The Basal Ganglia IX: 58 (Advances in Behavioral Biology)

Development of Neural Circuitry. Guidance Cues in the Developing Brain. Functional Organization of Vertebrate Plasma Membrane. Developmental Plasticity of Inhibitory Circuitry. Neurogenesis in the Adult Brain II. Neurobiology of the Locus Coeruleus. From Molecules to Networks. Handbook of the Behavioral Neurobiology of Serotonin.

Oxygen Homeostasis and Its Dynamics. New Horizons in Neurovascular Coupling: Translational Research in Environmental and Occupational Stress. Cytoskeleton of the Nervous System. International Review of Cell and Molecular Biology. From Neuroscience to Neurology. Exercise and Physical Functioning in Osteoarthritis. The Beagle Brain in Stereotaxic Coordinates. Annual, Lunar, and Tidal Clocks. Melanin-Concentrating Hormone and Sleep. The second Parkinsonian pattern, labeled Bursty, consists of a basal level of firing at 70 Hz interrupted by random bursts stepping to Hz.

The duration of each burst is selected from a Gaussian distribution with a mean of 30 ms and a variance of 10 ms. The time between bursts is selected from a Poisson distribution with a mean of 70 ms. The final input pattern, labeled Oscillatory Bursty, is constructed similar to the bursty case, however, the inter-burst-interval is selected from a Gaussian distribution with a mean of 30 ms and a variance of 10 ms. This results in more periodic bursts. These rate functions are then used to generate Poisson random spike trains. These patterns were selected by Reitsma et al.

Both interspike interval ISI distributions and power spectra were computed on the model TC cells for comparisons with the original work. The power spectra was computed for the TC model spike response as well as the corresponding GPi and cortical inputs using the point process multi-taper spectrum analysis from the Chronux software package Bokil et al.

The measure of correlation is calculated using the Pearson's correlation coefficient. This is a spike count measurement that compares the number of spikes that occur over a window of length T defined as. The correlation coefficient is used to calculate the correlation susceptibility that quantifies the degree to which correlations are transferred through the model.

This is computed using the equation. For each value of f , 30 simulations of were run for s each. This resulted in pairs of correlation coefficients. This was completed over a range of window sizes T. The pairs were then sampled with replacement to generate a new set correlation coefficients and S values.

With the exception of the correlation study, all of the models were simulated using the HRLSim neural simulator package Thibeault, It currently supports two different point neuron implementations, the Leaky Integrate-and-Fire LIF model and the simple hybrid Izhikevich model. It has also proven extremely useful as a general neural simulation environment for other studies Srinivasa and Cho, ; O'Brien and Srinivasa, ; Srinivasa and Jiang, The action-selection model of Figure 2 was first tuned to match the original model of Humphries et al.

Using the model-as-animal strategy, 15 simulations were completed with different randomly connected networks. From each of those simulations 3 cell indexes were randomly selected and the overall activity rate of the last 9 s of simulation were computed for those neurons.

This is presented in Figure 6. In addition, the spike rasters and binned spike count rate functions are included. The overall mean firing rate results are in good agreement with the original work as well as with the experimental results referenced there. Basal activity of the model of action-selection. The spike rasters for each of the nuclei are overlaid with the corresponding spike-count firing rates.

Using the protocol of Humphries et al. Figure 7A illustrates the two channel action-selection results. Initially the network is at its basal level of activity with a 3 Hz Poisson input. At 1 s the input for channel 1 is increased to 20 Hz, causing, through disinhibition, the selection of that channel. The activity of channel 1 is pushed up to its basal level of activity and the channel 2 output is inhibited causing it to be selected.

This selection mechanism is more decisive than the one presented in Humphries et al. In the original work the previously selected channel had an increase in activity that was only slightly above the selection limit. To build on this result we tested the selection capabilities of all three channels, something that was not part of the original work.

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The results of this are presented in Figure 7B as well as in Figure 8 where the spike rasters of the model nuclei are plotted with the overlaid spike count rate functions. This is an encouraging result and suggests that the functional anatomy of the original work can be extended to more than three channels. The model is capable of appropriate selecting the most salient input between two competing channels A as well as three competing channels B.

Network response to competing inputs; spike rasters of the major nuclei of the BG action-selection with the spike count rates overlaid. With this irregular pattern of activity the thalamus is capable of reliably transmitting the somatomotor signals see Figure 9A. Simulated recovery of TC relay fidelity. A Under normal BG activity the thalamus is capable of relaying somatomotor inputs. B Under Parkinsonian conditions the BG nuclei fall into oscillatory firing patterns TC relay capabilities are greatly diminished. In Parkinson's disease, the firing pattern of the BG neurons have been reported to have regular synchronous firing patterns Walters and Bergstrom, In Figure 9B it can be seen that the BG nuclei begin to fire synchronously.

The neurons of the STN separate into two distinct populations with different phases of bursting. The periods of bursting oscillate around 4 Hz which is consistent with synchronous oscillations observed in the Parkinsonian BG Walters and Bergstrom, This synchronous activity results in a marked loss of thalamic relay. This disruption in the oscillatory activity is sufficient to restore the relay fidelity of the thalamus see Figure 9C.

The results of Figure 9 are quantified in Figure Although the spreads are somewhat dissimilar, neither overlaps with the much higher values measured in the Parkinsonian state. Allowing the network connection weights to randomly change over 20 simulations results in the Normal and DBS modes operating with less errors than the PD mode. The modified RT network of Pirini et al. The results of this experiment are shown in Figure Parkinsonian fire patterns result in a loss of accurate selection capabilities. Validating the generated GPi input spike trains was completed by the spectral power analysis presented in Figure 12A.

As in Reitsma et al. As expected the cortical inputs lack a peak in the frequency range of interest see Figure 12B. The parameters for the model were selected based on the TC cells firing patterns and spectral analysis. Although the Normal and Bursty spectral powers do peak around 10 Hz, there are oscillations present in both see Figure 12C.

Consistent with the original work, the Oscillatory and Oscillatory Bursty cases both have more distinct peaks around 10 Hz. The discrepancies are likely due to analysis parameters and the way GPi inputs were generated, as discussed below. There is a clear bimodality to the interspike interval histogram of Figure 12D , which is consistent with the original work.

However, the first peak, at 10 ms, is lower than the 30 ms peak described by Reitsma et al.

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This may be a product of that model using a refractory period of 5 ms, possibly resulting in slower bursts. It may also be a product of the way the dynamical correlate of the T-current is produced in the hybrid model. This would cause the inputs to recruit the bursting regime of the model in a different or perhaps less efficient way than the IFB or conductance based models used in Reitsma et al. Despite the slight differences, the firing patterns of the hybrid model in this network are still in general agreement with Reitsma et al.

The general susceptibility analysis, Figure 12F , qualitatively matches the results of Reitsma et al. Similar results were found for our implementation of the IFB model not presented , suggesting that the discrepancy in the magnitude of the susceptibility may arise due to differences in the way the input signals are generated.

This is a product of generating the spike trains using a common time-dependent rate function.

In the work of Reitsma et al. The implications of this are unclear but they do not appear to affect the conclusion that the bursty inputs cause an increase in correlation susceptibility. In addition, this further supports the conclusion that the correlation results of Reitsma et al. That combined with the fire pattern results above, helps validate the use of the simple hybrid model in correlation studies. An interesting result of this work that was absent from Humphries et al.

Even with the added current source the LIF neuron employed by Humphries et al. It was argued that the most relevant dynamics are included and given that the model of Humphries et al. However, as illustrated by the results in Figure 7 , the model presented here was able to not only selected the most salient input but also drive the activity of the previously activated channel clearly away from the selection limit. The selection results presented by Humphries et al. The increased activity of our model is large enough to push the previous channel back to its basal level of firing; reducing the possibility of selecting undesired or multiple channels.

The mechanism for the improved selection capabilities is unclear and remains a focus of future studies. In addition, in the future this model will be extended to include a larger number of channels to determine how feasible it is to scale beyond the three presented here.

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The original rate based model of Gurney et al. It was then expanded to include both action-selection and reward learning Stewart et al. The combination of action-selection and reinforcement-learning is another aspect of this model we plan to explore. Rubin and Terman offered one of the first models providing an explanation for the paradoxical therapeutic effects of DBS in a Parkinsonian BG.

The data driven extension of this work presented by Guo et al. A similar extension was performed by Meijer et al. Similarly, Dorval et al. The majority of these studies support the results of the work presented here and the theory that oscillatory inputs into the thalamus from the GPi negatively affect relay fidelity of the thalamus. In addition, constant inputs from the GPi, arising from DBS application, result in more effective relay in the thalamus Rubin et al.

There have been a number of studies that have extended the RT model to explore the therapeutic effects of different DBS locations, protocols and strategies Hahn and McIntyre, ; Guo and Rubin, ; Agarwal and Sarma, , as well as closed loop configurations Feng et al. Similarly, the inverse relationship between frequency and stimulus amplitude in clinically effective DBS has been explored with the RT Model Cagnan et al.

Similar extensions are planned for the network model presented here. The correlation study of Reitsma et al. That firing patterns observed in the Parkinsonian BG result in increased correlation susceptibility of the thalamus was also found in the work presented here. This could provide an explanation for some of the pathological hallmarks of Parkinson's disease.

Although it was shown that the T-current, required for TC neuron bursting, is responsible for the spike pattern of the model, it does not appear to have an effect on the correlation transfer Reitsma et al. Here however, we were able to demonstrate both similar spiking patterns as well as similar correlation susceptibility as the models with higher biological fidelity.

These results open up a number of future studies employing the hybrid model. This includes a frequency space analysis of the correlation transfer as well as a more thorough mathematical analysis of the relationship between GPi inhibition and spike correlation.

The complexity of the neuron models explored in the original studies require a level of population specificity that is undesirable in generic hardware implementations. Although the LIF neurons of Humphries et al. The motivations for embedding BG models in hardware systems go beyond the obvious applications to intelligent agents and neurorobotics. It has been shown that the model based control concepts introduced in section 1 have a number of clinical and practical applications Schiff, In addition to the control system computations, are the numerical calculations required for simulating the model aspect of the observer.

Combining the control system with neuromorphic hardware, perhaps in a system on chip, would significantly reduce the power consumption and provide a solution appropriate for portable realization. As emphasized in Schiff , even if the results of closing the loop are a reduction in battery life the model-based paradigm would be beneficial. Ideally, extended battery life will be accompanied by clinical improvements and studies cited here support the presence of both in closed-loop strategies.

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Model based or model predictor control systems work as state estimators where the dynamics of the model are used to predict the state of the current system. That prediction is then corrected with new measurements. These allows us to incorporate the predictions of the system's state as well as sensor estimates with the real sensor information to get a better estimate of the actual state. Figure 13 is a simplified overview of how these models would fit into such a control system. This is a brief example of how these models and neuromorphic hardware fit in with model based control strategies, for a more extensive review see Schiff Simplified example of how these models fit in a model based control DBS paradigm.

There are a number of issues, however, beyond implementation difficulties that need to be resolved before model-based control strategies will prove useful. The level of realism required in the neuron model is still unclear at this point. Schiff was able to demonstrate model-based control of DBS using the simple neuron implementation of Rubin and Terman Although computationally cheaper than the full conductance based models, this still suffers from the problems discussed above.

A logical next step in this work will be to show that the simple hybrid neuron can also be effective in model-based control strategies of DBS. This concept may also prove efficacious in brain computer interfaces BCI. Rather than contributing to the dynamic changes in brain dynamics, BCI applications would be used in estimating state and decoding measurements. This is a concept that, although promising, has proven difficult to achieve Schiff, Low-power realizations of these systems, as suggested here, offer a cost-effective option as BCI theories mature.

Structure and Function

Finally, the most important point on the study of neural control engineering is that often the best model is not the most physiological one, but the one that best reduces error Schiff, This is important because focusing too much on model adequacy may take away from the more important task of producing better therapies. An important question that will need to be answered in this case is, how detailed does a BG network model need to be in order to prove effective in estimating pathological conditions?

The next step in this work is to begin developing strategies based on the these models and the control theoretic approaches of Voss et al. Ultimately, until models are capable of predicting therapeutic outcomes, either through realistic biological results or through a dimensionality reduced interpretations, the pathological BG models will remain just a complement to physiological experiments. The networks utilizing the simple hybrid neuron presented here may offer a mechanism for revealing mathematical details of BG function and dysfunction that are hidden by the complexity of other models.

An immediate extension that highlights that concept is in the parameter exploration of the RT model. The computational efficiency of the network presented in section 2. Sweeps can be completed in hours as opposed to months of computing it would take to explore the original RT Model. We hope to present details of this in future publications. Although we have chosen the Izhikevich hybrid neuron, there are other neuron models that could have been employed. The most obvious choice is the adaptive exponential integrate-and-fire neuron Brette and Gerstner, Given the similarities of the two models we would predict the existence of parameter sets that would provide similar results.

Rate or the population based models may also be an option. These, as well as the feasibility of their hardware implementations, are options that should be explored in the future. Using the simple hybrid neuron, or any point neuron model, in such small networks and deriving biologically significant meaning from them can be unreliable. Care must be taken when interpreting the results in the context of both pathological conditions as well as clinical therapies.

The traditional niche for the simple hybrid neuron has really been in large-scale modeling. The more biologically realistic conductance based neuron models are generally recommended for single and small-scale network studies Izhikevich, In addition to those presented above, one of the primary motivations for using the simple model lie in the intention to construct large-scale models of the BG. My interest for Neuroscience started at the end of my Bachelor Degree in Biology when I was learning the use of retrograde and anterograde neuronal tracers in the amphibian brain in the Department of Cell Biology of the Complutense University.

The main goal of the research I have been doing there was to investigate the glial responses to different injuries: In this laboratory I learned glial primary culture techniques and worked in a project that involved time lapse confocal scanning laser microscopy to study calcium signaling mechanisms in cultured astrocytes responding to different neurotransmitters. Also during this time and in collaboration with the Neurosurgery Department, I did some immunocytochemical studies GFAP and NF in tissue sections from the amygdale, hippocampus and cortex of epileptic patients.

This company was created to develop novel fluorescence screening methods for drug discovery that used primary cell culture. In this company I helped to develop high through-put screening assays that used fluid handling robots to produce uniform cultures of neurons from different regions of the central nervous system. These primary cultures were assayed for targets that pharmaceutical companies were using to elucidate the mode of action of drugs in preclinical experiments.

The ultimate goal of my projects in Yoland's lab is to establish if the synaptic plasticity GABA receptors localization in the thalamus may play a role in Parkinson's disease pathophysiology. The hypothesis is that in Parkinson's disease the lack of striatal dopamine leads to increased GABAergic basal ganglia outflow to the thalamus.

If so, postsynaptic GABA receptors could respond to this increased release of neurotransmitter by either downregulation or changes in pharmacological properties. To do so, I have been using pre-and post-embedding immunocytochemichal techniques for electron microscopy.