fMRI數(shù)據(jù)分析系統(tǒng)SPM原理與應(yīng)用

1、Statistical Parametric Mapping基本原理與使用北京師范大學(xué)認(rèn)知神經(jīng)科學(xué)與學(xué)習(xí)國家重點(diǎn)實(shí)驗(yàn)室朱朝喆 研究員fMRI研究框架實(shí)驗(yàn)設(shè)計(jì)被試招募與掃描科學(xué)問題結(jié)果解釋實(shí)驗(yàn)假設(shè)數(shù)據(jù)統(tǒng)計(jì)分析SPM, AFNI, FSL, VoxBoSPM 版本歷史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/線性代數(shù)統(tǒng)計(jì)理論GLM模型隨機(jī)場模型MR成像信號處理計(jì)算神經(jīng)解剖學(xué)神經(jīng)科學(xué)SPM數(shù)據(jù)分析基本流程預(yù)處理部分模型構(gòu)建與參數(shù)估計(jì)常用工具與參數(shù)設(shè)置講座提綱SPM I: PreprocessingSPM II: Single-subject analysesSPM III: Group analysesSPM I: 預(yù)處理.Slice timing (獲取時(shí)間校正)Realignment - (頭動校正)Normalisation - (空間標(biāo)準(zhǔn)化）Smoothing - (空間平滑)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)預(yù)處理 Slice Timing - SPM選擇參考slice拉齊其它slice預(yù)處理 Realign （頭動校正） 不同sc

4、an之間像素對應(yīng)關(guān)系遭到破壞。 血液動力學(xué)響應(yīng)被頭動引起的信號淹沒。預(yù)處理 Realign （頭動校正）剛體變換六個(gè)頭動參數(shù)估計(jì):3個(gè)方向的平移(mm)3個(gè)軸向的旋轉(zhuǎn)預(yù)處理 Realign - SPM將同一被試不同采樣時(shí)間點(diǎn)上的3D腦對齊空間標(biāo)準(zhǔn)化問題空間標(biāo)準(zhǔn)化問題個(gè)體大腦在形狀、大小等方面存在明顯差異，我們?nèi)绾芜M(jìn)行不同人之間的比較呢？ 使不同被試腦圖像中的同一像素代表相同的解剖位置一個(gè)標(biāo)準(zhǔn)腦空間標(biāo)準(zhǔn)腦空間- Talairach 坐標(biāo)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使不同被試腦圖像中的同一像素代表相同的解剖位置粗配準(zhǔn) 仿射變換精配準(zhǔn) 非線性變換Why使不同被試腦圖像中的同一像素代表相同的解剖位置一個(gè)公共的標(biāo)準(zhǔn)空間How先使用簡單的線性變換進(jìn)行粗配準(zhǔn)再用復(fù)雜的非線性變換精配準(zhǔn)Problems計(jì)算復(fù)雜度（高精度算法配準(zhǔn)一個(gè)腦需要幾個(gè)小時(shí)）個(gè)體之間的腦并非一一映射關(guān)系不可能有完全準(zhǔn)確的配準(zhǔn)Solutions對空間標(biāo)準(zhǔn)化后的腦圖像進(jìn)行適當(dāng)?shù)钠交褂米冃螆鲂畔㈩A(yù)處理 空間標(biāo)準(zhǔn)化 小結(jié)預(yù)處理 空間標(biāo)準(zhǔn)化

6、- SPM使不同被試腦圖像中的同一像素代表相同的解剖位置將每個(gè)個(gè)體腦放入一個(gè)公共的標(biāo)準(zhǔn)空間TemplateNormalised Image預(yù)處理 空間標(biāo)準(zhǔn)化 結(jié)果空間平滑的問題使殘差項(xiàng)更符合高斯分布假設(shè)減少標(biāo)準(zhǔn)化后剩余的個(gè)體間差異提高信噪比5-5 0預(yù)處理 空間平滑-SPMSPM預(yù)處理部分小結(jié).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基本過程與原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest and statistics個(gè)體水平分析的基本過程與目的實(shí)驗(yàn)設(shè)計(jì)個(gè)體掃描個(gè)體激活區(qū)檢測Spa

8、tial Memory Condition500 msec200 msec3000 msecTime1500 msec500 msec3000 msec200 msecSpatial Control Condition1500 msec對這個(gè)被試，你感興趣的effect在那些腦區(qū)出現(xiàn)，其強(qiáng)度如何？Single-subject Analyses基本過程與原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest & StatisticsExampleSingle-subject Analyses基本過程與原理GL

9、MPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest & StatisticsExampleIn Matrix FormGLM 的數(shù)學(xué)表示1:l:YJxJ 1 xJ lxJ LLJXY =觀測數(shù)據(jù)設(shè)計(jì)矩陣參數(shù)+ 殘差x1 lx1L1恐 懼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基本過程與原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffect of Interest & StatisticsExampleTimeTimeGLM：設(shè)計(jì)矩陣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 (干擾因素)H1Global activity: E.g. headmotion parametersHcLinear trendsGcstimulusGLM：設(shè)計(jì)矩陣X的結(jié)構(gòu)血氧系統(tǒng)對單次刺激的響應(yīng)刺激序列HRF設(shè)計(jì)矩陣中的刺激因素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：設(shè)計(jì)矩陣X的結(jié)構(gòu)為什么要考慮這些干擾因素？Linear TrendProbableRespirationArtifacthead motionparametersEffect/ErrorSingle-subject Analyses基本過程與原理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求解的幾何表示：勾股定理E用X線性組合Y近似表達(dá)YSingle-subject Analyses基本過程與原理GLMPrinciple of GLMDesign MatrixSolution to GLMEffe

14、ct of Interest & statistics多重比較Example構(gòu)造 Contrast對感興趣的解釋變量進(jìn)行比較X2X1Y=X + = 1 X1+2 X2+3 X3+N XN+X1 X2 X3 XN1 2 3 NT檢驗(yàn)：構(gòu)造 Contrast向量F檢驗(yàn)：構(gòu)造 Contrast矩陣實(shí)驗(yàn)設(shè)計(jì) =感興趣effect =contrast所以contrast在數(shù)據(jù)采集之前就定下了！本質(zhì)Effects 解釋空間Xs contrast 向量1 -1x1x2Ex1 x2(x1 x2)Single-subject Analyses基本過程與原理GLMPrinciple of GLMDesig

15、n MatrixSolution to GLMEffect of Interest & statisticsMultiple ComparisonsTimeY =X + IntensityYPreprocessing .The Problem of MultipleComparisonsTToPo=0.01200 activated噪聲腦的“激活”P=0.0120,000 voxs噪聲腦怎么辦？200 activated2 activated200 activated5 activated200 activated200 activatedUncorrected p=0.01我在進(jìn)行探

16、索性研究！探索性研究Bonferroni correction最嚴(yán)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數(shù)據(jù)分析中的問題Bonferroni 校正的假設(shè)pvoxel = poverall/N N為獨(dú)立觀測個(gè)數(shù)相鄰體元的BOLD信號會相互獨(dú)立的嗎？頭動等噪聲對同一腦區(qū)的影響很相似BOLD信號本身就對應(yīng)著一定空間范圍預(yù)處理中的平滑SPM 中的多重比較校正的原理根據(jù)數(shù)據(jù)的空間相關(guān)程度計(jì)算獨(dú)立觀測個(gè)數(shù)（獨(dú)立比較的次數(shù)Nindepentent）根據(jù)整體虛警概率poverall和Nindepentent得到單個(gè)體元的pvoxel值pvoxel = poverall/ NindepententSPM個(gè)體激活區(qū)檢測基本過程個(gè)體水平effec

18、t 計(jì)算的SPM實(shí)現(xiàn)（個(gè)體激活區(qū)檢測）模型定義Design Matrix Specification數(shù)據(jù)定義參數(shù)估計(jì)Data SpecificationParameter Estimation統(tǒng)計(jì)結(jié)果 Result參數(shù)估計(jì)常用工具與參數(shù)設(shè)置預(yù)處理部分First-level模型構(gòu)建與Second-levelLecture OutlineSPM I: Intro, PreprocessingSPM II: Single-subject analysesSPM III: Group analysesHow do we compare across subjects?建立不同人之間的可比性Normal

19、izationROI多個(gè)被試的統(tǒng)計(jì)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雙層統(tǒng)計(jì)First-level：個(gè)體水平effect 計(jì)算Second-level：群體水平effect 計(jì)算SPM個(gè)體激活區(qū)檢測基本過程Fixed- & Random- effects Model小結(jié)Fixed-effects ModelAssumes that effect is constant (“fixed”) in the populationUses data from all s