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Given a complex analytic germ $(X, 0)$ in $(\mathbb C^n, 0)$, the standard Hermitian metric of $\mathbb C^n$ induces a natural arc-length metric on $(X, 0)$, called the inner metric. We study the inner metric structure of the germ of an isolated complex surface singularity $(X,0)$ by means of an infinite family of numerical analytic invariants, called inner rates. Our main result is a formula for the Laplacian of the inner rate function on a space of valuations, the non-archimedean link of $(X,0)$. We deduce in particular that the global data consisting of the topology of $(X,0)$, together with the configuration of a generic hyperplane section and of the polar curve of a generic plane projection of $(X,0)$, completely determine all the inner rates on $(X,0)$, and hence the local metric structure of the germ. Several other applications of our formula are discussed in the paper., Comment: Proposition 5.3 strengthened, exposition improved, some typos corrected, references updated. 42 pages and 10 figures. To appear in Geometry & Topology

To evaluate the clinical value of 68Ga-PSMA PET/CT negativity in patients with biochemical recurrent prostate cancer (BCR). One hundred three BCR patients (median age, 70 years; median PSA, 0.47 ng/mL) with negative 68Ga-PSMA PET/CT, followed up for at least 1 year, were retrospectively identified in a database of 1003 consecutive patients undergoing 68Ga-PSMA PET/CT for BCR. Clinical recurrence (CR) was determined or excluded on follow-up imaging selected as per clinical practice. Clinical recurrence-free survival (CRFS) was computed from the date of negative 68Ga-PSMA PET/CT to the date of evident disease; frequencies of CRFS were described as per ISUP patient subset (subset 1: ISUP grades 1 and 2; subset 2: ISUP grade 3; subset 3: ISUP grades 4 and 5) and other conventional variables. In 57 patients out of 103 (55.3%), CR was detected in the prostatic fossa (45.6%), nodes (38.6%), and bone (15.8%). The median CRFS was 15.4 months (range, 12.1–20.5), with a CRFS at 12 months in 61.4% of cases (range, 50.9–70.4) whereas the 24-month CRFS was 34.8% (range, 24–45.8). ISUP subset 1 benefited from significantly longer CRFS compared to subset 2 and subset 3 (median CRFS, 20.5 months, 12.6 months, and 12.1 months, respectively). ISUP subset 3 had significantly poorer 24-month CRFS (9.3%) compared to subset 1 (47.8%) and subset 2 (33.5%). At the univariate and multivariate analyses, the ISUP subset was the only significant risk factor for clinical relapse; ISUP subset 3 and subset 2 patients held a higher risk of CR compared to subset 1 patients (HR of 2.75 [1.35–5.57] for subset 3 versus subset 1; HR of 2.08 [1.11–3.88] for subset 2 versus subset 1). 68Ga-PSMA PET/CT negativity in early BCR patients (PSA

Introduction: 68Ga-PSMA is a labelled ligand to a membrane protein overexpressed in many prostate cancer cells and has raised its interest to be highly specific in PET imaging for detection and staging of prostate cancers. DW-MRI is a standard technique that provides quantitative information about tumor cellularity and tissue structure is a useful tool for the detection and staging of prostate cancer in clinical practice. This study investigates the correlation between SUVmax and tumour heterogeneity computed from DWI sequences. Materials and Methods: 17 patients (age range, 49-75 years; mean, 64.3 years) of a prospective study aiming at multi-cohort investigation for clinical impact of mp-3TMRI and 68Ga-PSMA PET/CT in diagnosis of clinically-significant prostate cancer and presurgical staging. After co-registering MRI and PET sequences, Regions of Interest (ROIs) were manually delineated around prostate in MRI/T2 and the cancer lesion in the dominant sequence (high values of DWI or T2). SUVmax was computed on PET images and 60%-threshold of SUVmax was used for lesion contouring. A compound texture feature related to tumour heterogeneity (Hc) was computed within prostate ROIs in DWI and the outcome represented with colorimetric maps. The highest regions were extracted by automatic contouring. Average Hc (DWI) and SUVmax (PET) were computed on the co-registered slices and the Spearman rank correlation (ρ) was assessed. Results: SUVmax ranges from [1.6-101.0] and Hc through [37.9 -50.6]. Regions highlighted by Hc are usually much greater than those detected by SUVmax thresholding and always include the region outlined by radiologists. 13 patients show ρ≥0.7, 3 with ρ≥0.5 and 1 only with ρ≥0.25. For 11 patients (65% of cases) the amount of PET slices pointing out malignant SUV peaks is greater than DWI slices showing high Hc values, with Hc ROIs better depicting tumour extent. For 3 patients (17.5%) PET and Hc-DWI show equivalent performance in tumour detection and in 3 cases only, Hc points out more slices with suspect tumour ROIs. However, in all cases SUV and Hc show the same trend, with the highest values around central slices and a much greater increasing rate for SUV. Conclusions: The outcomes of this study reveal a rank correlation between heterogeneity of cellularization and the expression of the membrane receptor of PSMA. The reason of such correlation requires deeper investigations and could be confirmed after examining a wider cohort. Hc result a promising compound feature for outlining malignant ROIs extent to be employed together with PET sequences for validating tumour side. A deeper analysis is required for those few cases showing weak or even poor correlation between SUV and Hc.

We characterize sandwiched singularities in terms of their link in two different settings. We first prove that such singularities are precisely the normal surface singularities having self-similar non-archimedean links. We describe this self-similarity both in terms of Berkovich analytic geometry and of the combinatorics of weighted dual graphs. We then show that a complex surface singularity is sandwiched if and only if its complex link can be embedded in a Kato surface in such a way that its complement remains connected., 35 pages

We study the Galois descent of semi-affinoid non-archimedean analytic spaces. These are the non-archimedean analytic spaces which admit an affine special formal scheme as model over a complete discrete valuation ring, such as for example open or closed polydiscs or polyannuli. Using Weil restrictions and Galois fixed loci for semi-affinoid spaces and their formal models, we describe a formal model of a $K$-analytic space $X$, provided that $X\otimes_KL$ is semi-affinoid for some finite tamely ramified extension $L$ of $K$. As an application, we study the forms of analytic annuli that are trivialized by a wide class of Galois extensions that includes totally tamely ramified extensions. In order to do so, we first establish a Weierstrass preparation result for analytic functions on annuli, and use it to linearize finite order automorphisms of annuli. Finally, we explain how from these results one can deduce a non-archimedean analytic proof of the existence of resolutions of singularities of surfaces in characteristic zero., Comment: Exposition improved and minor modifications. 37 pages. To appear in Math. Z

Lu-DOTATATE (Lu-PRRT) is a valid therapeutic option in differentiated pancreatic neuroendocrine tumors (P-NETs). FDG PET seems to be an important prognostic factor in P-NETs. We evaluated the efficacy of Lu-PRRT and the role of FDG PET in 60 patients with advanced P-NETs. From March 2008 to June 2011, 60 consecutive patients with P-NETs were enrolled in the study. Follow-up lasted until March 2016. Eligible patients were treated with two different total cumulative activities (18.5 or 27.8 GBq in 5 cycles every 6–8 weeks), according to kidney and bone marrow parameters. Twenty-eight patients received a mean full activity (FA) of 25.9 GBq and 32 a mean reduced activity (RA) of 18.5 GBq. The disease control rate (DCR), defined as the sum of CR+PR+SD was 85.7 % in the FA group and 78.1 % in the RA group. Median progression-free survival (mPFS) was 53.4 months in the FA group and 21.7 months in the RA group (P = 0.353). Median overall survival (mOS) was not reached (nr) in FA patients and was 63.8 months in the RA group (P = 0.007). Fifty-five patients underwent an FDG PET scan before Lu-PRRT, 32 (58 %) showing an increased FDG uptake in tumor sites. mPFS was 21.1 months in FDG PET-positive patients and 68.7 months in the FDG PET-negative group (P

Urea-based prostate-specific membrane antigen (PSMA) ligands labelled with 68Ga or 177Lu are new tracers with great potential for theranostic approaches in prostate cancer. However, clinical studies have shown that the kidneys are one of the off-target organs along with the salivary and lacrimal glands. In the kidneys, PSMA is physiologically expressed in the apical epithelium of the proximal tubules, and mannitol acts as an osmotic diuretic in these tubules. We investigated the potential of mannitol to reduce renal uptake of 68Ga-PSMA. Kidney uptake (SUVmax) was calculated in nine patients undergoing 68Ga-PSMA PET/CT at baseline (b-PET/CT) and after intravenous infusion of 500 ml of 10% mannitol (m-PET/CT). Two different infusion schemes for mannitol were used: (1) 500 ml mannitol was infused over 40 min after 68Ga-PSMA administration (A-infusion) and (2) 250 ml mannitol was infused over 15 min before and again after 68Ga-PSMA administration (B-infusion). In patients receiving the A-infusion, mean SUVmax increased by 11.9% and 7.4% in the right and left kidney, respectively. In patients receiving the B-infusion, mean SUVmax decreased by 24.3% and 22.4% in the right and left kidney, respectively. Our preliminary findings indicate that mannitol may play a role in reducing off-target 68Ga-PSMA renal uptake. Administration of the osmotic diuretic should be rapid and start before 68Ga-PSMA injection. These results warrant dosimetric studies in patients treated with 177Lu-PSMA to find the best scheme for mannitol administration.

We define normalized versions of Berkovich spaces over a trivially valued field $k$, obtained as quotients by the action of $\mathbb R_{>0}$ defined by rescaling semivaluations. We associate such a normalized space to any special formal $k$-scheme and prove an analogue of Raynaud's theorem, characterizing categorically the spaces obtained in this way. This construction yields a locally ringed $G$-topological space, which we prove to be $G$-locally isomorphic to a Berkovich space over the field $k((t))$ with a $t$-adic valuation. These spaces can be interpreted as non-archimedean models for the links of the singularities of $k$-varieties, and allow to study the birational geometry of $k$-varieties using techniques of non-archimedean geometry available only when working over a field with non-trivial valuation. In particular, we prove that the structure of the normalized non-archimedean links of surface singularities over an algebraically closed field $k$ is analogous to the structure of non-archimedean analytic curves over $k((t))$, and deduce characterizations of the essential and of the log essential valuations, i.e. those valuations whose center on every resolution (respectively log resolution) of the given surface is a divisor., Several corrections and improvements. New result added, Theorem 10.8, proving a characterization of essential valuations. 51 pages. To appear in Transactions of the AMS

We study whether a given tropical curve $\Gamma$ in $\mathbb{R}^n$ can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented by $\Gamma$. We give an affirmative answer to this question for a large class of tropical curves that includes all trivalent tropical curves, but also many tropical curves of higher valence. We then deduce that for every metric graph $G$ with rational edge lengths there exists a smooth algebraic curve in a toric variety whose analytification has skeleton $G$, and the corresponding tropicalization is faithful. Our approach is based on a combination of the theory of toric schemes over discrete valuation rings and logarithmically smooth deformation theory, expanding on a framework introduced by Nishinou and Siebert., Comment: 16 pages, introduction improved and other minor modifications, to appear in IMRN, comments very welcome!

The aim of this work was to preliminarily evaluate the sensitivity, specificity, positive predictive value, negative predictive value, and overall accuracy of 68Ga-citrate PET/CT in a population of patients with suspected bone infections. Methods: We enrolled 31 patients with suspected osteomyelitis or diskitis who underwent a total of forty 68Ga-citrate PET/CT scans. The results were compared with different combinations of diagnostic procedures (MRI, radiography, CT, or white blood cell scintigraphy), biopsy (when diagnostic), and follow-up data (at least 1 y) to determine the performance of 68Ga-citrate PET/CT. Results: We found a sensitivity of 100%, a specificity of 76%, a positive predictive value of 85%, a negative predictive value of 100%, and an overall accuracy of 90%. Conclusion: Although preliminary, these data confirm a possible role for 68Ga-citrate in the diagnosis of bone infections, especially in consideration of its favorable characteristics.

Background SF-12™ Health Survey, and European Organisation for Research and Treatment of Cancer Quality of life Questionnaire-C30 are the two main questionnaires proposed and validated for assessing the quality of life in chronic pancreatitis. Aims To evaluate the role of the information furnished by both the SF-12™ Health Survey and European Organisation for Research and Treatment of Cancer Quality of life Questionnaire-C30 questionnaires, and to determine which of these two questionnaires may be considered more efficacious, in clinical practice, in describing the quality of life of patients with chronic pancreatitis. Patients We studied 163 consecutive patients with proven chronic pancreatitis. Methods The Italian version of the SF-12™ Health Survey and the Italian neutral version of the European Organisation for Research and Treatment of Cancer Quality of life Questionnaire-C30 Version 3.0 questionnaires were administered. Results Pancreatic pain was the only clinical variable able to significantly impair the SF-12™ Health Survey component summaries as well as all domains of the European Organisation for Research and Treatment of Cancer Quality of life Questionnaire-C30, while body mass index was positively related to the physical component summary-12 and to the domains of the European Organisation for Research and Treatment of Cancer Quality of life Questionnaire-C30. A high level of reliability of the domains/scores of the two questionnaires in evaluating the quality of life in patients with chronic pancreatitis was found and two main factors were identified. These two factors were mainly related to the two SF-12™ Health Survey summary components. Conclusions From a practical point of view, the SF-12™ Health Survey is more reliable and easier to use in routine clinical practice than the European Organisation for Research and Treatment of Cancer Quality of life Questionnaire-C30.

In recent years, a number of articles have been published on the treatment of acute pancreatitis in experimental models and most of them concerned animals with mild disease. However, it is difficult to translate these results into clinical practice. For example, infliximab, a monoclonal TNF antibody, was experimentally tested in rats and it was found to significantly reduce the pathologic score and serum amylase activity and also to alleviate alveolar edema and acute respiratory distress syndrome; however, no studies are available in clinical human acute pancreatitis. Another substance, such as interleukin 10, was efficacious in decreasing the severity and mortality of lethal pancreatitis in rats, but seems to have no effect on human severe acute pancreatitis. Thus, the main problem in acute pancreatitis, especially in the severe form of the disease, is the difficulty of planning clinical studies capable of giving reliable statistically significant answers regarding the benefits of the various proposed therapeutic agents previously tested in experimental settings. According to the pathophysiology of acute pancreatitis, the efficacy of the drugs already available, such as gabexate mesilate, lexipafant and somatostatin should be re-evaluated and should be probably administered in a different manner. Of course, also in this case, we need adequate studies to test this hypothesis.