Hi Jiang :

Dear spm experts,

I have some questions about the calculation of the latency of the BOLD response and the explaination of  the temporal derivative of parametric regressor.

(1) The latency is estimated by the ratio of derivative parameter (beta2) to canonical (beta1) parameter estimates and can be calculated by a function latency=2C/(1 + exp(D*beta2/ beta1))- C, C = 1.78 and D = 3.10 (Henson et al., 2002). However, the beta1 can either a positive or a negative value that lead to a response later than the canonical when the beta2 is positive and the beta1 is negative.

yes Henson is correct, the modelled hrf is simply obtained by summing the double gamma + derivative

beta2 + / beta1 + = early response (latency is negative)
beta2 - / beta1 - = early response (latency is negative)
beta2 - / beta1 + = delayed response (latency is positive)
beta2 + / beta1 - = delayed response (latency is positive)
-- see bottom for a simple script showing this

Therefore, is it right to use the abosolute value of beta1 in this function to calculate the latency and the earlier or later of the BOLD response only depends on whether the derivative parameter is positive or negative rather than the canonical parameter.

no

(2) When we get a significant effect in the temporal derivative of parametric regressor (reaction time – mean(reaction time)), is the explaination right that for a region with deactivation, when we only put “1” on the “paraRT_TD” regressors, the significant regions means that the in the regions, the larger the reaction time, the larger the temporal derivative, and the earlier the BOLD response appear in the region.

for a region with deactivation = you are already in an area where the hrf regressor is negative

when we only put “1” = I would never do that - always add an inclusive mask (with lenient threshold) for the hrf regressor

paraRT_TD” regressors = voxels that change trial to trial as a function of RT

interpretation = hrf peaks (earlier/latter, depends beta value) than expected by trial to trial variations

for be able to say 'the larger the reaction time,  the earlier the BOLD response appear ' you need to show a systematic change in the timing of the peak, the temporal derivative doesn't do that - it only 'moves' earlier or latter your RT regressor

Cyril


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For question 1, you can convince yourself running that simple example

xBF.dt = 0.5;
xBF.name = 'hrf (with time derivative)';
xBF.length = 20;
[xBF] = spm_get_bf(xBF)

beta1=2; beta2=3;
latency=2*1.78/(1 + exp(3.1*beta2/beta1))- 1.78;
figure; subplot(2,2,1); plot(beta1*xBF.bf(:,1),'--','LineWidth',2);
hold on; plot(beta2*xBF.bf(:,2),'g--','LineWidth',2);
plot(beta1*xBF.bf(:,1)+beta2*xBF.bf(:,2),'r','LineWidth',2);
title(['Beta1 +, Beta2 +, latency=' num2str(latency)],'FontSize',13');
axis tight; box on; grid on

beta1=2; beta2=-3;
latency=2*1.78/(1 + exp(3.1*beta2/beta1))- 1.78;
subplot(2,2,2); plot(beta1*xBF.bf(:,1),'--','LineWidth',2);
hold on; plot(beta2*xBF.bf(:,2),'g--','LineWidth',2);
plot(beta1*xBF.bf(:,1)+beta2*xBF.bf(:,2),'r','LineWidth',2);
title(['Beta1 +, Beta2 -, latency=' num2str(latency)],'FontSize',13');
axis tight; box on; grid on

beta1=-2; beta2=3;
latency=2*1.78/(1 + exp(3.1*beta2/beta1))- 1.78;
subplot(2,2,3); plot(beta1*xBF.bf(:,1),'--','LineWidth',2);
hold on; plot(beta2*xBF.bf(:,2),'g--','LineWidth',2);
plot(beta1*xBF.bf(:,1)+beta2*xBF.bf(:,2),'r','LineWidth',2);
title(['Beta1 -, Beta2 +, latency=' num2str(latency)],'FontSize',13');
axis tight; box on; grid on

beta1=-2; beta2=-3;
latency=2*1.78/(1 + exp(3.1*beta2/beta1))- 1.78;
subplot(2,2,4); plot(beta1*xBF.bf(:,1),'--','LineWidth',2);
hold on; plot(beta2*xBF.bf(:,2),'g--','LineWidth',2);
plot(beta1*xBF.bf(:,1)+beta2*xBF.bf(:,2),'r','LineWidth',2);
title(['Beta1 -, Beta2 -, latency=' num2str(latency)],'FontSize',13');
axis tight; box on; grid on

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http://www.sbirc.ed.ac.uk/cyril
http://www.ed.ac.uk/edinburgh-imaging


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