Estimating Nephron Number from Biopsies: Impact on Clinical Studies

Abstract

Significance Statement 

Total nephron number is a potentially important marker of susceptibility to kidney disease. This work demonstrates the effect of spatial variation in glomerular density on the estimation of whole-kidney nephron number from biopsy. We show here that a single needle biopsy does not accurately reflect whole-kidney nephron number on an individual level. However, in studies with a large number of subjects or samples, needle biopsies can reveal differences in nephron number between populations. There is a need for new technologies to directly measure nephron number at an individual level.

Background 

Accumulating evidence supports an association between nephron number and susceptibility to kidney disease. However, it is not yet possible to directly measure nephron number in a clinical setting. Recent clinical studies have used glomerular density from a single biopsy and whole kidney cortical volume from imaging to estimate nephron number and single nephron glomerular filtration rate. However, the accuracy of these estimates from individual subjects is unknown. Furthermore, it is not clear how sample size or biopsy location may influence these estimates. These questions are critical to study design, and to the potential translation of these tools to estimate nephron number in individual subjects.

Methods 

We measured the variability in estimated nephron number derived from needle or virtual biopsies and cortical volume in human kidneys declined for transplantation. We performed multiple needle biopsies in the same kidney, and examined the three-dimensional spatial distribution of nephron density by magnetic resonance imaging. We determined the accuracy of a single-kidney biopsy to predict the mean nephron number estimated from multiple biopsies from the same kidney.

Results 

A single needle biopsy had a 15% chance and virtual biopsy had a 60% chance of being within 20% of the whole-kidney nephron number. Single needle biopsies could be used to detect differences in nephron number between large cohorts of several hundred subjects.

Conclusions 

The number of subjects required to accurately detect differences in nephron number between populations can be predicted on the basis of natural intrakidney variability in glomerular density. A single biopsy is insufficient to accurately predict nephron number in individual subjects.

Visual Abstract

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.

Methods

Kidney Preparation

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.

MRI

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 (N_glom) 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.

Biopsies

Needle Biopsies

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).

Figure 1.: (A) Process to calculate N _glom from needle biopsy in a human kidney. (i) Segmentation of the histologic image. The densities of non-sclerotic glomeruli were calculated using area of their cross-sections (blue outline) and the cortical area (black outline) in each biopsy. Scale bar=0.5 mm. The volume of kidney cortex was estimated from 3D CFE-MRI. (ii) CF-labeled glomeruli were visible as black spots. Scale bar=10 mm. (iii) Segmented cortex (red area) and (iv) reconstructed entire kidney cortical volume that was used for N_glom calculation in both needle and virtual biopsy methods. Scale bar=10 mm. (B) Virtual biopsy of a human kidney from CFE-MRI. (i) 3D rendering and virtual resection of whole human kidney labeled with CF. Black ovals represent the clusters of virtual biopsies. White rectangular prisms represent individual virtual biopsies. In total, four cluster of virtual biopsies were created in bottom and upper poles, five clusters were created in midpole. Scale bar=10 mm. (ii) 3D visualization of single virtual biopsy of 10.25 mm³ in size. Black dots are CF-labeled glomeruli. Scale bar=1 mm. (ii) Segmentation of individual glomeruli from (B). Each glomerulus is shown as a colored sphere. Scale bar=1 mm.

Virtual Biopsies

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 N_glom

We estimated glomerular number from needle (N_{glom_NB}) and virtual biopsies (N_{glom_VB}). We used CFE-MRI to estimate whole kidney glomerular number (N_{glom_CFE}).

Needle Biopsies

Calculations were on the basis of previously published methods that used nonsclerotic glomerular number and cortical volumes measured from imaging to estimate whole kidney N_glom.^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 ($\#\mathit{NSG}$), total area of NSG ($TA\_\mathit{NSG}$), and cortical area of needle biopsy ($CA\_NB$). Partial NSG were counted as 0.5 NSG. We calculated $\mathit{NSG}\_\mathit{Density}$ using^37,49: Equation 1$$\mathit{NSG}\_\mathit{Density}=\frac{1}{1.382}.\sqrt{\frac{{\left(\raisebox{1ex}{$\#\mathit{NSG}$}\!\left/ \!\raisebox{-1ex}{$CA\_NB$}\right.\right)}^3}{\raisebox{1ex}{$TA\_\mathit{NSG}$}\!\left/ \!\raisebox{-1ex}{$CA\_NB$}\right.}}$$

We estimated N_glom from the needle biopsy (N_{glom_NB}) using: Equation 2$$N_{\mathit{glom}\_NB}=\frac{\mathit{NSG}\_\mathit{Density}.CV}{1.25}$$where 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 N_{glom_NB} for volume shrinkage. We did not correct for loss of perfusion pressure because all measurements were made ex vivo.

Virtual Biopsies

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 N_{glom_VB}, we used: Equation 3$$N_{\mathit{glom}\_VB}=(N_{\mathit{glom}\_vb}.CV)/BV,$$where N_{glom_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 N_{glom_VB} can be systematically overestimated by including glomeruli on the surface of the volume, we do not expect this to affect the variability of N_glom across multiple virtual biopsies.

Statistical Analysis

Variability

We estimated variability (defined as the observed difference in N_glom in each kidney) using needle and virtual biopsies from different regions: Equation 4$$\mathit{Variability}=100\text{\%}.\left(N_{\mathit{glom}\_(NBorVB)}-N_{\mathit{glom}\_\mathit{CFE}}\right)/N_{\mathit{glom}\_\mathit{CFE}}$$

Where N_{glom_(NB or VB)} is the glomerular number measured from needle biopsy (Equation 1) or virtual biopsy (Equation 3), N_{glom_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.

Reliability

We examined reliability to determine how much of the observed variation in measured N_glom 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 N_glom 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 N_glom (NB or VB) and N_{glom_CFE}. We defined the bias and variance in biopsy-measured N_glom as the median and variance of this distribution. We used a likelihood ratio test to determine the mean difference between N_{glom_VB} and N_{glom_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 N_{glom_NB} between the two cohorts.

Results

Donor characteristics are shown in Table 1.

Table 1. - Donor characteristics

Kidney ID	Age (yrs)	Race	Sex	KDPI	Cause of Death	Final Serum Creatinine (mg/dl)
CF1	68	White	M	91	Cardiac arrest	2.5
CF2	45	Black	F	93	Stroke	2.7
CF3	37	White	F	50	Cardiac arrest	6.1
CF21	21	Black	M	26	Brain tumor	1.08
CF38	83	White	F	100	Stroke	0.6
CF60	40	White	M	32	Anoxia	1.44

M, male; F, female.

Distribution and Variability of N_glom Estimated from Needle and Virtual Biopsies

Figure 2A shows the cortical volumes, whole kidney N_glom measured from CFE-MRI (N_{glom_CFE}), N_glom estimated from needle biopsies (N_{glom_NB}), and from virtual biopsies (N_{glom_VB}). As the number of biopsies per kidney increases, the average N_glom of all biopsies approximates N_{glom_CFE}. The slope of linear regression between N_{glom_NB} and N_{glom_CFE} was 1.17 (R²=0.40), whereas the slope for N_{glom_VB} and N_{glom_CFE} was 1.05 (R²=0.91) (Figure 1S, Supplemental Figure 1).

Figure 2.: Intra- and interkidney estimates of N _glom from needle biopsy (N _{glom_NB} ) and virtual biopsy (N _{glom_VB} ). (A) Cortical volumes, N_glom estimated from CFE-MRI, mean N_glom±SD estimated from needle biopsies (N_{glom_NB}), and virtual biopsies (N_{glom_VB}). (B) Distribution of N_glom within each kidney; gray “X” markers represent the N_glom estimated from individual (i) needle biopsies and (ii) virtual biopsies. The horizontal line is the mean N_{glom_NB} (i) and mean N_{glom_VB} (ii) for all biopsies within the kidney. Squares and circles are N_glom estimated by CFE-MRI and whole kidney stereology, respectively. (iii)–(iv) Variability in N_glom estimated from (iii) needle and (iv) virtual biopsies. Variability is defined as the difference between N_glom estimated from a single biopsy and the total glomerular number in whole kidney by CFE-MRI within the same kidney (Equation 4). (C) Variability in N_{glom_NB} (dotted bars) and N_{glom_VB} (gray bars). Both distributions contain results of all kidneys. Slightly larger but not statistically significant variability (P=0.07) was observed for N_{glom_NB} compared with N_{glom_VB}. (D) The mean N_glom±SD within the clusters of virtual biopsies along the kidney. Four clusters were created in lower and upper poles of the kidney; five clusters were created in the midpole as depicted in (i). Each cluster contains between 12–18 biopsies. The results are shown for CF1 (i), CF2 (ii), CF3 (iii), CF21 (iv), CF38 (v), and CF60 (vi) kidneys. Gray crosses represent the results of individual virtual biopsies. Bars and error bars are mean±SD of N_glom within each cluster of biopsies. Black line represents the N_glom estimated by CFE-MRI.

Figure 2, Bi and Bii shows the distributions of N_{glom_NB} and N_{glom_VB}. Figure 2, Biii–Biv shows the variability in N_glom in individual kidneys from different biopsies (Equation 4). N_glom was overestimated from a needle biopsy by <144% or underestimated by up to 71% (Figure 2Aiii). N_glom 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 N_{glom_NB} and N_{glom_VB} (two-sample t test, P=0.07), sho wn in Figure 2C. Figure 2D shows N_glom calculated from within clusters of virtual biopsies across the kidney. Within clusters, mean N_glom was overestimated by 12%–53% and underestimated by 8%–40%.

Reliability and Accuracy of Needle and Virtual Biopsies

Needle Biopsy

The reliability of needle biopsy was approximately 30%, indicating that 30% of the observed variance in N_glom was due to differences in N_glom between kidneys and 70% was due to measurement error. The bias in N_{glom_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 N_{glom_NB} approached N_{glom_CFE} with increasing numbers of needle biopsies. However, >200 needle biopsies would be required to be 95% certain the average N_{glom_NB} was within 20% of whole kidney N_{glom_CFE}. If a single needle biopsy were taken from the cortex of a kidney, the probability is <15% that N_{glom_NB} would be within 20% of N_{glom_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 N_{glom_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 N_{glom_NB} of around 310,000. When limited to a single biopsy, >100 kidneys per group would be needed to detect a difference in N_{glom_NB} between two groups.

Table 2. - Sample size required to detect a significant difference (P<0.05) in N_glom between two groups of subjects. Values in the table represent the difference in mean N_glom (divided by 100,000) that can be detected between two groups of n kidneys each with m biopsies.

Number of Biopsies per Kidney (m)	Number of Kidneys per Group (n)
	6	8	10	12	16	20	30	50
1	6.05	5.24	4.69	4.28	3.70	3.31	2.71	2.10
2	4.88	4.22	3.78	3.45	2.99	2.67	2.18	1.69
3	4.42	3.83	3.42	3.12	2.71	2.42	1.98	1.53
4	4.17	3.61	3.23	2.95	2.55	2.28	1.87	1.44
5	4.01	3.48	3.11	2.84	2.46	2.20	1.80	1.39
6	3.91	3.38	3.03	2.76	2.39	2.14	1.75	1.35
7	3.83	3.31	2.96	2.71	2.34	2.10	1.71	1.33
8	3.77	3.26	2.92	2.66	2.31	2.06	1.68	1.30
9	3.72	3.22	2.88	2.63	2.28	2.04	1.66	1.29
10	3.68	3.19	2.85	2.60	2.25	2.02	1.65	1.28
12	3.62	3.14	2.81	2.56	2.22	1.98	1.62	1.25
14	3.58	3.10	2.77	2.53	2.19	1.96	1.60	1.24
16	3.55	3.07	2.75	2.51	2.17	1.94	1.59	1.23
18	3.52	3.05	2.73	2.49	2.16	1.93	1.58	1.22
20	3.50	3.03	2.71	2.48	2.15	1.92	1.57	1.21
∞	3.32	2.87	2.57	2.34	2.03	1.82	1.48	1.15

Virtual Biopsy

The reliability of virtual biopsy was approximately 60%, indicating that 60% of the variance in observed N_{glom_VB} was due to true differences in N_glom between kidneys; 40% of the variance was due to sampling error. The bias in N_{glom_VB} was 78,000 with variance 474,000 (Equation 6, Supplemental Material).

Although we observed differences in variability and mean N_{glom_VB} across the kidney (Figure 2D), these differences were consistent with random variation. We found the variability in the difference between N_{glom_VB} and N_{glom_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 N_glom. On the basis of this study, approximately four virtual biopsies would be needed to be 95% certain the average N_{glom_VB} was within 20% of N_{glom_CFE}. The N_{glom_VB} estimated from single virtual biopsy has a 60% chance to be within 20% of N_{glom_CFE}.

Discussion

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 N_glom across the whole kidney. We used published methods to estimate N_glom 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 N_glom estimated by CFE-MRI. A large number of biopsies (>200 biopsies) was needed to accurately approximate N_glom in an individual kidney. There was no biopsy location that could systematically reduce the variability in N_glom.

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 N_glom 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 N_glom 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 N_{glom_VB} compared with N_{glom_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 N_glom. Estimates of N_glom 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, N_glom 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 N_glom of all biopsies approximated the N_{glom_CFE}. We observed a large distribution of N_glom 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 N_glom 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.

Disclosures

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.

Funding

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).