Description: This paper compares several commonly used state-of-the-art ensemble-based data assimilation methods in a coherent mathematical notation. The study encompasses different methods that are applicable to high-dimensional geophysical systems, like ocean and atmosphere and provide an uncertainty estimate. Most variants of Ensemble Kalman Filters, Particle Filters and second-order exact methods are discussed, including Gaussian Mixture Filters, while methods that require an adjoint model or a tangent linear formulation of the model are excluded. The detailed description of all the methods in a mathematically coherent way provides both novices and experienced researchers with a unique overview and new insight in the workings and relative advantages of each method, theoretically and algorithmically, even leading to new filters. Furthermore, the practical implementation details of all ensemble and particle filter methods are discussed to show similarities and differences in the filters aiding the users in what to use when. Finally, pseudo-codes are provided for all of the methods presented in this paper.

Description: The relation between the Agulhas Current retroflection location and the magnitude of Agulhas leakage, the transport of water from the Indian to the Atlantic Ocean, is investigated in a high-resolution numerical ocean model. Sudden eastward retreats of the Agulhas Current retroflection loop are linearly related to the shedding of Agulhas rings, where larger retreats generate larger rings. Using numerical Lagrangian floats a 37 year time series of the magnitude of Agulhas leakage in the model is constructed. The time series exhibits large amounts of variability, both on weekly and annual time scales. A linear relation is found between the magnitude of Agulhas leakage and the location of the Agulhas Current retroflection, both binned to three month averages. In the relation, a more westward location of the Agulhas Current retroflection corresponds to an increased transport from the Indian Ocean to the Atlantic Ocean. When this relation is used in a linear regression and applied to almost 20 years of altimetry data, it yields a best estimate of the mean magnitude of Agulhas leakage of 13.2 Sv. The early retroflection of 2000, when Agulhas leakage was probably halved, can be identified using the regression.

Description: Time series of transports in the Agulhas region have been constructed by simulating Lagrangian drifter trajectories in a 1/10 degree two-way nested ocean model. Using these 34 year long time series it is shown that smaller (larger) Agulhas Current transport leads to larger (smaller) Indian-Atlantic inter-ocean exchange. When transport is low, the Agulhas Current detaches farther downstream from the African continental slope. Moreover, the lower inertia suppresses generation of anti-cyclonic vorticity. These two effects cause the Agulhas retroflection to move westward and enhance Agulhas leakage. In the model a 1 Sv decrease in Agulhas Current transport at 32 degrees S results in a 0.7 +/- 0.2 Sv increase in Agulhas leakage

Description: In prostate cancer with biochemical failure after therapy, current imaging techniques have a low detection rate at the prostate-specific antigen (PSA) levels at which targeted salvage therapy is effective. 11 C-choline and 18 F-fluoromethylcholine, though widely used, have poor sensitivity at low PSA levels. 68 Ga-PSMA (Glu-NH-CO-NH-Lys-(Ahx)-[ 68 Ga- N,N '-bis[2-hydroxy-5-(carboxyethyl)benzyl]ethylenediamine- N,N '-diacetic acid]) has shown promising results in retrospective trials. Our aim was to prospectively compare the detection rates of 68 Ga-PSMA versus 18 F-fluoromethylcholine PET/CT in men who were initially managed with radical prostatectomy, radiation treatment, or both and were being considered for targeted therapy. Methods: A sample of men with a rising PSA level after treatment, eligible for targeted treatment, was prospectively included. Patients on systemic treatment were excluded. 68 Ga-PSMA, 18 F-fluoromethylcholine PET/CT, and diagnostic CT were performed sequentially on all patients between January and April 2015, and the images were assessed by masked, experienced interpreters. The findings and their impact on management were documented, together with the results of histologic follow-up when feasible. Results: In total, 38 patients were enrolled. Of these, 34 (89%) had undergone radical prostatectomy and 4 (11%) had undergone radiation treatment. Twelve (32%) had undergone salvage radiation treatment after primary radical prostatectomy. The mean PSA level was 1.74 ± 2.54 ng/mL. The scan results were positive in 26 patients (68%) and negative with both tracers in 12 patients (32%). Of the 26 positive scans, 14 (54%) were positive with 68 Ga-PSMA alone, 11 (42%) with both 18 F-fluoromethylcholine and 68 Ga-PSMA, and only 1 (4%) with 18 F-fluoromethylcholine alone. When PSA was below 0.5 ng/mL, the detection rate was 50% for 68 Ga-PSMA versus 12.5% for 18 F-fluoromethylcholine. When PSA was 0.5–2.0 ng/mL, the detection rate was 69% for 68 Ga-PSMA versus 31% for 18 F-fluoromethylcholine, and when PSA was above 2.0, the detection rate was 86% for 68 Ga-PSMA versus 57% for 18 F-fluoromethylcholine. On lesion-based analysis, 68 Ga-PSMA detected more lesions than 18 F-fluoromethylcholine (59 vs. 29, P 〈 0.001). The tumor-to-background ratio in positive scans was higher for 68 Ga-PSMA than for 18 F-fluoromethylcholine (28.6 for 68 Ga-PSMA vs. 9.4 for 18 F-fluoromethylcholine, P 〈 0.001). There was a 63% (24/38 patients) management impact, with 54% (13/24 patients) being due to 68 Ga-PSMA imaging alone. Histologic follow-up was available for 9 of 38 patients (24%), and 9 of 9 68 Ga-PSMA–positive lesions were consistent with prostate cancer ( 68 Ga-PSMA was true-positive). The lesion positive on 18 F-fluoromethylcholine imaging and negative on 68 Ga-PSMA imaging was shown at biopsy to be a false-positive 18 F-fluoromethylcholine finding ( 68 Ga-PSMA was true-negative). Conclusion: In patients with biochemical failure and a low PSA level, 68 Ga-PSMA demonstrated a significantly higher detection rate than 18 F-fluoromethylcholine and a high overall impact on management.

Description: 68 Ga-PSMA (prostate-specific membrane antigen) PET/CT is increasingly used in men with prostate-specific antigen (PSA) failure after radical prostatectomy (RP) to triage those who will benefit from salvage radiation treatment (SRT). This study examines the value of PSMA-informed SRT in improving treatment outcomes in the context of biochemical failure after RP. Methods: We analyzed men with rising PSA after RP with PSA readings between 0.05 and 1.0 ng/mL, considered eligible for SRT at the time of PSMA. For each patient, clinical and pathologic features as well as scan results, including site of PSMA-positive disease, number of lesions, and a certainty score, were documented. Subsequent management, including SRT, and most recent PSA were recorded using medical records. Treatment response was defined as both PSA ≤ 0.1 ng/mL and 〉50% reduction in PSA. Multivariate logistic regression analysis was performed for association of clinical variables and treatment response to SRT. Results: One hundred sixty-four men were included. PSMA was positive in 62% ( n = 102/164): 38 of 102 in the prostatic fossa, 41 of 102 in pelvic nodes, and 23 of 102 distantly. Twenty-four patients received androgen-deprivation therapy (ADT) and were excluded for outcomes analysis. In total, 99 of 146 received SRT with a median follow-up after radiation treatment of 10.5 mo (interquartile range, 6–14 mo). Overall treatment response after SRT was 72% ( n = 71/99). Forty-five percent ( n = 27/60) of patients with a negative PSMA underwent SRT whereas 55% (33/60) did not. In men with a negative PSMA who received SRT, 85% ( n = 23/27) demonstrated a treatment response, compared with a further PSA increase in 65% (22/34) in those not treated. In 36 of 99 patients with disease confined to the prostate fossa on PSMA, 81% ( n = 29/36) responded to SRT. In total, 26 of 99 men had nodal disease on PSMA, of whom 61% ( n = 16/26) had treatment response after SRT. On multivariate logistic regression analysis, PSMA and serum PSA significantly correlated with treatment response, whereas pT stage, Gleason score, and surgical margin status did not. Conclusion: PSMA PET is independently predictive of treatment response to SRT and stratifies men into a high treatment response to SRT (negative or fossa-confined PSMA) versus men with poor response to SRT (nodes or distant-disease PSMA). In particular, a negative PSMA PET result predicts a high response to salvage fossa radiotherapy.