Signal

Previously, parameterised HRFs limited to epochs of boxcar designs have been modelled in a Bayesian framework using MCMC (21,25). In this work we introduced a novel half-cosine parameterisation of the HRF, and implemented it in a framework allowing for general stimulation types (boxcar, single-event). We imposed no spatial regularisation of the signal to allow an investigation of what can be inferred at each voxel. Whilst the HRF signal model is voxel-wise, it is worth emphasising that the noise model used at the same time is fully spatio-temporal. The use of the half-cosine parameterised form produces easily interpretable parameters, which is useful for the specification of priors and for interpreting the results. The parameters which represent the size of the initial dip and post undershoot crucially had an ARD prior. An ARD prior will force to zero those parameters that are not supported by the model and the data. This allows us to identify whether or not the data supports the existence of these HRF features on a voxel-wise basis. One of the results on the HRF characterisation suggested that there is a negative correlation between activation height and HRF time to peak. The idea that activation height is negatively correlated with the HRF time to peak, was also found in (25) for boxcar designs only. However, we need to be careful. The apparent causality between activation height and time to peak is just as likely to be indirect, and merely reflect that for voxels with low activation heights, the uncertainty in the time to peak is larger and hence we get a spread of estimated posterior mean time to peaks around the true value. This is demonstrated in figure 15 with the marginal posterior distribution for a strongly activating voxel having a much tighter distribution than the weakly activating voxel (both from the visual boxcar stimulus). There is another possibility. We may have voxels passing the threshold which are not pure responses to the stimuli. This ``confound activation'' may be structured noise partially correlated with the assumed response by chance, or response/stimulus related confounds such as motion artefact. These ``confound activations'' will have apparent HRF shapes spread across a wide range. These could have been avoided by being more restrictive with the HRF shape, however, without knowing the exact shape of the true HRF response a priori, we might then have missed some of the true response to the stimulus. Figure 16 is a schematic suggesting how the activation height--time to peak ($m_1+m_2$) scatter plot maybe made up of all three of these effects. There is no clear way with the current model to distinguish between these effects.

Figure 15: Marginal posterior distribution of the time to peak, $m_1+m_2$, for the visual boxcar stimulation for (a) a voxel with large activation, (b) a voxel with small activation.

Figure 16: Schematic suggesting how the activation height--time to peak scatter plot maybe made up three different effects (1) The ``true activation'' is negatively correlated. (2) The uncertainty in the ``true activation'' increases with smaller activation height. (3) There are voxels with ``confound activation'' passing the threshold. This may be structured noise randomly correlated with the assumed response, or response/stimulus related confounds such as motion artefact -- these ``confound activations'' will have apparent HRF shapes spread across a wide range. There is no clear way with the current model to distinguish between these effects.

picture(3621,2603)(628,-2766) (2008,-2676)(0,0)[lb]Mean of $m_1+m_2$%