Algorithms for Spike Sorting and Source Localization of Mice Neuron Signals

本研究主要在探討以神經訊號 (spike) 為對象的分群演算法。神經訊號在無複 合電位或連續激發放電時，假設神經元訊號波形各不相同，在此基礎下，以四聯 電極(tetrode) 為訊號接收儀器，將訊號拆解出波形解析度(waveform resolution) 及空間解析度 (spatial resolution)。波形訊號往往受到生物體內複雜環境的干擾， 因此，本研究針對波形進行線性度前處理，並在頻域上去除高頻雜訊，留下平滑 訊號(low-pass)，並放大波形中差異性(difference) 較大的細節成分做為人工高頻， 使得波形保留大部分的原形又能突顯變化較大的特徵，最後以主成分分析(PCA) 降維，組成LDPCA 特徵；空間解析度來自於神經訊號在空間中傳輸造成的衰減， 因距離而有所不同。 神經訊號分群採用 AP (affinity propagation) 非監督式分群演算法，排除了主觀 判斷。在低SNR (3 dB) 的狀態下，分群正確率仍有70%以上，並且隨SNR 上升 正確率明顯改善，而傳統的k-means 分群演算法卻無法隨SNR 提升而進步。 而神經訊號分群的任務之一是要描述神經元活動的狀態，藉由掌握神經元放 電的模式及頻率，即可推估出一指數機率模型配適的神經元發射訊號模式。在低 SNR 的狀態下，只要訊號數量能多於50 個，即可以保證指數機率模型參數μ 的錯 誤率低於20%。 最後本研究中嘗詴解決共平面四聯電極無法定位神經元的問題，利用一虛擬 位移，使得共平面的數值方法有解，模擬實驗證實在高SNR 的環境中，可以看出 訊號在2 維平面上的散布狀態，而定位後的座標值和模擬神經元位置的平均均方 根差可以小於25 μm，有助於生物實驗人員判斷AP 分群結果之優劣程度。This study has developed a clustering algorithm for spike sorting. It assumes that neuron signal waveform is different from each neuron when there is not overlapping and bursting in neuron signal. Based on the previous hypothesis, tetrode, which is an instrument detecting a neuron signal consisting of waveform resolution and spatial resolution. Waveform that is detected from a tetrode is consisting of neuron signals and noise. This study has pre-processed the linearity of tetrode waveforms, and filtered the signal out high frequency component which usually is noise. In order to amplify the difference between different neuron waveform, we further add the artifical detail component into the waveform in time domain. This process will output waveform with noise-reduced and detail-included. Finally, the principal component analysis (PCA) is applied to reduce number of dimensionality. The feature which is extracted from these previous methods is called LDPCA (low-pass difference PCA) feature. On the other hand, the spatial resolution is defined as the decay which is a result of spatial distance from neuron to tetrode based on signal transmitting model. In clustering computing, an unsupervised clustering algorithm, affinity propagation (AP), is employed, and the result of this algorithm can output an objective clustering result. Even in low SNR environment (about 3 dB), the clustering accuracy is still higher than 70%, and the accuracy is getting better when the SNR is getting higher. Another clustering algorithm, k-means, can’t improve the accuracy even in higher SNR environment (about 10 dB). One of the advantages of the spike sorting is to express the model of neuron spikes firing. An exponential probability distribution and the main parameter μ can be used to describe the firing model. The false rate of μ is lower than 20% when the spike number is more than 50. Excepting the developed clustering algorithm, the method of signal source localization based on planar tetrode signal has been developed. The co-planar tetrode is virtually shifted from the 2-D tetrode to 3-D tetrode in this method. The error of distance from localization can be considered as noise interference. In high SNR environment, we can clearly observe the distribution of the localized points. The root mean square error is less than 25 μm. The result shows that the method of localization can help biological researchers to estimate the performance of spike sorting result