Dynamics of the Subthalamo-pallidal Complex in Parkinson’s Disease During Deep Brain Stimulation

Modolo, Julien; Henry, Jacques; Beuter, Anne

doi:10.1007/s10867-008-9095-y

Cited by 31 publications

(31 citation statements)

References 41 publications

(62 reference statements)

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“…1, the initial mathematical model of DBS appeared only 10 years ago [46] and involved phase oscillators. Over the last decade, other models have been published including among others an oscillator network model [50], a spiking neuron network model [41], and a population based model [33]. In the present paper, we illustrate the close interaction existing between mathematics and neuroscience through a model based on neural field equations.…”

Section: Brief Historical Developmentmentioning

confidence: 95%

“…Taking a different approach, a population based model of the complex formed by the STN and the GPe was developed [33,35], which overcomes the above issues. Population based models have been extensively developed along the lines of statistical mechanics [36,38], when the number of neurons in the population is very large (i.e., N → +∞).…”

Section: Population-based Modelmentioning

confidence: 99%

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Past, Present and Future of Brain Stimulation

Modolo

Edwards

Campagnaud

et al. 2010

Math. Model. Nat. Phenom.

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Abstract. Recent technological advances including brain imaging (higher resolution in space and time), miniaturization of integrated circuits (nanotechnologies), and acceleration of computation speed (Moore's Law), combined with interpenetration between neuroscience, mathematics, and physics have led to the development of more biologically plausible computational models and novel therapeutic strategies. Today, mathematical models of irreversible medical conditions such as Parkinson's disease (PD) are developed and parameterised based on clinical data. How do these evolutions have a bearing on deep brain stimulation (DBS) of patients with PD? We review how the idea of DBS, a standard therapeutic strategy used to attenuate neurological symptoms (motor, psychiatric), has emerged from past experimental and clinical observations, and present how, over the last decade, computational models based on different approaches (phase oscillator models, spiking neuron network models, population-based models) have started to shed light onto DBS mechanisms. Finally, we explore a new mathematical modelling approach based on neural field equations to optimize mechanisms of brain stimulation and achieve finer control of targeted neuronal populations. We conclude that neuroscience and mathematics are crucial partners in exploring brain stimulation and this partnership should also include other domains such as signal processing, control theory and ethics.

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Section: Brief Historical Developmentmentioning

confidence: 95%

Section: Population-based Modelmentioning

confidence: 99%

Past, Present and Future of Brain Stimulation

Modolo

Edwards

Campagnaud

et al. 2010

Math. Model. Nat. Phenom.

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“…The model described above has been introduced by J. Modolo in his Ph.D thesis; a full description of the model as well as extensions of it and numerical results can be found in [12], [13], [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Synchronization in a Neural Population by a Population Density Approach

Garenne¹,

Henry

Tarniceriu

2010

Math. Model. Nat. Phenom.

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Abstract. In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich's two -dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate the phase deviations of a weakly coupled population model.

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“…The authors were participants in the interdisciplinary workshop "From Complex System Theory to Clinical Neurology" which was held at the Max-Planck-Institute for the Physics of Complex Systems (MPIPKS) in Dresden, Germany from June 4 to 8,2007. This workshop was organised by the guest editors of this issue and has received significant support by the MPIPKS guest programme, not only financial but also including the local organisation which was overtaken by Mandy Lochar and Renate Seidel under the auspices of the MPIPKS Director Frank Jülicher.…”

mentioning

confidence: 99%

“…Modolo et al [8] compare the outcomes of a simple firing rate model and a population-based model of the subthalamopallidal complex for a better understanding and improved treatment of Parkinson's tremor. Popovych et al [9] propose nonlinear delayed feedback stimulations for the control of collective dynamics with specific regard to the prevention and interruption of the abnormal synchrony in clinical practice.…”

mentioning

confidence: 99%

Complexity in Neurology and Psychiatry

et al. 2008

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This special issue focuses on the most complex system we know: the brain. More precisely, it deals with the examination of the brain dynamics and disturbances which are clinically manifested in neurological and psychiatric disorders like epilepsy, Parkinson's disease or mental depression. These diseases are often associated with disturbances of autonomous functions like hormone secretion and sleep which also are under the control of the brain. Accordingly, the papers in this issue will refer to a diversity of physiological systems. Their common link is that they all are related to brain functions and dysfunctions and that these neurophysiological issues are addressed by physically based approaches of systems analysis with the use of computer models and tools for nonlinear data analysis.The high expectations in such interdisciplinary approaches towards a better understanding of brain dynamics is the major motivation for this issue. All the authors have expertise in interdisciplinary work and have already made essential contributions in their fields. Many of them are experimental physiologists or clinicians who have learnt to implement biophysical methods, mostly in cooperation with physicists and mathematicians. Vice versa, the physicists and mathematicians among the authors have successfully entered the life sciences in demonstrating that physical applications are not only of interest from a systems theoretical point of view; but can also have high physiological relevance.

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Dynamics of the Subthalamo-pallidal Complex in Parkinson’s Disease During Deep Brain Stimulation

Cited by 31 publications

References 41 publications

Past, Present and Future of Brain Stimulation

Past, Present and Future of Brain Stimulation

Analysis of Synchronization in a Neural Population by a Population Density Approach

Complexity in Neurology and Psychiatry

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