Navigated 3D Ultrasound in Brain Metastasis Surgery: Analyzing the Di ﬀ erences in Object Appearances in Ultrasound and Magnetic Resonance Imaging

: Background: Implementation of intraoperative 3D ultrasound (i3D US) into modern neuronavigational systems o ﬀ ers the possibility of live imaging and subsequent imaging updates. However, di ﬀ erent modalities, image acquisition strategies, and timing of imaging inﬂuence object appearances. We analyzed the di ﬀ erences in object appearances in ultrasound (US) and magnetic resonance imaging (MRI) in 35 cases of brain metastasis, which were operated in a multimodal navigational setup after intraoperative computed tomography based (iCT) registration. Method: Registration accuracy was determined using the target registration error (TRE). Lesions segmented in preoperative magnetic resonance imaging (preMRI) and i3D US were compared focusing on object size, location, and similarity. Results: The mean and standard deviation (SD) of the TRE was 0.84 ± 0.36 mm. Objects were similar in size (mean ± SD in preMRI: 13.6 ± 16.0 cm 3 vs. i3D US: 13.5 ± 16.0 cm 3 ). The Dice coe ﬃ cient was 0.68 ± 0.22 (mean ± SD), the Hausdor ﬀ distance 8.1 ± 2.9 mm (mean ± SD), and the Euclidean distance of the centers of gravity 3.7 ± 2.5 mm (mean ± SD). Conclusion: i3D US clearly delineates tumor boundaries and allows live updating of imaging for compensation of brain shift, which can already be identiﬁed to a signiﬁcant amount before dural opening.


Introduction
Metastases are the most common brain tumors [1], with an estimated incidence being 3-to 10-fold higher than in primary brain tumors [2]. Despite tremendous advances in therapy, such as chemotherapy, immunotherapy, and targeted therapies [3], surgery and radiotherapy remain important cornerstones of the therapy [3][4][5]. Furthermore, the European Association of Neuro-Oncology recommends surgical resection in patients with a maximum of three metastases, especially when reaching a diameter of 3 cm or more, in cases of necrotic or cystic lesions, a distinct edema or mass effect, or an imminent danger of hydrocephalus as in posterior fossa lesions [5]. The development of image-guided surgery within the last decades including intraoperative magnetic resonance imaging (iMRI), computed tomography (iCT), and ultrasound (iUS) allows gross total resection with lower morbidity [6]. A well-described limitation of image-guided neurosurgery is brain shift [7], which is, among others, due to influences of gravity, brain swelling, loss of cerebrospinal fluid, tissue removal during surgery, and brain retraction [8,9]. First attempts to address this issue reach as far back as 1986, differ under optimal conditions of a minimized brain shift, which is given at the earliest possible operative stage right after craniotomy. To specify this, we prospectively obtained navigated i3D US datasets in a series of 35 cases of brain metastasis, which shared the feature to have more delineated boundaries in US than, e.g., gliomas, as described by Unsgaard et al. before [34]. We compared i3D US to preoperative MRI, analyzing the tumor volume, shape, and distance of segmented objects.

Materials and Methods
The prospective study included initially 37 patients, who were operated between February 2019 and July 2020. In the course of the study, two cases had to be excluded due incomplete image acquisition.
In all participants, preoperative MRI detected at least one lesion suggestive of brain metastasis and an interdisciplinary tumor board recommended resection. We obtained informed consent from all patients included in this study and received ethics approval for prospectively archiving clinical and technical data applying intraoperative imaging and navigation (study no. 99/18).
All patients received an MRI within a few days before resection, typically encompassing a 3D data set of T1-weighted contrast-enhanced images. These were transferred to the navigational system (Brainlab, Munich, Germany), which consists of a ceiling mounted double monitor (Curve, Brainlab, Munich, Germany) and two displays (Buzz, Brainlab, Munich, Germany) and navigational software.
All patients were operated under general anesthesia. After narcosis induction the patients were positioned on the operating room (OR) table and the head was fixed to a radiolucent carbon Doro head clamp with metallic pins. A reference array with four reflective markers was attached to the head clamp. Three fiducial markers were placed on the head within the scanning area, which were not needed for registration. The OR table was rotated 90 • to the 32-slice mobile CT scanner (AIRO, Brainlab, Munich) and a low-dose registration scan of 62 mm scan length was performed. Reflective markers, which are permanently attached to the AIRO scanner, and the reference array must be in the field of view of the navigational camera during the scanning process. The CT scan was automatically transferred to the navigational system and fused with the preoperative imaging datasets, establishing automatic patient registration. The patient was rotated back, and registration accuracy was checked by placing the navigational pointer into the divot of each skin fiducial. This allows the calculation of a target registration error as the Euclidian offset of the pointer tip. The reference array was removed and replaced by a sterile one after draping. Details of the aforementioned set-up, scanning process, and patient registration were published before [35].
All patients received 40 mg of dexamethasone. After team time-out, skin disinfection, and sterile draping, the skin was incised. One-hundred-and-twenty-five milliliters of mannitol 15% was administered before craniotomy. After bone flap removal, and before dural opening, a navigated i3D US dataset was acquired using the bk5000 system (bk medical, Herlev, Denmark), which was connected to the navigational system. For acquisition, a reference array with three reflective markers is attached to the precalibrated bk medical transducer N13C5, which is fully immersible, can be sterilized and therefore be used without a sterile cover. The transducer offers a convex contact surface of 29 × 10 mm and has a scanning frequency of 5-13 MHz. Whenever possible, the patient's head was positioned in a way exposing the dura horizontally after bone removal, allowing a saline depot to be administered as a coupling fluid. During image acquisition the probe was smoothly swept over the dura, whilst the reference arrays attached to the head clamp and the transducer were in the line of sight of the navigational camera ( Figure A1). The bk5000 actually generated 2D slices of 0.3 mm, which were transformed into 3D image volumes and automatically registered by the navigational software (Figure 1a). Those 3D data sets, which were now available during the further surgical procedure, were displayed in an overlay or side-by-side fashion, or as a standalone and could be reformatted to an oblique plane matching the surgeon's view through the operating microscope (Figure 1b,c). A second image acquisition was performed after tumor removal as a resection control or if demanded at any timepoint during the surgery. Lesions were identified and segmented in the preMRI and pre-resectional ultrasound using the smart brush tool element (Brainlab, Munich, Germany) in the navigational software, which automatically calculates the tumor volume. The 3D datasets were exported to MeVisLab (MeVis Medical Solutions AG, Bremen, Germany) for further calculations. To assess similarity of the objects, the Dice coefficient [36] and the Hausdorff distances were computed. Lesions were identified and segmented in the preMRI and pre-resectional ultrasound using the smart brush tool element (Brainlab, Munich, Germany) in the navigational software, which automatically calculates the tumor volume. The 3D datasets were exported to MeVisLab (MeVis Medical Solutions AG, Bremen, Germany) for further calculations. To assess similarity of the objects, the Dice coefficient [36] and the Hausdorff distances were computed. The Dice coefficient (C DSC ) is a spatial overlap index that can be used for comparing segmented objects [37,38] and is calculated as where A US and B MR are number of voxels of the segmented objects. The Dice coefficient is restricted to values between 0 and 1, with a value of 0 indicating no overlap and a value of 1 representing an exact match [38]. The Hausdorff distance measures the extent to which each voxel of one segmentation lies near to some voxel of the other segmentation, and vice versa [39]. The calculated distance can be used to measure the degree of resemblance of the object contours [38,39].
The formula is defined as The Hausdorff distance is measured in mm; it is a small distance indicating a good resemblance of the segmented objects [38].
Furthermore, the geometric centers of gravity (CoG) were calculated, which have the advantage of being invariant under rotation, scaling and skewing, and a stable measurement even under random noise [40]. The CoG has been used for measuring the displacement of objects in different MRI sequences before [41]. Put simply, the geometric center of gravity is calculated by summing up the coordinates of voxels, divided by the number of voxels: The displacement is calculated by subtraction of the geometric centers of gravity, expressed as Euclidean distance.
For statistical analysis GrapPad Prism 8.4.3 (GrapPad Software, San Diego, CA, USA) for MacOS was used.
If necessary, testing for normal distribution was performed using the D'Agostino and Pearson test. For the analysis of not normally distributed data either the two-tailed Mann-Whitney test (un-paired) or the Wilcoxon matched-pairs signed rank test (paired data) were used.
A p-value < 0.05 was considered statistically significant.

Patient Characteristics
Of the 37 patients, two had to be excluded because the acquired i3D US did not capture the whole lesion due to artifacts. Of the remaining 35, 18 were females and 17 males. Mean patient age was 62.7 ± 12.1 (mean ± SD) years, ranging from 28.6 to 79.1 years. Thirty-one patients suffered from single brain metastasis and four were diagnosed with more than one lesion. The most common tumor location was in the frontal lobe (15), followed by the parietal (five, of which each one was temporo-parietal or parieto-occipital), occipital (five), and temporal (two). In six cases, the tumor was located cerebellar. One lesion was located at the head of the caudate nucleus, and one lesion was insular. Histopathological work-up revealed metastasis of an adenocarcinoma of the lung in eleven cases and neuroendocrine carcinoma of the lung in three cases. In seven patients, a melanoma was found as the primary site, three patients suffered from breast cancer, four were diagnosed with renal cell carcinoma, six with gastrointestinal adenocarcinoma encompassing colon (three), gall bladder (one), esophagus (one), and one which was not specified further. One lesion was defined as a carcinoma of unknown primary site. Table 1 summarizes patient characteristics.  Table 2 summarizes tumor object characteristics and reports the target registration error. Descriptive analysis of the segmented tumor volumes revealed a mean tumor volume of 13.6 ± 16.0 cm 3 (mean ± SD) and a median of 8.5 cm 3 in MRI, whereas it was 13.5 ± 16.0 cm 3 (mean ± SD) with a median of 8.8 cm 3 , when segmented in ultrasound. The data were not normally distributed (D'Agostino and Pearson test). For further analysis a two-tailed Wilcoxon matched pairs test was used (Figure 2), demonstrating a median of differences of 0.11 cm 3 , which was not significant (p = 0.0595). To take into account that some of the values were negative and thus the median of differences might be misleading, we also determined the median of the magnitude of the differences, which was 0.40 cm 3 . Descriptive analysis of the segmented tumor volumes revealed a mean tumor volume of 13.6 ± 16.0 cm 3 (mean ± SD) and a median of 8.5 cm 3 in MRI, whereas it was 13.5 ± 16.0 cm 3 (mean ± SD) with a median of 8.8 cm 3 , when segmented in ultrasound. The data were not normally distributed (D'Agostino and Pearson test). For further analysis a two-tailed Wilcoxon matched pairs test was used (Figure 2), demonstrating a median of differences of 0.11 cm 3 , which was not significant (p = 0.0595). To take into account that some of the values were negative and thus the median of differences might be misleading, we also determined the median of the magnitude of the differences, which was 0.40 cm 3 . The mean Dice coefficient C DSC was 0.68 ± 0.22 (mean ± SD) with a median of 0.75. As demonstrated in Figure 3, the Dice coefficient ranged from 0 (case no. 31) to 0.88 (case no. 11).

Tumor Object Characteristics
When looking at the cases with a Dice coefficient below 0.5, it is noteworthy that the median tumor size (segmented in MRI) was significantly (p = 0.0001, two-tailed Mann-Whitney test) smaller in this subgroup (0.7 cm 3 vs. 9. The mean Dice coefficient CDSC was 0.68 ± 0.22 (mean ± SD) with a median of 0.75. As demonstrated in Figure 3, the Dice coefficient ranged from 0 (case no. 31) to 0.88 (case no. 11). When looking at the cases with a Dice coefficient below 0.5, it is noteworthy that the median tumor size (segmented in MRI) was significantly (p = 0.0001, two-tailed Mann-Whitney test) smaller in this subgroup (0.7 cm 3 vs. 9.8 cm 3 ). MRI-segmented tumor volume and Dice coefficient correlated positively (r = 0.59, p = 0.0002, nonparametric Spearman correlation). The same applied when the Dice coefficient was correlated to the volume of the segmented US objects (r = 0.58, p = 0.0003, nonparametric Spearman correlation).
The Hausdorff distance was 8.1 ± 2.9 mm (mean ± SD), respectively, 8.1 mm (median), whereas the Euclidean distance of the geometric centers of gravity was 3.7 ± 2.5 mm (mean ± SD) with a median of 3.0 mm, see Figure 4.

Influence of Registration
The mean TRE was 0.84 ± 0.36 mm (mean ± SD) with a median of 0.79 mm, in three cases the TRE could not be quantified. The TRE did neither correlate with the Dice coefficient (r = 0.14, p = 0.4369, Spearman correlation) nor the Hausdorff distance (r = −0.04, p = 0.8242, Spearman correlation). TRE and the Euclidean distance of the geometric center of gravity correlated negatively (r = −0.3616, p = 0.0420, Spearman correlation), demonstration only a week association of the registration accuracy and brain shift.  The Hausdorff distance was 8.1 ± 2.9 mm (mean ± SD), respectively, 8.1 mm (median), whereas the Euclidean distance of the geometric centers of gravity was 3.7 ± 2.5 mm (mean ± SD) with a median of 3.0 mm, see Figure 4. When looking at the cases with a Dice coefficient below 0.5, it is noteworthy that the median tumor size (segmented in MRI) was significantly (p = 0.0001, two-tailed Mann-Whitney test) smaller in this subgroup (0.7 cm 3 vs. 9.8 cm 3 ). MRI-segmented tumor volume and Dice coefficient correlated positively (r = 0.59, p = 0.0002, nonparametric Spearman correlation). The same applied when the Dice coefficient was correlated to the volume of the segmented US objects (r = 0.58, p = 0.0003, nonparametric Spearman correlation).
The Hausdorff distance was 8.1 ± 2.9 mm (mean ± SD), respectively, 8.1 mm (median), whereas the Euclidean distance of the geometric centers of gravity was 3.7 ± 2.5 mm (mean ± SD) with a median of 3.0 mm, see Figure 4.

Influence of Registration
The mean TRE was 0.84 ± 0.36 mm (mean ± SD) with a median of 0.79 mm, in three cases the TRE could not be quantified. The TRE did neither correlate with the Dice coefficient (r = 0.14, p = 0.4369, Spearman correlation) nor the Hausdorff distance (r = −0.04, p = 0.8242, Spearman correlation). TRE and the Euclidean distance of the geometric center of gravity correlated negatively (r = −0.3616, p = 0.0420, Spearman correlation), demonstration only a week association of the registration accuracy and brain shift.

Influence of Registration
The mean TRE was 0.84 ± 0.36 mm (mean ± SD) with a median of 0.79 mm, in three cases the TRE could not be quantified. The TRE did neither correlate with the Dice coefficient (r = 0.14, p = 0.4369, Spearman correlation) nor the Hausdorff distance (r = −0.04, p = 0.8242, Spearman correlation). TRE and the Euclidean distance of the geometric center of gravity correlated negatively (r = −0.3616, p = 0.0420, Spearman correlation), demonstration only a week association of the registration accuracy and brain shift.

Discussion
Despite an enormous increase in ultrasound image quality in recent years, recognizing anatomical structures in oblique and narrow US sections can become tedious. The first attempts to address this issue date as far back as 1993, when Koivukangas et al. used intraoperative ultrasound as a control for reformatted CT and MRI image sets during neurosurgical procedures by establishing a common axes on which preoperative and intraoperative images where aligned [42]. However, only when trackable US probes were developed, US and navigational systems were able to coalesce to integrated systems [22,43,44], which allowed displaying preoperative and intraoperative image sets as overlays or side-by-side [23,28].
This baseline study was conducted to describe the obvious differences in object appearances in iUS and preoperative MRI at the earliest possible surgical stage after craniotomy. We chose to acquire the iUS-scan before dural opening, to keep the influence of brain shifting as low as possible and to enable a comparison of the imaging modalities under optimized conditions. Initial patient registration was achieved by an iCT scan and fusion to the preoperative MRI data sets with high accuracy (mean ± SD TRE: 0.84 ± 0.36 mm), which is comparable to our previously published data [35]. The US probes were precalibrated, meaning that they were fully implemented into the navigational system, and thus a co-registration was automatically established. This kind of MRI and US fusion is based on spatial position information and can be categorized as a rigid or non-deformable registration [45,46]. Alternatively, rigid registration can be performed image-based using different algorithms to match structures in MRI and US [47,48], but any non-deformable registration approach does not tackle the issue of brain deformation and distortion. However, rigid co-registration allowed the assessment of the spatial deviation and deformation of structures segmented in both modalities. Statistical analysis of the segmented tumor volumes in preoperative MRI and intraoperative US revealed a very similar mean ± SD (preMRI: 13.6 ± 16.0 cm 3 ; iUS: 13.5 ±16.0 cm 3 ) and median (preMRI: 8.5 cm 3 ; iUS: 8.8 cm 3 ), which did not differ significantly. The median of the magnitude of the differences was 0.40 cm 3 . These results indicate both modalities being comparable with respect to tumor delineation. This might be partially fostered by the study design that only included brain metastases, whose tumor boundaries could be clearly identified in both T1-enhanced MRI and US. Including gliomas in this study, especially low-grade gliomas, on the other hand, would have made tumor identification and subsequent analysis of data dependent on the segmentation much more difficult.
Spatial overlap was assessed using the Dice coefficient, which was 0.68 ± 0.22 (mean ± SD) with a median of 0.75, where 1.0 would indicate a perfect match and 0 no association at all [36]. Consistently, the Dice coefficient correlated positively to the tumor size. Even though the Dice coefficient is thought to allow straightforward comparison, interpretation of the coefficient in this study must take into account several factors. First, the calculated measures are influenced by segmentation inaccuracy, as shown by Zou et al., who found in a series of repeated segmentation of the prostate peripheral zone in patients with prostate cancer, a mean Dice coefficient of 0.883 in 1.5 T MRI and 0.838 in 0.5 T MRI segmentations [37]. 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, Nitsch et al. compared automatic segmentations of the falx 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 ± 2.5 mm (mean ± 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, Hill et al. reported a dural displacement of 1.2 mm right after craniotomy [12]. However, Ohue et al. found a brain shift of 3.4 ± 1.9 mm (range: 0.4-10.8 mm) at the tumor margins before dural opening, which was increased to 5.1 ± 2.7 mm (range: 0.9-15.7 mm) before tumor removal [23] and Letteboer 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]. Sastry 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 ± 0.33 mm (mean ± 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: ±2.9 mm) and a median of 8.1 mm. Interestingly, our computed value was lower than in the above citied study of Nitsch 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. Another drawback is the fact that the quality of the precalibration, respectively, the co-registration of the US probes was not sufficiently assessed for each case. When reflecting the results of the accuracy measurement in a phantom, which showed an offset of 1.3 mm, compared to the Euclidean distance of the geometric centers of gravity (mean ± SD: 3.7 ± 2.5 mm) and the partially small tumor volumes, we see the need for further improvement in future applications. However, we believe the influence of the precalibration error to be within a just acceptable range.
Summing up the results of this study, we found the segmented tumor objects in i3D US clearly delineated the tumor boundaries and was comparable to preMRI segmentations. Dice coefficient and Euclidean distance of geometric centers of gravity indicated a moderate brain shift even before dural opening, and the Hausdorff distance of 8.1 mm suggested a good resemblance of the objects with only moderate deformation. Both the measured shift and deformation might be partially affected by the pressure applied with the US probe during image acquisition and calibration inaccuracy to some extent. An additional feature of i3D US, which was not evaluated in this study, is the possibility of updating the navigation during surgery based on i3D US. The simplest way to do so is to rely solely on the i3D US data sets rigid co-registration of preoperative and intraoperative imaging is limited by brain deformation or distortion. Approaches addressing this problem utilize deformable methods [49], different mathematical algorithms [7], and deep learning with convolutional neural networks to improve registration and segmentations [50]. Yet, all of these share the common feature of an increase in computation time and registration uncertainty [51], making them less suitable for routine use in brain tumor resection when compared to fully implemented rigidly co-registrated US.
Taken together, even under optimal conditions, we found differences in object appearances in both modalities. Nevertheless, we conclude that our study contributes to the body of literature showing that the rigid co-registration of i3D US utilizing a precalibrated trackable transducer offers a valuable supplement to multimodal neuronavigational set-ups with high imaging quality allowing a precise depiction of pathologies, whereby it is straightforward in use and allows convenient integration in preexisting systems and workflows. Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
Taken together, even under optimal conditions, we found differences in object appearances in both modalities. Nevertheless, we conclude that our study contributes to the body of literature showing that the rigid co-registration of i3D US utilizing a precalibrated trackable transducer offers a valuable supplement to multimodal neuronavigational set-ups with high imaging quality allowing a precise depiction of pathologies, whereby it is straightforward in use and allows convenient integration in preexisting systems and workflows.