Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation

Parkinson’s Disease (PD) is currently the second most common neurodegenerative disease. One of the most characteristic symptoms of PD is resting tremor. Local Field Potentials (LFPs) have been widely studied to investigate deviations from the typical patterns of healthy brain activity. However, the inherent dynamics of the Sub-Thalamic Nucleus (STN) LFPs and their spatiotemporal dynamics have not been well characterized. In this work, we study the non-linear dynamical behaviour of STN-LFPs of Parkinsonian patients using ε-recurrence networks. RNs are a non-linear analysis tool that encodes the geometric information of the underlying system, which can be characterised (for example, using graph theoretical measures) to extract information on the geometric properties of the attractor. Results show that the activity of the STN becomes more non-linear during the tremor episodes and that ε-recurrence network analysis is a suitable method to distinguish the transitions between movement conditions, anticipating the onset of the tremor, with the potential for application in a demand-driven deep brain stimulation system.

[1]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[2]  Tipu Z. Aziz,et al.  Resting tremor classification and detection in Parkinson's disease patients , 2015, Biomed. Signal Process. Control..

[3]  M. A. J. van Gerven,et al.  Parkinsonian rest tremor can be detected accurately based on neuronal oscillations recorded from the subthalamic nucleus , 2017, Clinical Neurophysiology.

[4]  Robert M. May,et al.  Dynamical diseases , 1978, Nature.

[5]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[6]  C. Stam,et al.  Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field , 2005, Clinical Neurophysiology.

[7]  Tipu Z. Aziz,et al.  Prediction of Parkinson's Disease tremor Onset Using a Radial Basis Function Neural Network Based on Particle Swarm Optimization , 2010, Int. J. Neural Syst..

[8]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[9]  E Ray Dorsey,et al.  The Parkinson Pandemic-A Call to Action. , 2018, JAMA neurology.

[10]  M. Farrer.  Genetics of Parkinson disease: paradigm shifts and future prospects , 2006, Nature Reviews Genetics.

[11]  J. Kurths,et al.  Complex network approach for recurrence analysis of time series , 2009, 0907.3368.

[12]  Dorothea Wagner,et al.  Approximating Clustering Coefficient and Transitivity , 2005, J. Graph Algorithms Appl..

[13]  D. S. Russell,et al.  Benign tremulous parkinsonism. , 2006, Archives of neurology.

[14]  M. Small.  Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance , 2005 .

[15]  Erwan Bezard,et al.  Pathophysiology of levodopa-induced dyskinesia: Potential for new therapies , 2001, Nature Reviews Neuroscience.

[16]  Kevin Warwick,et al.  Parkinsonian tremor identification with multiple local field potential feature classification , 2012, Journal of Neuroscience Methods.

[17]  J. Parra,et al.  Epilepsies as Dynamical Diseases of Brain Systems: Basic Models of the Transition Between Normal and Epileptic Activity , 2003, Epilepsia.

[18]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[19]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[20]  Tipu Z. Aziz,et al.  Closed-loop deep brain stimulation based on a stream-clustering system , 2019, Expert Syst. Appl..

[21]  A. Priori,et al.  Adaptive deep brain stimulation (aDBS) controlled by local field potential oscillations , 2013, Experimental Neurology.

[22]  J. Donges,et al.  Signatures of chaotic and stochastic dynamics uncovered with ϵ-recurrence networks , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[23]  Jonathan O. Dostrovsky,et al.  Pathological subthalamic nucleus oscillations in PD: Can they be the cause of bradykinesia and akinesia? , 2009, Experimental Neurology.

[24]  D. Graupe,et al.  Pathological tremor prediction using surface electromyogram and acceleration: potential use in ‘ON–OFF’ demand driven deep brain stimulator design , 2013, Journal of neural engineering.

[25]  C. Goetz,et al.  Levodopa‐induced dyskinesias , 2007, Movement disorders : official journal of the Movement Disorder Society.

[26]  Michael Small,et al.  Recurrence-based time series analysis by means of complex network methods , 2010, Int. J. Bifurc. Chaos.

[27]  P. Brown,et al.  Reduction in subthalamic 8–35 Hz oscillatory activity correlates with clinical improvement in Parkinson's disease , 2006, The European journal of neuroscience.

[28]  Stiliyan Kalitzin,et al.  Dynamical diseases of brain systems: different routes to epileptic seizures , 2003, IEEE Transactions on Biomedical Engineering.

[29]  M. Merello,et al.  Deep Brain Stimulation of the Subthalamic Nucleus for the Treatment of Parkinson's Disease , 2008 .

[30]  Kazutaka Takahashi,et al.  Recurrence network analysis of wide band oscillations of local field potentials from the primary motor cortex reveals rich dynamics. , 2015, 2015 7th International IEEE/EMBS Conference on Neural Engineering (NER).

[31]  Juan E. Tapiador,et al.  Security and privacy issues in implantable medical devices: A comprehensive survey , 2015, J. Biomed. Informatics.

[32]  G. Curio,et al.  Functional and effective connectivity in subthalamic local field potential recordings of patients with Parkinson’s disease , 2013, Neuroscience.

[33]  C. Hammond,et al.  Closing the loop of deep brain stimulation , 2013, Front. Syst. Neurosci..

[34]  Jürgen Kurths,et al.  Recurrence networks—a novel paradigm for nonlinear time series analysis , 2009, 0908.3447.

[35]  Tipu Z. Aziz,et al.  A Fuzzy Inference System for Closed-Loop Deep Brain Stimulation in Parkinson’s Disease , 2015, Journal of Medical Systems.

[36]  Hayriye Cagnan,et al.  Bilateral adaptive deep brain stimulation is effective in Parkinson's disease , 2015, Journal of Neurology, Neurosurgery & Psychiatry.

[37]  J. A. Stewart,et al.  Nonlinear Time Series Analysis , 2015 .