THEMATIC PROGRAMS

September  2, 2014
THE FIELDS INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES
Focus Program on "Towards Mathematical Modeling of Neurological Disease from Cellular Perspectives"
Parkinson's Disease Workshop
May 22-23, 2012


Abtracts


Robert Chen, University of Toronto
Role of the basal ganglia in voluntary movements and mechanisms of deep brain stimulation

We investigated the role of the basal ganglia and thalamus in movement planning and preparation. In patients undergoing deep brain stimulation (DBS) surgery, we recorded simultaneously from scalp electrodes and from DBS electrodes implanted in the subthalamic nucleus (STN) or the pedunculopontine nucleus (PPN) in patients with Parkinson's disease, in the internal globus pallidus (GPi) in patients with dystonia and in the ventrointermediate (VIM) (cerebellar) nucleus of the thalamus in patients with tremor. When patients performed a self-paced wrist extension movement, bilateral premovment potentials or Bereitshaftspotential (BP) were recorded from the STN, PPN, GPi and the VIM about 1.5 to 2 seconds before movement onset, suggesting they are part of a network involved in movement preparation. Before and during self-paced movements, ß oscillations decreased bilaterally which may reflect general motor planning and ? oscillations increased only contralaterally in the GPi, which may reflect specific communications between the cortex and basal ganglia. Dystonia may be associated with excessive 5-18 Hz oscillations. In PD, dopaminergic medications increase the interactions between cortex and PPN. ß oscillations in the PPN increase rather than decrease during the movement planning period, suggesting that it is not antikinetic in the PPN and may explain why therapeutic DBS in the PPN used lower frequencies than in other nuclei in the basal ganglia. In a study in which PD patients received STN DBS at their individualized frequencies based on their local field potential recordings, ß frequency stimulation had no effect but ? frequency stimulation improve PD motor signs, suggesting the ? may be a prokinetic frequency in the STN. In a study that paired transcranial magnetic stimulation (TMS) and DBS, STN DBS was found to increase motor cortex excitability after ~3 ms and ~20 ms, demonstrating that STN DBS can increase motor cortex excitability and is potentially a mechanism of action of DBS. A TMS study also showed that VIM DBS facilitated rather than inhibit transmission in the cerebellothalamocortical pathway, showing that DBS activates rather than inhibit this target area.

Ming Cheng, Brown University
Pattern and Location of HFS-Induced Modulation of Pathological PD Dynamics

High-frequency stimulation (HFS) of the subthalamic nucleus (STN) is known to be effective in Parkinson's Disease (PD) patients, whereas low-frequency stimulation (LFS) is not. We examined single unit spike train activity in the contralateral STN during HFS and LFS of the STN in 8 PD patients during deep brain stimulation (DBS) surgery. We were able to record in the contralateral STN during STN stimulation, where stimulation pulses produce less artifactual interference with single unit data from the recording zone. Combined with the ability to cluster and remove stimulation-related artifact, we were able to better observe and define the features seen in HFS-induced changes to pathological beta oscillation, burstiness, and firing rate.
We hypothesized, and indeed found, that HFS drives a repetitive network-wide modulation that counteracts systemic pathologic neuronal activity that is not seen with LFS. We also found that this physiological modulation is greatest where DBS (with HFS) happens to make the greatest clinical impact, within the dorsal-most portion of the motor subunit, 1-2mm below the AC-PC plane, in posterolateral STN. We targeted this location based upon our prior observation (Cheng et. al. 2006, 2010) that patients with the most dramatic clinical improvements had their electrodes implanted within this location. We call this location the "sweet spot" for STN PD DBS. Within this "sweet spot", we find modulation of pathological PD dynamics as follows: 1) STN HFS appears to suppresses STN firing counteracting PD STN hyperactivity, whereas STN LFS does not reliably modulate firing rates; 2) firing rate suppression is accompanied by a stereotyped pulse-by-pulse decrement in the propensity to spike in the first 1-2 ms directly after each high frequency stimulation pulse; and 3) there is a stimulation frequency-locked increased probability to spike 3-4ms after each HFS pulse. These findings are not seen with LFS.
With our collaborators, we are now beginning to model the downstream effect of these findings upon beta power, burstiness, and firing rate using biophysical modeling methods and control algorithms. We believe that this work may lead to greater mechanistic understanding of why HFS, but not LFS, modulates the pathological dynamics of Parkinson's Disease. In addition, with the means to detect specific physiological signals related to HFS from the "sweet spot" that appear to correlate with clinical PD improvement, we hope to improve surgical localization and postoperative programming for DBS systems.

Mandar Jog, University of Western Ontario
New thoughts regarding pathogenesis of Parkinson disease

The concepts of brain organization and its architecture are rooted in the neurobiology of evolution itself. The laws that have governed the complexity of nature as we see it have all been applied to the nervous system as they have to every other complex system. As the nervous system currently exists, these laws seem to have been forgotten in the understanding of why the architecture may have become this way. In terms of the understanding of the physiology and function of the nervous system and then considering why the system fails as in neurodegenerative disease has therefore remained an enigma to a large extent. Two important concepts that are engrained within physics are those of thermodynamics and electrodynamics. While separate, these concepts are dependent on each other for the very existence of complex systems and especially applicable to the constituent elements of the nervous system.

These constructs result in a balance between multistate and nonequilibrium conditions that make the system rich at forming solutions. These states may exist at all levels of cellular biology. We present data using charge dynamics that show the transient existence of bistable states at the charge level and also at behavioral level.

Michelle M. McCarthy, Boston University
Striatum as a potential source of exaggerated beta rhythms in Parkinsons disease

Prominent beta frequency oscillations appear in the basal ganglia of Parkinsons disease patients. The dynamical mechanisms by which these beta oscillations arise are unknown. Using mathematical models, we show that robust beta frequency rhythms can emerge from inhibitory interactions between striatal medium spiny neurons. The interaction between the intrinsic membrane M-current and the synaptic GABAa current provides a cellular-level interaction that promotes the formation of the beta frequency rhythm. Our modeling studies propose that the pathologic beta oscillations in Parkinsons disease may arise as an indirect e ect of striatal dopamine loss on the striatal cholinergic system. Experimental testing of our model by infusion of the cholinergic agonist carbachol into normal, mouse striatum induced pronounced, reversible beta oscillations in the local eld potential. These results suggest the prominent beta oscillations in Parkinsons disease may be the result of an exaggeration of normal striatal network dynamics.

Cameron McIntyre, Cleveland Clinic Department of Biomedical Engineering
Neural Engineering Investigation of Deep Brain Stimulation

Chronic high frequency electrical stimulation of subcortical brain structures (or Deep Brain Stimulation (DBS)) is an effective treatment for several medically refractory neurological disorders. DBS is an established therapy for essential tremor, Parkinson’s disease, and dystonia, improving the lives of tens of thousands of people worldwide. DBS also shows promise in the treatment of epilepsy, obsessive-compulsive disorder, Tourette's syndrome, and depression. However, the clinical successes of DBS are tempered by limited understanding of the effects of the stimulation on the nervous system, and scientific definition of the therapeutic mechanisms of DBS remains elusive. In addition, it is presently unclear what electrode designs and stimulation parameters are optimal for maximum therapeutic benefit and minimal side effects. The focus of the McIntyre laboratory is to couple results from functional imaging, neurophysiology, neuroanatomy, and neurostimulation modeling to enhance our understanding of the effects of DBS. We combine human and animal experiments with detailed computer models of DBS. The computer models are parameterized by the experimental work and subsequently used to develop new experimental hypotheses; thereby creating a synergistic relationship of simulation and experimentation. We then use our growing knowledge on the therapeutic mechanisms of DBS to better engineer the next generation of DBS devices. We hope to improve DBS for the treatment of movement disorders and provide fundamental technology necessary for the effective application of DBS to new clinical arenas.

Rosalyn J Moran, University College London
Connectivity Changes in Parkinsonian Brain Networks through Dynamic Causal Modelling

In this talk I will propose Dynamic Causal Modelling as a 'mathematical microscope' that can provide regional, laminar, neurotransmitter and receptor specific assays of brain networks. In particular, I will examine the neuromodulatory chemical, Dopamine, in the context of healthy brain circuits and in Parkinson's disease. Understanding how Dopamine interacts with primary neurotransmitters in active brain networks is an important prerequisite for understanding pathological onset and progression. How this occurs and how brain connections change downstream of Dopamine loss is the focus of my results.
In particular, from a healthy human population, I will describe how DCM was used to link behavioural improvement under pro-dopaminergic (levodopa) modulation to changes in AMPA and NMDA mediated signalling in prefrontal regions. I will present data and a DCM of steady state responses analysis of Parkinsonian animal recordings that reveal changes in connectivity in basal ganglia-thalamo cortical circuits which exhibit enhanced beta oscillations. I will also show how this analysis is supported by a human patient population where pathological oscillations are linked to a similar connectivity profile.

Leonid Rubchinsky, Indiana University
Partially synchronous dynamics of parkinsonian basal ganglia and delayed feedback deep brain stimulation

Motor symptoms of Parkinson’s disease are associated with the excessive synchronized oscillatory activity in the beta frequency band (around 20Hz) in the basal ganglia and other parts of the brain. We study the dynamics of this synchrony in parkinsonian patients, as well as its potential mechanisms and functional implications with the computational models of basal ganglia circuits.

The study of neuronal units and LFP recorded in subthalamic nucleus of our group of patients revealed the specific temporal patterning of synchrony in time. If synchrony is present on the average, neural signals tend to go out of synch for a short (although potentially numerous) intervals. We developed time-series analysis approach, which quantifies this temporal patterning (and associated organization of the phase space), which allowed us to analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data. The experimentally observed intermittent synchrony can be generated just by moderately increased coupling strength in the basal ganglia circuits due to the lack of dopamine.

One particularly interesting aspect of this observed synchrony is the potential for desynchronizing deep brain stimulation. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation. This type of synchrony control was shown to destabilize synchronized state in networks of simple model oscillators as well as networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson’s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. When model parameters are such that the synchrony is unphysiologically strong, the feedback exerts desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson’s disease may boost rather than suppress synchronization. This also indicates that in general, desynchronizing stimulation may not necessarily exhibit a desynchronization effect, when acting on a physiologically realistic partially synchronous dynamics.

Jonathan Rubin, University of Pittsburg
Propagation of parkinsonian activity patterns and the effects of deep brain stimulation

Several major changes in activity patterns in the basal ganglia are associated with parkinsonism. These include enhanced bursting, changes in power and frequency of oscillations in firing, and increased correlation in neuronal activity. In this talk, I will focus in part on computational analysis of effects that these changes may induce in downstream basal ganglia and thalamic areas, which may lead to parkinsonian motor signs. These ideas provide a framework for understanding the mechanisms underlying the therapeutic efficacy of deep brain stimulation (DBS), and I will also discuss how the impact of DBS on bursting and synaptic transfer could contribute to this efficacy.

Sridevi Sarma, Johns Hopkins University
Performance Limitations of Thalamic Relay: Insights into Motor Signal Processing, Parkinson's Disease and Deep Brain Stimulation

Relay cells are prevalent throughout sensory systems and receive two types of inputs: driving and modulating. The driving input contains receptive field properties that must be transmitted while the modulating input alters the specifics of transmission. For example, the motor thalamus contains relay neurons that receive a driving input from motor cortex which encodes a motor plan, and a modulating input from the basal ganglia, which suppress movements that are not intended and vice-versa. In this paper, we analyze a biophysical based model of a relay cell and use systems theoretic tools to construct analytic bounds on how well the cell transmits a driving input as a function of the neuron’s electrophysiological properties, the modulating input, and the driving signal parameters. We assume that the modulating input belongs to a class of sinusoidal signals and that the driving input is an irregular train of pulses with inter-pulse intervals obeying an exponential distribution. Our analysis applies any nth order model as long as the neuron does not spike without a driving input pulse and exhibits a refractory period. Our bounds on relay reliability contain performance obtained through simulation of a second and third order model, and suggest, for instance, that if the frequency of the modulating input increases and the DC offset decreases, then relay increases. Our analysis shows how the biophysical properties of the neuron (e.g. ion channel dynamics) define the oscillatory patterns needed in the modulating input ( reflected by local field potentials) for appropriately timed relay of sensory information. We show how our bounds predict experimentally observed neural activity in the basal ganglia in (i) health, (ii) in Parkinson’s disease (PD), and (iii) in PD during therapeutic deep brain stimulation. Our bounds also predict different rhythms that emerge in the lateral geniculate nucleus in the thalamus during different attentional states.

Peter A. Tass, Research Center Juelich
Long-lasting neuronal desynchronization caused by coordinated reset neuromodulation

A number of brain diseases, e.g. movement disorders such as Parkinsons disease, are characterized by abnormal neuronal synchronization. Within the last years permanent high-frequency (HF) deep brain stimulation became the standard therapy for medically refractory movement disorders. To overcome limitations of standard HF deep brain stimulation, we use a model based approach. To this end, we make mathematical models of affected neuronal target populations and use methods from statistical physics and nonlinear dynamics to develop mild and efficient control techniques. Along the lines of a top-down approach we test our control techniques in oscillator networks as well as neural networks. In particular, we specifically utilize dynamical self-organization principles and plasticity rules. In this way, we have developed coordinated reset (CR) stimulation, an effectively desynchronizing brain stimulation technique. The goal of CR stimulation is not only to counteract pathological synchronization on a fast time scale, but also to unlearn pathological synchrony by therapeutically reshaping neural networks. According to computational studies, CR works effectively no matter whether it is delivered directly to the neurons' somata or indirectly via excitatory or inhibitory synapses. The CR theory, results from animal experiments as well as clinical applications will
be presented. MPTP monkey and human data will be shown on electrical CR stimulation for the treatment of Parkinsons disease via chronically implanted depth electrodes. Furthermore, acoustic CR neuromodulation for the treatment of subjective tinnitus will be explained. Subjective tinnitus is an acoustic phantom phenomenon characterized by abnormal synchronization in the central auditory system. In a proof of concept study it was shown that acoustic CR neuromodulation significantly and effectively counteracts tinnitus symptoms as well as the underlying pathological
neuronal synchronization processes. Furthermore, CR normalizes the pathologically altered interactions between different brain areas involved in the generation of tinnitus.

Charles Wilson, University of Texas-San Antonio
Chaotic Desynchronization and Deep Brain Stimulation for Parkinson’s Disease

Deep brain stimulation (DBS) of the subthalamic nucleus is a useful treatment for Parkinson's disease, but its therapeutic mechanism is unknown. There are three proposed mechanisms: (1) DBS may correct a pathological change the firing rate of basal ganglia output neurons, (2) It may correct a pathological pattern of firing (bursting), or (3) It may correct a pathological across-neurons firing pattern (synchrony).
To be effective, DBS requires high frequency stimulation (~100 Hz), well above the average firing rate of basal ganglia output neurons, (~60 spikes/s). Periodicity of DBS is also important; random stimulation patterns at the same mean frequency are ineffective.
Neither the rate nor the pattern model for the action of DBS adequately explains either the frequency or periodicity requirements. We suggest that that periodic stimulation may act to disrupt synchrony among basal ganglia output neurons. It is well known that oscillators (including neurons) driven by periodic inputs will exhibit chaotic oscillations over a specific range of stimulus frequencies and intensities. Small differences in phase among a group of forced oscillators are amplified and synchrony is disrupted. We used a one-dimensional reduction of a model basal ganglia output neuron to predict the frequency specificity of this mechanism, and its requirement for periodic stimulation.

Back to Top