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Hi John, I have a couple of questions regarding the same analysis. 1) What is the best way to do the analysis if there are three time points of data? Should I perform longitudinal registration between T1 and T2, T2 and T3 separately and do the long. registration on the resulting avg_*.nii images? 2) I have done the two group t test on the resulting smoothed and normalized c1.*jd images with contrasts, 1 and -1 (group 1 and group 2) the results would show if there is greater grey matter volume 'decline' in group 1 than in group 2. Is this correct? Thanks, Pradeep Is the subtraction as baseline – followup for JD calculation or the other way around. On Wed, Mar 12, 2014 at 5:09 AM, John Ashburner <[log in to unmask]> wrote: > I only said "this behaviour MAY introduce some sort of undesirable noise", > and wasn't 100% certain. > > As an example of the type of effect I was thinking of, try putting the > attached tstat.m function somewhere where MATLAB can find it, and pasting > the following into MATLAB. > > > N = 100; > > % Design matrix consisting of constant term, group difference, some > % covariate and an interaction between covariate and group > X = [ones(N*2,1) [ones(N,1); -ones(N,1)] [1:N, 1:N]'/(N/2)-(1+1/N)]; > X = [X X(:,2).*X(:,3)]; > > > Nrand = 10000; > p = zeros(Nrand,1); > for i=1:Nrand, > beta0 = [randn(3,1).*[1 0.5 0.5]'; 0]; % Interraction term set to > zero > y = exp(X*beta0 + randn(N*2,1)*0.5); % Assume 1st order kinetics > p(i) = tstat(X,y,[0 0 0 1]); % Test for interaction > % plot((1:N*2)',y,'.',(1:N*2)',X*inv(X'*X)*X'*y,'-') > end > > hist(p,100); % Should be flat > > > Even though the mechanism by which the data were generated does not > include any interaction, there appears to be one because of the > nonlinearity. For this reason, I'm slightly sceptical of the importance of > claims such as those about male brains atrophying faster than female brains > with age. My take on it is that the atrophy rate could be the same in both > groups, but brains that are slightly larger to begin with will lose more > tissue. > > Best regards, > -John > > > > On 11 March 2014 23:25, Chou Paul <[log in to unmask]> wrote: > >> Dear John >> >> Sorry to bother you, I don't understand why the Jacobian determinants >> introduce some sort of undesirable noise into the statistical analysis. >> Could you explain this concept more detail for me ? >> >> Thank you ! >> >> Best >> >> Paul >> >> ------------------------------ >> Date: Tue, 11 Mar 2014 11:59:56 +0000 >> From: [log in to unmask] >> Subject: Re: [SPM] Divergence rate vs Jacobian rate in Longitudinal >> Registration >> To: [log in to unmask] >> >> >> >> The Jacobian changes are easier to explain in a paper, so I would >> generally suggest using those for now. In practice, because longitudinal >> deformations are pretty small, it probably doesn't make so much difference >> which you use. >> >> Both measures are included because I actually don't know which is likely >> to be most useful over the long term. Having both options makes it >> possible to compare the effectiveness of the two different types of volume >> change representation. >> >> When some form of groupwise registration is run, one of the things we can >> expect is that these divergences should be zero on average. This is not >> the case for the Jacobian determinants. If an average of Jacobian >> determinants is computed for a population of subjects that have been >> aligned together, this average does not turn out to be uniformly 1. I >> figured that this behaviour may introduce some sort of undesirable noise >> into the statistical analysis, which is one reason why I kept the option of >> using the divergence. >> >> Divergence represents the rate of volumetric change according to the >> registration model ( http://en.wikipedia.org/wiki/Divergence ). >> Consider the following simple exponential growth model, where the volume of >> a structure atrophies at a constant rate. >> >> dt = 1; % Time interval >> r = -0.3; % Growth rate >> vol1 = 1; % Volume at first time point >> vol2 = vol1*exp(r*dt); % Volume at second time point >> >> jac_rate = (vol2 - vol1)/dt >> >> The divergence rate is analogous to "r", whereas the volume change rate >> computed from the Jacobian determinants is analogous to (vol2 - vol1)/dt. >> If r or dt are sufficiently small, then r and jac_rate are similar. In >> practice, the registration is slightly more complicated than this simple >> first order kinetic model, but similar principles apply. >> >> Best regards, >> -John >> >> >> >> >> >> >> Best regards, >> -John >> >> >> >> On 10 March 2014 20:36, Shashwath Meda <[log in to unmask]> wrote: >> >> Dear John & SPM'ers - I am in the midst of analyzing some longitudinal >> data via SPM12b and am trying to understand the differences between the >> divergence rate and the jacobian rate images that are produced via the >> pairwise longitudinal registration module. I am interested in looking at >> how volumetric changes correlate with drinking behavior in a cohort of >> normal adults. Which of the above metrics would be the best to look at from >> an morphometrics perspective? >> >> TIA >> >> -- >> Best, >> >> Shashwath >> >> >> >