this method was applied to segment the kidney arterial network from the intact human kidney from the imaging data at 50 µm per voxel, and portions of the same network in the 13 and 5. 2 µm per voxel datasets, approximately 250 – 300 h were needed to segment the kidney in this way. a second approach to independently and quantitatively validate the segmentation of the lowest resolution data was performed using segmented vois of the higher resolution, 13 µm per voxel dataset. here, the 13 µm per voxel vois were rigidly registered to the whole organ volume using the affine registration toolkit ( amira - avizo ) ( see supplementary note 1. 1, supplementary fig. 2 and supplementary tables 3 and 4 ). overlapping portions of the 13 µm voxel segmentations and 50 µm per voxel datasets were extracted, and the 50 µm per voxel datasets were upsampled to the resolution of the 13 µm voxel dataset. an overlap measure, termed topological precision and recall score, following paetzold et al., was applied ( see supplementary note 2. 1 and supplementary fig. 3 ). to quantify branching metrics of the human kidney vasculature, the segmented 3d vascular network at 50 µm per voxel was skeletonised using the centreline tree algorithm in amira - avizo v2021. 1. the choice of skeletonisation algorithm and the parameterising of the algorithm were optimised by utilising the super - metric approach, outlined by walsh and berg et al. ( tube parameters: slope = 4 and zeroval = 10, see supplementary note 2. 2 and supplementary fig. 4 for parameter optimisation results ). the resulting spatial graph describes the vessel network in terms of ‘ nodes ’, ‘ points ’, ‘ segments ’, and ‘ subsegments ’. a segment is defined as being between a start and end node, corresponding to either a branching point leading into another segment branch, or a terminal end where no further branches were detectable. between the start and terminal node of each segment lie subsegments with ‘ points ’, marking the start and end of each subsegment. each subsegment has an associated radius and length ( supplementary fig. 6a ). a multiscale smoothing approach was applied to the larger vessels ( those of truncated strahler order greater than 5 ). iterative weighted smoothing was performed, where the smoothed location of any point is given by iteratively calculating weighted average of the current and two neighbour points. parameter values were found empirically as 0. 8, 0. 1 and 15 for the neighbour points, current point and iterations, respectively. this reduced the tortuosity in the larger vessels ( fig. 2, step 4 ), which occurs artefactually due to noise on the surface of the segmented large vessels, and which if uncorrected, impacts severely on the correction for collapsed radius vessels. correction for collapsed vessels was delineated into two distinc t cases. one case is a scenario in which there is a small collapsed portion in an otherwise patent vessel ( supplementary fig. 5bi, bii ). the second case applied when the majority of the vessel is collapsed ( supplementary fig. 5cii ). the reduction in radius in the skeletonised form of the networks can be seen in supplementary fig. 5bii, cii. correction for short subsegment collapsed vessels was performed by plotting radius along each segment. subsegments where the radius was below the 5th percentile for that segment were replaced with the nearest neighbour. for larger collapsed vessels, the process is fully described in the “ results ” section. topological / morphological metrics of the network were calculated from the spatial graph as follows, with code provided at https: / / github. com / hipctproject / skeleton _ analysis: i. branching angle is calculated as either: ( a ) the angle between the two child segments from a common parent segment, or ( b ) the angle between a child segment and its parent segment. in both cases, the vector for the segment of parent and child were calculated between the start node and end node, irrespective of vascular tortuosity. tortuosity is defined as the euclidean distance between start and end node of a segment, divided by the sum of all subsegment lengths. radius is calculated per segment as the mean of all subsegment radii. in cases where larger vessels had fully collapsed ( see “ results ” for details ), the radius was defined as the equivalent radius for a circular vessel with the same length perimeter as the vessel cross - section in the binary image. length is defined as the sum of all subsegment lengths. v. inter - vessel distance is calculated by two approaches to facilitate different analyses. first, using the segmentation binary image, the distance of every non - vessel voxel from its nearest vessel voxel was calculated via a 3d distance transform ( imagej ) applied to the binary vessel segmentation. second, using the skeleton form, the euclidean distance between the midpoint of every segment to its nearest - neighbouring segment midpoint was calculated. branching angle is calculated as either: ( a ) the angle between the two child segments from a common parent segment, or ( b ) the angle between a child segment and its parent segment. in both cases, the vector for the segment of parent and child were calculated between the start node and end node, irrespective of vascular tortuosity. tortuosity is defined as the euclidean distance between start and end node of a segment, divided by the sum of all subsegment lengths. radius is calculated per segment as the mean of all subsegment radii. in cases where larger vessels had fully collapsed ( see “ results ” for details ), the radius was defined as the equivalent radius for a circular vessel with the same length perimeter as the vessel cross - section in the binary image. length is defined as the sum of all subsegment lengths. inter - vessel distance is calculated by two approaches to facilitate different analyses. first, using the segmentation binary image, the distance of every non - vessel voxel from its nearest vessel voxel was calculated via a 3d distance transform ( imagej ) applied to the binary vessel segmentation. second, using the skeleton form, the euclidean distance between the midpoint of every segment to its nearest - neighbouring segment midpoint was calculated. in addition to the above metrics, we also assessed vessel generation, or order, using two methods. first, we used a variation of the centripetal system, known as the strahler ordering system, wherein the most distal, smallest segments are assigned as the first order. if two segments with the same order intersect, the resulting segment has one strahler order greater. alternatively, if two segments with different orders intersect, the higher order of the two is given to the resulting segment ( supplementary fig. 6b ). we used a variant of the strahler order approach, which we term the truncated strahler approach. our 50 µm per voxel dataset does not provide sufficient resolution to image or segment down to afferent arterioles. thus, the network created from this 50 µm per voxel dataset is truncated at the interlobular arteries. we assigned the terminal ends of our network as the first strahler order, as opposed to applying statistical estimates to determine the strahler order of these terminal ends based on diameter relative to the afferent arterioles, as performed previously. detailed discussion of this approach and alternative ordering approaches are discussed in the supplementary note 3. second, we took a centrifugal, or ‘ topological ’ approach, starting with the most proximal artery as generation one. at each branching node the generation is increased, an approached which has been previously utilised ( supplementary fig. 6c ).