12This study presents a computational model of closed-loop control of deep brain stimulation (DBS) for 13Parkinson's disease (PD) to investigate clinically-viable control schemes for suppressing pathological 14 beta-band activity. Closed-loop DBS for PD has shown promising results in preliminary clinical 15 studies and offers the potential to achieve better control of patient symptoms and side effects with 16 lower power consumption than conventional open-loop DBS. However, extensive testing of algorithms 17in patients is difficult. The model presented provides a means to explore a range of control algorithms 18 in silico and optimize control parameters before preclinical testing. The model incorporates (i) the 19 extracellular DBS electric field, (ii) antidromic and orthodromic activation of STN afferent fibers, (iii) 20 the LFP detected at non-stimulating contacts on the DBS electrode and (iv) temporal variation of 21 network beta-band activity within the thalamo-cortico-basal ganglia loop. The performance of on-off 22 and dual-threshold controllers for suppressing beta-band activity by modulating the DBS amplitude 23 were first verified, showing levels of beta suppression and reductions in power consumption 24 comparable with previous clinical studies. Proportional (P) and proportional-integral (PI) closed-loop 25 controllers for amplitude and frequency modulation were then investigated. A simple tuning rule was 26 derived for selecting effective PI controller parameters to target long duration beta bursts while 27 respecting clinical constraints that limit the rate of change of stimulation parameters. Of the controllers 28 tested, PI controllers displayed superior performance for regulating network beta-band activity whilst 29 accounting for clinical considerations. Proportional controllers resulted in undesirable rapid 30 fluctuations of the DBS parameters which may exceed clinically tolerable rate limits. Overall, the PI 31 controller for modulating DBS frequency performed best, reducing the mean error by 83% compared 32 to DBS off and the mean power consumed to 25% of that utilized by open-loop DBS. The network 33 model presented captures sufficient physiological detail to act as a surrogate for preclinical testing of 34 closed-loop DBS algorithms using a clinically accessible biomarker, providing a first step for deriving 35 and testing novel, clinically-suitable closed-loop DBS controllers. 36 37 38
Recent studies have shown that specific motor symptoms of Parkinson's disease (PD) are correlated with oscillatory beta-band (12-30 Hz) activity in the basal ganglia. Deep brain stimulation (DBS) is an established therapy for PD, but is currently applied in an open-loop configuration. A computational model of the cortico-basal ganglia network was developed to systematically test the performance of five separate linear control schemes for closed-loop DBS. Each controller modulated the amplitude of DBS using the oscillatory activity in the basal ganglia as a biomarker. All controllers yielded a reduction in current and demonstrated a response to the suppression and resurgence of oscillations within the network. The model developed here can be further used to design and test more complex non-linear control schemes.
Models of the cortico-basal ganglia network and volume conductor models of the brain can provide insight into the mechanisms of action of deep brain stimulation (DBS). In this study, the coupling of a network model, under parkinsonian conditions, to the extracellular field distribution obtained from a three dimensional finite element model of a rodent's brain during DBS is presented. This coupled model is used to investigate the influence of uncertainty in the electrical properties of brain tissue and encapsulation tissue, formed around the electrode after implantation, on the suppression of oscillatory neural activity during DBS. The resulting uncertainty in this effect of DBS on the network activity is quantified using a computationally efficient and non-intrusive stochastic approach based on the generalized Polynomial Chaos. The results suggest that variations in the electrical properties of brain tissue may have a substantial influence on the level of suppression of oscillatory activity during DBS. Applying a global sensitivity analysis on the suppression of the simulated oscillatory activity showed that the influence of uncertainty in the electrical properties of the encapsulation tissue had only a minor influence, in agreement with previous experimental and computational studies investigating the mechanisms of current-controlled DBS in the literature.
Oscillatory neural activity in the beta frequency band (12-30 Hz) is elevated in Parkinson's disease and is correlated with the associated motor symptoms. These oscillations, which can be monitored through the local field potential (LFP) recorded by a deep brain stimulation (DBS) electrode, can give insight into the mechanisms of action, as well as treatment efficacy, of DBS. A detailed physiological model of the cortico-basal ganglia network during DBS of the subthalamic nucleus (STN) is presented. The model incorporates extracellular stimulation of STN afferent fibers, with both orthodromic and antidromic activation, and the LFP detected at the electrode. Pathological beta-band oscillations within the cortico-basal ganglia network were simulated and found to be attenuated following the application of DBS. The effects of varying DBS parameters, including pulse amplitude, duration and frequency, on the LFP at the DBS electrode were then assessed. The model presented here can be further used to understand the interaction of DBS with the complex dynamics of the cortico-basal ganglia network and subsequent changes observed in the LFP.
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