A Bayesian analysis of regularised source inversions in gravitational lensing

Strong gravitational lens systems with extended sources are of special interest because they provide additional constraints on the models of the lens systems. To use a gravitational lens system for measuring the Hubble constant, one would need to determine the lens potential and the source intensity distribution simultaneously. A linear inversion method to reconstruct a pixellated source brightness distribution of a given lens potential model was introduced by Warren & Dye. In the inversion process, a regularisation on the source intensity is often needed to ensure a successful inversion with a faithful resulting source. In this paper, we use Bayesian analysis to determine the optimal regularisation constant (strength of regularisation) of a given form of regularisation and to objectively choose the optimal form of regularisation given a selection of regularisations. We consider and compare quantitatively three different forms of regularisation previously described in the literature for source inversions in gravitational lensing: zeroth-order, gradient and curvature. We use simulated data with the exact lens potential to demonstrate the method. We find that the preferred form of regularisation depends on the nature of the source distribution.Comment: 18 pages, 10 figures; Revisions based on referee's comments after initial submission to MNRA

Outcomes of RAdium-223 and SABR vs. SABR for oligomEtastatic prostate caNcerS – The RAVENS Phase II Randomized Trial

The STOMP and ORIOLE randomized clinical trials (RCTs) showed progression-free survival (PFS) benefits of metastasis-directed therapy (MDT) alone without androgen-deprivation therapy (ADT) for oligometastatic hormone-sensitive prostate cancer (omHSPC). However, most patients with bone metastatic (BM) omHSPC recur with additional BM following MDT alone. We hypothesized the addition of BM-targeting alpha-emitter radium-223 (Ra223), approved for treatment of BM castration-resistant prostate cancer (mCRPC), could delay progression of disease. In addition, biomarkers to determine patients who benefit most from MDT are still poorly defined. We report on the first RCT to examine Ra223 and evaluate novel biomarkers in BM omHSPC. In this phase 2 multi-institutional RCT (NCT04037358), men with recurrent omHSPC (≥1 BM & ≤5 radiation fields) were: i) stratified by institution, primary management (radiotherapy vs surgery), PSA doubling time and prior ADT, and ii) randomized 1:1 to stereotactic ablative radiation (SABR) MDT or SABR and 6 monthly cycles of Ra223. The primary endpoint was composite PFS [(PSA ≥ 25% increase and ≥ nadir + 2 ng/mL) and/or (RECIST 1.1 or new lesion on bone scan) and/or (ADT initiation or symptomatic decline)]. Tissue, liquid and imaging correlative studies were obtained and analyzed as biomarkers. From 8/2019-3/2023, 64 patients were randomized (33 to SABR and 31 to SABR/Ra223). Arms were balanced for key covariates. 26 (87%) patients received the full 6 planned cycles of Ra223. Median PFS was 10.2 months with SABR and 10.4 months with SABR/Ra223 (stratified HR 1.7, 95% CI, 0.78-3.69, p = 0.18). 13 patients (20%) experienced grade 3 toxicity (no grade 4 or 5), of which 6 were non-treatment-related, 2 related to SABR, and 5 related to SABR/Ra223 (lymphopenia, back pain). Baseline circulating tumor cells (CTCs) were detected in 55% of patients, and prostate-specific membrane antigen (PSMA)+ CTCs at baseline were prognostic for PFS (p = 0.029). Compared with the observation arm from the ORIOLE RCT, T-cell receptor deep sequencing (TCR-seq) identified significantly more clonotypic expansions between baseline and day 90 with SABR (p = 0.009) and SABR/Ra223 (p = 0.0007). Greater unique productive TCR rearrangements (UPRs) were prognostic for PFS independent of treatment arm (aHR, 0.45; 95% CI, 0.21-0.96; p = 0.04). UPRs were also associated with PFS in the ORIOLE RCT (HR, 0.46; 95% CI, 0.19-1.05; p = 0.07). SABR alone for omHSPC affords PFS benefits, but emergence of additional BM in most patients remains a challenge. We report for the first time that the addition of Ra223 to SABR MDT in this low volume BM state does not delay progression of disease. CTCs are present in omHSPC, and SABR MDT induces a systemic adaptive immune response. We validate the TCR repertoire as a prognostic biomarker in omHSPC treated with SABR MDT. These results underline the importance of RCTs in omHSPC with concurrent collection of biological correlates