## 1 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,when [PERSON] et al. assessed brain movement during neurosurgical procedures. They placed stainless steel reference balls into the tumor and obtained radiographic images, which allowed computer adjustment for tumor location in three-dimensional space [10]. Subsequently, different methods to assess the extent of brain distortion were developed utilizing a navigated pointer [11; 12], microscope [9], optical scanning [13], or analysis of video images [9]. IMRI [14; 15] and iUS allow analyzation of brain shift and deformation of brain or tumor structures [8]. However, brain shift is a dynamic phenomenon occurring during the whole course of tumor resection, which can only be partially compensated by serially updated imaging [16]. While iMRI provides high-quality images, it is not widely available and has its drawbacks, such as an interruption of the surgical procedure, limitations in patient positioning, specific requirements on the organization of the operating theatre and staff [17], and, not least, high costs [18]. IUS, on the other hand, as introduced by [PERSON] et al. in 1982, who described the use of intraoperative brightness modulation (B-mode) ultrasound in 21 neurosurgical procedures [19] and began to use it routinely in their institution [20], provides real-time imaging without or at least with only minimal interruption of surgery, is nowadays widely available, and cost effective [21]. Initially, US did not receive much attention amongst neurosurgeons, probably mostly due to low imaging quality compared to other modalities, a lack of training and only few available specialized devices. The development of new integrative setups, combining neuronavigation and high quality ultrasound drew attention to this intraoperative imaging modality again [22; 23]. A major step forward in the practical application of these systems was the introduction of navigated intraoperative 3D ultrasound (i3D US) [24; 25], which allows updating of the 3D imaging data at several time points during surgery and delivers information on brain shift and resection extent with high specificity [24; 26]. A prerequisite for brain shift determination is an accurate registration of the preoperative imaging (e.g., MRI) and iUS. Using a navigational system, both modalities can be co-registered, reaching an average accuracy of less than 2 mm for deeply located reference structures, which are less prone to shifting, as demonstrated by [PERSON] et al. [27]. Co-registration is based on the assumption of a rigid connection between the coordinate frames of the equipment (e.g., US probe) and the object of interest (patient's head).