and Peter A. Tass
References
/
Nuorodos
[1] A. Stephenson, On a
new type of dynamical stability, Mem. Proc. Manch. Lit. Phil.
Soc.
52, 1–10 (1908),
http://www.biodiversitylibrary.org/item/39442#page/113/mode/1up
[2] A. Stephenson, On induced stability, Phil. Mag.
15,
233–236 (1908),
https://doi.org/10.1080/14786440809463763
[3] P.L. Kapitsa, Dynamic stability of a pendulum when its point
of suspension vibrates, Sov. Phys. JETP
21, 588–592
(1951) [in Russian]
[4] P.L. Kapitsa, Pendulum with a vibrating suspension, Usp.
Fiz. Nauk
44, 7–15 (1951) [in Russian],
http://ufn.ru/ru/articles/1951/5/b/
[5]
Selected Topics in Vibrational Mechanics, ed. I.
Blekhman (World Scientific, New Jersey, 2003),
https://doi.org/10.1142/5013
[6] A.L. Benabid, P. Pollak, C. Gervason, D. Hoffmann, D.M. Gao,
M. Hommel, J.E. Perret, and J. de Rougemont, Long-term
suppression of tremor by chronic stimulation of ventral
intermediate thalamic nucleus, Lancet
337, 403–406
(1991),
https://doi.org/10.1016/0140-6736(91)91175-T
[7] G. Deuschl, C. Schade-Brittinger, P. Krack, J. Volkmann, H.
Schäfer, K. Bötzel, C. Daniels, A. Deutschländer, U. Dillmann,
W. Eisner, et al., A randomized trial of deep-brain stimulation
for Parkinson's disease, N. Engl. J. Med.
1355, 896–908
(2006),
https://doi.org/10.1056/NEJMoa060281
[8] P. Krack, A. Batir, N. Van Blercom, S. Chabardes, V. Fraix,
C. Ardouin, A. Koudsie, P.D. Limousin, A. Benazzouz, J.F. LeBas,
A.L. Benabid, and P. Pollak, Five-year follow-up of bilateral
stimulation of the subthalamic nucleus in advanced Parkinson's
disease, N. Engl. J. Med.
349, 1925–1934 (2003),
https://doi.org/10.1056/NEJMoa035275
[9] P. Limusin, P. Krack, and P. Pollak, A. Benazzouz, C.
Ardouin, D. Hoffmann, and A.-L. Benabid, Electrical stimulation
of the subthalamic nucleus in advanced Parkinson's disease, N.
Engl. J. Med.
339, 1105–1111 (1998),
https://doi.org/10.1056/NEJM199810153391603
[10] P. Limousin, P. Pollak, A. Benazzouz, D. Hoffmann, J.F. Le
Bas, E. Broussolle, J.E. Perret, and A.L. Benabid, Effect of
parkinsonian signs and symptoms of bilateral subthalamic nucleus
stimulation, Lancet
345, 91–95 (1995),
https://doi.org/10.1016/S0140-6736(95)90062-4
[11] M.C. Rodriguez-Oroz, A. Gorospe, J. Guridi, E. Ramos, G.
Linazasoro, M. Rodriguez-Palmero, and J.A. Obeso, Bilateral deep
brain stimulation of the subthalamic nucleus in Parkinson's
disease, Neurology
55(12 Suppl 6), S45–S51 (2000)
[12] A.M. Lozano, J. Dostrovsky, R. Chen, and P. Ashby, Deep
brain stimulation for Parkinson's disease: disrupting the
disruption, Lancet Neurol.
1, 225–231 (2002),
https://doi.org/10.1016/S1474-4422(02)00101-1
[13] W.J. Marks, Deep brain stimulation for dystonia, Curr.
Treat. Options Neurol.
7, 237–243 (2005),
https://doi.org/10.1007/s11940-005-0017-z
[14] C. Hamani, J.M. Schwalb, A.R. Rezai, J.O. Dostrovsky, K.D.
Davis, and A.M. Lozano, Deep brain stimulation for chronic
neuropathic pain: Long-term outcome and the incidence of
insertional effect, Pain
125, 188–196 (2006),
https://doi.org/10.1016/j.pain.2006.05.019
[15] J.L. Viek, Mechanism of deep brain stimulation: excitation
or inhibition, Mov. Disord.
17(3), S69–S72 (2002),
https://doi.org/10.1002/mds.10144
[16] A.L. Benabid, A. Benazzous, and P. Pollak, Mechanisms of
deep brain stimulation, Mov. Disord.
17(3), S73–S74
(2002),
https://doi.org/10.1002/mds.10145
[17] A.M. Lozano and H. Eltahawy, How does DBS work? Suppl.
Clin. Neurophysiol.
57, 733–736 (2004),
https://doi.org/10.1016/S1567-424X(09)70414-3
[18] C. Beurrier, B. Bioulac, J. Audin, and C. Hammond,
High-frequency stimulation produces a transient blockade of
voltage-gated currents in subthalamic neurons, J. Neurophysiol.
85, 1351–1356 (2001),
http://jn.physiology.org/content/85/4/1351
[19] C. Magarinos-Ascone, J.H. Pazo, O. Macadar, and W. Buno,
High-frequency stimulation of the subthalamic nucleus silences
subthalamic neurons: a possible cellular mechanism in
Parkinson's disease, Neuroscience
115, 1109–1117 (2002),
https://doi.org/10.1016/S0306-4522(02)00538-9
[20] A. Benazzouz, D.M. Gao, Z.G. Ni, B. Piallat, R.
Bouali-Benazzouz, and A.L. Benabid, Effect of high-frequency
stimulation of the subthalamic nucleus on the neuronal
activities of the substantia nigra pars reticulata and
ventrolateral nucleus of the thalamus in the rat, Neuroscience
99,
289–295 (2000),
https://doi.org/10.1016/S0306-4522(00)00199-8
[21] T. Boraud, E. Bezard, B. Bioulac, and C. Gross, High
frequency stimulation of the internal Globus Pallidus (GPi)
simultaneously improves parkinsonian symptoms and reduces the
firing frequency of GPi neurons in the MPTP-treated monkey,
Neurosci. Lett.
215, 17–20 (1996),
https://doi.org/10.1016/S0304-3940(96)12943-8
[22] C.H. Tai, T. Boraud, E. Bezard, B. Bioulac, C. Gross, and
A. Benazzouz, Electrophysiological and metabolic evidence that
high-frequency stimulation of the subthalamic nucleus bridles
neuronal activity in the subthalamic nucleus and the substantia
nigra reticulata, FASEB J.
17, 1820–1830 (2003),
https://doi.org/10.1096/fj.03-0163com
[23] J.O. Dostrovsky, R. Levy, J.P. Wu, W.D. Hutchison, R.R.
Tasker, and A.M. Lozano, Microstimulation-induced inhibition of
neuronal firing in human globus pallidus, J. Neurophysiol.
84,
570–574 (2000),
http://jn.physiology.org/content/84/1/570
[24] M. Filali, W.D. Hutchison, V.N. Palter, A.M. Lozano, and
J.O. Dostrovsky, Stimulation-induced inhibition of neuronal
firing in human subthalamic nucleus, Exp. Brain. Res.
156,
274–281 (2004),
https://doi.org/10.1007/s00221-003-1784-y
[25] R. Levy, A.E. Lang, J.O. Dostrovsky, P. Pahapill, J. Romas,
J. Saint-Cyr, W.D. Hutchison, and A.M. Lozano, Lidocaine and
muscimol microinjections in subthalamic nucleus reverse
Parkinsonian symptoms, Brain
124, 2105–2118 (2001),
https://doi.org/10.1093/brain/124.10.2105
[26] M.L. Welter, J.L. Houeto, A.M. Bonnet, P.B. Bejjani, V.
Mesnage, D. Dormont, S. Navarro, P. Cornu, Y. Agid, and B.
Pidoux, Effects of high-frequency stimulation on subthalamic
neuronal activity in parkinsonian patients, Arch. Neurol.
61,
89–96 (2004),
https://doi.org/10.1001/archneur.61.1.89
[27] K. Pyragas, V. Novičenko, and P.A. Tass, Mechanism of
suppression of sustained neuronal spiking under high-frequency
stimulation, Biol. Cybern.
107, 669–684 (2013),
https://doi.org/10.1007/s00422-013-0567-1
[28] R. FitzHugh, Impulses and physiological states in
theoretical models of nerve membrane, Biophys. J.
1,
445–466 (1961),
https://doi.org/10.1016/S0006-3495(61)86902-6
[29] C. Morris and H. Lecar, Voltage oscillations in the
barnacle giant muscle fiber, Biophys. J.
35, 193–213
(1981),
https://doi.org/10.1016/S0006-3495(81)84782-0
[30] A.L. Hodgkin and A.F. Huxley, A quantitative description of
membrane current and its application to conduction and
excitation in nerve, J. Physiol.
117, 500–544 (1952),
https://doi.org/10.1113/jphysiol.1952.sp004764
[31] J. Kevorkian and J.D. Cole,
Multiple Scale and Singular
Perturbation Methods (Springer-Verlag, New York, 1996),
https://doi.org/10.1007/978-1-4612-3968-0
[32] W. Gerstner and W.M. Kistler,
Spiking Neuron Models.
Single Neurons, Populations, Plasticity (Cambridge
University Press, 2002),
https://doi.org/10.1017/CBO9780511815706
[33] A.L. Benabid, P. Pollak, A. Louveau, S. Henry, and J. de
Rougemont, Combined (thalamotomy and stimulation) stereotactic
surgery of the VIM thalamic nucleus for bilateral Parkinson
disease, Appl. Neurophysiol.
50, 344–346 (1987),
https://doi.org/10.1159/000100803
[34] A.L. Benabid, Deep brain stimulation for Parkinson's
disease, Curr. Opin. Neurobiol.
13, 696–706 (2003),
https://doi.org/10.1016/j.conb.2003.11.001
[35] D. Terman, J.E. Rubin, A.C. Yew, and C.J. Wilson, Activity
patterns in a model for the subthalamopallidal network of the
basal ganglia, J. Neurosci.
22, 2963–2976 (2002),
http://www.jneurosci.org/content/22/7/2963
[36] C. Hauptmann and P.A. Tass, Therapeutic rewiring by means
of desynchronizing brain stimulation, Biosystems
89,
173–181 (2007),
https://doi.org/10.1016/j.biosystems.2006.04.015
[37] P. Brown and D. Williams, Basal ganglia local field
potential activity: character and functional significance, Clin.
Neurophysiol.
116, 2510–2519 (2005),
https://doi.org/10.1016/j.clinph.2005.05.009
[38] A.A. Kühn, A. Kupsch, G.H. Schneider, and P. Brown,
Reduction in subthalamic 8–35 Hz oscillatory activity correlates
with clinical improvement in Parkinson's disease, Eur. J.
Neurosci.
23, 1956–1960 (2006),
https://doi.org/10.1111/j.1460-9568.2006.04717.x
[39] W.W. Alberts, E.W. Wright Jr, and B. Feinstein, Cortical
potentials and Parkinsonian tremor, Nature
221, 670–672
(1969),
https://doi.org/10.1038/221670a0
[40] H. Ben-Pazi, H. Bergman, J.A. Goldberg, N. Giladi, D.
Hansel, A. Reches, and E.S. Simon, Synchrony of rest tremor in
multiple limbs in Parkinson's disease: evidence for multiple
oscillators, J. Neural Transm.
108, 287–296 (2001),
https://doi.org/10.1007/s007020170074
[41] J.M. Hurtado, C.M. Gray, L.B. Tamas, and K.A. Sigvardt,
Dynamics of tremor-related oscillations in the human globus
pallidus: a single case study, Proc. Natl. Acad. Sci. USA
96,
1674–1679 (1999),
https://doi.org/10.1073/pnas.96.4.1674
[42] J.M. Hurtado, J.P. Lachaux, D.J. Beckley, C.M. Gray, and
K.A. Sigvardt, Inter- and intralimb oscillator coupling in
Parkinsonian tremor, Mov. Disord.
15, 683–691 (2000),
https://doi.org/10.1002/1531-8257(200007)15:4<683::AID-MDS1013>3.0.CO;2-%23
[43] J.M. Hurtado, L.L. Rubchinsky, K.A. Sigvardt, V.L.
Wheelock, and C.T. Pappas, Temporal evolution of oscillations
and synchrony in GPi/muscle pairs in Parkinson's disease, J.
Neurophysiol.
93, 1569–1584 (2005),
https://doi.org/10.1152/jn.00829.2004
[44] R. Levy, W.D. Hutchison, A.M. Lozano, and J.O. Dostrovsky,
High-frequency synchronization of neuronal activity in the
subthalamic nucleus of parkinsonian patients with limb tremor,
J. Neurosci.
20, 7766–7775 (2000),
http://www.jneurosci.org/content/20/20/7766
[45] P.A. Tass, D. Smirnov, A. Karavaev, U. Barnikol, T.
Barnikol, I. Adamchic, C. Hauptmann, N. Pawelcyzk, M. Maarouf,
V. Sturm, H.J. Freund, and B. Bezruchko, The causal relationship
between subcortical local field potential oscillations and
Parkinsonian resting tremor, J. Neural Eng.
7, 016009
(2010),
https://doi.org/10.1088/1741-2560/7/1/016009
[46] P. Brown, Oscillatory nature of human basal ganglia
activity: relationship to the pathophysiology of Parkinson's
disease, Mov. Disord.
18, 357–363 (2003),
https://doi.org/10.1002/mds.10358
[47] F. Alonso-Frech, I. Zamarbide, M. Alegre, M.C.
Rodríguez-Oroz, J. Guridi, M. Manrique, M. Valencia, J. Artieda,
and J.A. Obeso, Slow oscillatory activity and levodopa-induced
dyskinesias in Parkinson's disease, Brain
129, 1748–1757
(2006),
https://doi.org/10.1093/brain/awl103
[48] A.G. Androulidakis, A.A. Kuhn, C.C. Chen, P. Blomstedt, F.
Kempf, A. Kupsch, G.H. Schneider, L. Doyle, P. Dowsey-Limousin,
M.I. Hariz, and P. Brown, Dopaminergic therapy promotes
lateralized motor activity in the subthalamic area in
Parkinson's disease, Brain
130, 457–468 (2007),
https://doi.org/10.1093/brain/awl358
[49] M. Cassidy, P. Mazzone, A. Oliviero, A. Insola, P. Tonali,
V. Di Lazzaro, and P. Brown, Movement-related changes in
synchronization in the human basal ganglia, Brain
125,
1235–1246 (2002),
https://doi.org/10.1093/brain/awf135
[50] D. Williams, M. Tijssen, G. Van Bruggen, A. Bosch, A.
Insola, V. Di Lazzaro, P. Mazzone, A. Oliviero, A. Quartarone,
H. Speelman, and P. Brown, Dopamine-dependent changes in the
functional connectivity between basal ganglia and cerebral
cortex in humans, Brain
125, 1558–1569 (2002),
https://doi.org/10.1093/brain/awf156
[51] G. Foffani, G. Ardolini, B. Meda, M. Egidi, P. Rampini, E.
Caputo, G. Baselli, and A. Priori, Altered subthalamo-pallidal
synchronisation in parkinsonian dyskinesias, J. Neurol.
Neurosurg. Psych.
76, 426–428 (2005),
https://doi.org/10.1136/jnnp.2004.043547
[52] J. Lopez-Azcarate, M. Tainta, M.C. Rodriguez-Oroz, M.
Valencia, R. González, J. Guridi, J. Iriarte, J.A. Obeso, J.
Artieda, and M. Alegre, Coupling between beta and high-frequency
activity in the human subthalamic nucleus may be a
pathophysiological mechanism in Parkinson's disease, J.
Neurosci.
30, 6667–6677 (2010),
https://doi.org/10.1523/JNEUROSCI.5459-09.2010
[53] T.E. Özkurt, M. Butz, M. Homburger, S. Elben, J. Vesper, L.
Wojtecki, and A. Schnitzler, High frequency oscillations in the
subthalamic nucleus: a neurophysiological marker of the motor
state in Parkinson's disease, Exp. Neurol.
229, 324–331
(2011),
https://doi.org/10.1016/j.expneurol.2011.02.015
[54] H. Tan, A. Pogosyan, A. Anzak, K. Ashkan, M. Bogdanovic,
A.L. Green, T. Aziz, T. Foltynie, P. Limousin, L. Zrinzo, and P.
Brown, Complementary roles of different oscillatory activities
in the subthalamic nucleus in coding motor effort in
Parkinsonism, Exp. Neurol.
248, 187–195 (2013),
https://doi.org/10.1016/j.expneurol.2013.06.010
[55] J. Wang, J. Hirschmann, S. Elben, C.J. Hartmann, J. Vesper,
L. Wojtecki, and A. Schnitzler, High-frequency oscillations in
Parkinson's disease: spatial distribution and clinical
relevance, Mov. Disord.
29, 1265–1272 (2014),
https://doi.org/10.1002/mds.25962
[56] T. Yanagisawa, O. Yamashita, M. Hirata, H. Kishima, Y.
Saitoh, T. Goto, T. Yoshimine, and Y. Kamitani, Regulation of
motor representation by phase–amplitude coupling in the
sensorimotor cortex, J. Neurosci.
32, 15467–15475
(2012),
https://doi.org/10.1523/JNEUROSCI.2929-12.2012
[57] A.I. Yang, N. Vanegas, C. Lungu, and K.A. Zaghloul,
Beta-coupled high-frequency activity and beta-locked neuronal
spiking in the subthalamic nucleus of Parkinson's disease, J.
Neurosci.
34, 12816–12827 (2014),
https://doi.org/10.1523/JNEUROSCI.1895-14.2014
[58] B.C. van Wijk, M. Beudel, A. Jha, A. Oswal, T. Foltynie,
M.I. Hariz, P. Limousin, L. Zrinzo, T.Z. Aziz, A.L. Green, P.
Brown, and V. Litvak, Subthalamic nucleus phase-amplitude
coupling correlates with motor impairment in Parkinson's
disease, Clin. Neurophysiol.
127, 2010–2019 (2016),
https://doi.org/10.1016/j.clinph.2016.01.015
[59] H. Bronte-Stewart, C. Barberini, M.M. Koop, B.C. Hill, J.M.
Henderson, and B. Wingeier, The STN beta-band profile in
Parkinson's disease is stationary and shows prolonged
attenuation after deep brain stimulation, Exp. Neurol.
215,
20–28 (2009),
https://doi.org/10.1016/j.expneurol.2008.09.008
[60] E.J. Quinn, Z. Blumenfeld, A. Velisar, M.M. Koop, L.A.
Shreve, M.H. Trager, B.C. Hill, C. Kilbane, J.M. Henderson, and
H. Brontë-Stewart, Beta oscillations in freely moving
Parkinson's subjects are attenuated during deep brain
stimulation, Mov. Disord.
30, 1750–1758 (2015),
https://doi.org/10.1002/mds.26376
[61] P.A. Tass, Stochastic phase resetting: a theory for deep
brain stimulation, Prog. Theor. Phys. Suppl. (Kyoto)
139,
301–313 (2000),
https://doi.org/10.1143/PTPS.139.301
[62] P.A. Tass, Effective desynchronization by means of
double-pulse phase resetting, Europhys. Lett.
53, 15–21
(2001),
https://doi.org/10.1209/epl/i2001-00117-6
[63] P.A. Tass, A model of desynchronizing deep brain
stimulation with a demand-controlled coordinated reset of neural
subpopulations, Biol. Cybern.
89, 81–88 (2003),
https://doi.org/10.1007/s00422-003-0425-7
[64] S. Little and P. Brown, What brain signals are suitable for
feedback control of deep brain stimulation in Parkinson's
disease? Ann. N. Y. Acad. Sci.
1265, 9–24 (2012),
https://doi.org/10.1111/j.1749-6632.2012.06650.x
[65] S. Little, A. Pogosyan, S. Neal, B. Zavala, L. Zrinzo, M.
Hariz, T. Foltynie, P. Limousin, K. Ashkan, J. FitzGerald, A.L.
Green, T.Z. Aziz, and P. Brown, Adaptive deep brain stimulation
in advanced Parkinson disease, Ann. Neurol.
74, 449–457
(2013),
https://doi.org/10.1002/ana.23951
[66] M. Rosa, M. Arlotti, G. Ardolino, F. Cogiamanian, S.
Marceglia, A. Di Fonzo, F. Cortese, P.M. Rampini, and A. Priori,
Adaptive deep brain stimulation in a freely moving Parkinsonian
patient, Mov. Disord.
30, 1003–1005 (2015),
https://doi.org/10.1002/mds.26241
[67] S. Little, M. Beudel, L. Zrinzo, T. Foltynie, P. Limousin,
M. Hariz, S. Neal, B. Cheeran, H. Cagnan, J. Gratwicke, T.Z.
Aziz, A. Pogosyan, and P. Brown, Bilateral adaptive deep brain
stimulation is effective in Parkinson's disease, J. Neurol.
Neurosurg. Psychiatr.
87, 717–721 (2016),
https://doi.org/10.1136/jnnp-2015-310972
[68] P.A. Tass,
Phase Resetting in Medicine and Biology
(Springer Verlag, Berlin, 1999),
https://doi.org/10.1007/978-3-540-38161-7
[69] W. Gerstner, R. Kempter, J. van Hemmen, and H. Wagner, A
neuronal learning rule for submillisecond temporal coding,
Nature
383, 76–81 (1996),
https://doi.org/10.1038/383076a0
[70] H. Markram, J. Lübke, M. Frotscher, and B. Sakmann,
Regulation of synaptic efficacy by coincidence of postsynaptic
APs and EPSPs, Science
275, 213–215 (1997),
https://doi.org/10.1126/science.275.5297.213
[71] P.A. Tass and M. Majtanik, Long-term anti-kindling effects
of desynchronizing brain stimulation: a theoretical study, Biol.
Cybern.
94, 58–66 (2006),
https://doi.org/10.1007/s00422-005-0028-6
[72] P.A. Tass and C. Hauptmann, Therapeutic modulation of
synaptic connectivity with desynchronizing brain stimulation,
Int. J. Psychophysiol.
64, 53–61 (2007),
https://doi.org/10.1016/j.ijpsycho.2006.07.013
[73] C. Hauptmann and P.A. Tass, Cumulative and after-effects of
short and weak coordinated reset stimulation – a modeling study,
J. Neural Eng.
6, 016004 (2009),
https://doi.org/10.1088/1741-2560/6/1/016004
[74] P.A. Tass, L. Qin, C. Hauptmann, S. Dovero, E. Bezard, T.
Boraud, and W.G. Meissner, Coordinated reset neuromodulation has
sustained after-effects in parkinsonian monkeys, Ann. Neurol.
72,
816–820 (2012),
https://doi.org/10.1002/ana.23663
[75] J. Wang, S. Nebeck, A. Muralidharan, M.D. Johnson, J.L.
Vitek, and K.B. Baker, Coordinated reset deep brain stimulation
of subthalamic nucleus produces long-lasting, dose-dependent
motor improvements in the
1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine non-human primate
model of parkinsonism, Brain Stimul.
9, 609–617 (2016),
https://doi.org/10.1016/j.brs.2016.03.014
[76] I. Adamchic, C. Hauptmann, U.B. Barnikol, S. Dovero, E.
Bezard, T. Boraud, and W.G. Meissner, Coordinated reset has
lasting aftereffects in patients with Parkinson's disease, Mov.
Disord.
29, 1679–1684 (2014),
https://doi.org/10.1002/mds.25923