Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T13:52:02.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Past, Present and Future of Brain Stimulation

Published online by Cambridge University Press:  10 March 2010

J. Modolo ,
R. Edwards ,
J. Campagnaud ,
B. Bhattacharya  and
A. Beuter
J. Modolo
Affiliation:
Lawson Health Research Institute, Department of Medical Biophysics University of Western Ontario, N6A 4V2 London, ON Canada Laboratoire IMS, Site ENSCPB, Institut Polytechnique de Bordeaux 16 avenue Pey-Berland, 33607 Pessac, France
R. Edwards
Affiliation:
Department of Mathematics and Statistics, University of Victoria V8W 3R4 Victoria, B.C. Canada
J. Campagnaud
Affiliation:
Laboratoire IMS, Site ENSCPB, Institut Polytechnique de Bordeaux 16 avenue Pey-Berland, 33607 Pessac, France
B. Bhattacharya
Affiliation:
Laboratoire IMS, Site ENSCPB, Institut Polytechnique de Bordeaux 16 avenue Pey-Berland, 33607 Pessac, France
A. Beuter*
Affiliation:
Laboratoire IMS, Site ENSCPB, Institut Polytechnique de Bordeaux 16 avenue Pey-Berland, 33607 Pessac, France
*
* Corresponding author. E-mail:[email protected]
Get access

Abstract

Recent technological advances including brain imaging (higher resolution in space andtime), miniaturization of integrated circuits (nanotechnologies), and acceleration ofcomputation speed (Moore’s Law), combined with interpenetration between neuroscience,mathematics, and physics have led to the development of more biologically plausiblecomputational models and novel therapeutic strategies. Today, mathematical models ofirreversible medical conditions such as Parkinson’s disease (PD) are developed andparameterised based on clinical data. How do these evolutions have a bearing on deep brainstimulation (DBS) of patients with PD? We review how the idea of DBS, a standardtherapeutic strategy used to attenuate neurological symptoms (motor, psychiatric), hasemerged from past experimental and clinical observations, and present how, over the lastdecade, computational models based on different approaches (phase oscillator models,spiking neuron network models, population-based models) have started to shed light ontoDBS mechanisms. Finally, we explore a new mathematical modelling approach based on neuralfield equations to optimize mechanisms of brain stimulation and achieve finer control oftargeted neuronal populations. We conclude that neuroscience and mathematics are crucialpartners in exploring brain stimulation and this partnership should also include otherdomains such as signal processing, control theory and ethics.

Keywords

brain stimulationspiking neuronsneural field models
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 2: Mathematics and neuroscience , 2010 , pp. 185 - 207
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C. Ajmone Marsan. Focal electrical stimulation. In: Experimental Models of Epilepsy: A manual for the laboratory worker. Eds D. P. Purpura, J. K. Penry, D. Tower, D. M. Woodbury and R. Walter, Raven Press, New York, 1972.
Amari, S.. Dynamics of pattern formation in lateral-inhibition type neural fields . Biol. Cybern., 27 (1977), No. 2, 77–87.CrossRefGoogle ScholarPubMed
Atay, F. Hutt, A.. Stability and bifurcations in neural fields with finite propagation speed and general connectivity . SIAM J. Appl. Math., 65 (2005), No. 2, 644–666.CrossRefGoogle Scholar
Barnikol, U. B., Popovych, O. V., Hauptmann, C., Sturm, V., Freund, H. J. Tass, P. A.. Tremor entrainment by patterned low-frequency stimulation . Philos. Transact. A Math. Phys. Eng. Sci., 366 (2008), No. 1880, 3543–3573.CrossRefGoogle ScholarPubMed
Bartolow, R.. Experimental investigations into the functions of the human brain . AM. J. Med. Sci., 1874, 305–313. CrossRefGoogle Scholar
Bechtereva, N. P., Bondarchuk, A. N. Smirnov, V. M.. Therapeutic electrostimulations of deep brain structures . Vopr Neirokhir, 1 (1972), 115–120.Google Scholar
Benabid, A. L., Pollak, P., Louveau, A., Henry, S. de Rougemont, J.. Combined (thalamotomy and stimulation) stereotactic surgery of the Vim thalamic nucleus for bilateral Parkinson disease . Appl. Neurophysiol., 50 (1987), No. 1-6, 344–346.Google ScholarPubMed
Benabid, A. L., Bradley, W., Mitrofanis, J., Xia, C., Piallat, B., Fraix, V., Batir, A., Krack, P., Pollak, P. Berger, F.. Therapeutic electrical stimulation of the central nervous system . C. R. Biologies, 328 (2005), 177–186.CrossRefGoogle ScholarPubMed
S. A. Chkhenkeli. Direct deep brain stimulation: first steps toward the feedback control of seizures. In: Epilepsy as a dynamical disease, p. 249-262. Eds J. Milton and P. Jung, Springer-Verlag, New York, 2003.
J. Echauz, H. Firpi, G. Georgoulas. Intelligent control strategies for neurostimulation. In: Applications of intelligent control of engineering systems. Ed P. K. Valavanis, Springer, 2009.
Edwards, R.. Approximation of neural network dynamics by reaction-diffusion equations . Math. Meth. App. Sci., 19 (1996), 651–677.3.0.CO;2-S>CrossRefGoogle Scholar
Ermentrout, G. B. Cowan, J. D.. A mathematical theory of visual hallucination patterns . Biol. Cybern., 34 (1979), No. 3, 137–150.CrossRefGoogle ScholarPubMed
Eusebio, A., Pogosyan, A., Wang, S., Averbeck, B., Gaynor, L. D., Cantiniaux, S., Witjas, T., Limousin, P., Azulay, J. P. Brown, P.. Resonance in subthalamo-cortical circuits in Parkinson’s disease . Brain, 132 (2009), No. 8, 2139–2150.CrossRefGoogle ScholarPubMed
Gerstner, W., Kempter, R., van Hemmen, J. L. Wagner, H.. A neuronal learning rule for sub-millisecond temporal coding . Nature, 383 (1996), 76–81.CrossRefGoogle ScholarPubMed
Gibbs, F. A., Gibbs, E. L. Lennox, W. G.. The likeness of the cortical dysrhythmias of schizophrenia and psychomotor epilepsy . Am. J. Psychiatry, 95 (1938), 255–269.CrossRefGoogle Scholar
Gildenberg, P. L.. History of electrical neuromodulation for chronic pain . Pain Medicine, 7 (2006), S7–S13.CrossRefGoogle Scholar
Gluckman, B. J., Neel, E. J., Neto, T. I., Ditto, W. L., Spano, M. L. Schiff, S. J.. Electric field suppression of epileptiform activity in hippocampal slices . J. Neurophysiol., 6 (1996), 4202–4205.Google Scholar
Gluckman, B. J., Nguyen, , Weinstein, S. L. Schiff, S. J.. Adaptive electric field control of epileptic seizures . J. Neurosci., 21 (2001), No. 2, 290–600.Google ScholarPubMed
Grillner, S., Kozlov, A. Kotaleski, J. H.. Integrative neuroscience: linking levels of analyses . Curr. Opin. Neurobiol., 15 (2005), No. 5, 614–621.CrossRefGoogle ScholarPubMed
Hassler, R., Mundiger, F. Riechert, T.. Correlations between clinical and autoptic findings in stereotaxic operations in parkinsonism . Confin. Neurol., 26 (1965), 282–290.CrossRefGoogle ScholarPubMed
Hodgkin, A. L. Huxley, A. F.. A quantitative description of membrane current and its application to conduction and excitation in nerve . J. Physiol., 117 (1952), No. 4, 500–544.CrossRefGoogle ScholarPubMed
Horton, J. C., Adams, D. L.. The cortical column: a structure without a function . Phil. Trans. of the Royal Soc. B, 360 (2005), No. 1456, 837–862. CrossRefGoogle ScholarPubMed
Huang, X., Troy, W. C., Yang, Q., Ma, H., Laing, C. R., Schiff, S. J. Wu, J. Y.. Spiral waves in disinhibited mammalian neocortex . J. Neurosci., 24 (2004), 9897–9902.CrossRefGoogle ScholarPubMed
Izhikevich, E. M.. Simple model of spiking neurons . Transactions on Neural Networks, 14 (2003), 1569–1572.CrossRefGoogle ScholarPubMed
Izhikevich, E. M.. Polychronization: computation with spikes . Neural Computation, 18 (2006), 245–282.CrossRefGoogle ScholarPubMed
Jasper, H. H.. Recording from microelectrodes in stereotactic surgery for Parkinson’s disease . J. Neurosurg., 24 (1966), 219–221.Google Scholar
E. I. Kandel. Functional and stereotactic neurosurgery. Plenum Medical Book Co, New York, 1966.
Llinas, R. R., Ribary, U., Jeanmonod, D., Kronberg, E., Mitra, P. P.. Thalamocortical dysrhythmia: a neurological and neuropsychiatric syndrome characterized by magnetoencephalography . Proc. Natl. Acad. Sci. USA, 96 (1999), No 26, 15222–15227. CrossRefGoogle ScholarPubMed
H. O. Lüders. Deep brain stimulation and epilepsy. Martin Dunitz, New York, 2004.
McIntyre, C. C., Mori, S., Sherman, D. L., Thakor, N. V. Vitek, J. L.. Electric field and stimulating influence generated by deep brain stimulation of the subthalamic nucleus . Clin. Neurophysiol., 115 (2004), No. 3, 589–595.CrossRefGoogle ScholarPubMed
Meissner, W., Leblois, A., Hansel, D., Bioulac, B., Gross, C. E., Benazzouz, A. Boraud, T.. Subthalamic high frequency stimulation resets subthalamic firing and reduces abnormal oscillations . Brain, 128 (2005), No. 10, 2372–2382.CrossRefGoogle ScholarPubMed
JMilton, P. Jung. Epilepsy as a dynamical disease. Springer-Verlag, New York, 2003.
Modolo, J., Henry, J. Beuter, A.. Dynamics of the subthalamo-pallidal complex in Parkinson’s disease during deep brain stimulation . J. Biol. Phys., 34 (2008), No. 3-4, 351–366.CrossRefGoogle ScholarPubMed
J. Modolo, A. Beuter. Contribution of cortical inputs to subthalamic activity during deep brain stimulation. Proceedings of the Neurocomp 2008 conference, Marseille, France (2008).
Modolo, J. Beuter, A.. Linking brain dynamics, neural mechanisms and deep brain stimulation in Parkinson’s disease: an integrated perspective . Med. Eng. Phys., 31 (2009), 615–623.CrossRefGoogle Scholar
Nykamp, D. Q. Tranchina, D.. A population density approach that facilitates largescale modeling of neural networks : analysis and an application to orientation tuning . J. Comput. Neurosci., 8 (2000), No. 1, 19–50.CrossRefGoogle Scholar
J. Olszewski. The thalamus of the Macaca Mulatta. An atlas for use with the stereotactic instrument. Basel Karger, 1952.
Omurtag, A., Knight, B. W., Sirovich, L.. On the simulation of large populations of neurons . J. Comput. Neurosci., 8 (2000), No. 5, 51–63. CrossRefGoogle ScholarPubMed
Pascual, A., Modolo, J., Beuter, A.. Is a computational model useful to understand the effect of deep brain stimulation in Parkinson’s disease? J. Integr. Neurosci., 5 (2006), No. 4, 541–559. CrossRefGoogle ScholarPubMed
Richmond, J.. The 3Rs-Past, present and future . Scand. J. Lab. Anim. Sci., 27 (2000), 84–92.Google Scholar
Rubin, J. E. Terman, D.. High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model . J. Comput. Neurosci., 16 (2004), No. 3, 211–235.CrossRefGoogle Scholar
Rubino, D., Robbins, K. A. Hatsopoulos, N. G.. Propagating waves mediate information transfer in the motor cortex . Nature Neurosci., 9 (2006), No. 12, 1549–1557.CrossRefGoogle ScholarPubMed
Speelman, J. D. Bosch, D. A.. Resurgence of functional neurosurgery for Parkinson’s disease: a historical perspective . Mov. Disord., 13 (1998), No. 3, 582–588.CrossRefGoogle ScholarPubMed
Spiegel, E. A., Wycis, H. T., Marks, M. Lee, A. S.. Stereotaxic apparatus for operations on the human brain . Science, 106 (1947), 349–350.CrossRefGoogle ScholarPubMed
A. A. Spiegel, H. T. Wycis. Stereoencephalotomy (thalamic related procedures) part 1: Methods and atlas for the human brain. Grune and Stratton, New York, 1952.
P. A. Tass. Phase Resetting in Medicine and Biology. Stochastic Modelling and Data Analysis. Series: Springer Series in Synergetics, 1999.
Terman, D., Rubin, J. E., Yew, A. C. Wilson, C. J.. Activity patterns in a model for the subthalamopallidal network of the basal ganglia . J. Neurosci., 22 (2002), No. 7, 2963–2976.Google Scholar
Timmermann, L., Gross, J., Dirks, M., Volkmann, J., Freund, H. J. Schnitzler, A.. The cerebral oscillatory network of parkinsonian resting tremor . Brain, 126 (2003), No. 1, 199–212.CrossRefGoogle ScholarPubMed
Timmermann, L., Florin, E., Reck, C.. Pathological cerebral oscillatory activity in Parkinson’s disease: a critical review on methods, data and hypotheses . Expert Rev. Med. Dev., 4 (2007), No 5, 651–61. CrossRefGoogle ScholarPubMed
Titcombe, M. S., Glass, L., Guehl, D. Beuter, A.. Dynamics of Parkinsonian tremor during deep brain stimulation . Chaos, 11 (2001), No. 4, 766–773.CrossRefGoogle ScholarPubMed
Velazquez, J. L. P.. Brain, behaviour and mathematics: Are we using the right approaches? Physica D, 212 (2005), 161–182. CrossRefGoogle Scholar
Vilensky, J. A. Gilman, S.. Horsley was the first to use electrical stimulation of the human cerebral cortex intraoperatively . Surg. Neurol., 58 (2002), 425–426.CrossRefGoogle ScholarPubMed
Wilson, H. R. Cowan, J. D.. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue . Kybernetik, 13 (1973), No. 2, 55–80.CrossRefGoogle ScholarPubMed
Wichmann, T. Delong, M. R.. Deep brain stimulation for neurologic and neuropsychiatric disorders . Neuron, 52 (2006), No. 1, 197–204.CrossRefGoogle ScholarPubMed
A. Winfree. Are cardiac waves relevant to epileptic waves propagation? In: Epilepsy as a dynamical disease, p. 165-188. Eds J. Milton and P. Jung, Springer-Verlag, New York, 2003.
J. S. Yeomans. Principles of Brain Stimulation. Oxford University Press, New York, 1990.