Fig 1.
Schematic of the closed-loop DBS system.
(A) Case of advanced PD; LFP: local field potential; HFOs: high-frequency oscillations; head model reproduced with permission from Inserm /Eric Bardinet, Jerome Yelnik and Luc Mallet. (B) Case of treatment-refractory OCD. Applicability of cross-frequency coupling as a biomarker for feedback control in case of treatment-refractory OCD may be subject-specific. Accordingly, the presence of bursting neuronal activity was included as an alternative biomarker for feedback control in the respective closed-loop neuromodulation scheme; *short interburst interval and high intraburst frequency. (C) Exemplary identification of a bursting firing pattern of neuronal activity at Central, -2.56mm, Left STN, case O2 (top) based on the interspike interval (ISI) histogram (bottom). The histogram is characterized by a positively skewed distribution indicating a large fraction of short ISIs and a high intraburst frequency (μISI = 0.0179s; VarISI = 0.00069).
Fig 2.
Performance comparison between the modulation index and the 0–1 test outcome.
(A) Exemplary LFP signals acquired along the lateral MER trajectory for the identification of the right STN in a case of PD (P8). (B) The respective instantaneous angular frequency series are characterized by a high rate of singularities. Here, angular frequency is defined as the derivative of the (unwrapped) phase estimated by means of the Hilbert transform after linear band-pass filtering the signal between 13 and 30 Hz. By setting as thresholds the limits of the band-pass filter (red horizontal lines), slip occurences are identified at the time points of threshold crossing (inset). (C) Comparative assessment of the modulation index and the 0–1 test outcome in four representative cases of PD. Results obtained by means of both measures are in good agreement in case of a relatively high signal to noise ratio (SNR) (cases P5 and P6: identification of significant cross-frequency coupling at +0.5 mm). On the contrary, in the presence of increased noise levels, the high rate of artificial phase slips renders the calculation of cross-frequency coupling by means of the modulation index unreliable. In particular, the index fails to discriminate sites with significant non-linear coupling from sites without, in case of a low SNR (cases P7 and P8: significant cross-frequency coupling at -3 mm and at -1.5 mm/+1 mm, respectively, identified only by means of the 0–1 test for chaos).
Fig 3.
Exemplary and cumulative results of the methodology applied for the assessment of cross-frequency coupling as a biomarker for feedback control.
(A) Exemplary results corresponding to a case of PD and a case of OCD. Figures at the top display the power spectrum of the filtered signals (13-30Hz) along each exemplary trajectory. (B) Determination of parameter h (Eq (3)), based upon optimization of the outcome of the 0–1 test for chaos across a subset of 12 MER trajectories in PD and 12 MER trajectories in OCD. According to the results, in case of PD, sensitivity to measurement noise had to be further decreased by assigning a unitary value to parameter h. (C) Cross-frequency coupling was identified at at least 1 site within the STN of each patient with PD (total:18 MERs). Approximately 67% of these sites was located at the dorsal border of the STN, while at 72.2% of these sites neuronal activity followed a bursting or burst-like firing pattern and was considered for further processing in the phase-reduced bursting neuron model. Contrary to the case of PD, cross-frequency coupling was identified within the STN of only 2 patients with treatment-refractory OCD (total:4 MERs).
Fig 4.
Implementation results of the model-based vs. the non-model-based approach.
The model-based direct search method (SID-PSM) was compared with a non-model-based direct search method ([72]; Matlab, Mathworks, Natick, MA) in terms of the acquired parameters of stimulation, based on 13 MERs acquired during STN-DBS surgery for advanced PD and 12 MERs acquired during STN-DBS surgery for treatment-refractory OCD. For each site, we acquired five sets of parameter values, by means of each distinct solver, and assessed the respective mean values displayed in (A)-(C). The current amplitude, after application of both optimization procedures, was consistently maintained at its minimal value (I0 = 0.001A). (D) Mean values of the optimal stimulation settings following the application of the model-based direct search method. The mean optimal stimulation frequency proved to be significantly higher in case of OCD compared with PD (*p = 0.02, Mann—Whitney U test). Errorbars indicate standard error mean.
Fig 5.
Performance of the model-based vs. the non-model-based approach in terms of efficiency of stimulation and computational speed.
Comparison of the model-based direct search method (SID-PSM) with a non-model-based direct search method ([72]; Matlab, Mathworks, Natick, MA) corroborated a significantly higher performance of the former method, in terms of both stimulation power and computation time (*p<0.0001, Mann—Whitney U test), while an almost equivalent effect was observed on the invariant density measure (pPD = 0.3299, Mann—Whitney U test). Errorbars indicate standard error mean.
Table 1.
Stimulation settings determined post-operatively during the last follow-up visit for patients with advanced PD.
Table 2.
Stimulation settings determined post-operatively during the last follow-up visit for patients with treatment-refractory OCD.
Fig 6.
Performance of the model-based control strategy in terms of efficiency of stimulation.
(A)-(B) Statistical analysis corroborated the ability of the model-based control strategy (combined application of the stochastic phase-reduced model and the model-based direct search method) to identify stimulation settings that yield significantly lower values of the invariant density measure and stimulation power compared with the respective values obtained by simulating application (through employment of the stochastic phase-reduced model) of the stimulation settings determined post-operatively, during the last follow-up of patients with PD and OCD (*p<0.0001, Mann—Whitney U test). Errorbars indicate standard error mean. (C)-(D) The depicted stochastic kernels were acquired by fitting the phase-reduced bursting neuron model to an exemplary set of MERs acquired during STN-DBS surgery for PD and OCD, respectively, and simulating application of the post-operative (left panels) vs. the model-based stimulation settings (right panels). The stronger desynchronizing effect on neuronal activity exerted by the model-based stimulation settings is qualitatively reflected in the intense form of the respective stochastic kernels.
Fig 7.
Possible correlation between the invariant density measure and clinical effectiveness of stimulation in OCD.
Assessment of the mean ± standard error mean value of the invariant density measure based on a total of 39 MERs of subthalamic neuronal activity acquired during DBS surgery for treatment-refractory OCD and characterized by a high mean discharge rate (39.7 ± 14.71 Hz), a high intraburst frequency and a short interburst interval (μISI = 0.0289 ± 0.0114s, VarISI = 0.0038 ± 0.0056) vs. a total of 39 MERs of subthalamic neuronal activity characterized by a low mean discharge rate (13.53 ± 7.13 Hz), a low intraburst frequency and a long interburst interval (μISI = 0.1072 ± 0.093s, VarISI = 0.0265 ± 0.0542). The mean desynchronizing effect of standard 130Hz stimulation proved to be significanlty stronger in the former case compared with the latter (*p< 0.01, Mann—Whitney U test).