[PDF]    http://dx.doi.org/10.3952/physics.v56i4.3419

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 56, 223–238 (2016)


SUPPRESSION OF SPONTANEOUS OSCILLATIONS IN HIGH-FREQUENCY STIMULATED NEURON MODELS
Kęstutis Pyragasa and Peter A. Tassb,c,d
aCenter for Physical Sciences and Technology, Saulėtekio 3, LT-10222 Vilnius, Lithuania
bInstitute of Neuroscience and Medicine – Neuromodulation, Jülich Research Center, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
cDepartment of Neurosurgery, Stanford University, 450 Serra Mall, Stanford, CA 94305, USA
dDepartment of Neuromodulation, University of Cologne, Albertus-Magnus-Platz, 50923 Cologne, Germany
E-mail: pyragas@pfi.lt

Received 13 July 2016; accepted 23 September 2016

We analyze the influence of high-frequency current stimulation on spontaneous neuronal activity and show that it may cause a death of spontaneous low-frequency oscillations. We demonstrate the universality of this effect for typical neuron models such as FitzHugh–Nagumo, Morris–Lecar, and Hodgkin–Huxley neurons as well as for the normal form of the supercritical Hopf bifurcation. Using a multiple scale method we separate the solutions of the neuron equations into slow and fast components and derive averaged equations for the slow components. The mechanism of suppression of neuronal activity is explained by an analysis of the bifurcations in the averaged equations governing the dynamics of the slow motion. Our results may contribute to the understanding of therapeutic effects of high-frequency deep brain stimulation, the golden standard for the treatment of medically refractory patients suffering from Parkinson’s disease. Furthermore, our study enables hypotheses concerning possible improvements of high-frequency deep brain stimulation.
Keywords: neuron models, high-frequency stimulation, Parkinson’s disease, nonlinear dynamics, multiple scale method, averaging method
PACS: 05.45.Xt, 87.19.La

SAVAIMINIŲ VIRPESIŲ SLOPINIMAS AUKŠTU DAŽNIU ŽADINAMUOSE NEURONUOSE

Kęstutis Pyragasa, Peter A. Tassb,c,d
aFizinių ir technologijos mokslų centras, Vilnius, Lietuva
bJulicho tyrimų centras, Julichas, Vokietija
cStanfordo universitetas, Stanfordas, Kalifornija, JAV
dKelno universitetas, Kelnas, Vokietija

Nagrinėjame aukšto dažnio srovės įtaką savaiminiam neuronų aktyvumui ir parodome, kad ši srovė gali nuslopinti neuronų savaiminius žemo dažnio virpesius. Šio reiškinio universalumą demonstruojame naudodami standartinius neuronų modelius (FitzHugh-Nagumo, Morris-Lecar ir Hodgkin-Huxley) ir normalinę superkrizinės Hopfo bifurkacijos formą. Taikydami skirtingų laiko mastelių metodą, mes atskiriame greitus ir lėtus neuroninių lygčių sprendinius ir lėtoms sprendinių komponentėms išvedame vidurkintas lygtis. Neuroninio aktyvumo slopinimo mechanizmą aiškiname remdamiesi vidurkintų lygčių bifurkacijų analize. Gauti rezultatai padeda suprasti giluminės smegenų aukšto dažnio stimuliacijos (high-frequency deep brain stimulation) gydomąjį efektą. Šiuo metu giluminė aukšto dažnio smegenų stimuliacija yra standartinė procedūra gydant Parkinsono ir kitas neurologines ligas. Mūsų tyrimai leidžia toliau tobulinti giluminės aukšto dažnio smegenų stimuliacijos metodą.


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