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Source paper: PMC12408821 Vascular network geometric properties, including vessel diameters, lengths and branching angles, are key metrics for quantitative and objective comparison of vascular networks in health or disease .
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Thus, we extracted and reported the metrics for the human kidney vasculature.
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Data were grouped according to truncated Strahler order (Fig. 4 , Table 1 ) to enable quantitative comparison to rat and other human organ data.
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The raw data for each segment, which may serve as inputs for computational models, have been provided as Supplementary Information .
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Table 1 Human kidney vascular branching metrics by truncated Strahler generation (means with standard deviation are shown) Truncated Strahler order No. of segments Radium (µm) Length µm × 10 Tortuosity Length:diameter Vol.
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× 10 µm Branching angle IVD µm × 10 1 5105 45 ± 5 2.6 ± 1.7 1.2 ± 0.20 57.4 ± 36 0.18 ± 0.22 129 ± 28 1.1 ± 0.4 2 3030 56 ± 15 1.8 ± 1.4 1.1 ± 0.16 32.3 ± 26 0.21 ± 0.46 128 ± 29 0.9 ± 0.4 3 1295 95 ± 37 1.8 ± 1.4 1.1 ± 0.14 20.2 ± 18 6.7 ± 10.3 128 ± 29 1.1 ± 0.4 4 516 165 ± 60 2.3 ± 1.9 1.1 ± 0.13 14.6 ± 12 25.5 ± 34.9 135 ± 29 1.4 ± 0.5 5 150 294 ± 110 3.3 ± 2.6 1.1 ± 0.05 12.2 ± 9.4 11.3 ± 17.1 142 ± 25 1.8 ± 0.7 6 69 684 ± 250 4.3 ± 3.1 1.1 ± 0.06 6.5 ± 4.5 84.6 ± 104 149 ± 21 2.9 ± 0.7 7 20 839 ± 251 7.2 ± 4.9 1.1 ± 0.05 8.5 ± 4.8 223 ± 302 148 ± 24 6.1 ± 1.5 8 4 877 ± 188 8.1 ± 4.7 1.1 ± 0.07 9.6 ± 6.3 227 ± 159 141 ± 6 4.7 ± 1.5 9 1 2923 669 1.0 0.2 180 - - Source paper: PMC12408821 Further quantitative analysis of the human kidney vascular network revealed that, as truncated Strahler order increased, there was a reduction in the ratio of vessel length:diameter (Fig. 4B ).
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In contrast, the mean radius (Fig. 4E ) and inter-vessel distance increased (Fig. 4F ).
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Tortuosity did not vary significantly with truncated Strahler order (Fig. 4D ); with most segments possessing tortuosity close to 1, thus implying limited deviation from a straight path.
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These findings are consistent with anticipated trends for a healthy tissue, wherein a vascular network is assumed to be a fractal structure, with branching pattern driven by optimised delivery of blood to the whole organ.
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Interestingly, within truncated Strahler orders 8–6, the mean branching angle was approximately 150°, decreasing to 130° for truncated Strahler orders 3–1 (Fig. 4C ).
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Importantly, the latter value of 130° is the predicted optimal theoretical branching angle for volume-constrained vascular growth .
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Source paper: PMC12408821 Simulation of kidney haemodynamics has previously been performed using μCT data from the rat kidney.
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To facilitate comparison between existing rat data and our human HiP-CT results, we aligned our network based on the Strahler order allocated to the segmental arteries, thus aligning Strahler order 9 in the previously published rat dataset to truncated Strahler order 8 of our human data.
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We then related normalised vessel metrics from each species, matching anatomically defined vessel types.
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The expected increase in vessel radius with order followed a similar trend between human and rat kidney (Fig. 5A ).
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However human kidney vessel radii increased to a greater extent across Strahler orders than in the rat kidney, evaluated based on a fit of log(radius) to Strahler order (Fig. 5B ), ( p < 0.0001 Sum-of-F test F (DFn, DFd) = 700.6 (2, 12)).
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To provide additional insights into this difference observed between human and rat kidneys, we extracted radial scaling exponents of the human vascular network.
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The radial scaling exponent provides insight into how the network has structurally developed with respect to its functions such as the efficiency of blood flow and nutrient delivery to meet metabolic demands and minimise flow resistance .
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Exponents of 0.33 and 0.5 each have theoretical bases in different models, (i) Murray’s law (expected exponent of 0.33 for all the whole network, derived from considering the energy balance between energy of flow and viscous drag), (ii) the West-Brown-Enquist (WBE) model which predicts 0.5 in larger vessels and 0.33 in smaller vessels, resulting from balancing the energy for metabolic distribution of blood across a fractal-like network.
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However, deviations from these exponent values and other variants of vascular scaling models have been widely reported .
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Source paper: PMC12408821 Previously in the rat kidney, Nordsletten et al. demonstrated a deviation from Murray’s law by ~1% for the rat kidney .
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Figure 5Ci shows the cubed parent radius plotted against the cube sum of the child radii for our dataset, the theoretical Murray’s law is overlaid (orange hatched) to allow qualitative comparison to previous literature.
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To quantitatively evaluate whether our data are better represented by Murray’s law (expected radial scaling exponent 0.33) the WBE model (radial scaling exponent 0.33 in small and 0.5 in large vessels) or another model, we extracted the number of downstream terminal ends of the network for each vessel segment and the radius of that segment.
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Through a log-log plot of the data (Fig. 5Cii ), the theoretical value of the exponent a was found to be 0.55.
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This value is higher than Murray’s law and closer to the WEB model and the values found in ref.
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for the human pulmonary artery system.
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Source paper: PMC12408821 We then sought to compare heterogeneity in morphology of the human kidney vasculature according to anatomical regions within the human kidney, which may reflect specialised vascular functions.
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For example, the medulla of the kidney is predominantly vascularised by vasa recta; specialised capillaries which possess low oxygen tension.
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This configuration leads to physiological hypoxia that is inherent to the medulla’s urinary concentration mechanisms .
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Further reflecting the importance of vascular morphology is the longstanding hypothesis, supported by blood oxygenation level-dependent MRI studies , that vascular rarefaction in CKD results in hypoxia within the kidney cortex.
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In turn, this stimulates neighbouring cells into a pro-fibrotic phenotype, manifesting in replacement of normal kidney tissue by fibrosis and heralding loss of organ function .
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Thus, regional heterogeneity of vascular morphology is fundamental for sustaining local microenvironmental features, such as hypoxia, that influence specialised organ functions.
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However, regional heterogeneity in vascular structure has not been quantitatively explored in the human kidney.
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Source paper: PMC12408821 Leveraging the contrast-free approach of HiP-CT, we were able to segment the kidney into known anatomical compartments, including hilum, medulla, intramedullary kidney columns and cortex (Fig. 6Ai ).
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We compartmentalised the vascular network according to these anatomical compartments (Fig. 6Aii ).
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The total tissue volume of each compartment, in addition to the number of vessels, length, radius and volume of segmented vessels within each compartment, were quantified (Table 2 ).
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Most of the tissue volume of the human kidney was occupied by the cortex (63.7%) as compared with the medulla (23.5%), hilum (8.7%) or intermedullary pillars (4.1%).
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The number of segments of the vascular network within each compartment followed this trend.
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We then quantified (Fig. 6Aiii ) and mapped (Fig. 6Bi–Biii ) the inter-vessel distance, compartmentalised by hilum, medulla, cortex, and intermedullary pillars.
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Mean inter-vessel distances were calculated for each compartment, assessing the distribution of inter-vessel distance from the renal artery down to interlobular arteries (Table 2 ).
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The medulla had the highest inter-vessel distance.
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Whilst the cortex had a comparatively smaller inter-vessel distance than medulla and hilum, a large standard deviation for this value was noted within the cortex.
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This is illustrated by the heatmap in Fig. 6Bi, Bii , which identified small areas with inter-vessel distance >4.5 mm localised towards the kidney capsule.
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Table 2 Human kidney vascular branching metrics compartmentalised by spatial zone with the organ Cortex Medulla Hilum Intermedullary pillars Organ Volume of tissue, ×10 µm (% of total) 8.70 (63.7%) 3.21 (23.5%) 1.18 (8.66%) 0.57 (4.14%) 13.7 (100%) Number of segments* (% of total) 6141 (60.27%) 554 (5.4%) 151 (1.5%) 727 (7.1%) 10,190 (100%) Mean segment length, µm ± STD 1999 ± 1374 1493 ± 1113 3993 ± 3568 1720 ± 1386 2260 ± 1720 Mean segment radius, µm ± STD 48 ± 12.6 95 ± 49 496 ± 335 136 ± 80 71 ± 87 Mean inter-vessel distances, ×10 µm ± STD 1.10 ± 0.677 1.55 ± 0.881 1.55 ± 1.312 0.664 ± 0.543 1.2 ± 0.833 Mean segment volume, ×10 µm ± STD 0.148 ± 0.116 0.623 ± 1.12 69.0 ± 147 1.73 ± 4.48 1.65 ± 20.6 Mean segment tortuosity ± STD 1.14 ± 0.17 1.08 ± 0.13 1.08 ± 0.1 1.1 ± 0.12 1.15 ± 0.18 *Segments that crossed over two regions were excluded.
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Source paper: PMC12408821 Human kidney vascular branching metrics compartmentalised by spatial zone with the organ Source paper: PMC12408821 Owing to the limited volume of tissue that can be imaged at high resolution using ex vivo 3D imaging modalities, such as μCT and lightsheet microscopy, and insufficient resolution of technologies routinely used in clinical practice, such as CT and MRI; it had previously been impractical to capture the vascular network of the intact adult human kidney beyond the very largest arteries.
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Here, using a synchrotron-phase contrast tomography technique, termed HiP-CT, we were able to image, segment and quantify the human kidney arterial network within an intact human kidney from renal artery to down to the level of interlobular arteries, without the need for exogenous contrast agents.
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Source paper: PMC12408821 With HiP-CT, we show that vessels which have not been imaged in the intact human kidney previously, namely the interlobar to interlobular arteries, occupy approximately 20% of the arterial vascular volume of the organ.
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By imaging VOIs in the intact kidney at higher resolution, and aligning this with our lower resolution scans, we further demonstrate that, akin to rat , and varying from the traditional hierarchy of the kidney vasculature observed in nephrology and anatomical textbooks, glomeruli in humans can originate from non-terminal arterioles.
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In further comparisons with the rat kidney vasculature, we found that although similar trends in vascular radius were seen, there was a significant difference in the change in radius with vessel order between species.
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This may be explained by the larger radii range in the human kidney between renal artery and afferent arterioles, relative to the volume of the human kidney; but could also be dependent on the difference in approach to calculation of the Strahler order for each study.
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Source paper: PMC12408821 We also found that the exponent for radial scaling is closer to the WBE model (0.5) than Murray’s law value of 0.33.
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This is broadly in alignment with previous work , where exponents of 0.47–0.58 were found for trees with vascular diameters ≥200 µm and 70–20≥ µm, respectively.
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Wide variation between theoretical exponents and those derived from real imaging data is widely accepted and often attributed to the complexity of real vessels including factors such as mechanical strain, the elastic nature of arteries during pulsatile flow and turbulent flow patterns .
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Specific to the kidney, while Murray’s law or the WBE model assume idealised flow-optimised network, or ideal fractal scaling, kidneys likely exhibit non-optimal but functional scaling due to their high-resistance, low-compliance vascular network which is needed to support hemodynamic fluctuations due to changes in glomerular filtration and autoregulation .
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However, it should also be noted that due to the ex vivo nature of HiP-CT, and the consequent lack of vascular tone, extracting such radial scaling laws from these data may have additional sources of error compared to in vivo imaging techniques.
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Source paper: PMC12408821 Deviations from theoretical laws support the idea that vascular systems adapt based on tissue-specific demands rather than universal optimisation principles.
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This idea can be further supported by examining regional heterogeneity of vascular morphology in different anatomical zones of the kidney.
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The segmentation of hilar, medullary, intramedullary and cortical zones of HiP-CT images from the same kidney support this hypothesis.
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For example, the increased inter-vessel distance observed within the medulla, as compared to the cortex, is pertinent.
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The medulla experiences physiological hypoxia, and increased inter-vessel distance, paired with the oxygen diffusion limit, provides a potential anatomical rational for this phenomenon, in addition to the unique solute and gas exchange mechanisms that take part in this region of the kidney .
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The data provided in this study, and resultant insights into how morphology of the kidney vasculature varies by different renal compartments, could shed light on the mechanisms underpinning the unique cellular and molecular adaptations of specialised endothelia across the kidney vascular network .
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Our pipeline and the HiP-CT data provide a framework to potentially study how the vasculature within each anatomical compartments is differentially affected by kidney disease, with potential for understanding the basis of vascular rarefaction and pathological hypoxia .
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Further studies with higher resolution HiP-CT or with microfill of the human kidney could potentially preserve vessel radius more accurately and resolve capillaries allowing extension of the work.
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Such information is important to acquire in human samples, as it could potentially influence simulations of haemodynamics, oxygenation or drug delivery ; and generation of synthetic vessel trees for in silico experiments .
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Source paper: PMC12408821 The human kidney vasculature is exquisitely specialised to meet the physiological demands of the kidney.
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Underpinning this specialisation is the cellular and molecular heterogeneity of endothelial beds within the renal vasculature , of which we are gaining an increasing understanding due to the advent of improved techniques such as single-cell and spatially-resolved transcriptomics.
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The rapid and recent advances in our understanding of cellular and molecular heterogeneity of the kidney vasculature has not been matched by structural insights, likely because of limitations in imaging technologies.
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We have overcome many of these limitations using HiP-CT, where the exceptional contrast, coupled with appreciable spatial resolution at scale, allows us to capture and segment the 3D vascular architecture of an intact human kidney.
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Furthermore, within high-resolution VOIs, HiP-CT allows glomeruli and afferent arterioles to be segmented and, in selected cases, be connected back to the vascular tree of the intact whole organ.
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Source paper: PMC12408821 Robust and reproducible analysis of vascular networks relies on the careful application of a multi-stage image processing pipeline, which we have outlined in this paper.
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We have developed an approach which utilises multiple annotators and comparison to higher resolution scans to validate segmentation accuracy as a crucial first step.
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Following segmentation, we have developed a skeletonisation approach, which can be scaled to large datasets, and also provides corrections for radius estimation when portions of the vasculature have collapsed.
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Finally, we applied a truncated Strahler ordering to the vessel spatial graph, providing a meaningful ordering system with respect to known anatomical vessel descriptions, as well as facilitating quantification of individual vessels within the vascular hierarchy.
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By developing and applying this pipeline, we have produced quantitative vascular branching metrics from an intact human organ for the first time.
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These metrics exceed other studies on cadaveric human kidney cast and dye injections, which report arterial branches corresponding to truncated Strahler orders 7–9 .
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We provide quantitative comparison between the human kidney vasculature and that of the rat, the latter of which has been key for inputs to generate biophysical models of kidney haemodynamics .
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Source paper: PMC12408821 The quantitative analysis pipeline performed in this paper serves multiple purposes.
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First, it allows the whole kidney vasculature dataset to be represented in a single spatial graph, comprising only kilobytes of data.
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This spatial graph, which is provided as Supplementary Data , is readily quantifiable.
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Whereas prior simulations of kidney haemodynamics and perfusion have relied on seminal μCT studies performed in rat, we provide, for the first time, a map of the kidney arterial network from renal artery to interlobular arteries.
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We demonstrated our segmentation approach to be accurate, with 97% of vessels of >50 µm radius captured across the intact human kidney.
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These data thus provide vital inputs for biophysical modelling of kidney physiology.
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The data also serves as a reference to study kidney diseases, in which vascular rarefaction is a pathophysiological hallmark .
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The pipeline described could be used to generate vascular maps from multiple kidneys, or other human organs, potentiating spatial ‘atlases’ of human organ vasculature across healthy and pathological contexts.
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Beyond these, our openly available dataset has immediate practical applications, such as providing inputs for bioprinting and tissue engineering of artificial kidneys or planning surgical resection of kidney tumours whilst preserving kidney function .
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These datasets can also be used as a tool for medical education and training, as well as for the creation and advancement of surgical methods.
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Source paper: PMC12408821 There are several limitations of this work.
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Firstly, the low throughput of HiP-CT vascular segmentation warrants discussion.
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Here, we present the complete analysis from a single kidney as a framework for future studies of kidneys in health and disease or other intact human organs.
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The accuracy of the segmentation, however, lays a foundation for tools such as machine learning methods for automated segmentation of blood vasculature from imaging data .
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HiP-CT imaging still cannot resolve afferent arteriole or capillary resolution across the whole organ, meaning that the contributions of peritubular capillaries or vasa recta are not incorporated.
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This also creates challenges for applying ordering schemes such as the Strahler order, where the true 0th order is the capillary bed.
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Previous approaches to estimating the distance of a terminal end in a truncated network from the capillary bed have relied on utilising diameter measurements of vessels to iteratively update the Strahler order of terminal ends .
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This facilitates the creation of a connectivity matrix to estimate the downstream network .
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However, diameter estimation is less accurate for HiP-CT, where vascular collapse makes radius estimates less consistent than, for example, when using microfill techniques.
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Using the high-resolution VOIs, we also demonstrated that glomeruli frequently emanate from non-terminal arterioles.
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Without connecting on the order of 1000s of glomeruli back to the main vascular tree as performed for small portions of rat kidney , a connectivity matrix cannot be developed.
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However, the utility of any vascular classification scheme relies upon the ability to distinguish morphologically distinct vessel types, and to show logarithmic relations between morphology and classification orders .
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Our truncated Strahler approach creates vessel orders which are able to separate morphologically distinct vessels (Supplementary Note 4 ), as well as demonstrating logarithmic relationships for radius and vessel number.
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We also found that truncated Strahler ordering also aligns well with the anatomically defined vessel classifications, as was the case for rat kidney .
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