Background: Inhibitors of the sodium-glucose cotransporter 2 (SGLT2) slow the progression of diabetic kidney disease, possibly by reducing the proximal tubule transport workload with subsequent improvement of renal oxygenation. We aimed to test this hypothesis in individuals with type 1 diabetes and albuminuria. Methods: A randomised, double-blind, placebo-controlled, crossover trial with a single 50 mg dose of the SGLT2 inhibitor dapagliflozin and placebo in random order, separated by a two-week washout period. Magnetic resonance imaging (MRI) was used to assess renal R 2 * (a low value corresponds to a high tissue oxygenation), renal perfusion (arterial spin labelling) and renal artery flow (phase contrast imaging) at baseline, three-and six hours from tablet ingestion. Exploratory outcomes, including baroreflex sensitivity, peripheral blood oxygen saturation, peripheral blood mononuclear cell mitochondrial oxygen consumption rate, and biomarkers of inflammation were evaluated at baseline and 12 h from medication. The study is registered in the EU Clinical Trials Register (EudraCT 2019À004,557À92), on ClinicalTrials.gov (NCT04193566), and is completed. Findings: Between February 3, 2020 and October 23, 2020, 31 individuals were screened, and 19 eligible individuals were randomised. Three dropped out before receiving any of the interventions and one dropped out after receiving only placebo. We included 15 individuals (33% female) in the per-protocol analysis with a mean age of 58 (SD 14) years, median urinary albumin creatinine ratio of 46 [IQR 21À58] mg/g and an eGFR of 73 (32) ml/min/1¢73m 2 . The mean changes in renal cortical R 2 * from baseline to six hours were for dapagliflozin -1¢1 (SD 0¢7) s À1 and for placebo +1¢3 (0¢7) s À1 , resulting in a difference between interventions of -2¢3 s À1 [95% CI -4¢0 to -0¢6]; p = 0¢012. No between-intervention differences were found in any other MRI outcomes, physiological parameters or exploratory outcomes. There were no adverse events. Interpretation: A single dose of 50 mg dapagliflozin acutely improved renal cortical R 2 * without changing renal perfusion or blood flow. This suggests improved renal cortical oxygenation due to a reduced tubular transport workload in the proximal tubules. Such improved oxygenation may in part explain the long-term beneficial renal effects seen with SGLT2 inhibitors, but it remains to be determined whether the observed effects can be achieved with lower doses, with chronic treatment and if they occur in type 2 diabetes as well.

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The analysis of point patterns with linear structures is of interest in many applications. To detect anisotropy in such cases, in particular in case of a columnar structure, we introduce a functional summary statistic, the cylindrical K-function, which is a directional K-function whose structuring element is a cylinder. Further we introduce a class of anisotropic Cox point processes, called Poisson line cluster point processes. The points of such a process are random displacements of Poisson point processes defined on the lines of a Poisson line process. Parameter estimation based on moment methods or Bayesian inference for this model is discussed when the underlying Poisson line process is latent. To illustrate the methodologies, we analyze twoand three-dimensional point pattern data sets. The three-dimensional data set is of particular interest as it relates to the minicolumn hypothesis in neuroscience, claiming that pyramidal and other brain cells have a columnar arrangement perpendicular to the surface of the brain.

Background: Spatial characterization of vertical organization of neurons in human cerebral cortex, cortical columnarity or minicolumns, and its possible association with various psychiatric and neurological diseases has been investigated for many years. New method: In this study, we obtained 3D coordinates of disector sampled cells from layer III of Brodmann area 4 of the human cerebral cortex using light microscopy and 140μm-thick glycolmethacrylate sections. A new analytical tool called cylindrical K-function was applied for spatial point pattern analysis of 3D datasets to see whether there is a spatially organized columnar structure. In order to demonstrate the behaviour of the cylindrical K-function, the result from brain tissues was compared with two models: A homogeneous Poisson process exhibiting complete spatial randomness, and a Poisson line cluster point process. The latter is a point process model in 3D space, which exhibits spatial structure of points similar to minicolumns. Results: The data show in three out of four samples nonrandom patterns in the 3D neuronal positions with the direction of minicolumns perpendicular to the pial surface of the brainwithout a priori assuming the existence of minicolumns. Comparison with existing methods: Studies on columnarity are difficult and have mainly been based on two-dimensional images analysis of thin sections of the cerebral cortex with the a priori assumption that minicolumns existed. Conclusions: A clear difference from complete spatial randomness in the data could be detected with the new tool, the Correspondence to: Jens R. Nyengaard, Professor of Stereology and EM Laboratory,