## 1 Introduction  
Globlastoma (GBM) and cerebral metastasis (cMET) are the most common brain tumors in adult patients [1]. Reliably differentiating GBM and cMET based on their conventional magnetic resonance imaging (MRI) characteristics has proven difficult [2, 3], as both tumor types can show necrotic centers, contrast-enhancing peripheral areas and peritumoral edema (Figure 1) [4]. However, studies employing advanced MR-imaging techniquesfocusing on the tumor microenvironment and hypoxia-induced changes in the microvasculature found that an elevated cerebral blood flow (CBF) and proxies for increased metabolic activity including a higher resulting cerebral metabolic rate of oxygen (CMRO2) were associated with high-grade gliomas [5; 6]. Therefore, we performed a prospective feasibility study to differentiate between GBM and cMET by using an artificial neural network (ANN) approach for non-invasive estimation of CMRO2, combining quantitative susceptibility mapping (QSM) and the quantitative blood-oxygenation-level-dependent effect (qBOLD). To the best of the authors' knowledge, the concept of using the combined QSM + qBOLD approach for estimation of CMRO2 is new for differentiating these two entities. GBMs constitute between 60% and 70% of all malignant gliomas [7]. Median survival for this highly malignant, infiltratively growing tumor is between 12 and 15 months with optimal treatment [7; 8; 9]. A higher median survival of 22 months has been reported for patients with recurrent glioblastoma undergoing a second surgical therapy [10]. The metabolism of GBM cells is adapted to the increased uptake of nutrients by utilizing aerobic glycolysis [11], thereby linking glucose metabolism to oxygen metabolism [12]. Although benefiting from a greater supply of components for cell upkeep and increased perfusion, GBMs frequently grow too fast for their vasculature, eventually resulting in the typical central necrosis with peripheral ring-enhancement [7; 8]. Similarly, cMETs can also become ring-enhancing after developing a necrotic center due to them outgrowing their blood and nutrient supply [13; 14]. Over 20% of cancer patients develop disseminations to the central nervous system [15]. One study identified that 55% of cMET cases had no known primary at diagnosis [16], while between 30% to 50% of cMETs have been found to first appear as solitary lesions, further complicating their correct identification [2; 17; 18]. Accurately discriminating between GBM and cMET is of great clinical importance because therapy approach and surgical decisions are quite different and directly affect patient outcomes [9; 17; 19]. The current diagnostic standard is an invasive tissue biopsy with subsequent histopathological examination [4], a procedure that is not without inherent risks with a complication rate of about 6% [20]. Figure 1: Axial contrast-enhanced magnetization prepared rapid gradient echo (MP-RAGE) brain images comparing (**a**) a right temporal metastasis from known esophageal cancer in a 50-year-old male patient and (**b**) a glioblastoma in the frontal lobe of the left hemisphere of a 71-year-old male patient. Both tumors show cystic elements and peripheral contrast enhancement, complicating a differentiation based on solely morphological criteria. Hence, the discrimination of GBM and cMET has been attempted many times using a variety of different radiological approaches [4; 19; 21; 22; 23; 24]. Perfusion-based studies showed relative cerebral blood volume (rCBV) in the proximal peritumoral non-enhancing T2 FLAIR hyperintensity (NET2) to be significantly higher in GBM than in cMET [21; 22; 23; 24]. In the distal parts of NET2, GBM and cMET showed similar rCBV values which may reflect a lack of GBM cell infiltration and angiogenesis, supporting the notion that angiogenesis follows a gradient around the tumor and is highest on the surface of the contrast-enhancing tumor region (CET) [24; 25].