Functional,Connectivity, (PPI,&,PLS), · PPI in Event-Related Designs • Low,power, –...

NeuroImaging,Training,Program,UCLA,

July,13,,2016,

Agatha,Lenartowicz,,Ph.D.,

,

,

Functional,Connectivity,(PPI,&,PLS),

“Connectivity”,

•  Being,joined,together,

•  Ability,to,communicate,(transfer,of,information),

Member,Units,+,Paths,

Network,

“Connectivity”,

•  Being,joined,together,

•  Ability,to,communicate,(transfer,of,information),

Connectivity,in,Neuroscience,

1881,International,Medical,Congress:,Segregation,(Ferrier),vs,

Integration,(Goltz),

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1000,

2000,

3000,

4000,

5000,

6000,

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1855, 1875, 1895, 1915, 1935, 1955, 1975, 1995, 2015,YEAR%

Cumulative%Manuscripts%Published%(brain%OR%neural%OR%cortical)%AND%(connectivity)%

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2000,

3000,

4000,

5000,

6000,

7000,

1855, 1875, 1895, 1915, 1935, 1955, 1975, 1995, 2015,YEAR%


0,1000,2000,3000,4000,5000,6000,7000,8000,

YEAR%


1881,International,Medical,Congress:,Segregation,(Ferrier),vs,

Integration,(Goltz),

Ogawa,1990,BOLD,Filler,,LeBihan,1991/2,DTI,

McIntosh,,Horwitz,,Friston,1990,Biswal,1997,RSN,

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0,

1000,

2000,

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7000,

1855, 1875, 1895, 1915, 1935, 1955, 1975, 1995, 2015,YEAR%



Petrides M., (2005) Phil. Trans. R. Soc. B;360:781-795

Felleman & Van Essen, (1991), Cereb Cortex;1(1);1-47

Transition,from,architectonic,analysis,and,neurophysiological,recordings,in,the,animal,model,to,inWvivo,human,(and,nonWhuman),experiments.,

Fox et al., (2005) Proc. Natl. Acad. Sci. USA. 102; 967-9678

Image Courtesy of Jesse Brown, Ph.D.

Categories,of,Connectivity,

Thanks to SPM group for slide images.

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Physical,Connections,(tracing,*DTI/DWI,*dissections)*

Statistical,Connections,(correlation,*coherence,*mutual*information)*Sporns*2007*(Scholaropedia,*2*(10):4695)*

Categories,of,Connectivity,

Thanks to SPM group for slide images.

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Physical,Connections,(tracing,*DTI/DWI,*dissections)*

Statistical,Connections,(correlation,*coherence,*mutual*information)*Sporns*2007*(Scholaropedia,*2*(10):4695)*

No,information,about,direction,of,information,flow,(causal,relationships).,

Bird’s,Eye,View,of,Methods,Sp

atial,S

cale,of,N

etwork,

Degree,of,Causal,Inference,

ICA PCA

Graph Analysis

Bivariate Correlation

Connectome Virtual Brain

Granger Causality, Bayes Nets, SEM, DCM

Lesions, TMS

PPI

Seed-Analysis

Partial Correlation

Partial Least Squares MVPA

Model,Free,

Model,Based,

DTI


atial,S

cale,of,N

etwork,


ICA PCA

Graph Analysis




Lesions, TMS

PPI

Seed-Analysis

Partial Correlation


Model,Free,

Model,Based,

DTI

“effective,connectivity”,


atial,S

cale,of,N

etwork,


ICA PCA

Graph Analysis




Lesions, TMS

PPI

Seed-Analysis

Partial Correlation


Model,Free,

Model,Based,

DTI

Psychophysiological,Interaction,

Slide*images*courtesy*of*UCL*group,Friston, K.J., et al., (1997), NeuroImage, 6: 218-229

attention%

•  PPI,is,an,interaction,term,between,a,

task,regressor,and,a,time,series,from,

an,ROI,(β3,=,β1,*,β2),

•  test,of,slopes,

Y%=%β1%%%%%+%%β2%%%%%%%%+%β3%%%%%%+%error%%%%

Attention,No,Attention,

β3,=,β1,*,β3,,

Attention,

No,Attention,

β1,

β2,V1,

Corr(V1,PPI),=,.05,

Corr(PSY,PPI),=,.97,

Corr(V1,PSY),=,.03,

,

,,,,,NonWFactorial,

,

V1,

PSY:,Att,vs,NoAtt,

PPI:,Interaction,

Corr(V1,PPI),=,.02,

Corr(PSY,PPI),=,.01,

Corr(V1,PSY),=,.02,

,

,,,,,,,,,,,,Factorial,

,

Speed,1, Speed,2,

A, A,NA, NA,

A, A,NA, NA,

•  Collinearity,in,this,model,will,decrease,power,of,detecting,β3,

•  Factorial,designs,are,preferable,because,they,ensure,variance,

in,PPI,independent,of,main,effects,–  2,crossed,independent,variables,in,design,(e.g.,,attention,,speed),

–  identify,seed,using,one,of,the,factors,(e.g.,,speed***),

–  replace,factor,(speed),with,activity,of,seed,

,

No,Attention,

β3,=,β1,*,β3,,

Attention,

β1,

β2,V1,

•  Must,include,main,effect,regressors,(β1,and,β2),to,test,unique,

variance,due,to,interaction,term,

–  If,don’t,include,main,effects,=>,spuriously,significant,interaction,term,

–  If,do,include,main,effects,=>,may,have,poor,power,(collinearity),to,detect,interaction,

,

No,Attention,

β3,=,β1,*,β3,,

Attention,

β1,

β2,V1,

•  PPI,“concept”,can,be,used,to,test,for,differences,in,connectivity,

comparing,preFpost%intervention,and,subject%groups,

•  ‘psychological’,variable,is,now,a,between,subject,variable;,compare,ROI,connectivity,between,sessions,or,groups,

No,Attention,

β3,=,β1,*,β3,,

Attention,

β1,

β2,V2,

Heinz, A., et al., (2005), Nat Neuro, 8(1): 20—21

EXAMPLE: AMY-PFC interactions vary as a function of depression

correlated genotype

•  PSY,=,genotype,(group),,ROI,=,AMY,,no,PPI,

•  Response,of,AMY,to,task,(aversive/pleasant),also,greater,in,ls/ss,genotypes,•  If,compare,y=AMY+e,across,groups,,will,observe,differences,primarily,due,to,

task,response,of,AMY,to,aversive,stimuli,•  If,compare,y=AMY+task+e,across,groups,,will,obtain,estimate,of,taskW

independent,difference,in,AMY,connectivity,between,groups,

PSY, l/l,s/s,

PPI in Event-Related Designs •  Low,power,

–  Smaller,signal,and,poorer,model,fit,than,in,block,designs,–  Layering,on,top,of,this,variability,is,the,structured,variability,that,we,test,

with,PPI,–  Convolution,with,HRF,impacts,interaction,term,(hrf(A)*hrf(B)),vs,hrf(A*B),–  Recommended,with,caution,in,fast,designs;,alternate,approach,beta,

series,correlation,(Rissman),

PPI in Event-Related Designs •  Low,power,

–  Smaller,signal,and,poorer,model,fit,than,in,block,designs,–  Layering,on,top,of,this,variability,is,the,structured,variability,that,we,test,

with,PPI,–  Convolution,with,HRF,impacts,interaction,term,(hrf(A)*hrf(B)),vs,hrf(A*B),–  Recommended,with,caution,in,fast,designs;,alternate,approach,beta,

series,correlation,(Rissman),

Gitelman et al., (2003), NeuroImage, 19: 200-207 hrf(A)*hrf(B) ≠ hrf(A*B)

ROIA, ROIB,

Generalized PPI Model •  1997,subtraction,model,is,limited,

–  Limited,to,2,conditions,–  Dependent,on,accurate,centering,of,PSY,and,PPI,regressors,–  Doesn’t,make,interpretation,easy,

Y,=,c,+,β1,(X1WX2),+,β2,,ROI,+,β3,(X1WX2)*ROI,

No,Attention,

Attention,

If,you,were,to,mean,center,and,there,were,more,time,points,in,Attention,condition,than,in,No,Attention,condition,,the,zero,point,would,be,biased,upwards.,ZeroWcenter,(minWmax),more,appropriate.,

No,Attention,

Attention,

+X1,0,X1,

+X1,

0,X2,WX2,

WX2,

Generalized PPI Model •  Generalized,form,of,the,model,

–  Initially,developed,by,Jeanette,Mumford,~2010,(not,published),–  Independently,formalized,by,McLaren,et,al.,(2012),NeuroImage,61:,1277W1286,

Y,=,c,+,β1a,X1,+,β1bX2,+,β2,,ROI,+,β3a,(X1)*ROI,+,β3b,(X1)*ROI,,To,test,for,slope,difference:,β3a,W,β3b,To,test,for,within,condition,ROI,correlations:,β3a,,β3b,

+X1,0,X1,

+X1,

0,X2,WX2,

WX2,

PhysWPhys,Interactions,

•  Can,use,PPI,to,evaluate,physioWphysiological,interactions,(Friston,

et,al.,,1997)%

Friston, K.J., et al., (1997), NeuroImage, 6: 218-229

PhysWPhys,Interactions,

•  β1,=,L,Motor,,β2,=,R,Motor,,β3,,=,L,Motor,*,R,Motor,

•  Does,connectivity,within,one,region,vary,with,activation,level,of,

another,region,in,resting,state,data,

Di & Biswal, (2013), PLOS ONE, 8(8): e71163

β1% β2%

β1%

β2%

PPI,Summary,•  PPI,is,accessible,and,powerful,as,a,tool,to,study,connectivity,across,context,

(condition,,intervention,,group,,activity,of,another,region),

–  Requires,attention,to,model,,inclusion,of,‘task’,regressors,,regressor,collinearity,and,

centering,(for,differenceWbased,regressors),,,

–  Typically,limited,to,single,region,(except,for,physioWphysio,interactions),and,so,,not,as,

powerful,as,other,multivariate,techniques,such,as,MVPA,or,PLS,

•  Direction,of,modulation,is,ambiguous,

attention%

attention%

Images*courtesy*of*UCL*group,

More on PPI?

Partial,Least,Squares,

•  PLS,seeks,to,identify,a,profile,of,voxels,(and,timepoints),that,

covary,as,a,function,of,task,,group,etc.,

•  ModelWfree,(unlike,PPI)*,

•  Multivariate,(unlike,PPI),

•  Singular,Value,Decomposition,of,CrossWBlock,Variance,Matrix,

,

McIntosh,et.,al,,1996,,2004ab,(adapted,to,PET/fMRI/EEG),

SVD,on,CrossWBlock,Variance,voxels, task,conditions,

voxe

ls,

task,con

ditio

ns,

Cross,Block,Variance,PLS,

Within,Block,Variance,Voxels,PCA,

Within,Block,Variance,Task,PCA,(Factor,Analysis),

voxels, task,conditions,e.g.,,attend,,nonWattend,

SVD,on,CrossWBlock,Variance,X=USVT,

=,

voxels,(v),

cond

ition

,(c), k,

c,Data(X), U,

k,

k, k,

v,

V,

•  Least*squares*decomposition*of*data*matrix*into*orthogonal*basis*

function*k,latent,variables,produced,(LVs),•  LV,=,saliences,+,singular*value*•  Conceptually,similar,to,PCA,,ICA,etc.,maybe,even,FFT,because,we,

reNexpress*matrix*as*a*series*of*orthogonal*vectors*that*can*be*

recombined*to*recreate*the*original*matrix,

S,

%,cov,

SVD,on,CrossWBlock,Variance,X=USVT,

=,

voxels,(v),

cond

ition

,(c), k,

c, U,

k,

k, k,

v,

V,S,

%,cov,

Data(X),

Examples,

Spreng*et*al.,*2011,*Neuroimage*53(1):*303N317,

Examples,

Lenartowicz*et*al.,*2011,*CABN,*10(2):*298N315*,

Note:*256*electrodes***500*time*points*=*128k*variables,

Flexibility,of,Technique,voxels,(v),

cond

ition

,(c),

Data(X),


cond

ition

,(c),

Data(X),

Data(Y),

cond

ition

,(c),

GRO

UP1

,GRO

UP2

,


cond

ition

,(c),

Data(X),

Data(Y),

cond

ition

,(c),

GRO

UP1

,GRO

UP2

,

Data(X),

cond

ition

,(c), voxels,(v),*,time,(event,related,design),

Examples,

Spreng*et*al.,*2011,*Neuroimage*53(1):*303N317,


cond

ition

,(c),

Data(X),

Data(Y),

cond

ition

,(c),

GRO

UP1

,GRO

UP2

,

Data(X),

cond

ition


cond

ition

,(c),

r(perf,,seed,,EEG,,symptoms,…),

voxels,(v),


cond

ition

,(c),

Data(X),

Data(Y),

cond

ition

,(c),

GRO

UP1

,GRO

UP2

,

Data(X),

cond

ition


cond

ition

,(c),


voxels,(v),

Data(X),

cond

ition

,(c),


voxels,(v),

cond

ition

,(c),

Model,Free*,

•  We,can,steer,analysis,to,various,contrasts,by,demeaning,cross,block,matrix,selectively,

Group1, Group2,

10, 5,W5, W10,

7.5,

W7.5,

Model,Free*,

Group1, Group2,

10, 5,W5, W10,

2.5,

W2.5,

•  We,can,steer,analysis,to,various,contrasts,by,demeaning,cross,block,matrix,selectively,

Statistics,

•  Resampling,methods,are,used,in,Matlab,batch/GUI,PLS,implementation,(distribution,free),

,•  Permutation,(resampling,without,replacement/shuffling,assignment,between,e.g.,,conditions,and,subjects),approach,for,testing,overall,significance,of,singular,value,(i.e.,,%,covariance,accounted,for),–,depends,on,exchangeability,

,•  Bootstrap,(resampling,with,replacement/varying,which,subjects,are,in,sample),approach,to,calculate,confidence,intervals,,on,the,saliences,(weights),

PLS,Summary,•  Similar,idea,to,PPI,in,seeking,task,related,patterns,of,functional,

connectivity,however:,

–  Multivariate,

–  Model,Free,

–  Flexible,to,incorporate,time,,covariates,,seeds,,beta,maps,etc.,

–  Nonparametric,statistical,assessment,

•  Originally*designed*for*between*subject*analyses*whereas*PPI*is*designed*for*

within*subject*connectivity;*natural*extensions*for*withinNsubject*designs*do*

exist*

•  May,not,produce,the,contrast,you,*want*,(modelWfree),,but,often,that,

should,be,informative,in,itself,

For,more,on,PLS,

https://www.rotmanWbaycrest.on.ca/index.php?section=84,

PLS,Summary,•  Similar,idea,to,PPI,in,seeking,task,related,patterns,of,functional,

connectivity,however:,

–  Multivariate,

–  Model,Free,

–  Flexible,to,incorporate,time,,covariates,,seeds,,beta,maps,etc.,

–  Nonparametric,statistical,assessment,

•  Originally*designed*for*between*subject*analyses*whereas*PPI*is*designed*for*

within*subject*connectivity;*natural*extensions*for*withinNsubject*designs*do*

exist*

•  May,not,produce,the,contrast,you,*want*,(modelWfree),,but,often,that,

should,be,informative,in,itself,

Within,vs,Between,Ss,Variance,

•  FC,has/can,assessed,using,withinW,&,betweenWsubject,variance,,

–  Within:,across,time,(e.g.,,continuous,–,RSN,or,trials,–,PPI),

–  Between:,across,individuals,on,mean,withinWsubject,values,(e.g.,,PLS),

–  Not,unique,to,FC,analyses,,true,in,general,when,multiple,measures,

obtained,(e.g.,,EEGWfMRI,,BOLDWRT,etc.),


•  Does,between,subject,variance,recapitulate,within,subject,

variance?,Not,always.,

–  No,e.g.,,positive,correlation,between,DMN,and,visual,cortex,across,people,

greater,for,visual,flashes,than,for,,passive,,could,be,because,some,people,

have,overall,greater,activation,(in,all,regions);,may,in,fact,have,negative,

correlation,within,individuals,

–  Yes,if,measuring,the,same,processes,and,the,effects,are,consistent,over,

time,and,across,individuals,(ergodicity),e.g.,*Molenaar*&*Campbell*2009*

Curr*Directions*in*Psych*Science.18(2),*112N117*


•  Example,in,FC,–,Roberts,et,al.,(2016),Neuroimage,135,,1W15,

•  Moderate,prediction,of,(“ws”),withinWsubject,FC,from,betweenWsubject,(“as”),FC,(DMN),

Within,vs,Between,Ss,Variance,•  Better,prediction,for,regions,within,network,than,between,network,(DAN,,DMN),

•  BetweenWsubject,FC,has,more,negative,relationships,between,networks,

•  BetweenWsubject,FC,is,more,variable,

Within,vs,Between,Ss,Variance,•  Simpson’s,Paradox,


•  FC,analysis,requires,analysis,of,withinWsubject,variance,

•  This,is,not,unlike,hierarchical,GLM,approach,(study,effect,within,individual),

•  Holds,true,for,correlations,with,external,variables,like,RT,,or,EEG,

Which,method?,MVPA,,PPI,,PLS,grouped,as,taskWrelated,connectivity,methods,

ML,

PPI,

PLS,

Y(label),=,b1X1,+,b2X2,+,b3X3,….,*

Multivariate*(however*voxels*independent*variables)*and*model*based.*Objective*is*to*predict*class*label,*not*

to*understand*the*correlations*(connectivity*patterns)*and*weights*may*or*may*not*be*related*to*interpretable*

brain*phenomena.*General*class*prediction*tool*(decoder),*not*a*functional*connectivity*method.*User*defined*

interpretation*based*on*choice*of*features*(EEG,*fMRI,*PET,*connectivity,*activity,*etc.)*

Y=,b1X1,+,b2X2,+,b3ROI,+,b4X1*ROI,…,,Mass*univariate*(GLM),*but*bound*by*ROI*correlation*across*conditions.*We*are*testing*FC*hypotheses.*Model*

based.*Conceptually*a*precursor*to*causality.*Subject*to*standard*regression*assumptions.*Excellent*for*

factorial*designs*where*precise,*largeNpower,*wellNdefined*network*hypotheses*exist.*

a1Y1,+,a2Y2,+,a3Y3,…,=,b1X1,,+b2x2,+,b3x3,,Multivariate*(voxels*dependent*variables),*aiming*to*discover*combination*of*activity*patterns*that*covary*

across*context*(e.g.,*condition*X1*levels).*Not*model*based.*Precursor*to*causality*analyses.*Relatively*

assumption*free.**Excellent*for*high*dimensional*data,*with*or*without*priors*on*network*architecture,*and*

flexible*across*multiple*modalities.*

Questions?,

Lab,•  DOWNLOAD,TO,YOUR,OWN,DESKTOP,(as,well,as,to,the,virtual,box),

in,order,to,open,the,instruction,guides,(docx,files),,as,the,VB,does,not,have,a,Word,reader,

•  Lab,will,be,demo,format,and,I,will,move,quickly,in,order,to,focus,on,higher,level,concepts,

,•  If,you,get,stuck,,stop,,follow,along,with,a,colleague,or,presenter,,•  If,you,are,unfamiliar,with,shell,,Matlab,,and,possibly,FSL,,follow,

along,with,a,colleague,or,presenter,i.e.,*don’t*waste*time*trouble*

shooting*trivial*problems*during*the*lab*to*get*conceptual*

understanding*of*lab*objective*

*

•  Each*lab*has*a*readme*with*complete*instructions*for*performing*all*

steps*demonstrated*

,

Lab,,•  OBJECTIVE1:,Using,1,subject’s,data,from,Friston,97,paper,(attend/

nonattend,,motion/nomotion),we,will,replicate,the,steps,needed,to,set,up,a,PPI,analysis,of,the,V1,connectivity,as,it,varies,with,attention,condition,–,using,FSL,(ppi_lab/ppi_fsl_lab_2012.docx),

,•  OBJECTIVE2:,Appreciate,how,to,set,up,this,analysis,using,subtraction,

versus,generalized,PPI,model.,(ppi_lab/pls_fsl_lab_2014ADDENDUM.docx),

,•  OBJECTIVE3:,Appreciate,how,to,set,up,this,analysis,using,PLS,(not,to,

validate,analysis,but,to,experience,the,PLS,code/GUI),(pls_lab/pls_lab_2015.docx).,

,

Functional,Connectivity, (PPI,&,PLS), · PPI in Event-Related Designs • Low,power, –...

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