第三章 基於CCA的fMRI信號生理噪聲抑制方法

3.1 引言

　　典型相關分析作為一種多元變量相關分析方法，可以用來提取出自相關的信號子空間，因而被廣泛地用來做激活信號的提取及噪聲成分的估計^[48][55]。基於CCA，Churchill等人^[10]提出了對fMRI殘差數據做成分分解，進而估計出具有自相關特性的生理噪聲成分，並在真實數據集上取得了較為顯著的噪聲抑制效果。但該方法需要先知道實驗的刺激範式作為先驗知識，然後去除fMRI信號中刺激範式相關的成分以得到殘差數據。這裏對功能信號與噪聲信號進行分離，可以使得噪聲成分子空間與功能信號子空間保持正交化，則所得殘差數據中基本不包含功能激活信號，以防止由於對生理噪聲的處理導致對BOLD

為了能夠實現對生理噪聲盲分離的目的，基於Churchill等人在殘差數據中提取生理噪聲信號成分的思想，本章提出一種新的基於CCA的無監督生理噪聲抑制方法。由於功能BOLD信號主要產生於灰質區域的大腦皮層，故該方法首先利用CCA從大腦灰質中粗略地提取得到一個大致的功能激活信號集，將其作為估計的實驗刺激範式。然後，在全腦fMRI數據中利用GLM對上一步估計得到的實驗刺激範式進行回歸並去除與其相關的成分，以得到殘差數據。最後，由於生理噪聲主要作用於大腦的非神經區域，故利用CCA從殘差數據對應的非神經組織區域提取出自相關的生理噪聲集。這裏得到的噪聲成分能夠與功能信號保持正交，並且具有較強的自相關特性。通過在真實fMRI數據上的實驗分析，證明了該方法的有效性及可靠性。並且該方法無需心跳或呼吸等外部測量數據，也不需要已知任務刺激範式作為先驗知識，因而具有靈活度高、成本低的優勢。

3.2 CCA的基本思想

圖3-1 CCA算法原理圖示說明^[64]

3.3 時域CCA的基本原理

　　由於fMRI數據是一種包含時間維的四維數據集，同時包含時間域和空間域信息。故在具體分析時，CCA信號分析可分為時域CCA和空域CCA兩種。而基於時域CCA可以很好地提取出時間自相關的信號成分^[48]，因而被廣泛地用來做fMRI激活分析及噪聲分離。時域CCA中數據矩陣的組成如圖3-2(a)所示。

　　圖3-2 時域CCA算法模型^[48]。(a) 時域CCA數據矩陣的組成，其中每一行代表一次樣本觀察得到的成分；(b) 在時域CCA中，y(t)一般是x(t)

3.4 基於CCA的生理噪聲抑制方法模型

　　無監督生理噪聲抑制方法一般需要考慮三個方面因素：一、受噪聲幹擾區域如何確定；二、如何從噪聲幹擾區域中估計和構造生理噪聲子空間；三、采取何種機制對fMRI數據中的生理噪聲進行抑制。首先針對第一個問題，利用本章3.5節實驗部分的公式(3-15)所描述的方法構造非神經組織模板，相較於傳統的基於腦脊液模板的方法在精度上具有一定的提升。之所以主要選取腦脊液區域作為噪聲幹擾區域，是因為腦脊液區域是大腦的非神經區域，會同時受到心臟和呼吸等噪聲影響，基本沒有與大腦皮質層神經活動相關的BOLD功能信號。此外，由於心跳或呼吸具有一定的周期性，因而具有較高的自相關性，而時域CCA在自相關成分的提取上具有一定優勢。針對第二個問題，采取的解決辦法是利用CCA從殘差對應的非神經組織區域中提取若幹顯著性成分構造生理噪聲集。最後，采用GLM從fMRI數據中抑制生理噪聲相關成分，這一步在相關文獻中一般稱之為多余變量正則(Nuisance Variable Regression，NVR)。本章所提生理噪聲抑制方法流程圖，如圖3-3所示。

圖3-3 基於CCA的生理噪聲抑制方法流程圖

3.5 實驗

　　本章的視覺刺激實驗數據利用SENSE 2T EPI掃描儀進行成像采集，數據分辨率為，體素的大小為，TR參數為2s。被試實驗之前已被告知實驗之目的，並簽署同意書。作為一個任務態的數據，視覺刺激範式的模式為OFF–ON–OFF–ON–OFF–ON–OFF，每一個OFF–ON的block持續時間為20個TR，最後一個OFF階段持續10個TR，所以共采集了70個時間點數據。在ON狀態，被試會被要求盯住一副藍黃相間的棋盤格畫面，整幅畫面以7Hz的頻率進行翻轉。實驗刺激範式block如圖3-4所示。

圖3-4 實驗刺激範式block

3.5.1 實驗數據的預處理

本章實驗數據的預處理主要基於SPM8工具箱，包含如下步驟：(1)首先，對被試的功能像數據進行剛體頭動矯正，在此過程中會得到一個頭動矯正後的功能平均像；(2)對被試的結構像和功能平均像進行協配準；(3)對協配準後的結構像進行組織分割提取腦脊液模板與灰質模板；(4)將被試頭動矯正後的功能像配準到MNI空間；(5)對配準後的功能像數據按照全寬半高參數為8的高斯核進行平滑。

3.5.2 實驗刺激範式的估計

首先，利用時域CCA方法對大腦灰質區域的數據進行自相關分析，提取出具有自相關結構的源信號成分。實驗中發現偏移1至5個時間點所提取出的信號源成分差別不具有顯著性，故本實驗選取偏移1個時間點進行信號提取。提取的前三個自相關結構性最強的成分如圖3-5所示，將此三個成分作為功能激活信號集。由圖3-5可發現，其中第一個成分可認為是低頻漂移信號成分，第二個信號成分與實驗的刺激範式相似度較高，可認為是激活成分。

圖3-5 CCA從灰質中提取的信號成分

3.5.3 非神經組織區域的噪聲成分提取

圖3-6 提取非神經組織模板示意圖。(a) 非神經組織空域模板；(b) 非神經組織時域模板；(c) 空域模板與時域模板兩者交集結果。圖中腦殼內黑色部分為灰質區域，白色部分為腦脊液區域。

為得到殘差數據，需要利用GLM從全腦fMRI數據中回歸並去除掉估計的實驗刺激範式。然後從殘差數據對應的非神經組織區域(如圖3-6(c)的區域)中，再利用CCA提取出自相關結構性較強的生理噪聲集，如圖3-7所示。

圖3-7 CCA從殘差數據對應的非神經組織區域中提取的噪聲信號

3.5.4 實驗結果

為驗證本章所提出的生理噪聲抑制方法對fMRI數據分析產生的差異影響，所以統一采用SPM來對視覺數據進行激活統計分析。而前期的預處理操作中，設置了經過生理噪聲處理和不經過生理噪聲處理的兩個對照組數據。這裏，SPM統計分析時的總體誤差率p值設定為0.05，最小激活簇大小閾值設定為0。

在空域上，經過噪聲抑制處理之後，大部分激活體素的位置仍保持不變，如圖3-8所示。圖3-8(a)為沒有噪聲抑制處理的數據經過SPM分析所得激活圖，圖3-8(b)為加入噪聲抑制處理的數據經過SPM分析所得激活圖。

圖3-8 噪聲抑制前後激活圖對比。

(a)無噪聲抑制處理的SPM所得激活圖；(b)有噪聲抑制處理的SPM所得激活圖。

在圖3-8中fMRI數據加入噪聲抑制處理之後，在新激活圖中減少的激活體素，主要是集中在原有激活區的邊緣部分。而新增加的激活體素，主要是集中在原有激活區的中心區域。所以，經過生理噪聲抑制處理後的數據所提取的激活區域，能更集中於大腦枕葉部分，而枕葉區域在醫學上被認為是大腦控制視覺反應的區域。這在一定程度上說明，針對該視覺刺激實驗數據，生理噪聲的抑制處理操作能夠突出視覺刺激實驗的激活效果。

在時域上評價視覺任務態實驗的分析效果時，可通過比較全部激活體素的平均時間過程與實驗刺激範式之間的相似度，如圖3-9所示。通過圖3-9可表明，經過生理噪聲抑制處理後，所提取激活體素的平均時間過程與時間刺激範式波形的相似度更高，二者的相關系數由0.4415升至0.5347。

圖3-9 噪聲抑制前後激活體素的平均時間過程對比

並且，計算每個激活體素與實驗刺激範式之間的相關系數可得到激活體素的相關系數分布直方圖，如圖3-10所示。在圖3-10中，原始數據所提取激活體素的相關系數分布是一個以0.45為均值的正太分布。而經過噪聲抑制之後，相關系數分布整體向右傾斜，且分布更加集中，主要局限在0.3至0.6之間，與實驗刺激範式相關性大的體素占整體大多數。

圖3-10 噪聲抑制前後激活體素時間過程與實驗刺激範式相關系數分布。

(a)噪聲抑制前激活體素相關系數分布；(b)噪聲抑制後激活體素相關系數分布。

3.6 本章小結

本章提出了一種基於CCA結合fMRI信號在時間域與空間域上的綜合特征，以抑制腦功能成像過程中的心跳和呼吸等生理噪聲的方法。通過在真實fMRI數據上進行實驗，表明了該方法能有效提高激活體素與任務刺激範式之間的相關性，進而提升後續數據激活檢測方法的靈敏性。並且所提方法不需要任何實驗先驗信息，實現了對fMRI生理噪聲的無監督抑制，具有成本低的優勢。

謝謝我的導師曾先生，讓我知道，讀碩士、做學術不會投機是沒有前途的，做任何事情沒有RMB是沒有出路的。

當時的我比較幼稚，還對學術充滿了向往，還總以為自己在創造知識的新邊疆，這些東西始終學不來。

所以，我是沒有出路的，只能幹幹苦力。

那就好好做個苦力吧。

好好做個苦力。

本文單獨的權限聲明：未經許可，嚴禁任何形式的轉載。

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基於CCA的fMRI信號生理噪聲抑制方法