fMRI数据分析系统SPM原理与应用PPT

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,1,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, VoxBo,2,SPM 版本历史,The forthcoming version is SPM5 The current version is SPM2 Previous versions,SPM2b released 21st November 2002 SPM99 released 25th January 2000 SPM

2、96 released 9th April 1997,http:/www.fil.ion.ucl.ac.uk/spm/,3,线 性 代 数,统 计 理 论,GLM模型,随机场模型,M R 成 像,信 号 处 理,计算神经解剖学,神 经 科 学,4,SPM数据分析基本流程,5,预处理部分,模型构建与,参数估计,常用工具与,参数设置,6,讲座提纲,SPM I: Preprocessing,SPM II: Single-subject analyses SPM III: Group analyses,7,SPM I: 预处理,1. 2. 3. 4.,Slice timing (获取时间校正) Rea

3、lignment - (头动校正) Normalisation - (空间标准化） Smoothing - (空间平滑),8,MRI vs. fMRI, neural activity, blood oxygen, fMRI signal,MRI,fMRI,one image,high resolution (1 mm),low resolution (3 mm but can be better),fMRI Blood Oxygenation Level Dependent (BOLD) signal indirect measure of neural activity, many ima

4、ges (e.g., every 2 sec for 5 mins),9,预处理 Slice Timing - SPM,选择参考slice 拉齐其它slice,10,预处理 Realign （头动校正）, 不同scan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。,11,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,12,预处理 Realign - SPM,将同一被试不同采样时间点上的3D脑对齐,13,空间标准化问题,14,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？

5、,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,15,标准脑空间- Talairach 坐标系,Source: Brain Voyager course slides,Talairach & Tournoux, 1988, squish or stretch brain into “shoe box” extract 3D coordinate (x, y, z) for each activation focus,16,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,17,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

6、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,18,预处理 空间标准化 - 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,19,Template,Normalised Image,预处理 空间标准化 结果,20,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

7、比,5,-5 0,21,预处理 空间平滑-SPM,22,SPM预处理部分小结,1. 2. 3. 4.,Slice timing (adjust time difference among different slice) Realignment - (adjust for movement between slices) Normalisation - (warp functional data into template space) Smoothing - (to increase signal to noise ratio),23,Lecture Outline,SPM I: Prepr

8、ocessing,SPM II: Single-subject analyses SPM III: Group analyses,24,Single-subject Analyses,基本过程与原理,GLM,Principle of GLM Design Matrix,Solution to GLM,Effect of Interest and statistics,25,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,Spatial Memory Condition 500 msec 200 msec 3000 msec Time 1500 msec

9、 500 msec 3000 msec 200 msec Spatial Control Condition 1500 msec 对这个被试，你感兴趣的effect在那些脑区出现，其强度如何？,26,Single-subject Analyses,基本过程与原理,GLM,Principle of GLM Design Matrix,Solution to GLM,Effect of Interest & Statistics,Example,27,Single-subject Analyses,基本过程与原理,GLM,Principle of GLM Design Matrix,Solutio

10、n to GLM,Effect of Interest & Statistics,Example,28,In Matrix Form,GLM 的数学表示, ,1 : l,:,:,:,:,:,:,YJ,xJ 1, xJ l,xJ L,L,J,X,Y = 观测数据, 设计矩阵, 参数,+ 残差,x1 l,x1L,1 恐 惧,Y1 :,x1 1 :,Yj,= xj1 1 + . . . + xj l l + . . . + xjL L+j,: : Y1 x11 x1 l : YJ : x : Yj = xj 1 xj l,J1,x1 L : xJ l xj L,1 : xJL + j,J,Y,Y,2

11、9,Single-subject Analyses,基本过程与原理,GLM,Principle of GLM Design Matrix,Solution to GLM,Effect of Interest & Statistics,Example,30,Time,Time,GLM：设计矩阵X,X2,X1,Y= X + SPM represents time as going down SPM represents predictors within the design matrix as grayscale plots (where black = low, white = high) o

12、ver time SPM includes a constant to take care of the average activation level throughout each run,X,Intensity,Y,31,G (刺激因素）,Design matrix X,G1,H (干扰因素),H1,Global activity: E.g. head,motion parameters,Hc,Linear trends,Gc,stimulus,GLM：设计矩阵X的结构,32,血氧系统对单次刺激的响应,33,刺激序列,HRF,设计矩阵中的刺激因素X,34,G (stimulating)

13、,Design matrix X,G1,H (non-interesting),H1,E.g.(1) head motion parameters (2) breathing (3) heartbeat,Hc,Linear trends,due to MRI scanner Global activity:,Gc,stimulus,GLM：设计矩阵X的结构,35,为什么要考虑这些干扰因素？,Linear Trend,Probable,Respiration,Artifact,head motion parameters,Effect/Error,36,Single-subject Analys

14、es,基本过程与原理,GLM,Principle of GLM Design Matrix,Solution to GLM,Effect of Interest and statistics,37,0,100,-10,+10,0,1 2,-0.01,+0.01,=,+,*,5 +,Y,=,X1 * 1 + +,Xn * ,+ e,* 50,Fitting X to Y gives you one (parameter estimate) for each column of X, a and e. Betas provide information about fit of regressor

15、 X to data, Y, in each voxel,38,GLM求解的几何表示：勾股定理,E,用X线性组合Y近似表达Y,39,Single-subject Analyses,基本过程与原理,GLM,Principle of GLM Design Matrix,Solution to GLM,Effect of Interest & statistics,多重比较,Example,40,构造 Contrast 对感兴趣的解释变量进行比较,X2,X1,Y=,X + ,= 1 X1+2 X2+3 X3+N XN+ X1 X2 X3 XN 1 2 3 N T检验：构造 Contrast向量 F检

16、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！,41,本质 Effects 解释空间Xs contrast 向量,1 -1,x1x2,E x1 x2 (x1 x2),42,Single-subject Analyses,基本过程与原理,GLM,Principle of GLM Design Matrix,Solution to GLM,Effect of Interest & statistics Multiple Comparisons,43,Time,Y =,X + ,Intensity,Y,Preproce

17、ssing .,The Problem of Multiple,Comparisons,TTo Po=0.01,44,200 activated,噪声脑的“激活” P=0.01,20,000 voxs 噪声脑,45,怎么办？,200 activated,2 activated,200 activated 5 activated,46,200 activated,200 activated,Uncorrected p=0.01 我在进行探 索性研究！,探索性研究,47,Bonferroni correction 最严格的校正,200 activated,2 activated,one voxel

18、 Type I error p = ？ number of voxels ： N= 50,000 overall correct detection = (1-p) (1-p) (1-p) = (1-p)N overall Type I error = 1 - (1-p)N = Np Desired overall Type I error： Np = .05 Required one voxel Type I error p = .05 / 50,000 = .000001,48,Bonferroni Correction的思想及其在,fMRI数据分析中的问题,Bonferroni 校正的假

19、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,49,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/ Nindepentent,50,SPM个体激活区检测基本过程,51,个体水平effect 计算的SPM实现 （个体激活区检测）,模型定义,Design Matr

20、ix Specification,数据定义 参数估计,Data Specification Parameter Estimation,统计结果 Result,52,参数估计,常用工具与 参数设置,预处理部分 First-level 模型构建与,Second-level,53,Lecture Outline,SPM I: Intro, Preprocessing SPM II: Single-subject analyses SPM III: Group analyses,54,How do we compare across subjects?,建立不同人之间的可比性,Normalizatio

21、n ROI,多个被试的统计分析,Fixed-effects Model,Random-effects Model,55,Fixed-effects Model,Assume that the experimental manipulation has same effect in each subject,Uses data from all subjects to construct statistical test,Averaging/connecting across subjects before a t-test,Sensitive to extreme results from i

22、ndividual subject,strong effect in one subject can lead to significance even when others show weak or no effects,Allows inference to subject sample,you can say that effect was significant in your group of subjects but cannot generalize to other subjects that you didnt test,How about,the population?,

23、56,Random effect analysis,Assumes that effect varies across the population Accounts for inter-subject variance in analyses,Allows inferences to population from which subjects are drawn,Especially important for group comparisons Required by many reviewers/journals,57,SPM双层统计,First-level：个体水平effect 计算,Second-level：群体水平effect 计算,58,SPM个体激活区检测基本过程,59,Fixed- & Random- effects Model,小结,Fixed-effects Model,Assumes that effect is constant (“fixed”)