Thalamocortical relay reliability varies across subthalamic nucleus deep brain stimulation protocols in a data driven computational model

Transcription

1 Thalamocortical relay reliability varies across subthalamic nucleus deep brain stimulation protocols in a data driven computational model Yixin Guo * Jonathan E. Rubin # Department of Mathematics Department of Mathematics Drexel University University of Pittsburgh Philadelphia, PA, USA Pittsburgh, PA, USA Cameron C. McIntyre Department of Biomedical Engineering Cleveland Clinic Cleveland, OH, USA Jerrold L. Vitek Department of Neuroscience Cleveland Clinic Cleveland, Ohio, USA David Terman Department of Mathematics The Ohio State University Columbus, OH, USA Running head: Thalamocortical relay across STN DBS protocols * The first two authors contributed equally to this work. # corresponding author: rubin@math.pitt.edu

2 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 2 Abstract. The therapeutic effectiveness of deep brain stimulation (DBS) of the subthalamic nucleus (STN) may arise through its effects on inhibitory outputs of the basal ganglia, including those from the internal segment of the globus pallidus (GPi). Changes in GPi activity will impact its thalamic targets, suggesting a possible pathway for STN DBS to modulate basal gangliathalamocortical processing. To study the effect of STN DBS on thalamic activity, we examined the reliability of the response of a computational model thalamocortical (TC) relay cell to an excitatory input train, under a variety of inhibitory signals. These inhibitory signals were obtained from single unit GPi recordings from monkeys rendered parkinsonian through arterial 1 methyl 4 phenyl 1,2,3,6 tetrahydropyridine (MPTP) injection, under three conditions: in the absence of STN DBS, under sub therapeutic STN DBS, and under therapeutic STN DBS. Our simulations show that inhibition generated from parkinsonian GPi activity compromised the reliability of TC relay of excitatory inputs, whereas TC relay fidelity was significantly improved under inhibition arising from therapeutic, but not sub therapeutic, STN DBS GPi activity. Further, in a heterogeneous model TC cell population, response failures to the same input occurred across multiple TC cells significantly more often in the no DBS case than in the therapeutic case. Inhibitory signals preceding successful TC relay tended to be relatively constant, whereas those before failed responses exhibited rapid changes. Consistent with this result, systematic variation of the burstiness and correlations of computationally generated inhibitory signals applied to the same model TC cell showed a compromise of TC relay under phasic, correlated inhibition, with improved reliability under more tonic inhibition. These results support the hypothesis that STN DBS may alter parkinsonian GPi activity patterns in a way that has the potential to promote reliable TC processing.

3 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 3 1. Introduction The delivery of high frequency stimulation to the subthalamic nucleus (STN) or other target areas, through a surgically implanted electrode, has become a widely used therapeutic option for the treatment of Parkinson's disease (PD) and other neurological disorders (Benabid et al. 2006). The mechanisms underlying the effectiveness of deep brain stimulation (DBS), however, remain unclear and under debate. Multiple studies have shown that pathological rhythmicity emerges in certain subsets of cells within the basal ganglia in parkinsonism (Bergman et al. 1994, Nini et al. 1995, Hurtado et al. 1999, Levy et al. 2000, Magnin et al. 2000, Raz et al. 2000, Brown et al. 2001, Hurtado et al. 2005). Therefore, DBS for PD may work by eliminating such pathological signals. Initial attempts to address this concept focused on the possibility that DBS blocks neural activity near the electrode, creating a physiologic lesion (Beurrier et al. 2001, Levy et al. 2001, Magarinos Ascone et al. 2002, Tai et al. 2003, Filali et al. 2004, Welter et al. 2004, Meissner et al. 2005). According to this theory, the DBS induced loss of inhibition from basal ganglia output areas frees up the thalamus to engage in appropriate movement related activity (Benazzouz et al. 2000, Obeso et al. 2000, Olanow et al. 2000, Benabid et al. 2001, Olanow and Brin 2001). Recent experimental and computational results, however, suggest that neurons directly downstream from stimulated regions may in fact be activated by DBS (Paul et al. 2000, Windels et al. 2000, Jech et al. 2001, Anderson et al. 2003, Hashimoto et al. 2003, Hershey et al. 2003, Windels et al. 2003, McIntyre et al. 2004, Miocinovic et al. 2006). These results support the alternative idea that DBS works by replacing pathological rhythms with regularized firing activity (Ryan and Sanders 1993, Obeso et al. 1997, Brown and Marsden 1998, Montgomery and Baker 2000, Vitek 2002, Grill et al. 2004, Garcia et al. 2005, Meissner et al. 2005). In past theoretical work, we offered a computational implementation of this idea (Rubin and Terman 2004). We used Hodgkin Huxley type models of cells in the indirect pathway of the basal ganglia (Terman et al. 2002) to generate inhibitory output trains, which served as synaptic inputs to a model thalamocortical (TC) relay cell. In this previous model system, we assessed TC cell activity under stereotyped representations of normal, parkinsonian, and DBS conditions. Our simulations and analysis demonstrated and explained how pathological rhythmic inhibition from the internal segment of the globus pallidus (GPi) to TC cells can compromise the fidelity of TC relay of excitatory signals, whereas regularization of this inhibition, even at levels that are elevated relative to normal conditions, can restore TC cells' relay capabilities.

4 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 4 In this study, we use GPi spike trains recorded from parkinsonian monkeys (Hashimoto et al. 2003), with or without DBS of the STN region, as the source of drive to our model TC cells. By doing so, we circumvented the controversy surrounding the effects of DBS at the stimulation site. Within this theoretical framework, we were able to test how biologically observed changes in GPi firing affect TC relay, both in a single model TC cell and in a heterogenous population of model TC cells. TC relay reliability is evaluated using a train of external excitatory stimuli applied to the same model TC cells that receive the recorded inhibitory synaptic inputs from GPi. Our results show that there is a significant improvement in the ability of the TC cells to relay the excitatory stimuli when they are exposed to GPi signals recorded under therapeutically effective DBS, relative to GPi data recorded in the absence of DBS or GPi data recorded from therapeutically ineffective DBS. Moreover, while response failures across a population of TC cells tend to occur on similar trials in the parkinsonian and therapeutically ineffective cases, failures occur asynchronously under effective STN DBS, which would moderate their downstream effect. Finally, to extend these results, we harness a purely computational approach that allows us to systematically vary the rhythmicity and degree of correlation within the inhibitory inputs that TC cells receive. Our results show that moderately increasing the burstiness and correlation of inhibitory spike trains, as might be expected in a transition from normal to parkinsonian conditions, leads to a gradual loss of relay reliability, while a further transition to tonic high frequency, highly correlated inhibitory signals, as may occur in clinically effective DBS (Hashimoto et al. 2003), leads to significant restoration of relay reliability. 2. Materials and Methods 2.1 Proposed Mechanism for DBS Effectiveness In awake states, TC cells serve to relay excitatory inputs (Steriade et al. 1997). The TC population targeted by GPi cells likely is involved in the relay of excitatory inputs between cortical areas (Guillery and Sherman 2002a, Guillery and Sherman 2002b, Haber 2003). The basic idea being explored in this paper is that changes in inhibitory output from the GPi to its target TC cell population affect the relay reliability of these TC cells, defined in terms of the generation of TC activity patterns that match the inputs to TC cells. Specifically, parkinsonian conditions induce oscillations, burstiness, and enhanced correlations in GPi outputs, and these effects are hypothesized to compromise relay reliability. We hypothesize that the effectiveness of DBS arises when DBS replaces the pathological GPi firing patterns with more regular activity.

5 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 5 While this regular activity may in fact be overly regular, and may occur at a higher frequency, relative to the activity that occurs in non parkinsonian states, it nonetheless restores thalamocortical relay reliability. This concept is illustrated schematically in Figure 1. These effects on TC relay in parkinsonian and DBS conditions remain to be demonstrated experimentally, but they were shown to arise in a previous, purely computational study (Rubin and Terman 2004), where a possible dynamical mechanism that could yield these results was also explained. The fundamental hypothesis from our original study was that DBS leads to tonic, regular inhibitory input to the TC cells, and this allows the activation and inactivation levels of TC cell membrane ionic currents to equilibrate, such that reliable relay can occur, as long as excitatory inputs are not excessively rapid. During parkinsonian conditions, the inhibitory output of GPi features synchronized bursting oscillations. When a significant increase in the level of inhibition associated with such oscillations occurs, a period of re equilibration of the TC ionic currents ensues. During this time, it is difficult for the TC cells to respond to excitation (Jahnsen and Llinas 1984a). Further, after currents have equilibrated to a high level of inhibition, a relatively abrupt decrease in inhibition can lead to an excessive or bursty TC response to excitation, due to increased availability of spike generating and sustaining currents (Jahnsen and Llinas 1984a, Jahnsen and Llinas 1984b). 2.2 Model TC Cells The model used for the TC cells is a slightly modified version of that used in our earlier study (Rubin and Terman 2004), which is itself a simplification of an earlier formulation (Sohal et al. 2000, Sohal and Huguenard 2002). In this model, the current balance and ionic activation equations take the form C m v' = I L I Na I K I T I G Th I E + I ext h' = (h (v) h)/τ h (v) (1) r' = (r (v) r)/τ r (v). 3 In system (1), the terms I L = g L [v E L ], I Na = g Na m (v)h[v E Na ], and I K = g K [.75(1 h)] 4 [v E K ] are leak, sodium, and potassium spiking currents, respectively, with square brackets denoting multiplication. Note that we use a standard reduction in our expression for the potassium current, which decreases the dimensionality of the model by one variable (Rinzel 1985). The current I T = 2 g T p (v)r[v E T ] is a low threshold calcium current. For these intrinsic currents, the forms of the

6 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 6 functions and the values of the parameters used appear in Table 1. Note that reversal potentials are given in mv, conductances in µs/cm 2, and time constant in msec. Further, we have scaled the parameters such that the capacitance is C m = 1 µf/cm 2. Additional terms in (1) refer to inputs to the TC cell model. I ext corresponds to a constant background input, chosen at I ext =0.44 na/cm 2 to yield a firing rate of roughly 12 Hz in the absence of other inputs. I Gi Th denotes the inhibitory input current from the GPi and will be discussed below. I E encodes excitatory signals to the TC cell and takes the form g E s[v v E ] where g E = 0.06 µs/cm 2, v E = 0 mv, and s'=α(1 s)exc(t) βs. (2) In (2), α = 0.1 msec 1 and β = 0.22 msec 1. The form of exc(t) depends on whether the excitatory input is periodic or stochastic. In the periodic case, exc(t) = i 0 H(sin(2πt/p))(1 H(sin(2π(t+d)/p))), where the dimensionless amplitude i 0 = 5, period p = 50 msec, duration d=5 msec, and where H(x) is the Heaviside step function, such that H(x)=0 if x<0 and H(x)=1 if x>0. In the stochastic case, input times are selected from a Poisson distribution, with an enforced pause of 20 msec between inputs to avoid excessive firing, with the same input duration and amplitude as in the periodic case.

7 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 7 In some simulations, we feed the same input currents I Gi Th and I E into all members of a heterogeneous population of model TC cells. The heterogeneous population is formed by selecting g Na, g L, and g T from normal distributions with means given by the values in Table 1 and with standard deviations given by 20% of these values. 2.3 Experimental Data Single unit extracellular recordings of neurophysiologically identified GPi neurons were acquired in parkinsonian monkeys that also had scaled down clinical DBS systems implanted (Hashimoto et al. 2002, Hashimoto et al. 2003, Elder et al. 2005). The monkeys were treated with 1 methyl 4 phenyl 1,2,3,6 tetrahydropyridine (MPTP) via a single injection through the internal carotid artery. They developed a stable parkinsonian state characterized by contralateral rigidity and bradykinesia (Hashimoto et al. 2003). Metal head chambers were placed aseptically under isofluorane anesthesia, and a chronic DBS electrode was implanted in the STN region. The chronic stimulating electrode was connected to a programmable pulse generator (Itrel II, Medtronic Inc.) implanted subcutaneously in the monkey's back. The stimulating lead was a scaled down version of the chronic stimulation electrode used in humans (Model 3387, Medtronic Inc.). The cylindrical lead consisted of four metal contacts each with a diameter of 0.75 mm, height of 0.50 mm, and separation between contacts of 0.50 mm. The most effective pair of stimulating electrode contacts in the STN region was chosen for bipolar stimulation in each animal after evaluation of the clinical effects of the stimulation (Hashimoto et al. 2003). Following establishment of the DBS animal model, neuronal activity was recorded extracellularly in the GPi using glass coated platinum iridium microelectrodes. Spontaneous neuronal activity (with the animal at rest and the head fixed) was recorded with and without DBS. To analyze neural activity during stimulation, a template of the stimulus artifact was constructed by averaging across all peristimulus segments. The stimulus artifact template was then subtracted from the individual traces, and neuronal spikes were detected (Hashimoto et al. 2002, Hashimoto et al. 2003). Stimulation parameters were selected to address two conditions in each animal: 1) stimulation parameters that produced therapeutic benefit, and 2) stimulation parameters subthreshold for therapeutic effect. Neuronal recordings of GPi activity were acquired under three conditions: 1) OFF stimulation (parkinsonian state), 2) ON therapeutic (clinically effective) stimulation, and 3) ON sub therapeutic (clinically ineffective) stimulation. 2.4 Inhibitory Inputs to TC Cells

8 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 8 In most simulations, we used experimentally recorded data, as discussed above, to represent the GPi spike times. For systematic exploration of the effects of particular features of the inhibitory input, however, we used computationally generated GPi spike times. In both cases, the synaptic inhibition from the GPi to a single model TC cell in our simulations has the form I Gi Th = g syn [ j s j ][v E syn ] (3) where the summation is over the synaptic activation variables s j of the presynaptic GPi cells, and where the inhibitory synaptic reversal potential E syn = 85 mv. At each spike time of the corresponding GPi cell, the variable s j is reset to 1, after which it decays via the equation s j ' = β inh s j (4) with β inh = 8 msec 1. Note that the experimental GPi data used in this study consists of single unit recordings, acquired with a single electrode. Therefore, it was not possible to use this data directly to explore how correlations among multiple GPi inputs to TC cells contribute to the TC cell relay reliability. However, in some simulations, we used the single unit GPi recordings to generate multiple GPi signals to each TC cell. To do this, we first formed N identical copies of a single GPi spike train, typically with N=2. We indexed the spike times within this train as {t 1, t 2,..., t p }. Next, we introduced jitter by selecting values ξ ij, i=1,..., N, j=1,...,p, from a normal distribution with amplitude σ (see Results for σ values used). These were used to form the new spike trains s 1 = {t 11, t 12,..., t 1p },..., s N = {t N1, t N2,..., t Np }, with t ij = t j + ξ ij. For simulated GPi inputs, each signal s j was formed by filtering a nonlinear combination of 5 independent random signals, w ij, i=1,..., 5. Each w ij was produced by a pair of Poisson processes. One Poisson process was used to generate a set of isolated spike times. A second, doubly stochastic Poisson process was used to generate bursting activity that was superimposed on the isolated spikes. In the doubly stochastic process, a primary Poisson process selects burst onset times with rate r b, while within bursting episodes, a secondary process produces spike times. Finally, burst durations were selected randomly from an independent Poisson process, with a minimum duration of 10 msec and a mean duration of 25 msec, for all r b. This approach allows for parametric control of the degree of burstiness and the spike rate of each input w ij, and hence of each s j (Tateno and Robinson 2006). The reason that we used multiple signals w ij for each s j is

9 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 9 that this allowed us to control the correlation across the s j, by using some of the same signals w ij for different j (Galan et al. 2006), as discussed further below (see Figure 7). We refer to the number of signals w ij shared by two GPi cells as the number of overlaps between them. Finally, at each spike time within any of the w ij, the variable s j was reset to 1, after which it decayed via equation (4). 2.5 Computational and Analytical Tools The computations in this paper were performed using customized codes simulated in XPPAUT (Ermentrout 2002; see and Matlab (The MathWorks, Inc., Natick, MA). We compute an error index to measure the reliability and accuracy with which the TC cells respond to excitatory inputs, similar to the error index described previously (Rubin and Terman 2004). In brief, the error index consists of the total number of errors divided by the total number of excitatory inputs. Errors can take the form of bad responses or misses. Specifically, for each excitatory stimulus, we record a miss if no TC spike occurs within a designated window of time, which we typically take as 10 msec, after the input arrives. If more than one TC spike occurs during this window, then we record a bad response. Finally, if exactly one TC spike occurs during the window, then we record a bad response if there are one or more additional TC spikes before the next input arrives (see Figure 1). Note that we use excitatory input rates that are sufficiently high such that in normal conditions, TC cells rarely recover and fire spontaneous spikes between inputs. This algorithm counts at most one error per input. An error index of 0 results if one TC spike occurs within 10 msec of each excitatory input and no other TC spikes occur until the next input, corresponding to optimal relay performance. Much of our analysis concerns ways in which the error index depends on the burstiness and correlation of the inhibitory GPi signals s j. Based on the method that we use to generate them, we take the burst rate r b as the measure of the burstiness of the purely computational GPi signals. It is important to note that based on this measure, what we call burstiness corresponds to the portion of time that a cell is engaged in high frequency activity. As shown in Figure 2A C, increases in burstiness lead first to rhythmicity and eventually, at sufficiently high values, to high frequency, nearly tonic spiking. That is, in the case of very high burstiness as we define it for computational GPi signals, a cell is actually engaged in high frequency spiking almost all of the time. To form an analogous measure for the GPi signals derived from experimentally recorded GPi spike trains, we perform a simple burst detection algorithm. In this approach, we detect all

10 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 10 spikes that are preceded by a silent period of at least 12 msec. Each such spike is considered to be the start of a burst if the next spike follows it by less than 8 msec. Each subsequent spike is counted as part of the burst if and only if it occurs within 8 msec of its predecessor. The burst duration is the time from the first spike in the burst to the last spike in the burst; see Figure 2. More involved statistical methods exist to compensate for chance epochs of high frequency spikes that fit within a given set of burst criteria of the type given here (Legendy and Salcman 1985); however, since such epochs would generate similar inhibitory inputs to TC cells as those produced by bursts, there is no reason to distinguish them for the purposes of our study. When burstiness is zero, the GPi signal consists of low frequency isolated spikes. The aspect of the correlation between pairs of GPi signals that is most relevant for our study is the temporal relationship of the bursts across the two signals. To obtain a single number that represents this relationship over a simulation of duration T msec, we simply sum the durations of all epochs during which both GPi cells are bursting simultaneously and divide by T (Figure 2). In the purely computational case, increases in r b tend to increase input correlation, in addition to burstiness, by this definition, since coincident bursts naturally become more likely when individual bursts themselves are more likely. If a single input signal w ij is represented more than once within the set of GPi inputs s j to a TC cell, however, then every burst of signal w ij contributes to this correlation measure. Thus, correlation can be manipulated for fixed r b by increasing the number of repeated signals w ij (overlaps) within the GPi input population for a TC cell. An additional computational procedure that we performed on GPi data was averaging. In this procedure, we first collected 25 msec segments of the GPi input signal to a TC cell. Each such segment extended from 20 msec before the start of an excitatory input to 5 msec after the start of this input. Segments were classified into three sets, based on whether the corresponding excitatory input was immediately followed by a missed, bad, or successful (i.e., neither missed nor bad) TC cell response. Finally, all segments within each set were averaged to produce miss, bad or success triggered GPi signals. 3. Results 3.1 With Experimentally Obtained GPi Inputs, Clinically Effective DBS Improves TC Relay Reliability

11 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 11 We generated GPi inputs to our model TC cell using GPi spike trains obtained from experimental recordings (Hashimoto et al. 2003), as described in Materials and Methods. In each simulation, a single GPi train was used, and hence the sum j s j in equation (3) became simply s 1. At each recorded GPi spike time, the synaptic activation term s 1 in equation (3) was set to 1, and s 1 decayed according to equation (4) between spikes. Figures 3A, 3B, and 3C show typical results from three second simulations using data collected in the absence of DBS, in the case of subtherapeutic DBS, and in the case of therapeutic DBS, respectively. The top trace in each figure (green) is the input signal, s 1, generated from the GPi spike train, while each middle trace (red) is the excitatory input current I E used in the simulation. The excitatory input is the same for the three simulations shown. Note, however, that the pattern of GPi activity in the absence of DBS leads to a much more phasic GPi signal in the top trace of Figure 3A than appears in the top trace of Figure 3C, with therapeutic DBS present. The bottom traces (black) in Figures 3A C show the membrane potential of the model TC cell in each condition. In perfect relay, the TC cell would exhibit one voltage spike for each input pulse. Figures 3A B illustrate that in the absence of DBS and with sub clinical DBS, however, the TC cell fails to respond to many of the inputs and generates bursts of multiple spikes to other inputs. The results in Figure 3C contrast strongly with Figures 3A B, showing a near perfect relay performance. In Figures 3D and 3E, we show the error index calculated based on the computational TC cell's relay performance for each of the three cases, labeled as PD (no DBS), subtherapeutic DBS, or therapeutic DBS, both for periodic excitation and for stochastically timed excitation. Each data point represents five seconds of simulation time, with non overlapping five second GPi data segments used, and is plotted as a function of the burstiness of the GPi input signal, computed as described in Materials and Methods. It is important to note that for the GPi recordings involved, all available data was used; that is, we did not select out particular simulation periods based the resulting error indices. These calculations show a strong difference in TC cell relay success across all three cases. Indeed, in both the periodic and the stochastic excitation cases, the mean performances across the three regimes were statistically significantly different (ANOVA, p <.0001), and a posteriori pairwise comparisons yielded significant differences across all pairs of regimes in both cases as well (Tukey's Honestly Significant Difference, p <.0002 for all pairs with periodic excitation and for PD/subDBS with stochastic excitation; p <.01 for PD/subDBS and subdbs/dbs with stochastic excitation). 3.2 Differences in GPi Signals Precede Different TC Cell Responses

12 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 12 TC cell responses were classified as misses and bad responses, both of which raised the error index, and successful responses, which did not. All three types of responses were found, in differing proportions, in the three scenarios of no DBS, subtherapeutic DBS, and therapeutic DBS. To analyze further the way in which the inhibitory signal to the TC cell contributed to its responses, we performed the averaging procedure described in Materials and Methods on the same GPi input signals used to generate Figures 3D E. In doing so, we combined signals from the no DBS, subtherapeutic DBS, and therapeutic DBS scenarios, after verifying that similar signals emerged in all three cases. As shown in Figure 4, there are important differences across the resulting miss, bad, and success triggered GPi signals. GPi inputs that preceded TC cell misses showed a substantial rise in strength over the 25 msec time interval considered. In the face of such a rise in inhibition, the TC cell would require additional deinactivation of its spike generating currents, namely I Na and I T in the TC model (1), in order to respond to an incoming excitatory stimulus (Rubin and Terman 2004, Rubin and Josic 2007). This deinactivation occurs relatively slowly, however, and thus would typically require more than the 25 msec available here. Conversely, GPi inputs that preceded bad TC cell responses showed a substantial decline in strength over the 25 msec interval considered. Recall that what we classify as bad responses consist of multiple spikes fired in response to single excitatory inputs, since such responses do not reflect the content of the input signals. In the presence of a strong inhibitory input, deinactivation of a TC cell's spike generating currents will occur. The resulting enhanced availability of these currents will allow for successful responses in the presence of sustained inhibition. When followed by a relatively rapid drop in inhibition, however, as seen in the bad signal in Figure 4, this additional deinactivation will lead to an excessive response to excitatory inputs (Rubin and Terman 2004), until it can be negated by a subsequent slow inactivation of the currents involved. Finally, GPi inputs that preceded successful TC cell responses were relatively constant and therefore avoided the generation of current imbalances. Interestingly, the roughly constant averaged inhibition level in this case was relatively high. This is consistent with the notion that DBS of the subthalamic nucleus promotes GPi activity (Hashimoto et al. 2003). However, the level of an approximately constant inhibitory signal has relatively little impact on TC cell responsiveness to excitatory inputs, because the cell's spike generating currents can equilibrate over time to whatever inhibition level is present (Rubin and Terman 2004). 3.3 DBS Leads to Dispersion in TC Cell Failure Times

13 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 13 The functional relevance of relay failures in TC cells will depend on how these failures are distributed across the TC population. In particular, if one TC cell bursts or fails to respond to an input but other TC cells in the population respond to this input appropriately, then the single aberrant response is unlikely to have a significant downstream effect. On the other hand, if multiple TC cells respond inappropriately to the same input, then this would be more likely to impact downstream activity. To test the degree of temporal coincidence of TC response errors, we used a single experimental GPi recording to generate an inhibitory signal that was input to each member of a population of 40 model TC cells. All TC cells also received an identical excitatory input, consisting of 59 pulses at a frequency of 20 Hz. To enhance the realism of this computational experiment, we introduced significant heterogeneity into the TC population, as described in Materials and Methods. Figures 5A1,B1,C1 show the number of TC cells responding to each excitatory input with a single spike, as a function of the position of each input within the excitatory train, for inhibitory signals recorded without DBS (PD), with subtherapeutic DBS, and with therapeutic DBS, respectively. Visual inspection of these plots shows that there were small numbers of successful TC cell responses on many more trials in the absence of DBS than with either form of DBS, while coincident TC cell failures were more prevalent in the case of subtherapeutic DBS than in the case of therapeutic DBS. Figures 5A2,B2,C2 summarize this data in three histograms, one for each case. In each histogram, results are binned according to the frequency with which different numbers of TC cells responded to excitatory inputs. For example, of the 59 excitatory inputs, there were 25 inputs to which 0 8 TC cells responded successfully in the PD case. Inspection of these plots reinforces the observation that there are many more instances of coincident TC response failures, across a large subset of the TC cell population, in the absence of DBS than with either form of DBS. In contrast, the response failures in the presence of DBS tend to be temporally dispersed. This trend is a gradual one, with subtherapeutic DBS representing an intermediate case between PD and therapeutic DBS. Similar results were obtained when noise was introduced into the TC model, in addition to heterogeneity (results not shown). We tested the statistical significance of the differences between these results in two different ways. First, for each histogram bin with a midpoint x, we can use the bin heights µ i (x), for i {PD, subdbs, DBS}, as estimates for the means of binomial distributions, each with standard deviation (µ i (x)(1 µ i (x)/59)) 1/2. We can then consider the probability that the sample values µ PD (x), µ subdbs (x), µ DBS (x) were in fact taken from the same distribution. Specifically, to

14 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 14 compare µ i (x) to µ j (x), we consider the likelihood that the values µ i (x), µ j (x) were drawn from a binomial distribution with mean (µ i (x)+µ j (x))/2 and standard deviation max {(µ k (x)(1 µ k (x)/59)) 1/2, (µ i (x)(1 µ i (x)/59)) 1/2 }. Using this calculation, we find statistically significant differences, with p <.01, between the bin heights of (PD,subDBS), (PD,DBS), and (subdbs,dbs) for x=4 and of (PD,DBS) for x=36, with p <.02, between the bin heights of (subdbs,dbs) for x=12 and for x=36, and with p <.05, between the bin heights of (PD,DBS) for x=28 and of (PD,subDBS) for x=36. Thus, we conclude that the overall distribution of the number of TC cells responding to each input is significantly different, with p <.01, across each pair of scenarios. The above statistical analysis suggests that erroneous responses by TC cells are more likely to occur together in the PD case than in subtherapeutic DBS, and in subtherapeutic DBS than in therapeutic DBS. However, this conclusion may depend on the fact that there are more errors overall in PD than in subtherapeutic DBS and in subtherapeutic DBS than in therapeutic DBS, which implies that purely by chance, the distributions in the PD and subtherapeutic DBS cases will be skewed toward coincident TC cell errors, relative to the therapeutic DBS case. To address this, we noted that there were 828 more errors in PD than in therapeutic DBS, which is approximately twice the total number of errors from therapeutic DBS. We started from the therapeutic DBS data and assigned an additional 828 errors randomly across excitatory inputs, while ensuring that the number of TC cell responses to each input remained non negative. This procedure yielded histogram totals of (9,11,22,16,1) for therapeutic DBS, which differs significantly in every bin from the totals of (25,3,5,6,20) seen in the PD data shown in Figure 5A2. Hence, we conclude that the significant difference in the dispersion of TC cell response failures between PD and therapeutic DBS is not attributable to the higher number of errors made in PD. 3.4 Burstiness and Correlation of GPi Inputs Both Affect TC Cell Relay Relability Experimental Case Experimental results have shown an increase in bursting activity, as well as an increase in correlations across GPi neurons, in parkinsonian conditions, relative to normal states (Bergman et al. 1994, Nini et al. 1995, Magnin et al. 2000, Raz et al. 2000, Brown et al. 2001). It is interesting to consider to what extent both burstiness and correlations within the GPi inputs to TC cells contribute to the differences that we observed in TC cell relay reliability. Since our experimental GPi data consisted of single cell recordings, we could not use this data to test this relationship

15 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 15 directly. However, in our simulations up to this point, we had set g syn for I Gi Th sufficiently high so that a single GPi input train could significantly impact TC firing. Based on this, we reasoned that the single GPi input train could be thought of as a collection of more than one, perfectly synchronized GPi signals. Correspondingly, we generated two copies of each GPi input train and divided the amplitude of the corresponding signal for each copy in half, and then we proceeded to introduce independent, normally distributed jitter into the input timing in each copy, as described in Materials and Methods. Figure 6A1 shows an example of a GPi input signal, an excitatory input train, and a TC cell response to this pair of inputs, in the DBS case with no jitter. Figure 6A2 shows the same GPi input signal after the introduction of a moderate jitter, of amplitude σ=0.05 (see Materials and Methods), as well as the TC cell response when this input is combined with the excitatory input train used previously. Figures 6B1,B2 show similar plots for GPi signals from the therapeutic PD case, with and without jitter. While it is difficult to detect differences across Figures 6A2,B1,B2 visually, systematic simulations yielded some interesting findings. First, the introduction of jitter within the therapeutic DBS input train had little effect on the already good TC response reliability (Figure 6C), although a slight smoothing of the GPi input signal, and corresponding relay enhancement, did result. Figures 6D,E show that jitter did have some effect on the burstiness and correlation of the input signals in the therapeutic DBS case. However, the burstiness level in the presence of jitter remained high (approximately 0.35, relative to 0.23 in the PD case without jitter), indicating that GPi inputs remained in a regime with high rates of high frequency spiking. In contrast, the inclusion of moderate amounts of jitter resulted in smoothing of the GPi input signal and yielded significant improvement in TC response reliability in the absence of DBS (Figure 6C). It is important to note that the introduction and gradual increase of jitter decreased the correlation between the GPi inputs to levels near zero, but it only diminished the burstiness in these signals by about one third, as shown in Figures 6F,G, such that significant burstiness remained. Therefore, the fact that the error index dropped with increased jitter in the PD case, as can be seen in Figure 6C, shows that input correlations likely play a role in the compromise of TC cell relay in the absence of DBS. At the same time, comparison of the PD and therapeutic DBS cases in Figures 6C G shows that the error index for the PD case remains substantially above that for the DBS case, even as jitter becomes relatively large. This comparison demonstrates that the phasic nature of GPi inputs in PD, indicated here by moderate burstiness levels (Figure 6F), also contributes significantly to the loss of TC cell reliability. In summary, based on these findings, we

16 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 16 predict that both significant correlations in GPi activity and phasic burstiness in GPi activity contribute to the compromise of TC relay reliability in parkinsonian conditions. 3.5 Burstiness and Correlation of GPi Inputs Both Affect TC Cell Relay Reliability Computational Case To further explore the effect on TC responses induced by changes in input burstiness, measured by the rate r b at which high frequency episodes occur, and in input correlation, corresponding to the proportion of time featuring simultaneous high frequency spiking of GPi cells, we performed simulations with computationally generated GPi input trains, for which we could control these input characteristics directly. As discussed in Materials and Methods, each computationally generated GPi signal s j was formed by combining spike trains w ij, which contained low frequency epochs and high frequency bursts, and filtering the result. We considered simulations with two GPi inputs (j=1,2) onto a single TC cell, with input sets W 1 = {w i1 : i=1,..., 5}, W 2 = {w i2 : i=1,..., 5}. In addition to varying the burst rate r b, we could vary the number of overlaps, or shared elements, in the sets W 1, W 2, as shown in Figure 7. In each simulation, we measured input correlation as the amount of time during which both of the GPi inputs to the TC cell were in the burst state, divided by the total simulation time, yielding a number between 0 and 1. For a fixed number of overlaps, we could achieve a full range of correlation times by varying r b. However, with fewer overlaps, a larger r b would be required to achieve a fixed correlation level. Hence, allowing different numbers of overlaps allowed us to consider more than just a one dimensional curve in the two dimensional space corresponding to burstiness and correlation of the inputs. We performed simulations with a range of r b values and different numbers of input overlaps. For each simulation, we counted the number of TC misses and bad spikes (i.e., bursts or spikes not aligned with inputs, as described in Materials and Methods) and used the results to compute the error index. Figure 8A shows how the error index depends on the input correlation, for a variety of numbers of overlaps, with g syn =0.06 µs/cm 2. For each fixed number of overlaps, the relation is non monotonic: for small correlation times, increases in input correlations are associated with more relay errors, while for large correlation times, further increases reduce errors in relay. Note that for small correlation times, the error index increases as the number of overlaps decreases. As mentioned above, to get the same degree of correlation with fewer overlaps requires larger r b. But larger r b corresponds to more burstiness in each of the GPi input trains. Thus, we deduce that at the low end of the correlation scale, more burstiness leads to

17 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 17 worsened TC relay. On the other hand, for large correlation times, the error index decreases as the number of overlaps decreases. At this end of the scale, increasing r b actually switches input trains from rhythmically bursty to high frequency tonic states. Together, these results on the impact of overlaps on error index suggest that rhythmic, bursty inputs lead to high error rates, while more high frequency, tonic inputs, as seem to occur in therapeutic DBS (Figures 3,6), reduce the error index back toward normal levels. The relationship between input burstiness and correlation and the error index is examined more thoroughly in Figure 8B, which shows color coded error index values as a function of both input burstiness and correlation. Each point was generated by running at least 100 simulations, with fixed r b and overlap number, and averaging the resulting correlations and error indices. Error index values peak for moderate input burst rate, with higher error rates for higher correlations at each fixed burst rate. As noted above, as burst rate increases beyond moderate levels, the proportion of time during which high frequency spikes are present in the input trains increases, such that inputs approach a high frequency, tonic spiking state (see Figure 2). In this regime, error index values decrease significantly, particularly when there are no overlaps (blue circles for large rates), which is consistent with Figure 8A. Finally, we decomposed the error index into the fraction of excitatory inputs for which the TC cell fails to respond (missed spikes; see Figure 8C) and the fraction of excitatory inputs to which the TC cell does respond but does so excessively (bad spikes; see Figure 8D). The number of missed spikes rises significantly from low to moderate burst rates and then drops again at high burst rates. This number depends much more weakly on correlation, for fixed burst rate, than on burst rate itself. Unlike missed spikes, the number of bad spikes depends strongly both on correlation and on burst rate, with the highest bad spike rate occurring for relatively high correlation and moderate burst rate. For each fixed burst rate, increased input correlations yield a noticeably higher rate of bad spikes. This trend makes sense, since bad spikes tend to arise via a rebound effect upon the relatively abrupt withdrawal of inhibition (Rubin and Terman 2004), and such an abrupt withdrawal would be more likely with higher input correlations (also see Figure 4). Similarly, for fixed correlation level, higher burst rates yield much lower bad spike rates, likely corresponding to the fact that with higher burst rates, the TC cell is subject to significant inhibition from at least one of its GPi inputs more of the time, making rebound less likely. Taken together, the results shown in Figure 8 all support three main ideas. First, TC cell relay reliability is compromised by inhibitory inputs that display a moderate or phasic burstiness with a significant correlation, or alignment of bursts, across inputs. This effect occurs through a

18 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 18 combination of increased missed spikes and increased bad, or excessive, responses. Second, the presence of a rather tonic, high frequency inhibitory signal, corresponding to high burstiness and correlation in our measures, reduces both missed and bad responses and thereby restores TC cell reliability. Third, both the burstiness and the correlations in the input structure contribute to this effect, yet the contributions that these features make are distinct. 4. Discussion The fundamental goal of this study was to quantify how different patterns of GPi inhibition affect TC relay reliability. We subjected a Hodgkin Huxley type model TC cell to stereotyped excitatory signals and evaluated its ability to relay that excitatory input while under the influence of inhibitory pallidal modulation. Experimental parkinsonian non human primate recordings of GPi activity, with and without DBS, were used to generate the inhibitory model inputs. We also explored a broader parameter space with computationally generated inhibitory trains in which the degree of burstiness and correlation structure were varied systematically. Our results show that parkinsonian GPi firing patterns and, more generally, phasic inhibitory signals with correlations in burst timing across cells, tend to compromise the fidelity of TC cell responses to excitatory signals. The principal motivation of our work was to investigate the possibility that therapeutic DBS restores the ability of the thalamus to integrate and relay excitatory inputs. Our simulations showed that relay fidelity was significantly improved under clinically effective, but not clinically ineffective, DBS conditions. More generally, improvement in TC relay reliability was achieved by either smearing out the arrival times of correlated, rhythmic inhibitory signals or by converting inhibitory inputs from rhythmic to tonic and high frequency. Moreover, across a model TC cell population, response failures tended to coincide temporally in parkinsonian conditions, even when the population was heterogeneous, whereas under DBS, these failures, when they occurred, were temporally dispersed. Excitatory inputs to the thalamic targets of basal ganglia are likely to arise from cortical areas, such as layer 5 of the motorcortex (Guillery and Sherman 2002a, Guillery and Sherman 2002b, Haber 2003). Smith and Sherman (Smith and Sherman 2002) have suggested that while excitatory inputs drive TC cells, inhibitory inputs generally act as modulatory signals to these cells, with their presence detectable primarily through their influence on TC cell responses to excitation. Our hypothesis about the mechanism through which parkinsonian conditions and DBS impact motor performance is consistent with this viewpoint. Specifically, our computational

19 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 19 analysis demonstrates that differing inhibitory basal ganglia output patterns, as arise in differing parkinsonian conditions, lead to significant differences in the modulation of TC relay of excitation. Further, we note that the impact of inhibition on TC relay in our model is mediated by the inactivation/deinactivation of spike promoting currents, namely a sodium current (I Na ) and a low threshold calcium current (I T ) (see also Rubin and Terman 2004). In normal conditions, with a relatively constant inhibition from the basal ganglia to TC cells, the TC cells act in tonic mode to relay excitatory inputs, with little I T participation (Rubin and Terman 2004). In parkinsonian conditions, however, rhythmic inhibition leads to two effects that compromise relay, both of which are evident in Figure 4. First, relatively abrupt rises in inhibition lead to failed relay, when excitatory inputs arrive before I Na and I T can deinactivate sufficiently to overcome the inhibition. Second, subsequent deinactivation of I Na and I T followed by relatively abrupt release from inhibition leads to activity bursts that do not represent excitatory input content. Finally, in therapeutic DBS conditions, although the level of inhibition to TC cells is generally higher than normal and may partially deinactivate I Na and I T, the lack of inhibitory rhythmicity leaves I T relatively constant and renders it fairly inconsequential for TC relay performance (Rubin and Terman 2004). Within the literature, substantial evidence has been presented that DBS of the subthalamic nucleus (STN) suppresses somatic activity (Beurrier et al. 2001,Levy et al. 2001, Magarinos Ascone et al. 2002, Tai et al. 2003, Filali et al. 2004, Welteret al. 2004, Meissner et al. 2004). Often, this has been interpreted to mean that the efficacy of DBS stems from such suppression, through a removal of excessive inhibition from the targets of basal ganglia outputs (Benazzouz et al. 2000, Obeso et al. 2000, Olanow et al. 2000, Benabid et al. 2001, Olanow and Brin 2001). While this hypothesis is consistent with classical, firing rate based representations of information flow through the basal ganglia (Albin et al. 1989, Wichmann and DeLong 1996), it is at odds with a variety of studies showing that DBS activates areas downstream from its target site (Paul et al. 2000, Windels et al. 2000, Jech et al. 2001, Anderson et al. 2003,Hashimoto et al. 2003, Hershey et al. 2003, Windels et al. 2003, McIntyre et al.2004, Miocinovic et al. 2006). From a rate based perspective, the idea that both parkinsonian and DBS conditions lead to increased thalamic inhibition represents a paradox. This paradox may be resolved, however, by considering that DBS changes the pattern, along with the firing rate, of inhibitory inputs to thalamus (Ryan and Sanders 1994, Obeso et al. 1997,Brown and Marsden 1998, Montgomery and Baker 2000, Terman et al. 2002,Vitek 2002, Rubin and Terman 2004, Garcia et al. 2005, Meissner et al. 2005). There have been some previous computational efforts to explore the details of how these varying firing patterns emerge and depend on a variety of neuronal and stimulus

20 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 20 related parameters (Grill et al. 2004, McIntyre et al. 2004). Building on one previous study (Rubin and Terman 2004), the work presented in this paper fills in important details of how specific changes in activity patterns induced downstream from the STN DBS site can lead to changes in information processing through the basal ganglia thalamocortical loop (Rubchinsky et al. 2003, Leblois et al. 2006), which would likely impact motor outcomes. The incorporation of experimentally recorded GPi firing patterns into our model represents a significant advance in the computational exploration of the mechanism underlying the efficacy of DBS. One important limitation of our study, however, was the lack of simultaneous multi unit recordings from GPi. While we were able to use computational techniques to generate simulated multi unit inputs (Figure 6) and to consider the impact of the experimental data on a multi cell target population (Figure 5), future work involving simultaneously recorded data would allow for a more direct consideration of the activity patterns across the GPi network and the thalamic responses that these patterns induce. Another limitation of our study was the use of a relatively simple TC cell model. We felt that it was appropriate to perform our analysis on a model that, while based on experimental data (Sohal et al. 2000, Sohal and Huguenard 2002, Rubin and Terman 2004), did not introduce undue complexity. The promising results of this study lay the groundwork for future efforts to further evaluate TC relay reliability during DBS in more detailed, multi compartmental TC cell models (Destexhe et al. 1998, Emri et al. 2000). In addition, the concepts considered in this work should be further explored in network models that account for the interactions of TC cells and the globus pallidus with other brain areas, such as the thalamic reticular network (Golomb et al. 1994, Destexhe et al. 1996). In this vein, we have not assigned a specific source to the excitatory signals to the TC cell in our model, and we therefore have not considered any source specific patterns that might be present in these signals. Further, we have not analyzed the downstream responses to changes in relay across a TC cell population nor their relevance for motor performance. Future experimental work to flesh out the details of the functionally relevant inputs to, and output targets of, the thalamic cells receiving inhibition from the GPi would prove quite useful in pursuing such extensions of this work. Acknowledgments. The research was partially supported by the NSF under the grants (JR), DMS (DT), and and NIH under grants NS (JV) and NS (CM). The authors thank Philip Hahn and Gary Russo for assistance in selecting representative GPi recordings.

21 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 21 Figure legends. Figure 1. Hypothesized mechanism for DBS effectiveness. In each of the three cases shown, the TC target receives inhibitory inputs from the GPi, which affects its relay of an excitatory drive. In the normal case, the inhibition is irregular and relatively weak, due to low correlation levels (represented by the grey boxes), and the TC cell successfully relays its inputs. In the parkinsonian case, inhibition is rhythmic and stronger (black boxes), due to enhanced correlations. During each inhibitory burst, the TC cell fails to respond to its drive (i.e., misses), while its response is excessive (i.e., bad) between bursts. In the case of supra clinical DBS, inhibition is strong but quite regular. Despite the strength of the inhibition, successful TC relay is restored. Figure 2. Examples of inputs from GPi cells to TC cells. A) C). Examples of the high frequency burst portions from computationally generated GPi signals. A) A low burst rate r b and 2 overlaps (shared w ij ) were used to generate these signals, and correspondingly, there are relatively few bursts. Moreover, the amount of time during which the traces simultaneously exhibit high frequency firing is small, yielding a small correlation time. B) A moderate burst rate r b and 2 overlaps were used to generate these signals, and correspondingly, each GPi trace shows high frequency oscillations for about half of the total simulation time. Although the times at which these occur are somewhat correlated, due to the overlaps and chance, the fraction of the total simulation time during which the traces simultaneously exhibit high frequency firing is less than 1/2, which yields a moderate correlation time. C) With a high r b and 4 overlaps, each trace exhibits high frequency oscillations for most of the simulation time, and the fraction of time during which the traces simultaneously show high frequency activity is much closer to 1, yielding a high correlation time. D) Illustration of the algorithm for burst detection, applied to experimental data. Bursts are detected, and the times at which bursts occur are read off of GPi spike trains (indicated with red/green segments in all panels). Next, burst times are compared and times when both cells are bursting are captured (black segments in top panel). Figure 3. TC relay reliability improves with clinically effective DBS. A) C) Top traces (green): inhibitory GPi input generated from filtering of the experimentally recorded GPi spike trains. Middle traces (red): simulated excitatory input signals. Bottom traces (black): model TC cell membrane potential in mv, over time in msec. Note that the vertical scale is not relevant for the input traces (green and red). A) MPTP without DBS. B) MPTP with subtherapeutic DBS (subdbs). C) MPTP with therapeutic DBS (DBS). D) E) Error index and burstiness calculated from simulations of 5 second blocks of data from all three cases. D) Results from 20 Hz periodic excitatory inputs. E) Results from excitatory inputs generated by a Poisson process, with a minimum time interval of 20 msec imposed between inputs. Figure 4. Average GPi signals preceding excitatory inputs to a TC cell vary depending on the resulting TC cell response. The three traces shown were formed by averaging over 25 msec segments of GPi signals, spanning the arrival times of excitatory inputs to a TC cell (see Materials and Methods). The excitatory input arrival times were aligned at 20 msec, as indicated by the dashed line in the figure. Signals were averaged separately for excitatory inputs that produced TC cell misses, bad responses, or successful responses. Figure 5. TC cell failures coincide without DBS and are dispersed with DBS. A1,B1,C1) Numbers of TC cells, from a heterogeneous population of 40 cells, responding successfully to each excitatory input in a train of 59 inputs (numbered 2 through 60, with input 1 discarded due to spurious transients), delivered at 20 Hz. The same excitatory input train was used in all three cases, while the GPi data used to generate the inhibition was taken either from a recording

22 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 22 without DBS (A1), a recording with subtherapeutic DBS (B1), or a recording with therapeutic DBS (C1). In all cases, a successful response was defined as a response without a miss or an extra spike, as discussed in Materials and Methods. A2,B2,C2) For each scenario, TC responses are collected in a histogram. To form each histogram, excitatory inputs were binned by the number of TC cells responding successfully to them. Each histogram thus shows the number of trials in which various numbers of TC cells responded successfully. Figure 6. Introducing jitter across multiple GPi signals reduces but does not eliminate the distinction between parkinsonian and DBS relay performance. Note that DBS here refers to supra clinical deep brain stimulation. A,B) The top four panels show GPi input signals (green), excitatory inputs (red), and TC cell voltage traces (black). The top two panels (A1, A2) correspond to the DBS case, with 0 jitter on the left and σ=0.05 on the right, while the bottom two (B1, B2) correspond to the PD case, with 0 jitter on the left and σ=0.05 on the right. C) Error index as a function of the level of jitter amplitude σ for DBS (red) and PD (non DBS, blue) simulations. D) Burstiness versus jitter amplitude for DBS. While burstiness drops with increasing jitter, it stays above baseline PD levels and remains at a level corresponding to significant periods of high frequency firing. E) Correlation versus jitter amplitude for DBS. F) Burstiness versus jitter amplitude for PD. While burstiness drops with increasing jitter, a significant burst rate remains. G) Correlation versus jitter amplitude for PD. Note that the fraction of time spent with both GPi cells bursting simultaneously drops almost completely to zero when jitter is introduced. Figure 7. Schematic representation of the numerical generation of GPi spike times. Each GPi cell receives and filters a combination of five independent random signals. Each signal is generated by a pair of Poisson processes that determine the signal's spike times and degree of burstiness (see Materials and Methods). An individual signal may belong to the input set of more than one GPi cell; in this example, there are two such overlaps, or shared signals. Varying the number of overlaps allows for control of the correlation across the GPi inputs to the TC cell. Figure 8. The error index rises and then falls again with increasing inhibitory input correlation and burst rate. A) Error index versus correlation, demonstrating the dependence of error index and correlation on the number of overlapping signals w ij in the GPi input sets W 1, W 2. B) Error index versus burst rate and correlation. The error index values are color coded such that warm colors, which occur here for moderate burst rate/correlation points, correspond to high error rates and cool colors, visible here for low and high burst rate/correlation points, correspond to low error rates. Note that for moderate burst rates, GPi firing is phasic, while for high burst rates, it is high frequency and more tonic. C),D) The error index is decomposed into missed spikes and bad spikes (see Materials and Methods), and their dependences on burst rate and correlation are plotted separately.

23 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 23 Figure 1

24 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 24 A B C D Figure 2

25 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 25 Figure 3

26 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 26 Figure 4

27 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 27 Figure 5

28 THALAMOCORTICAL RELAY ACROSS STN DBS PROTOCOLS 28