第三章 基于CCA的fMRI信号生理噪声抑制方法
3.1 引言
典型相关分析作为一种多元变量相关分析方法，可以用来提取出自相关的信号子空间，因而被广泛地用来做激活信号的提取及噪声成分的估计[48][55]。基于CCA，Churchill等人[10]提出了对fMRI残差数据做成分分解，进而估计出具有自相关特性的生理噪声成分，并在真实数据集上取得了较为显著的噪声抑制效果。但该方法需要先知道实验的刺激范式作为先验知识，然后去除fMRI信号中刺激范式相关的成分以得到残差数据。这里对功能信号与噪声信号进行分离，可以使得噪声成分子空间与功能信号子空间保持正交化，则所得残差数据中基本不包含功能激活信号，以防止由于对生理噪声的处理导致对BOLD响应信号的破坏。
为了能够实现对生理噪声盲分离的目的，基于Churchill等人在残差数据中提取生理噪声信号成分的思想，本章提出一种新的基于CCA的无监督生理噪声抑制方法。由于功能BOLD信号主要产生于灰质区域的大脑皮层，故该方法首先利用CCA从大脑灰质中粗略地提取得到一个大致的功能激活信号集，将其作为估计的实验刺激范式。然后，在全脑fMRI数据中利用GLM对上一步估计得到的实验刺激范式进行回归并去除与其相关的成分，以得到残差数据。最后，由于生理噪声主要作用于大脑的非神经区域，故利用CCA从残差数据对应的非神经组织区域提取出自相关的生理噪声集。这里得到的噪声成分能够与功能信号保持正交，并且具有较强的自相关特性。通过在真实fMRI数据上的实验分析，证明了该方法的有效性及可靠性。并且该方法无需心跳或呼吸等外部测量数据，也不需要已知任务刺激范式作为先验知识，因而具有灵活度高、成本低的优势。
3.2 CCA的基本思想
图3-1 CCA算法原理图示说明[64]
3.3 时域CCA的基本原理
由于fMRI数据是一种包含时间维的四维数据集，同时包含时间域和空间域信息。故在具体分析时，CCA信号分析可分为时域CCA和空域CCA两种。而基于时域CCA可以很好地提取出时间自相关的信号成分[48]，因而被广泛地用来做fMRI激活分析及噪声分离。时域CCA中数据矩阵的组成如图3-2(a)所示。
图3-2 时域CCA算法模型[48]。(a) 时域CCA数据矩阵的组成，其中每一行代表一次样本观察得到的成分；(b) 在时域CCA中，y(t)一般是x(t)移动一步所得结果。
3.4 基于CCA的生理噪声抑制方法模型
无监督生理噪声抑制方法一般需要考虑三个方面因素：一、受噪声干扰区域如何确定；二、如何从噪声干扰区域中估计和构造生理噪声子空间；三、采取何种机制对fMRI数据中的生理噪声进行抑制。首先针对第一个问题，利用本章3.5节实验部分的公式(3-15)所描述的方法构造非神经组织模板，相较于传统的基于脑脊液模板的方法在精度上具有一定的提升。之所以主要选取脑脊液区域作为噪声干扰区域，是因为脑脊液区域是大脑的非神经区域，会同时受到心脏和呼吸等噪声影响，基本没有与大脑皮质层神经活动相关的BOLD功能信号。此外，由于心跳或呼吸具有一定的周期性，因而具有较高的自相关性，而时域CCA在自相关成分的提取上具有一定优势。针对第二个问题，采取的解决办法是利用CCA从残差对应的非神经组织区域中提取若干显著性成分构造生理噪声集。最后，采用GLM从fMRI数据中抑制生理噪声相关成分，这一步在相关文献中一般称之为多余变量正则(Nuisance Variable Regression，NVR)。本章所提生理噪声抑制方法流程图，如图3-3所示。
图3-3 基于CCA的生理噪声抑制方法流程图
3.5 实验
本章的视觉刺激实验数据利用SENSE 2T EPI扫描仪进行成像采集，数据分辨率为，体素的大小为，TR参数为2s。被试实验之前已被告知实验之目的，并签署同意书。作为一个任务态的数据，视觉刺激范式的模式为OFF–ON–OFF–ON–OFF–ON–OFF，每一个OFF–ON的block持续时间为20个TR，最后一个OFF阶段持续10个TR，所以共采集了70个时间点数据。在ON状态，被试会被要求盯住一副蓝黄相间的棋盘格画面，整幅画面以7Hz的频率进行翻转。实验刺激范式block如图3-4所示。
图3-4 实验刺激范式block
3.5.1 实验数据的预处理
本章实验数据的预处理主要基于SPM8工具箱，包含如下步骤：(1)首先，对被试的功能像数据进行刚体头动矫正，在此过程中会得到一个头动矫正后的功能平均像；(2)对被试的结构像和功能平均像进行协配准；(3)对协配准后的结构像进行组织分割提取脑脊液模板与灰质模板；(4)将被试头动矫正后的功能像配准到MNI空间；(5)对配准后的功能像数据按照全宽半高参数为8的高斯核进行平滑。
3.5.2 实验刺激范式的估计
首先，利用时域CCA方法对大脑灰质区域的数据进行自相关分析，提取出具有自相关结构的源信号成分。实验中发现偏移1至5个时间点所提取出的信号源成分差别不具有显著性，故本实验选取偏移1个时间点进行信号提取。提取的前三个自相关结构性最强的成分如图3-5所示，将此三个成分作为功能激活信号集。由图3-5可发现，其中第一个成分可认为是低频漂移信号成分，第二个信号成分与实验的刺激范式相似度较高，可认为是激活成分。
图3-5 CCA从灰质中提取的信号成分
3.5.3 非神经组织区域的噪声成分提取
图3-6 提取非神经组织模板示意图。(a) 非神经组织空域模板；(b) 非神经组织时域模板；(c) 空域模板与时域模板两者交集结果。图中脑壳内黑色部分为灰质区域，白色部分为脑脊液区域。
为得到残差数据，需要利用GLM从全脑fMRI数据中回归并去除掉估计的实验刺激范式。然后从残差数据对应的非神经组织区域(如图3-6(c)的区域)中，再利用CCA提取出自相关结构性较强的生理噪声集，如图3-7所示。
图3-7 CCA从残差数据对应的非神经组织区域中提取的噪声信号
3.5.4 实验结果
为验证本章所提出的生理噪声抑制方法对fMRI数据分析产生的差异影响，所以统一采用SPM来对视觉数据进行激活统计分析。而前期的预处理操作中，设置了经过生理噪声处理和不经过生理噪声处理的两个对照组数据。这里，SPM统计分析时的总体误差率p值设定为0.05，最小激活簇大小阈值设定为0。
在空域上，经过噪声抑制处理之后，大部分激活体素的位置仍保持不变，如图3-8所示。图3-8(a)为没有噪声抑制处理的数据经过SPM分析所得激活图，图3-8(b)为加入噪声抑制处理的数据经过SPM分析所得激活图。
图3-8 噪声抑制前后激活图对比。
(a)无噪声抑制处理的SPM所得激活图；(b)有噪声抑制处理的SPM所得激活图。
在图3-8中fMRI数据加入噪声抑制处理之后，在新激活图中减少的激活体素，主要是集中在原有激活区的边缘部分。而新增加的激活体素，主要是集中在原有激活区的中心区域。所以，经过生理噪声抑制处理后的数据所提取的激活区域，能更集中于大脑枕叶部分，而枕叶区域在医学上被认为是大脑控制视觉反应的区域。这在一定程度上说明，针对该视觉刺激实验数据，生理噪声的抑制处理操作能够突出视觉刺激实验的激活效果。
在时域上评价视觉任务态实验的分析效果时，可通过比较全部激活体素的平均时间过程与实验刺激范式之间的相似度，如图3-9所示。通过图3-9可表明，经过生理噪声抑制处理后，所提取激活体素的平均时间过程与时间刺激范式波形的相似度更高，二者的相关系数由0.4415升至0.5347。
图3-9 噪声抑制前后激活体素的平均时间过程对比
并且，计算每个激活体素与实验刺激范式之间的相关系数可得到激活体素的相关系数分布直方图，如图3-10所示。在图3-10中，原始数据所提取激活体素的相关系数分布是一个以0.45为均值的正太分布。而经过噪声抑制之后，相关系数分布整体向右倾斜，且分布更加集中，主要局限在0.3至0.6之间，与实验刺激范式相关性大的体素占整体大多数。
图3-10 噪声抑制前后激活体素时间过程与实验刺激范式相关系数分布。
(a)噪声抑制前激活体素相关系数分布；(b)噪声抑制后激活体素相关系数分布。
3.6 本章小结
本章提出了一种基于CCA结合fMRI信号在时间域与空间域上的综合特征，以抑制脑功能成像过程中的心跳和呼吸等生理噪声的方法。通过在真实fMRI数据上进行实验，表明了该方法能有效提高激活体素与任务刺激范式之间的相关性，进而提升后续数据激活检测方法的灵敏性。并且所提方法不需要任何实验先验信息，实现了对fMRI生理噪声的无监督抑制，具有成本低的优势。
当我在读研究生时，是一个十分幼稚的学生。
我始终没能让自己的导师——曾先生 满意。
曾先生在很多方面都是成功人士，所以很喜欢以过来的人姿态教育我。
他总是在直接或间接地告诉我，或者试图点醒我：不会投机是没有前途的，做事情没有RMB是没有出路的。
可能，曾先生后来觉得我实在是根朽木，在学生们面前给我的评价是：“有思想”。
呵呵，
我好好做个苦力吧。
本文单独的权限声明：未经许可，严禁任何形式的转载。
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