For over a century, there has been great interest in understanding the effect of nephron number in human health and disease. Increasing evidence indicates a relationship between the number of nephrons and susceptibility to kidney disease.12345–6 Brenner and colleagues postulated that individuals with a congenital or acquired deficit in nephrons would have a greater risk of developing hypertension or kidney disease.7
Nephron number varies widely in humans, from 210,000 to 2.7 million at autopsy.8910111213–14 Nephron endowment is affected by genetic, epigenetic, and environmental factors, in utero and ex utero, and nephron number likely varies by sex and ethnicity.1516–17 Humans naturally lose nephrons as they age, but nephron loss may be accelerated due to systemic diseases or medical interventions.18,19 Although nephron number cannot yet be measured directly in living humans, surrogate markers have been used. These include birth weight, prematurity status, kidney size,15,18 glomerulomegaly, and reduced glomerular density in biopsy.20
Nephron number may also be an important marker of the health of kidneys donated for transplantation. In preclinical models, nephron number influences allograft outcomes.21,22 In the clinic, markers to predict the likelihood of graft failure after transplant are typically based on patient demographics. These factors have been incorporated into the Kidney Donor Profile Index (KDPI),23 which has been widely adopted to guide allocation. An unintended consequence of this scoring system has been that nearly 50% of donated kidneys with KDPI >85 are discarded.242526–27 Histologic evaluation of biopsied tissue has also been used to measure kidney quality.28,29 However, several studies suggest a histologic evaluation may not provide substantial improvement in determining organ quality.303132–33 There is still an unmet need to accurately measure donor kidney health.
To investigate the link between nephron number and human health, several groups have estimated nephron number in patients for whom a kidney biopsy was a part of clinical care. They used glomerular density estimated from the biopsy and cortical volume measured from radiologic imaging.343536–37 In a study of 39 subjects who underwent a protocol allograft biopsy 4 months after transplant, estimated nephron number correlated with GFR.38 Denic and colleagues also estimated nephron number to report the average single-nephron GFR in healthy patients being evaluated for living kidney donation.37 The cohort was large, and the authors limited their conclusions to population-level, not individual-level, inferences.
In smaller studies, accurate estimates of nephron number from biopsies are potentially limited by intrakidney variation in glomerular density. Although variations have been observed in animals,39,40 little is known about the intrakidney variation in glomerular density within a single human kidney or between subjects.41,42 Moreover, the effect of these variations on estimates of nephron number in individuals or across populations has not been quantified. To date, it is unknown how accurately a single biopsy can be used to predict nephron number in an individual, or how many subjects or biopsies would be required to detect differences in nephron number between populations.
Here, we investigated the variation of estimated nephron number derived from biopsy in the human kidney. We examined kidneys from deceased donors that had been rejected for transplantation, allowing us to perform multiple needle biopsies in each kidney. We estimated nephron number by measuring glomerular density from each biopsy37 and measured cortical volume by magnetic resonance imaging (MRI). We then used cationized ferritin enhanced–MRI (CFE-MRI)41,4344–45 to visualize the three-dimensional (3D) distribution of glomeruli and glomerular densities. We created “virtual biopsies” from the CFE-MR images to determine whether there were locations within the kidney where glomerular density would most accurately represent nephron number in the whole kidney. Finally, we compared measurements from needle and virtual biopsy to determine the precision and accuracy in nephron number estimated from biopsies in individuals and between cohorts of subjects.
Kidneys from deceased donors, declined for transplant, were acquired from the International Institute for the Advancement of Medicine (Edison, NJ). The institutional review boards (University of Virginia, Washington University in St. Louis, and Arizona State University) determined this project was exempt from review because the deidentified kidneys did not qualify as human-subject research. The kidneys were perfused with heparinized saline, stored in a kidney preservation solution, and transported on ice.
Cohort 1 (CF1, CF2, and CF3): the renal artery was catheterized and the kidneys were perfused with 120 ml of 1× PBS followed by 30 mg/100 g kidney weight of cationic ferritin (CF, cationized ferritin from horse spleen; Sigma-Aldrich).41 The unbound CF was removed from vasculature by perfusion with 120 ml of PBS, followed by 10% neutral buffered formalin at 4°C.
Cohort 2 (CF21, CF38, and CF60): CF-labeled glomeruli could be accurately detected and measured at higher magnetic field scanner using a lower dose of CF (not shown). Three additional kidneys were perfused with 120 ml of kidney perfusion solution, followed by CF (5.75 mg/100 g kidney weight), kidney perfusion solution, and formalin. Kidneys were stored in 10% neutral buffered formalin at 4°C.
All kidneys were immersed in PBS for ≥24 hours before MRI scans and were imaged in a sealed plastic container of PBS.
Kidneys from Cohort 1 were scanned using a Bruker 7T/35 MRI scanner with a 72 mm ID quadrature transmit/receive radiofrequency coil (Bruker, Billerica, MA).41 We performed T2*-weighted 3D gradient echo (3D-GRE) with TE/TR = 39/20 ms, flip angle of 30°, field-of-view=6 × 6×10.5 cm3, 512 × 512×896 matrix, and voxel resolution of 117 × 117×117 µm3. Five averages (NA=5) were acquired, with total acquisition time of approximately 10.5 hours/kidney. Glomerular number (Nglom) from CFE-MRI was validated using dissector-fractionator stereology,4647–48 and was previously published.41
Kidneys from Cohort 2 were scanned using a Bruker 9.4T/20 MRI scanner with an 86 mm ID quadrature transmit/receive radio frequency coil (Bruker, Billerica, MA). The higher magnetic field strength allowed a shorter imaging time compared to Cohort 1.41 The 3D-GRE experiment was conducted using the following parameters: TR/TE=100/15 ms, flip angle of 30°, and NA=1. Due to differences in kidney size, field-of-view and matrix size of 5.5 × 6×9.2 cm3 and 470 × 512×786, 5 × 5.5 × 9.2 cm3 and 428 × 470×786, or 5 × 6×10 cm3 and 426 × 470×856 were used for CF21, CF38, and CF60, respectively; thus, voxel resolution in all kidneys was 117 × 117×117 µm3. Imaging time was 5.5–6.5 hours/kidney.
Needle biopsies (n=8–11 biopsies/kidney) were performed using a clinical grade needle (Monopty Disposable Core Biopsy Instrument, 16 g × 10 cm, 22 mm penetration; Tempe, AZ, USA). Kidney tissue was dehydrated in a graded series of ethanol solutions, embedded in paraffin, sectioned at 4 μm, and mounted on glass slides (Figure 1Ai). Sections were stained with Periodic acid–Schiff, counterstained in Mayer’s hematoxylin, and imaged using a Grundium Ocus scanner (Grundium, Tampere, Finland) with a 20× objective (pixel resolution of 0.48 µm).
A series of virtual biopsies were created to simulate needle biopsies. A virtual biopsy represents the “best case scenario,” in which the challenges of needle biopsy are avoided. Such challenges include tissue fragmentation or a small number of sampled glomeruli. Virtual biopsies were created using the 3D MR images using the “Extract Subvolume” module in Amira 2019.3 (Thermo Fisher Scientific, Waltham, MA) at approximately equal distances around the cortex of each kidney. Four clusters of virtual biopsies were taken from the upper and lower poles and five clusters from the midpole. The differentiation between three poles is highlighted in Figure 1Bi. Each cluster consisted of 12–18 virtual biopsies (Figure 1Bi). The distance between neighboring virtual biopsies was <0.5 mm and a glomerulus was not included in more than one biopsy. Each virtual biopsy volume was 7.17–10.25 mm3. We performed 211–227 virtual biopsies/kidney. A representative virtual biopsy is shown in Figure 1, Bii and Biii.
Estimation of Nglom
We estimated glomerular number from needle (Nglom_NB) and virtual biopsies (Nglom_VB). We used CFE-MRI to estimate whole kidney glomerular number (Nglom_CFE).
Calculations were on the basis of previously published methods that used nonsclerotic glomerular number and cortical volumes measured from imaging to estimate whole kidney Nglom.34,37 We excluded globally sclerotic glomeruli and sections containing <4 glomeruli or areas >2 mm2, consistent with previous studies.34,37 We did not exclude glomeruli with focal sclerosis, mesangial expansion, or other pathology. Image segmentation and histologic analyses were performed using Amira with confirmation, (JRC, pediatric nephrologist). Figure 1Ai shows the segmentation of nonsclerotic glomeruli (NSG, blue outline) and cortical area (black outline). In each kidney, the cortex was segmented from the medulla. We used “Material Statistics” in Amira to measure total number of NSG (), total area of NSG (), and cortical area of needle biopsy (). Partial NSG were counted as 0.5 NSG. We calculated using37,49:
We estimated Nglom from the needle biopsy (Nglom_NB) using:
Equation 2where CV is the volume of the kidney cortex estimated from CFE-MRI (mm3). We found that dehydration in a section of tissue from the cortex for paraffin embedment resulted in volume shrinkage of 25%. The volume shrinkage was calculated from samples measured by caliper as previously described.50 We used a coefficient of 1.25 to correct Nglom_NB for volume shrinkage. We did not correct for loss of perfusion pressure because all measurements were made ex vivo.
Kidney CV was estimated from MRI. The cortex was manually segmented from the medulla for each kidney in Amira. Figure 1, Aii–Aiv shows this segmentation and a 3D visualization. Glomerular number in each virtual biopsy volume was measured using MIPAR 3.2.2 (MIPAR Software LLC, Worthington, OH).51 A single two-dimensional (2D) image from one representative biopsy was windowed and leveled manually. Next, an adaptive threshold was used to identify CF-labeled glomeruli. The same algorithm was applied to all 2D sections of virtual biopsies within the kidney using Batch Processor in MIPAR. The total glomerular number in the biopsy volume was measured using the watershed function in the 3D Toolbox in MIPAR. To estimate Nglom_VB, we used:
Equation 3where Nglom_vb is the number of segmented glomeruli in the individual biopsy, and BV is the volume of the virtual biopsy (mm3). Glomeruli detected at the boundaries of the volume of the virtual biopsy were always considered to be within the volume. Although Nglom_VB can be systematically overestimated by including glomeruli on the surface of the volume, we do not expect this to affect the variability of Nglom across multiple virtual biopsies.
We estimated variability (defined as the observed difference in Nglom in each kidney) using needle and virtual biopsies from different regions:
Where Nglom_(NB or VB) is the glomerular number measured from needle biopsy (Equation 1) or virtual biopsy (Equation 3), Nglom_CFE is the total number of glomeruli in the whole kidney as measured by CFE-MRI. We used a two-sample student’s t test and statistical significance was defined by P<0.05.
We examined reliability to determine how much of the observed variation in measured Nglom between subjects can be attributed to actual differences in glomerular number rather than sampling error. For example, a reliability of 30% means 30% of the variance in the observed Nglom is due to a true difference in glomerular number; the remaining 70% of the variance is due to measurement error. This analysis was based on a replication reliability study52 and was used to establish the effect of measurement error on statistical power for comparison between groups of subjects. A detailed description of the reliability analysis is presented in the Supplemental Analysis.
We calculated the distribution of differences between Nglom (NB or VB) and Nglom_CFE. We defined the bias and variance in biopsy-measured Nglom as the median and variance of this distribution. We used a likelihood ratio test to determine the mean difference between Nglom_VB and Nglom_CFE, the variability of the difference between clusters, and the variability of the difference within clusters.
We used a two-sample t test with a power of 80% and P<0.05 to calculate the total number of kidneys and biopsies from each kidney required to detect a significant difference in mean Nglom_NB between the two cohorts.
Donor characteristics are shown in Table 1.
Table 1. -
||Cause of Death
||Final Serum Creatinine (mg/dl)
Distribution and Variability of Nglom Estimated from Needle and Virtual Biopsies
Figure 2A shows the cortical volumes, whole kidney Nglom measured from CFE-MRI (Nglom_CFE), Nglom estimated from needle biopsies (Nglom_NB), and from virtual biopsies (Nglom_VB). As the number of biopsies per kidney increases, the average Nglom of all biopsies approximates Nglom_CFE. The slope of linear regression between Nglom_NB and Nglom_CFE was 1.17 (R2=0.40), whereas the slope for Nglom_VB and Nglom_CFE was 1.05 (R2=0.91) (Figure 1S, Supplemental Figure 1).
Figure 2, Bi and Bii shows the distributions of Nglom_NB and Nglom_VB. Figure 2, Biii–Biv shows the variability in Nglom in individual kidneys from different biopsies (Equation 4). Nglom was overestimated from a needle biopsy by <144% or underestimated by up to 71% (Figure 2Aiii). Nglom was overestimated from a virtual biopsy by up to 90% or underestimated by up to 80% (Figure 2Aiv). There was no statistically significant difference in variability between Nglom_NB and Nglom_VB (two-sample t test, P=0.07), sho wn in Figure 2C. Figure 2D shows Nglom calculated from within clusters of virtual biopsies across the kidney. Within clusters, mean Nglom was overestimated by 12%–53% and underestimated by 8%–40%.
Reliability and Accuracy of Needle and Virtual Biopsies
The reliability of needle biopsy was approximately 30%, indicating that 30% of the observed variance in Nglom was due to differences in Nglom between kidneys and 70% was due to measurement error. The bias in Nglom_NB was -56,000, with a variance of 1,770,000 (Equation 6, Supplemental Material); this indicates that needle biopsy is relatively unbiased, but highly variable. The mean Nglom_NB approached Nglom_CFE with increasing numbers of needle biopsies. However, >200 needle biopsies would be required to be 95% certain the average Nglom_NB was within 20% of whole kidney Nglom_CFE. If a single needle biopsy were taken from the cortex of a kidney, the probability is <15% that Nglom_NB would be within 20% of Nglom_CFE.
Reliability is directly related to sample size.52Table 2 shows the total number of kidneys and biopsies from each kidney required to detect a significant difference (P<0.05) in mean Nglom_NB between two groups of subjects. For example, eight kidneys with 14 biopsies/kidney, 10 kidneys with five biopsies/kidney, or 12 kidneys with three biopsies/kidney would be required in each of the two groups to detect a statistically significant (P<0.05) difference in Nglom_NB of around 310,000. When limited to a single biopsy, >100 kidneys per group would be needed to detect a difference in Nglom_NB between two groups.
Table 2. -
Sample size required to detect a significant difference (P
<0.05) in Nglom
between two groups of subjects. Values in the table represent the difference in mean Nglom
(divided by 100,000) that can be detected between two groups of n
kidneys each with m
|Number of Biopsies per Kidney (m)
||Number of Kidneys per Group (n)
The reliability of virtual biopsy was approximately 60%, indicating that 60% of the variance in observed Nglom_VB was due to true differences in Nglom between kidneys; 40% of the variance was due to sampling error. The bias in Nglom_VB was 78,000 with variance 474,000 (Equation 6, Supplemental Material).
Although we observed differences in variability and mean Nglom_VB across the kidney (Figure 2D), these differences were consistent with random variation. We found the variability in the difference between Nglom_VB and Nglom_CFE, within and between the clusters of virtual biopsies, was not statistically significant (likelihood ratio test=4.1, 6 df, P=0.66). There was no preferred location for biopsy to more accurately predict Nglom. On the basis of this study, approximately four virtual biopsies would be needed to be 95% certain the average Nglom_VB was within 20% of Nglom_CFE. The Nglom_VB estimated from single virtual biopsy has a 60% chance to be within 20% of Nglom_CFE.
We investigated the use of biopsies to estimate nephron number in individual kidneys, and how these data may inform the rigor and reproducibility of future clinical studies using the outcome of estimated nephron number. We used needle biopsies and created comparable virtual biopsies using CFE-MRI to estimate Nglom across the whole kidney. We used published methods to estimate Nglom from needle biopsies.34,37,49 This work generated several key findings. For a single needle biopsy, there was a 15% chance to be within 20% of the whole kidney Nglom estimated by CFE-MRI. A large number of biopsies (>200 biopsies) was needed to accurately approximate Nglom in an individual kidney. There was no biopsy location that could systematically reduce the variability in Nglom.
This work shows that estimated nephron number in an individual kidney from a single biopsy can often be imprecise, with potential error of >90%. A single biopsy appears insufficient to accurately predict nephron number in an individual. However, needle biopsies in aggregate can accurately estimate Nglom when the number of subjects in each cohort is large enough to reveal differences between the populations (Table 2).
The reliability of the estimate of Nglom from a single virtual biopsy was better than from a single needle biopsy. This may be due to the larger number of glomeruli observed in virtual biopsy compared with needle biopsy. This larger sample leads to a smaller sampling error and greater reliability of the virtual biopsy compared with needle biopsy. Greater reliability of Nglom_VB compared with Nglom_NB may be also attributed to difference in sampling between the two methods. For example, a histologic section may be fragmented, contain only a few glomeruli, or predominantly medulla.37 Virtual biopsies contained only cortex with observed glomeruli. The virtual biopsy provides the minimum expected error in estimation of Nglom. Estimates of Nglom from wedge biopsies might exhibit similar inaccuracies, because wedge biopsies are similar in size to the clusters of virtual biopsies.
This study has several limitations. It is possible that histology and CFE-MRI measure different subpopulations of glomeruli, because CF labels only perfused, functional glomeruli.53 However, Nglom from CFE-MRI and stereology were similar in three kidneys (squares and circles, respectively, Figure 2, Bi and Bii),41 and, as number of biopsies per kidney increased, the average Nglom of all biopsies approximated the Nglom_CFE. We observed a large distribution of Nglom estimated from single needle biopsies, as shown in Figure 2Bi. Future studies may reveal populations of subjects for whom these error rates are lower or more spatially defined. Therefore, the estimates from virtual biopsy here may provide a basis for comparison to other populations. This study was limited to six kidneys, but they exhibited a wide range in KDPI scores typical of both transplanted and rejected kidneys. There were also large differences in final serum creatinine (Table 1), with unknown baseline kidney function before the death of the patients. Finally, although the kidneys examined here represent a range of donor characteristics (KDPI, 26–100), they may not reflect the variability measured in Nglom in patients from other demographic groups. There is still a strong need for tools to measure nephron number in living subjects as an early marker for risk of chronic kidney disease.
A relatively large number of biopsies is required to accurately estimate nephron number in an individual human kidney. Although a single biopsy may not be sufficient to accurately predict nephron number in an individual kidney in a clinical setting, it may be used to detect specified differences in nephron number between cohorts of at least approximately 100 subjects.
E.J. Baldelomar and K.M. Bennett are co-owners of XN Biotechnologies. J.R. Charlton and K.M. Bennett are co-owners of Sindri Technologies, LLC. K.M. Bennett reports having a sponsored research agreement with Janssen Pharmaceuticals and XN Biotechnologies, LLC; reports having consultancy agreements with Janssen; reports receiving honoraria from Janssen Pharmaceuticals. K.M. Bennett has a grant from the Mid-America Transplant Foundation; and reports other interests/relationships Nephrodiagnostics (co-owner). S. Beeman reports having an ownership interest in Nephrodiagnostics; and reports receiving honoraria from the Mayo Clinic of Arizona and Vanderbilt University. All remaining authors have nothing to disclose.
This work was supported by National Institute of Diabetes and Digestive and Kidney Diseases grants R01DK111861 and R01DK110622, and National Center for Advancing Translational Sciences grant TL1TR002344 (to E.J. Baldelomar).
We gratefully acknowledge our colleague Dr. John F. Bertram for a critical and constructive review of this work. Studies were performed, in part, using the Small Animal MR Facility of the Mallinckrodt Institute of Radiology, Washington University in St. Louis. K. Bennett, J. Charlton, and D. Morozov designed the study; E. Baldelomar, S. Beeman, J. Charlton, A. Cwiek, K. deRonde, and D. Morozov conducted experiments; M. Conaway, D. Morozov, G. Oxley, and N. Parvin analyzed the data; J. Charlton and K. Bennett supervised the data analysis; K. Bennett, J. Charlton, and D. Morozov drafted and revised the paper; and all authors critically reviewed and edited the manuscript, and approved the final version.
This article contains the following supplemental material online at http://jasn.asnjournals.org/lookup/suppl/doi:10.1681/ASN.2021070998/-/DCSupplemental.
Statistical Analysis. Reliability of needle and virtual biopsies.
Supplemental Figure 1. Linear regression plots.
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