the number of observations at any given time window during a trial (e.g., MV– is a 350 ms window right before MV onset) that are above the median, which follow a binomial distribution with

*p* = 1/2 and

*n* equals the total number of observations above the mean and below the mean. We considered each patient separately and computed the number of observations (across all neurons in patient) that collectively were above or below the patient’s baseline for each STN characteristic (bursts, high-frequency oscillations (HFOs), and directional tuning) and for each epoch. We then computed either 1, if the probability of observing something greater if the number of observations were greater than the baseline under the null hypothesis, or 2, if the probability of observing something less if the number of observations were less than the baseline under the null hypothesis. These probabilities are the

*p*-values.

We make the following observations from and . Most neurons in both species exhibit refractoriness. Bursting is prevalent across all epochs in neural activity of PD patients (on average 39% of PD STN neurons burst). In contrast, neural activity in the healthy primate exhibits little bursting (14% on average) across all epochs. Ten to thirty hertz oscillations are prevalent in neural activity of PD patients during across all epochs (on average 36%) and significantly decrease relative to this baseline post movement as denoted by “+” symbols in the solid curve at the top of . Beta oscillations have been observed experimentally in both Parkinsonian primates and PD patients [

7], [

8], [

10], [

17], [

29], [

32], and attenuation of these oscillation post movement have also been observed [

4], [

36]. In contrast, an average of 12% of the primate neurons exhibit 10–30 Hz oscillations, which does not significantly modulate across the entire trial. Directional tuning is more prevalent in the healthy primate across the trial. In particular, directional tuning increases significantly above baseline right after the GA is shown in the primate case (see “+” in solid curve at the bottom of at GA+). This makes sense as the primate knows and moves to one of the four possible directions shown. Tuning increased further in the primate neurons after the TC appears, as now the subject knows which direction to move when cued to move. In contrast, directional tuning fails to increase significantly above baseline until right before MV onset (see “+” in solid curve at the top plot of at MV–) in PD STN neurons. The lack of significant increase in directional tuning in PD STN neurons early on in the trial may reflect the lack of a dynamic range in the STN neurons of PD patients, which may cause their slow and impaired movements.

For comparison, we also computed spiking characteristics using traditional methods. Next, we describe these computations.

A. Beta Oscillations

To analyze beta oscillations, we computed spectrograms for each epoch window (e.g., 350 ms window right before the GA appears), each neuron and each trial. Then, for each spectrogram, we computed the oscillation density of the spectrogram in the 10–30 Hz range as the integral of the spectrogram in the 10–30 Hz range divided by the integral of the spectrogram across all frequencies. That is, both were double integrals computed across specified frequencies in the 10–30 Hz range and across all time samples in the epoch. Then, for a given neuron and a given epoch, we computed the fifth percentile across all trials as a lower confidence bound on oscillation density (LBOS). We determined the neuron as exhibiting 10–30 Hz oscillations if LBOS > 0.155.

B. Bursting

To analyze bursting in these neurons, we computed interspike interval (ISI) histograms across each epoch during the trial for all neurons and all trials. We then normalized each histogram, so that it is summed to 1, and then, computed the bursting density of the histogram in the 2–10 ms range by taking the sum of the normalized histogram in the 2–10 ms range. Once we computed densities across all trials for a given neuron and epoch, we computed the fifth percentile as a lower confidence bound (LBBU). For a given neuron and epoch, we determined that the neuron bursts if the LBBU > 0.15.

C. Directional Tuning

To analyze directional tuning in these neurons, we computed tuning vectors [

20], [

21], [

33] across each epoch during the trial for all neurons and all trials. If the vector sum in all four directions lies within 20° from one of the four directions, we determined that the neuron is directionally tuned.

The population summary using traditional statistics is shown in for each subject group. When comparing and , we see similar trends in the spiking characteristics of primate STN neurons though absolute percentages slightly differ. In particular, we see that for the primate, we have a steady average of 17% neurons bursting and 19% neurons oscillating in the 10–30 Hz range over the entire trial. We also see significantly increased directional tuning relative to baseline right after the GA appears (GA+). One visible difference between the two analyses (in the primate case) is that the point process models show directional tuning continuously increasing after the TC is shown (solid curve at the bottom of ), whereas, the tuning vector analysis shows a decrease in directional tuning around the GC epoch (solid curve at the bottom of ). The reason for this discrepancy is due to the fact that tuning vectors are only capturing first-order statistics of the point process. The point process model parameters take into account the stimulus parameters (α’s) probability distributions (not just the mean values), and directional tuning is determined from these distributions as described earlier. Therefore, making inferences from average tuning vectors can be misleading.

In the human case, we see significant differences between the two analyses. The point process models show significant bursting and oscillations throughout the trial (an average of 39% and 36%, respectively), while traditional methods lead us to believe that there is much less bursting than 10–30 Hz oscillations (an average of 10% and 37%, respectively). The reason the ISI histogram does not show as much bursting in the neurons is precisely because there are also 10–30 Hz oscillations in the spiking activity. Therefore, there are secondary peaks in the ISI histograms between 30–100 ms range. These secondary peaks result in less bursting density, leading us to believe that bursting may not be prevalent. The fact is, PD STN neurons often burst and oscillate in the beta frequency range and this is captured by the point process model parameters as described earlier, since our GLM separates the contributions of short-term intrinsic factors and long-term intrinsic factors on the propensity of the neuron to spike (5).

Another drawback of using traditional statistics is that they are significantly different from one another, and therefore, using them to define whether a neuron bursts, oscillates, or exhibits directional tuning over a certain epoch is not straightforward. In fact, the population summary shown in varies significantly as we change thresholds. In contrast, for point process models, we can use the same threshold to determine whether a neuron oscillates and bursts as the threshold is on how model parameters modulate the overall probability that the neuron spikes at any given time.