帕金森氏病（PD）是一種慢性進行性的神經退行性疾病，長期藥物治療通常效果較差甚至不利。它的主要病症包括靜息性震顫，僵硬，運動遲緩和姿勢不穩。深部腦刺激（DBS）是緩解晚期PD患者運動症狀的一種有前途的治療方法。然而傳統的開環“open-loop”DBS中持續的電刺激會引起神經精神病副作用，並縮短電池壽命。閉環 “closed-loop” DBS（cDBS）克服了這些副作用，並且僅在病理發作狀態下通過精確刺激大腦來進一步提高治療效果。異常同步高電壓震盪（HVS）與6-羥基多巴胺損傷和PD大鼠的運動功能障礙有關。 HVSs是在5-13 Hz頻帶中具有隨時間變化的、尖峰波動的、有韻律性的振盪。與β同步波段相反，儘管HVSs是在PD大鼠中的基底神經節-丘腦皮層網內的多巴胺耗竭後盛行，HVSs在cDBS中是相對被忽略的。為了研究cDBS抑制HVS對治療帕金森氏病是否至關重要，需要一種僅在HVS出現時才刺激大腦的自適應刺激器。
本論文的主要貢獻如下：（1）提出了一種基於希爾伯特-黃變換的算法來標記四隻PD大鼠不同腦區的1,273例HVSs的開始和結束。（2）提出offline-learning和online-learning算法，可在非常短的先前數據（144 ms）與低運算時間（<150 ms）內偵測HVS；（3）通過計算機模擬，評比所提出的CWT與FFT演算法的性能； （4）在8位元微計算器中實現優化的offline-learning來實現closed-loop控制器； （5）在PD大鼠的動物實驗實現了具有closed-loop控制器的cDBS系統，並且探討了cDBS在不同刺激的持續時間內對HVS的影響。
所提出的算法是基於間隔的自回歸建模的，其參數是透過常規的offline Kalman濾波器或online的自適應Kalman濾波器學習的。在包含來自四隻PD大鼠不同大腦區域的1,131個HVS的LFP中，兩種方法均以100％的靈敏度檢測所有HVS。Online-learning對背景噪聲的抵抗性更佳，並實現了更低的運算時間（61毫秒）和更高的精準度（96％），同時比連續小波變換需要更少的計算時間。另一方面，offline-learning的平均等待時間為72毫秒，精度為94％，與online-learning相比，計算時間減少了95％。模擬結果表明，兩種方法均能以在比HVS事件的平均持續時間（4.3 s）短得多的時間內可靠地檢測出HVS。
傳統的DBS可以抑制PD大鼠的HVS，但是在刺激後抑製效果並不會一直持續下去。實驗結果的時頻分析顯示了cDBS的潛在優勢如下：（1）對於不同的刺激（0.2–2 s）， cDBS引發的HVS抑制，即使在刺激結束後也可持續超過0.5 s; （2）僅刺激0.2 s可以抑制刺激後的HVS超過0.5 s，儘管需要多次刺激才能完全抑制HVS發作； （3）更長的刺激（0.5–2 s）可以達到更佳的HVS抑制，並且一次刺激就可以完全抑制HVS發作； （4）與PD大鼠的未刺激狀態（3.1 ± 1.4 s）相比，cDBS將HVS持續時間顯著縮短至0.15 ± 0.12 s。這些結果表明，cDBS可以長期有效地抑制HVS，以恢復帕金森氏運動障礙。

Parkinson’s disease (PD) is a chronic, progressive neurodegenerative disease for which long-term medication usually becomes less or even adversely effective. Its major motor symptoms include resting tremor, rigidity, bradykinesia, and postural instability. Deep brain stimulation (DBS) is a promising treatment for mitigating motor symptoms in advanced PD patients. However, the continuous electrical stimulation in the conventional “open-loop” DBS induces neuropsychiatric side effects and shortens the battery life. The “closed-loop” DBS (cDBS) overcomes these side effects and further improves the therapeutic efficacy by precisely stimulating the brain only during the pathological state.
Abnormally-synchronized high-voltage spindles (HVSs) are associated with motor deficits in 6-hydroxydopamine lesioned PD rats. HVSs are spike-and-wave, rhythmic oscillations with time-varying spectrum in the 5–13 Hz band. In contrast to beta-band synchrony, HVSs are relatively neglected in cDBS despite its prevalence in the basal-ganglia-thalamocortical network after dopamine depletion in PD rats. To investigate whether suppressing HVSs by cDBS is crucial for treating PD, an adaptive stimulator able to stimulate the brain only upon the occurrence of HVSs is demanded.
The major contributions of this thesis are as follows: (1) Proposing an algorithm based on Hilbert-Huang transform to label the onset and end of 1,273 HVS episodes from different brain regions of four PD rats; (2) Proposing the offline-learning and online-learning algorithms for detecting HVSs with low latency (< 150 ms) from very-short prior data (144 ms); (3) Evaluating the performance of the proposed algorithms in comparison with continuous wavelet transform and Fourier transform through computer simulations; (4) Realizing the closed-loop controller by implementing the optimized offline-learning algorithm in an 8-bit microcontroller; (5) Realizing the cDBS system with the closed-loop controller and investigating the effects of cDBS on HVSs across different stimulation durations through animal experiments with two parkinsonian rats.
The proposed algorithms are based on autoregressive modeling at interval, whose parameters are learnt by a conventional Kalman filter offline or an adaptive Kalman filter online. In the LFPs containing 1,131 HVSs from different brain regions of four PD rats, both methods detect all HVSs with 100% sensitivity. The online-learning method is more robust against background noise and achieves lower latency (61 ms) and higher precision (96%), while requiring less computation time than the continuous wavelet transform method. On the other hand, the offline-learning method results in the mean latency of 72 ms and precision of 94%, while achieving a 95% reduction in computation time compared to the online-learning method. The simulation results reveal that the proposed predictive model-based methods reliably detected the HVSs with latencies that are much shorter than the average duration of an HVS episode (4.3 s).
The conventional DBS suppressed the HVSs in PD rats, but the suppression did not persist after the stimulation is turned off. The time-frequency analysis of in vivo experimental results reveals the promising advantages of cDBS as follows: (1) For different stimulation durations (0.2–2 s), the cDBS-induced HVS suppression sustains for more than 0.5 s even after the stimulation is turned off; (2) Stimulating only for 0.2 s could suppress HVSs for more than 0.5 s post-stimulation, although multiple stimulations are required to completely suppress an HVS episode; (3) Longer stimulation (0.5–2 s) achieved stronger HVS suppression and could completely suppress an HVS episode with a single stimulation; (4) cDBS significantly shortened the HVS duration to only 0.15 ± 0.12 s compared with the unstimulated state (3.1 ± 1.4 s) of a PD rat. These results suggest that cDBS could effectively suppress the HVSs to restore the parkinsonian motor impairments with more therapeutic efficacy in the long term.

Contents xi
List of Figures xv
List of Tables xxi
List of Notations xxiii
1 Introduction 1
1.1 Parkinson’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Epidemiology and Symptomatology . . . . . . . . . . . . . 1
1.1.2 Pathophysiology . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Deep Brain Stimulation . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Side Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Closed-Loop Deep Brain Stimulation . . . . . . . . . . . . . . . . 4
1.3.1 Feedback Signal . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Data Recording, Analysis, and Modeling 12
2.1 Animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Stereotaxic Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 Fourier Spectral Analysis . . . . . . . . . . . . . . . . . . 17
2.4.2 Time-Frequency Analysis by Continuous Wavelet Transform 20
2.4.3 Time-Frequency Analysis by Hilbert-Huang Transform . . 23
2.5 Data Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5.1 Autoregressive Modeling . . . . . . . . . . . . . . . . . . . 30
2.5.2 System Identification . . . . . . . . . . . . . . . . . . . . . 30
2.5.3 Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Methodology 35
3.1 State-Space Representation of Time-Varying ARτ Model . . . . . 35
3.2 Offline-Learning Method . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Online-Learning Method . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 FFT-based Detection Methods . . . . . . . . . . . . . . . 45
3.4.2 CWT-based Detection Method . . . . . . . . . . . . . . . 45
3.4.3 Performance Metrics . . . . . . . . . . . . . . . . . . . . . 46
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4 Simulation Results 48
4.1 The Offline-Trained ARτ Model . . . . . . . . . . . . . . . . . . . 48
4.2 The Online-Learning ARτ Model . . . . . . . . . . . . . . . . . . 49
4.3 Cross-Validation on the Detection Performance of ARτ Model Parameters
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Performance Comparisons . . . . . . . . . . . . . . . . . . . . . . 53
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.5.1 Motivation towards Predictive Modeling Approach . . . . 60
4.5.2 Advantages of the Online-Learning Method . . . . . . . . 60
4.5.3 Advantages of the Offline-Learning Method . . . . . . . . 61
4.5.4 Applicability to Closed-Loop DBS Systems . . . . . . . . . 62
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5 Effects of Closed-Loop Deep Brain Stimulation on HVSs in Parkinsonian
Rats 64
5.1 Closed-Loop Controller . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1.1 Firmware . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1.2 Performance Evaluation . . . . . . . . . . . . . . . . . . . 68
5.2 Closed-Loop DBS Experiment . . . . . . . . . . . . . . . . . . . . 69
5.3 In-Vivo Experimental Results . . . . . . . . . . . . . . . . . . . . 71
5.3.1 Suppression of HVSs by cDBS . . . . . . . . . . . . . . . . 71
5.3.2 Statistical Comparison . . . . . . . . . . . . . . . . . . . . 77
5.4 Implications of the Closed-Loop DBS Experiments . . . . . . . . 81
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6 Conclusion and Future Work 84
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Bibliography 87

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