臺灣博碩士論文加值系統

在分析大腦功能性核磁共振(fMRI:functional Magnetic Resonance Imaging)資料時,血液反應函數(HRF:Haemodynamic Response Function)描述活化過程中腦部反應的時間動態,而一般慣用形式的血液反應函數是對於簡短刺激的一個理想且不受到噪音干擾的反應,多數較傳統的統計分析方法在解釋訊號時會使用期望的血氧濃度反應(expected BOLD response),而這個期望的反應是慣用的血液反應函數和刺激函數的褶積而得到,一般將它放入設計矩陣當作迴歸式。

在試驗相關的功能性核磁共振實驗中,期望的血氧濃度反應的使用會遇到不明噪音的嚴重干擾,另外我們也認為說,對於有刺激反應的立體像素(Voxel),在某些時間點會因為失去專注或是其他的因素而導致有不反應或是不顯現出反應的情況,為了增加血液反應函數使用上的靈活性,我們考慮了兩種方法；首先是我們在一般線性模型的架構下(GLM:General Linear Model),引用了對係數做壓縮和選取
(LASSO: Least Absolute Shrinkage and Selection Operator)的概念；其次,我們也使用了貝氏無母數模型建立混和效應模型(MEM:Mixed Effects Model),當中對於隨機效應的分布我們引用了Dirichlet process作為先驗的資訊,我們將兩種方法的結果做一些討論。

透過血液反應函數使用上的靈活性,我們能夠獲得更準確的活化反應區域,對係數做壓縮和選取的方法能夠選取對刺激有反應的群聚區域,混和效應模型則是能夠辨識對刺激具有相同反應的像素,且這些像素在此架構下會被分類為同一個群集,混和效應模型也可以應用在找出訊號被嚴重干擾的時間區段。

In functional magnetic resonance imaging (fMRI) data analysis, haemodynamic response function (HRF) describes the
temporal dynamic of the brain region response during activations. Canonical HRF is described as the ideal, noiseless response to an infinitesimally brief stimulus. Most conventional statistical methods employ the canonical HRF which is convolved with the stimuli function as the regressor called expected BOLD response in design matrix.

In fact, the usage of expected BOLD response encounters a severe interference of uncertain noise, especially in fast event-related fMRI experiment. We expect that certain voxels will not activate at some time point because of losing concentration or other unknown reasons. In order to increase the flexibility in temporal dynamic of the HRF, we consider two methods to estimate the effect of stimuli. First, we use LASSO which is combined with a general linear model (GLM). Second, we use the Bayesian semi- and non-parametric modeling on our data and build a mixed effects model with a Dirichlet process prior for the distribution of the random effects. The selected activated voxels will be compared by these two methods.

We can acquire more accurate and reasonable activated region than the previous methods on these fMRI data set through the usage of the flexible HRF. LASSO help us selecting the clustered area where the voxels have the real response to the stimulus. Non-parametric model can identify the similar pattern in the voxels and these voxels are classified into the same cluster. It can also be applied to find the period of time points where the BOLD signals had a severe impact by
unknown nuisance.

1. Introduction ...... 1
1.1 Background and Motivation ...... 1
1.2 Data Description and Experimental Procedure ...... 3
1.2.1 Introduction of fMRI ...... 3
1.2.2 Case One ...... 8
1.2.3 Case Two ...... 17
1.3 Research Problems and Proposed Methods ...... 27
1.3.1 Research Problems ...... 27
1.3.2 Proposed Methods ...... 27
1.3.3 Overview ...... 28
2. Literature Review ...... 29
2.1 The Statistical Analysis of fMRI Data ...... 29
2.2 Estimation of HRF ...... 30
2.3 LASSO on fMRI ...... 30
2.4 Mixed Effects Model ...... 31
2.5 Software and Package ...... 31
3. Methods ...... 33
3.1 Analysis fMRI Data ...... 33
3.1.1 Generalized Linear Model ...... 33
3.1.2 LASSO ...... 35
3.1.3 Mixed Effects Model ...... 35
3.1.4 Denoise Method ...... 36
3.2 New Methods ...... 37
3.2.1 Usage of LASSO ...... 37
3.2.2 Usage of Mixed Effects Model ...... 40
4. Applications to Real Data Sets ...... 44
4.1 Case One ...... 45
4.1.1 Results by LASSO ...... 45
4.1.2 Results by Mixed Effects Model ...... 66
4.2 Case Two ...... 75
4.2.1 Results by LASSO ...... 75
4.2.2 Results by Mixed Effects Model ...... 91
4.3 Comparison of Methods in Two Cases ...... 96
4.3.1 The Different Characters of Two Data Sets ...... 96
4.3.2 The Different Results in Using LASSO ...... 96
4.3.3 The Different Results in Using Mixed Effects Model ...... 96
5. Conclusions and Future Work ...... 98
5.1 Conclusions ...... 98
5.2 Future Work ...... 99
Bibliography ...... 101
Appendix ...... 104
Appendix A. AF-BOLD Responses and Motion Correction by GLM after AFNI Process in Two Cases ...... 105
Appendix B. Results by Using LASSO ...... 110
Appendix C. Results by Mixed Effects Model ...... 127

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