## 4 Discussion
Interestingly, the same work group compared manual segmentations of brain tumors to a semi-automated probabilistic fractional segmentation and found wide ranges of the Dice coefficients (0.487-0.972) [37]. Additionally, [PERSON] et al. compared automatic segmentations of the falk and tentorium to manual segmentations of an expert in US and found an average Dice coefficient of 0.74. They also found a very high inter-observer variability in segmentations resulting in a Dice coefficient of 0.52-0.83 [38]. Secondly, spatial overlap is influenced by brain shift. With respect to this, we determined the Euclidean distance of the geometric centers of gravity, which were 3.7 \(\pm\) 2.5 mm (mean \(\pm\) SD) with a median of 3.0 mm, indicating a relevant shift of the segmented objects. Although the main shifting takes place after dural opening, [PERSON] et al. reported a dural displacement of 1.2 mm right after craniotomy [12]. However, [PERSON] et al. found a brain shift of 3.4 \(\pm\) 1.9 mm (range: 0.4-10.8 mm) at the tumor margins before dural opening, which was increased to 5.1 \(\pm\) 2.7 mm (range: 0.9-15.7 mm) before tumor removal [23] and [PERSON] et al. reported an average brain shift of 3.0 mm parallel to the direction of gravity and 3.9 mm perpendicular to the direction of gravity before dural opening. They described only an additional shift of 0.2 mm to the direction of gravity respectively 1.4 mm in the perpendicular plane after durotomy [29]. [PERSON] et al. discussed this unexpected finding of a larger extent of brain shift before dural opening to be attributed to calibration errors rather than true brain shift [21]. Although our study incorporated the evaluation of the registration procedure,the quality of the co-registration of the precalibrated US probes was not determined for each single case. To overcome this issue, we performed an accuracy measurement using a tracked ultrasound phantom containing wires. The expected positions of the wires were displayed within the US image and the offset was calculated to be \(1.33\pm 0.33\) mm (mean \(\pm\) SD). To evaluate object deformation possibly caused by either brain shift or the pressure applied with the US probe on the tissue during i3D US image acquisition, we analyzed the resemblance of segmented tumor objects in preMRI and iUS by calculating the Hausdorff distance [38; 39], resulting in a mean of 8.1 mm (SD: \(\pm 2.9\) mm) and a median of 8.1 mm. Interestingly, our computed value was lower than in the above citied study of [PERSON] et al., who compared automatic and manual segmentations of rigid and deeply located anatomic structures in one and the same US and found a Hausdorff distance of 12.2 mm [38]. Thus, segmentations were similar in preMRI and iUS and the deformation of the US objects was only moderate. We conclude that the brain shift is on the one hand partially due to the craniotomy and on the other hand influenced by the probe placement. However, unraveling the impact of each of these factors is virtually impossible, because first the iUS can only be performed after craniotomy and second the acquisition of ultrasound images requires contact to the brain's surface. Finally, the influence of the initial registration procedure expressed as TRE on the Dice coefficient, the Hausdorff distance, and the Euclidean distance of the geometric centers of gravity was evaluated facilitated by correlation analysis. Solely TRE and Euclidean distance of the geometric centers of gravity showed a significant (\(p=0.0420\)), but only moderate negative correlation (r = \(-0.3616\)). Taken together, the influence of the initial registration procedure was low, which is not surprising, given the very low TRE. Among the limitations of this study was the exclusion of two cases, in which the acquired i3D US datasets did not fully cover the lesions, and three cases, in which the TRE was not available. However, the amount of collected data is still large enough to allow a reliable evaluation.