Using our normative model, we explored several aspects of normal cortical variability.  First, we calculated our similarity metrics of Euclidean distance ($d_e$) and cosine similarity ($cos$) between: 1) pairs of homotopic patches across subjects  ($d_e$=$2.67\pm0.73$, $cos$=$0.45\pm0.28$), 2) heterotopic patches across subjects ($d_e$=$3.69\pm0.79$, $cos$=$0.00\pm0.29$).  In both distance and cosine similarity, the resulting distributions were all significantly different ($p<0.001$); homotopic patches appear more similar to each other than contralateral ($d=0.88$ and $d=1.01$ for $d_e$ and $cos$, respectively)  and heterotopic patches ($d=1.35$ and $d=1.59$ for $d_e$ and $cos$, respectively) with a large effect size.
The pre-normalization FCD similarity map, averaged across healthy controls, further demonstrates some overlap with areas of normal cortex (fig xxx), with reproducibly high similarities in regions such as the insula, temporal pole, parahippocampal gyrus, and anterior cingulate cortex. These reproducible similarities are no longer seen following local normalization, as seen in the individual patient FCD similarity maps in figure XX.
In healthy volunteers, as described above, we found that homotopic patches appeared more similar to each other than heterotopic patches as measured by both Euclidean distance and cosine similarity; as expected, these differences between homotopic and hetereotopic patches are minimal after carrying out local normalization, with $d_e$ = $2.67\pm0.73$ vs. $d_e$=$2.65\pm0.65$ ($d=0.04$), and $cos$=$-0.03\pm0.34$ vs. $cos$=$0.00\pm0.29$ ($d=0.11$).  Accordingly, following local normalization the average distance between pairs of FCD patches and normal cortex appears similar regardless of the location of the cortex ($d_e$=$3.63\pm0.94$ and$d_e$=$3.61\pm0.92$, between pairs of FCD patches and homotopic or heterotopic patches, respectively ($d=0.02$)). Interestingly, these distances are quite similar to the within class distance of FCD patches across individuals ($3.48\pm0.96$, $d=0.16$ and $d=0.14$ for FCD vs homotopic and heterotopic patches, respectively).  For cosine similarity, there is again little difference when comparing FCD to homotopic ($cos$=$0.00\pm0.30$) or heterotopic ($cos$=$0.00\pm0.28$) patches, but cosine similarity across FCDs ($0.39\pm0.26$) is much greater than between FCDs and normal cortex ($d=1.38$ and $d=1.41$ for FCD vs homotopic and heterotopic patches, respectively).  This suggests that FCDs are located in a relatively consistent direction, but are not clustered tightly, as their distances from each other are similar to that of randomly selected pairs of patches.  This can be observed in graphic form in figure XX, in which the center of each FCD is shown, as well as the average center and direction of the average FCD vector.  Additionally, in figure XX, the MRI appearance as well as the patch values within individual FCDs are demonstrated, highlighting the variable appearances of FCDs both visually and in this 2D space.