Testing the IED Basis Set

The main aim of the current study was to extract a representative HRF basis set of our paediatric epilepsy patient group to provide future EEG-fMRI studies with more sensitive localisation maps. To do so we tested the model sensitivity of various basis sets in patients with a well-defined epileptogenic region, but who had non- concordant maps when applying the canonical HRF (see Table 3.1).

The fMRI data was analysed using a General Linear Model (GLM) where IEDs were used as temporal regressors and convolved with the basis set. There were three basis sets which were tested (see Figure 3.2): the standard canonical HRF (cHRF) with

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time and dispersion derivatives, the extracted smooth FIR for IEDs (IED-HRF) described previously and the nested model in which both are merged together (cHRF + IED-HRF). FMRI signal changes significantly related to IEDs were subsequently measured with an F-test (see Equation 3.5-3.9). The statistical threshold was defined based on previous work on EEG-fMRI localisation maps (Centeno et al., 2016) at p<0.001 uncorrected with a minimum of 5 continuous voxels, which provides a reasonable balance between specificity and sensitivity. Further work dealing with statistical thresholds in random field theory (RFT) have indicated overly conservative values (Tierney et al., 2016b), which supports the use of this threshold level in the context of this study.

The size of both the cHRF and IED-HRF basis sets was three, resulting in three regressors for each event type. However the nested model has double the number of regressors. Therefore, model comparisons could only be quantified in cHRF and IED-HRF models. A one-tailed test of proportions was done in R (R Core Team, 2016) to test whether there were significant differences in resulting F-statistics and distances (to foci) in cHRF and IED-HRF epileptogenic clusters.

The total yield of each model was also calculated. This was defined as the likelihood that each model would provide an accurate localisation map, which refers to the number of patients with significant SPMs over the total number of patients tested (where significant here means an SPM with a cluster of p<0.001, k=5). Finally, the sensitivity of each basis set to reveal signal changes in the epileptogenic zone. The epileptogenic zone was defined within subjects whose localisation in the EEG-fMRI maps was improved with the use of IED-HRF/nested basis sets in comparison to the standard cHRF. Sensitivity was defined as the proportion of true positives in defining the focus. In the current study this refers to the number of concordant patients over the number of patients with significant SPMs.

𝑭_{𝒅𝒇𝟏,𝒅𝒇𝟐}= 𝑩̂𝑻𝒄(𝑯_{𝑹𝒔𝒔𝑻𝒐𝒕𝒂𝒍}𝑻𝑯)−𝒄𝑻𝜷̂

𝒅𝒇𝑻𝒐𝒕𝒂𝒍

Equation 3.5

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Where 𝐹 is the f-test output, 𝛽̂ represents the predicted betas, 𝑐 represents the contrast matrix, 𝑋 represents the design matrix, and the +

denotes a (Moore-Penrose) pseudo-inverse. This implementation is ideal for large data sets, as the alternative (Equation 3.7) can be computationally demanding.

The alternative to Equation 3.5 can also be described as the F-ratio, or the magnitude of difference between different conditions (see Equation 3.7-3.9). Both options will yield the same results.

𝑭 = _{𝒖𝒏𝒆𝒙𝒑𝒍𝒂𝒊𝒏𝒆𝒅 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆}𝒆𝒙𝒑𝒍𝒂𝒊𝒏𝒆𝒅 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 = 𝑹𝒔𝒔𝑹𝒆𝒅𝒖𝒄𝒆𝒅−𝑹𝒔𝒔𝑻𝒐𝒕𝒂𝒍 𝒅𝒇𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝑹𝒔𝒔𝑻𝒐𝒕𝒂𝒍 𝒅𝒇𝑻𝒐𝒕𝒂𝒍 Equation 3.7 𝒅𝒇𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = 𝒅𝒇𝑹𝒆𝒅𝒖𝒄𝒆𝒅 - 𝒅𝒇𝑻𝒐𝒕𝒂𝒍 Equation 3.8 𝑹𝒔𝒔 = ∑(𝒀 − 𝒀̂) Equation 3.9

Where 𝑅𝑠𝑠 is the residual sum of squares, 𝑑𝑓 refers to the degrees of freedom, Y refers to obtained data and 𝑌̂ refers to the predicted data. The 𝑅𝑠𝑠 and 𝑑𝑓 of both the reduced model (not including regressors of interest) and the total model (including regressors of interest) are calculated.

The global maxima of the SPM map derived from EEG-fMRI has been shown to be a relatively poor indicator of the epileptic focus (Dongmei et al., 2013; Centeno et al., 2016b). Here, the results are presented for both the global maxima as well as the local maxima within the concordant cluster (local maxima of the cluster within closest range of the epileptogenic region).

96 Figure 3.1 Methods for training the basis set

The first step in the analysis is training the basis set, which requires three processing steps: pre-processing the data (a), single subject analysis using smooth finite impulse response (sFIR) deconvolution (b) and group analysis using principal components analysis (c). Step ‘a’ involves slice time correction, realignment, and FIACH noise correction (see Tierney et al., 2016 for more details), and normalisation and smoothing. The single subject analysis step ‘b’ only uses patients with concordant maps (EEG-fMRI maps that have significant clusters in the focus) when using the canonical haemodynamic response function (cHRF). After which, a sFIR deconvolution is done for each patient to determine their HRF also including time prior to event onset. The group analysis step ‘c’ combines the patient HRFs extracted in step ‘b’ and performs a principal components analysis using three components as representatives HRFs for paediatric epilepsy patients.

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Figure 3.2 Methods for testing the basis set

The second step in the analysis is testing the IED basis set. This requires pre-processing the data (a) and performing a single subject analysis in the general linear model (b). The pre-processing in step ‘a’ is the same as in Step 1 for training the basis set. The single subject analysis is done in a general linear model (GLM) by defining three different types of basis sets (bottom panel, far left): the canonical haemodynamic response function (cHRF) in red, the IED-HRF (Interictal Epileptiform Discharge HRF) in green, and the nested model which includes both cHRF and IED-HRF in blue. These models are described in the design matrices (bottom panel, middle). Finally, a statistical parametric map can be used to identify the efficacy of each basis set in defining epileptogenic cortices.

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3.5 Results