Application of non-linear control theory to a model of deep brain stimulation

Davidson, Clare M.; Lowery, Madeleine M.; Paor, Annraoi M. de

doi:10.1109/iembs.2011.6091673

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…In order to analyze the fourth-order series model (reduced) shown in Fig. 2, the applied high-frequency stimulation, representative of DBS, is mathematically combined with the nonlinear element NL1 resulting in an equivalent nonlinear element [50], [51]. As described in [40], describing function analysis techniques from [52] (27) Combining this with (26) gives (28) which sets the critical value of the composition of describing functions to that for which oscillations will occur in the fourth order series model (reduced).…”

Section: B Fourth-order Series Model (Reduced)mentioning

confidence: 99%

Analysis of Oscillatory Neural Activity in Series Network Models of Parkinson's Disease During Deep Brain Stimulation

Davidson

Paor

Cagnan

et al. 2016

IEEE Trans. Biomed. Eng.

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Parkinson's disease is a progressive, neurodegenerative disorder, characterized by hallmark motor symptoms. It is associated with pathological, oscillatory neural activity in the basal ganglia. Deep brain stimulation (DBS) is often successfully used to treat medically refractive Parkinson's disease. However, the selection of stimulation parameters is based on qualitative assessment of the patient, which can result in a lengthy tuning period and a suboptimal choice of parameters. This study explores fourth-order, control theory-based models of oscillatory activity in the basal ganglia. Describing function analysis is applied to examine possible mechanisms for the generation of oscillations in interacting nuclei and to investigate the suppression of oscillations with high-frequency stimulation. The theoretical results for the suppression of the oscillatory activity obtained using both the fourth-order model, and a previously described second-order model, are optimized to fit clinically recorded local field potential data obtained from Parkinsonian patients with implanted DBS. Close agreement between the power of oscillations recorded for a range of stimulation amplitudes is observed ( R(2)=0.69-0.99 ). The results suggest that the behavior of the system and the suppression of pathological neural oscillations with DBS is well described by the macroscopic models presented. The results also demonstrate that in this instance, a second-order model is sufficient to model the clinical data, without the need for added complexity. Describing the system behavior with computationally efficient models could aid in the identification of optimal stimulation parameters for patients in a clinical environment.

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Section: B Fourth-order Series Model (Reduced)mentioning

confidence: 99%

Analysis of Oscillatory Neural Activity in Series Network Models of Parkinson's Disease During Deep Brain Stimulation

Davidson

Paor

Cagnan

et al. 2016

IEEE Trans. Biomed. Eng.

View full text Add to dashboard Cite

show abstract

“…Nevertheless, this entirely relies on a likely oversimplified computational model [41]. To conclude, several strength-duration curves have been developed based on experiments, theoretical models and clinical observations [23][24][25]41,42]. As…”

Section: Stimulation Amplitude Conversionmentioning

confidence: 99%