fMRI数据分析系统SPM原理与应用

1、Statistical Parametric Mapping基本原理与使用北京师范大学认知神经科学与学习国家重点实验室朱朝喆 研究员fMRI研究框架实验设计被试招募与扫描科学问题结果解释实验假设数据统计分析SPM, AFNI, FSL, VoxBoSPM 版本历史The forthcoming version is SPM5The current version is SPM2Previous versionsSPM2b released 21st November 2002SPM99 released 25th January 2000SPM96 released 9th April 199

2、7http:/www.fil.ion.ucl.ac.uk/spm/线性代数统计理论GLM模型随机场模型MR成像信号处理计算神经解剖学神经科学SPM数据分析基本流程预处理部分模型构建与参数估计常用工具与参数设置讲座提纲SPM I: PreprocessingSPM II: Single-subject analysesSPM III: Group analysesSPM I: 预处理.Slice timing (获取时间校正)Realignment - (头动校正)Normalisation - (空间标准化）Smoothing - (空间平滑)MRI vs. fMRI neura

3、l activity blood oxygen fMRI signalMRIfMRIone imagehigh resolution(1 mm)low resolution(3 mm but can be better)fMRIBlood Oxygenation Level Dependent (BOLD) signalindirect measure of neural activitymany images(e.g., every 2 sec for 5 mins)预处理 Slice Timing - SPM选择参考slice拉齐其它slice预处理 Realign （头动校正） 不同sc

4、an之间像素对应关系遭到破坏。 血液动力学响应被头动引起的信号淹没。预处理 Realign （头动校正）刚体变换六个头动参数估计:3个方向的平移(mm)3个轴向的旋转预处理 Realign - SPM将同一被试不同采样时间点上的3D脑对齐空间标准化问题空间标准化问题个体大脑在形状、大小等方面存在明显差异，我们如何进行不同人之间的比较呢？ 使不同被试脑图像中的同一像素代表相同的解剖位置一个标准脑空间标准脑空间- Talairach 坐标系Source: Brain Voyager course slidesTalairach & Tournoux, 1988 squish or stre

5、tch brain into “shoe box” extract 3D coordinate (x, y, z) for eachactivation focus使不同被试脑图像中的同一像素代表相同的解剖位置粗配准 仿射变换精配准 非线性变换Why使不同被试脑图像中的同一像素代表相同的解剖位置一个公共的标准空间How先使用简单的线性变换进行粗配准再用复杂的非线性变换精配准Problems计算复杂度（高精度算法配准一个脑需要几个小时）个体之间的脑并非一一映射关系不可能有完全准确的配准Solutions对空间标准化后的脑图像进行适当的平滑使用变形场信息预处理 空间标准化 小结预处理 空间标准化

6、- SPM使不同被试脑图像中的同一像素代表相同的解剖位置将每个个体脑放入一个公共的标准空间TemplateNormalised Image预处理 空间标准化 结果空间平滑的问题使残差项更符合高斯分布假设减少标准化后剩余的个体间差异提高信噪比5-5 0预处理 空间平滑-SPMSPM预处理部分小结.Slice timing (adjust time difference among different slice)Realignment - (adjust for movement between slices)Normalisation - (warp functional dat

7、a into template space)Smoothing - (to increase signal to noise ratio)Lecture OutlineSPM I: PreprocessingSPM II: Single-subject analysesSPM III: Group analysesSingle-subject Analyses基本过程与原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest and statistics个体水平分析的基本过程与目的实验设计个体扫描个体激活区检测Spa

8、tial Memory Condition500 msec200 msec3000 msecTime1500 msec500 msec3000 msec200 msecSpatial Control Condition1500 msec对这个被试，你感兴趣的effect在那些脑区出现，其强度如何？Single-subject Analyses基本过程与原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest & StatisticsExampleSingle-subject Analyses基本过程与原理GL

9、MPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest & StatisticsExampleIn Matrix FormGLM 的数学表示1:l:YJxJ 1 xJ lxJ LLJXY =观测数据设计矩阵参数+ 残差x1 lx1L1恐 惧Y1:x1 1:Yj= xj1 1 + . . . + xj l l + . . . + xjL L+j: :Y1 x11 x1 l: YJ : x :Yj = xj 1 xj lJ1x1 L: xJ lxj L1: xJL+ jJYYSingle-subject Analyse

10、s基本过程与原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest & StatisticsExampleTimeTimeGLM：设计矩阵XX2X1Y= X + SPM represents time asgoing downSPM representspredictors within thedesign matrix asgrayscale plots (whereblack = low, white = high)over timeSPM includes a constantto take care

11、 of theaverage activation levelthroughout each runXIntensityYG (刺激因素）Design matrix XG1H (干扰因素)H1Global activity: E.g. headmotion parametersHcLinear trendsGcstimulusGLM：设计矩阵X的结构血氧系统对单次刺激的响应刺激序列HRF设计矩阵中的刺激因素XG (stimulating)Design matrix XG1H (non-interesting)H1E.g.(1) head motion parameters(2) breathi

12、ng(3) heartbeatHcLinear trendsdue to MRI scannerGlobal activity:GcstimulusGLM：设计矩阵X的结构为什么要考虑这些干扰因素？Linear TrendProbableRespirationArtifacthead motionparametersEffect/ErrorSingle-subject Analyses基本过程与原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest and statistics0100-10+1001 2-0.01

13、+0.01=+*5 +Y=X1 * 1 + +Xn * + e* 50Fitting X to Y gives you one (parameter estimate) for each column of X, a and e. Betas provide information about fit of regressor X to data, Y, in eachvoxelGLM求解的几何表示：勾股定理E用X线性组合Y近似表达YSingle-subject Analyses基本过程与原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffe

14、ct of Interest & statistics多重比较Example构造 Contrast对感兴趣的解释变量进行比较X2X1Y=X + = 1 X1+2 X2+3 X3+N XN+X1 X2 X3 XN1 2 3 NT检验：构造 Contrast向量F检验：构造 Contrast矩阵实验设计 =感兴趣effect =contrast所以contrast在数据采集之前就定下了！本质Effects 解释空间Xs contrast 向量1 -1x1x2Ex1 x2(x1 x2)Single-subject Analyses基本过程与原理GLMPrinciple of GLMDesig

15、n MatrixSolution to GLMEffect of Interest & statisticsMultiple ComparisonsTimeY =X + IntensityYPreprocessing .The Problem of MultipleComparisonsTToPo=0.01200 activated噪声脑的“激活”P=0.0120,000 voxs噪声脑怎么办？200 activated2 activated200 activated5 activated200 activated200 activatedUncorrected p=0.01我在进行探

16、索性研究！探索性研究Bonferroni correction最严格的校正200 activated2 activatedone voxel Type I error p = ？number of voxels ： N= 50,000overall correct detection = (1-p) (1-p) (1-p) = (1-p)Noverall Type I error = 1 - (1-p)N = NpDesired overall Type I error： Np = .05Required one voxel Type I error p = .05 / 50,000 = .0

17、00001Bonferroni Correction的思想及其在fMRI数据分析中的问题Bonferroni 校正的假设pvoxel = poverall/N N为独立观测个数相邻体元的BOLD信号会相互独立的吗？头动等噪声对同一脑区的影响很相似BOLD信号本身就对应着一定空间范围预处理中的平滑SPM 中的多重比较校正的原理根据数据的空间相关程度计算独立观测个数（独立比较的次数Nindepentent）根据整体虚警概率poverall和Nindepentent得到单个体元的pvoxel值pvoxel = poverall/ NindepententSPM个体激活区检测基本过程个体水平effec

18、t 计算的SPM实现（个体激活区检测）模型定义Design Matrix Specification数据定义参数估计Data SpecificationParameter Estimation统计结果 Result参数估计常用工具与参数设置预处理部分First-level模型构建与Second-levelLecture OutlineSPM I: Intro, PreprocessingSPM II: Single-subject analysesSPM III: Group analysesHow do we compare across subjects?建立不同人之间的可比性Normal

19、izationROI多个被试的统计分析Fixed-effects ModelRandom-effects ModelFixed-effects ModelAssume that the experimental manipulation has same effect ineach subjectUses data from all subjects to construct statistical testAveraging/connecting across subjects before a t-testSensitive to extreme results from individu

20、al subjectstrong effect in one subject can lead to significance even when others showweak or no effectsAllows inference to subject sampleyou can say that effect was significant in your group of subjects but cannotgeneralize to other subjects that you didnt testHow aboutthe population?Random effect a

21、nalysisAssumes that effect varies across the populationAccounts for inter-subject variance in analysesAllows inferences to population from which subjectsare drawnEspecially important for group comparisonsRequired by many reviewers/journalsSPM双层统计First-level：个体水平effect 计算Second-level：群体水平effect 计算SPM个体激活区检测基本过程Fixed- & Random- effects Model小结Fixed-effects ModelAssumes that effect is constant (“fixed”) in the populationUses data from all s