Discrimination of cortical laminae using MEG

Abstract

Typically MEG source reconstruction is used to estimate the distribution of current flow on a single anatomically derived cortical surface model. In this study we use two such models representing superficial and deep cortical laminae. We establish how well we can discriminate between these two different cortical layer models based on the same MEG data in the presence of different levels of co-registration noise, Signal-to-Noise Ratio (SNR) and cortical patch size. We demonstrate that it is possible to make a distinction between superficial and deep cortical laminae for levels of co-registration noise of less than 2mm translation and 2° rotation at SNR > 11 dB. We also show that an incorrect estimate of cortical patch size will tend to bias layer estimates. We then use a 3D printed head-cast (Troebinger et al., 2014) to achieve comparable levels of co-registration noise, in an auditory evoked response paradigm, and show that it is possible to discriminate between these cortical layer models in real data.

Fig. 1

Outline of the simulation process. We use FreeSurfer to extract the pial and white matter surfaces for a single male subject. The pial and the white matter surfaces define the superficial and deep generative surface models. Activity is simulated by randomly selecting source locations from a list of 21401 possible patch centres. Data are generated using two different patch sizes; corresponding to either FWHM = 5 mm or FWHM = 10 mm (top left inset panel). Sources are simulated on both surfaces, followed by co-registration of each dataset to both cortical models. To add coregistration error, a random perturbation is added to the fiducial locations at this stage, either taking the form of rotation or pure translation of zero mean and specified standard deviation (0, 1, 2, 5, 10, 20 mm/degrees). Finally, we use the MSP algorithm to perform source reconstruction. This yields a free energy value as an outcome, which approximates the log model evidence, allowing us to compare between reconstructions based on the ‘correct’/‘incorrect’ surface models, as well as ‘correct’/‘incorrect’ patch sizes.

Fig. 2

An example to show the link between the free energy metric used in this paper and traditional cross-validation approaches. The basic approach we used is illustrated in Panel A. Here, we simulate 3 sources on the deep surface, and reconstruct these data onto two candidate cortical models (superficial and deep). In this case the free energies (or log model evidences) for the two models differ by 4.3. This suggests that the pial candidate model is more likely with a probability of 1/(1 + exp(− 4.3)) = 0.9866. An alternative method to judge between models would be to use cross-validation to see which model predicts new data more accurately. Based on the original set up we simulated a further 101 data sets, using the same source locations on the superficial surface (in other words these data had exactly the same underlying signal but different noise realisations). We now use the two candidate models to generate data and compare these predictions with new test data. Panel B shows the signal for a single MEG channel, for a single test dataset (blue solid) and predictions from the two candidate reconstructions (deep model green crosses, superficial model red circles). Note that the error between the superficial candidate model and the test model (based on superficial) is smaller than that of the deep. Panel C shows the ratio of these errors (over all channels and time points) for the two candidate models over 101 test datasets. The red line is at unity, points above the line show smaller error for the candidate deep surface model, points below indicate that the superficial model provides a better prediction of the test data. The incorrect model (deep surface model) is favoured in only two cases. This means that the deep model is more likely with a probability of 2/101 = 0.9802, in accord with the analytically derived posterior probability based on free energy (0.9866).

Fig. 3

A: The effect of lateral coregistration error (shift). The bars shows the average (over triplet simulations) free energy difference between true and incorrect surface models (evidence in favour of the true model is positive) for source triplets simulated on the superficial (left) and deep (right) surface models. Different coloured bars show different levels of co-registration error in mm. Both plots indicate that the ability to discriminate between models representing different cortical surfaces is destroyed once coregistration error exceeds 2 mm (free energy differences < 3). B: The effect of rotational coregistration error. The bars shows the average (over triplet simulations) free energy difference between true and incorrect surface models (evidence in favour of the true model is positive) for source triplets simulated on the superficial (left) and deep (right) surface models. Both for simulations based on the superficial as well as the deep surface model, the cut-off for being able to distinguish between the true/incorrect surface models (with 95% certainty or free energy > 3.0) lies around the 2-degree-mark.

Fig. 4

The effect of varying SNR. The ability to distinguish between surface models improves with SNR. At 1 dB SNR, it is not possible to make a significant distinction between cortical models (free energy < 3). However, at a higher, yet still moderate SNR of 11 dB, there is strong evidence in favour of the correct surface model.

Fig. 5

Investigating the effect of patch extent. Data were simulated on the superficial (left) or deep (right) surfaces models using either a patch extent of FWHM = 10 mm (upper panels), or FWHM = 5 mm (lower panels). Three sources were modelled, at a per trial SNR of 0 dB. In addition, rotational coregistration errors of 0, 2 and 5° were simulated. Panel A in the top row shows relative free energy differences for simulations based on the superficial surface and using a patch extent of FWHM = 10 mm. Looking at the leftmost set of bars (corresponding to reconstructions using FWHM 10 mm), we observe strong evidence in favour of the correct model (positive values) for reconstructions at true patch extent, both for 0 and 1, but not 5° of coregistration error. This pattern is destroyed when underestimating patch extent (FWHM = 5 mm), as illustrated by the rightmost set of bars where no clear difference between surfaces emerges. However, looking at Panel B, which shows the comparison based on the same patch size (10 mm), but using the deep surface model, it is clear that even if we underestimate patch extent (5 mm), the strong evidence in favour of the true model is preserved. This suggests that when we underestimate patch extent, we are introducing a bias towards deeper surface models. The bottom row shows relative free energy differences for simulations based on smaller patch extent (FWHM = 5 mm). Panels C and D correspond to the true surface models being superficial and deep, respectively. Here, in the case of superficial-surface-based data, when overestimating patch size, the evidence in favour of the superficial surface model is preserved (Panel C). On the other hand, as shown in Panel D, in the case of deep-surface-based simulations, overestimating patch size decreases the evidence in favour of the deep surface model. This indicates that by overestimating patch extent, we are introducing a bias towards superficial surface models.

Fig. 6

Investigation of layer and patch size models for an auditory evoked response paradigm in one subject over eight recording sessions. Panel A shows the difference in log model evidence between deep and superficial layer models for each of the eight runs for 5 (blue bars) and 10 mm (red bars) patch sizes. Positive values mean that the deep surface model is more likely; this is the case in six of the eight runs for both patch sizes. Panel B shows the probability of the two layer models based on all eight runs and both patch sizes. Note that the deeper cortical surface is more likely with a posterior probability of 0.9834. Panel C shows the probability of the different patch size models this time marginalising over layer models, the 5 mm patch size being more likely with a posterior probability of 0.8238. Panels D and E show the average posterior probability (probability that the current at any point is non zero) map for t = 0.92 s post stimulus over the eight sessions (combining both patch sizes) for deep and superficial layer models respectively.