Math. Model. Nat. Phenom.
Volume 5, Number 2, 2010Mathematics and neuroscience
|Page(s)||185 - 207|
|Published online||10 March 2010|
Past, Present and Future of Brain Stimulation
Lawson Health Research Institute, Department of Medical Biophysics
University of Western Ontario, N6A 4V2
2 Department of Mathematics and Statistics, University of Victoria V8W 3R4 Victoria, B.C. Canada
3 Laboratoire IMS, Site ENSCPB, Institut Polytechnique de Bordeaux 16 avenue Pey-Berland, 33607 Pessac, France
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 92B20 / 82C32
Key words: brain stimulation / spiking neurons / neural field models
© EDP Sciences, 2010
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