Measurement of glomerular volume in needle biopsy specimens

Jean M. Macleod1, Kathryn E. White1, Helen Tate2, Rudolf W. Bilous1,3 and on behalf of the Esprit Study Group

1 Department of Medicine, University of Newcastle upon Tyne, Framlington Place, Newcastle upon Tyne, 2 Clinical Data Operations, Merck, Sharp and Dohme Ltd, Hoddesdon, Hertfordshire and 3 Division of Medicine, South Tees Acute Hospitals NHS Trust, South Cleveland Hospital, Middlesbrough, Cleveland, UK

Correspondence and offprint requests to: Dr Jean M. MacLeod, c/o Secretary to Dr Bilous, Audrey Collins Teaching Unit, Education Centre, South Cleveland Hospital, Marton Road, Middlesbrough, Cleveland TS4 3BW, UK.

Abstract

Background. Various methods have been used to determine mean glomerular volume, some requiring measurement of over 30 glomerular profiles for a satisfactory estimate. Needle biopsies are useful diagnostically, but if small, provide insufficient tissue for the use of such methods.

Methods. We performed glomerular volume measurements on renal biopsies from 10 normotensive, non-uraemic patients with Type 1 diabetes. Sections were taken at 10 µm intervals through 10 glomeruli per biopsy and points landing on glomerular tuft counted under light microscopy. Volume was calculated from the measured cross-sectional area and known section thickness using the Cavalieri principle.

Results. Estimating the volume of 10 glomeruli per biopsy gave an overall mean glomerular volume of 4.21x106 µm3 and standard deviation between patient means 1.23x106 µm3. Using a sample size of five glomeruli per biopsy only increased the standard deviation between patient mean values by 3%. Using sections taken at 20 µm intervals made little difference to the mean glomerular volume and standard deviation estimates (MGV 4.20x106 µm3±1.24). Further increases in the sectioning interval resulted in an appreciable increase in the variance of the estimate.

Conclusions. The results suggest that a satisfactory estimate of mean glomerular volume can be obtained from a sample size of five glomeruli per biopsy using a sectioning interval of 20 µm. This represents a great saving in analysis time and effort, making widespread use of this method of glomerular volume measurement in renal disease more practicable, in both research and clinical settings.

Keywords: Cavalieri principle; glomerulopathy; glomerular volume; light microscopy; diabetes mellitus

Introduction

Glomerular volume increases seven-fold during development from infancy to adulthood with a subsequent decline during senescence [1]. Racial differences in glomerular volume have been shown with larger volumes found in Pima Indians than in white individuals, independent of the presence of diabetes [2]. Alterations in glomerular volume have been demonstrated in several different disease states. In adults with Type 1 diabetes mellitus, glomerular volume may be increased by almost two-fold after 15 years [3]. Increased glomerular volume has also been shown in human mesangiocapillary glomerulonephritis [4]. Studies of renal ischaemia on the other hand show a reduction in glomerular volume followed by glomerular hyalinization in response to decreased renal blood flow [5].

An estimate of glomerular volume is essential to derive absolute values for volume dependent parameters such as filtration surface area and capillary length [6,7]. Abnormalities of these parameters have been demonstrated in Type 1 and Type 2 diabetes, Alport syndrome and glomerulonephritis [3,4,8,9] and structural–functional relationships have been described [4,7,10].

Several methods have been used to calculate mean glomerular volume, each having reported coefficients of variation >40% and requiring relatively large numbers of glomeruli for an adequate estimate [3,7,11,12]. Needle biopsy specimens provide an insufficient number of glomeruli to derive a reasonable estimate of mean volume using these approaches. The Cavalieri method of glomerular volume estimation has been used in studies of diabetic nephropathy [13,14] and has the advantage of requiring relatively small numbers of glomeruli. What is not clear, however, is how few glomeruli are needed. As the method is time consuming this is an important issue of efficient use of resources.

Our aim was to assess the application of the Cavalieri method to the analysis of Trucut biopsy specimens from patients with Type 1 diabetes and address ways in which the efficiency of the method could be improved without sacrificing precision.

Methods

Biopsies from 10 normotensive, non-uraemic patients with Type 1 diabetes mellitus and abnormal albumin excretion recruited to the ESPRIT study were examined for the present morphometric analysis [15]. The biopsies were fixed by immediate immersion in 2% glutaraldehyde [11] in modified phosphate buffer. Blocks of tissue (1 mm3) were embedded in coffin moulds using TAAB Premix Kit (medium) T028 resin (TAAB, Aldermaston, Berkshire, UK). The embedding procedure ensures random orientation, in 3D, of any glomerulus within the block. The resin blocks were sectioned on a Reichert ultracut microtome with 1-µm sections taken at approximately 10-µm intervals throughout the tissue block and stained with 1% toluidine blue. Sections were cut at this predetermined interval of 10 µm until renal tissue was visible in the section. This section then formed the baseline, or level 0, from which all subsequent sections through the glomerulus were numbered (Figure 1Go). This sectioning regime provides sections which are systematically random with respect to individual glomeruli, thus satisfying the stereological requirement for an equal probability of any section through a glomerulus in any plane in 3D [6].



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Fig. 1. Schematic representation of sectioning through a renal glomerulus using a sampling interval of 10 and 20 µm. The first section where glomerular tissue is visible is level 0. in our series of 98 glomeruli in 10 patients 14–22 sections at 10 µm intervals were obtained. (Adapted from Junquiera and Carneiro [27].)

 
In order to perform the Cavalieri volume estimation, only complete, non-occluded glomeruli which were clearly surrounded by Bowman's capsule, with open capillary loops visible under light microscopy, were used for analysis [3,11]. When the first such open glomerulus was encountered in the block, the knife was advanced and a terrace cut into the resin at a depth of approximately 400 µm and measured, to allow later estimation of section thickness. As each glomerulus disappeared from the block, the distance to the terrace was measured again. The actual interval between sections was then determined from the known number of sections taken and the measured terrace depth. The calculated section `thickness', t, was used in the calculation of Cavalieri glomerular volume. Processing of each biopsy continued in this way until 10 complete glomeruli had been sectioned in nine of the biopsies, but in the remaining one patient only eight complete glomeruli were found in the biopsy. This regime yielded 14–22 profiles per glomerulus for analysis.

The stained 1-µm sections were examined by light microscopy at a magnification of 333x. A drawing tube attachment was used, under which was placed a tessellation of points, with an area of 225 mm2 pertaining to each point. The resulting grid appeared superimposed on the profile image and was randomly oriented with respect to the image. Points landing on the glomerulus were counted using a digitizing tablet, on each section through the whole glomerulus. Each complete glomerulus was measured in this way and glomerular volume calculated by the Cavalieri principle:


(1)

Statistical analysis
In addition to presenting simple summary statistics, a variance components analysis was performed. For this, the contributions of patients and glomeruli (i.e. the degree to which patients differ inherently in their glomerular volume and, for any given patient, the variability between glomeruli) to the overall variance of glomerular volume were estimated using the method of restricted maximum likelihood (REML) applied to a nested random model [16]. The total variability in the data is broken down into its individual components: the variability between patients ({sigma}2p) and the variability between glomeruli within a given patient ({sigma}2g). The results from the variance components analysis were used to assess the precision which might be associated with alternative sampling schemes. For example, if ng glomeruli are sampled from each biopsy, then the variation between the mean patient values would be estimated by {sigma}2p)+{sigma}2g/ng (Formula 1). The standard deviation is the square root of this. The effect of reducing the number of glomeruli per biopsy is estimated by substituting different values for ng into Formula 1. The effect on precision of reducing the number of levels from which each glomerular volume was calculated was examined empirically, by using alternate, every fourth and every sixth sections, while increasing the calculated section thickness t in the Cavalieri formula. The volume estimates from the reduced data were then analysed by variance components analysis, as described above. In summary, the full analysis involved all sections from 10 glomeruli per biopsy, the effect of reducing the number of glomeruli was assessed from Formula 1, and the effect of reducing the number of sections was assessed by repeating the analysis using only systematically selected sections and increasing the section thickness in the Cavalieri estimation.

Results

The results from the full analysis are shown in Table 1Go. Overall mean glomerular volume (MGV) was 4.21x106 µm3 with range 2.08–5.91x106 µm3, between patient mean standard deviation 1.23x106 µm3 and coefficient of variation 29.3%. The variance components analysis estimated the variability between patients ({sigma}2p) to be 1.417 and between glomeruli ({sigma}2g) to be 0.936, indicating that the inherent between patient differences in this series were by far the more important. Using these values, the standard deviation of the between patient mean values was estimated to be 1.238 for a sample size of eight glomeruli per biopsy, 1.266 for five glomeruli and 1.315 for three glomeruli.


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Table 1. Mean glomerular volumes and summary statistics for 10 patients with Type 1 diabetes and increased urinary albumin excretion (section interval 10 µm)
 
Halving the number of glomeruli examined would not be expected to increase the standard deviation of the between patient mean values by more than 3% (mean 4.20x106 µm3; SD 1.27; CV 30.2%).

The effect of increasing section thickness to approximately 20 µm is shown in Table 2Go. The mean values are very similar to those for 10 µm sections (MGV=4.20x106 µm3; SD 1.24; CV 29.5%). The components of variance analysis reinforces this observation with estimates of {sigma}2p and {sigma}2g being 1.437 and 0.911, respectively. Thus, it appears that there is little evidence for any increase in measurement error from examining half the number of sections. If five glomeruli per patient are examined, the standard deviation between patients was estimated as 1.273.


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Table 2. Mean glomerular volumes and summary statistics for 10 patients with Type 1 diabetes and increased urinary albumin excretion (section interval 20 µm)
 
The analysis of the effect of reducing the number of sections examined per glomerulus was taken further. Use of every fourth section would increase the variance in the estimate of glomerular volume ({sigma}2g) to 0.986, which effectively increases the standard deviation of the mean. In addition, using a sectioning interval of >=40 µm would result in sampling fewer than five sections per glomerulus, inevitably increasing the coefficient of error of the estimate.

A time analysis was performed to assess the impact of reducing the number of glomeruli sectioned and increasing the section thickness `t'. For 10 glomeruli with t 10 µm, sectioning and staining employed 48 h of technician time and counting of the results took a further 11 h. For five glomeruli with t=20 µm, these times were reduced to 17 and 2.5 h, respectively. This represents an overall saving of 67% in total time taken for processing and analysing each biopsy.

Discussion

Our aim in performing the present analysis was to develop a more efficient method for estimating glomerular volume from needle biopsies while maintaining precision with a limited sample size. In some previous studies a relatively large volume of tissue was available for analysis [7,11,12]. The point-counting and line-sampling methods of glomerular volume estimation employed by these studies require the measurement of numerous glomerular profiles from which mean glomerular volume can be estimated. Use of the Trucut needle or similar device yields only a limited volume of cortical tissue. With fewer glomeruli then available for measurement those methods of measurement requiring over 30 glomeruli for an adequate estimate of glomerular volume become impracticable. The data from this series show that a mean volume derived from five glomeruli serially sectioned with an interval of 20 µm produces a reasonable estimate with an acceptable coefficient of error of >=10%. Further reduction in the number of glomeruli examined or of the number of sections examined per glomerulus, although reducing the time spent in the analysis, would increase the error of the estimate.

Attempts have been made to estimate glomerular volume in normal subjects using cadaveric specimens [11], but as differences in volume may occur post-mortem and the degree of delay in obtaining the kidneys after death is unclear, it is probably not reasonable to use a normal range established in cadavers as a comparative to needle biopsy specimens of the diseased kidney. Studies performed as part of a kidney transplant programme would provide a valid comparison however, as donor biopsies were taken prior to removal of the donor kidney. Bilous et al. demonstrated glomerular volumes of 0.50-1.75x106 µm3 [17] compared to the mean in our diabetic group of 4.20x106 µm3. However, these workers reported results from tissue embedded in paraffin which results in substantially decreased glomerular volumes with differences of up to 40% reported compared to resin embedding [18]. Extrapolating from these data, it can be calculated that a section thickness t of 20 µm would yield a sample of 4–9 sections per normal glomerulus using the current methods. The suggested sectioning interval of 20 µm is still useful in those conditions not associated with glomerular enlargement.

The unbiased estimator of the volume of an arbitrary object based on Cavalieri's principle which we have employed [19] is accepted as the `gold standard' against which other methods of glomerular volume estimation have been compared [13]. These various methods of volume estimation involve assumptions regarding the size distribution of the glomeruli with corrections made for shape. Correction factors have been used to compensate for this based upon the model of the glomerulus as a flattened sphere [6]. However, after fixation and embedding such assumptions are not valid as not all glomeruli approach sphericity, as has been shown by assessment of mean tuft shape factor. Furthermore, shape factor appears to change with age or disease [20]. Alternatively, glomerular cross sectional area has been used as an indicator of glomerular size in membranous and minimal change nephropathy without conversion to volume [21], but the relationship between mean glomerular cross-sectional area and volume is neither consistent nor precise because the glomerular tuft at this magnification shows marked irregularity of contour [20]. The Cavalieri method makes no assumptions regarding the size distribution or the shape of particles, therefore no correction factors are required [19]. While the current analysis relates to the diseased state, where glomerular enlargement would be expected, with a contour tending to sphericity [3,10,20], the methods of analysis are applicable to normal biopsies and other disease states, as they are not influenced by size or shape of the glomerular tuft.

Some bias is inevitable when using needle biopsy specimens as glomerular volume varies according to the depth within the cortex [22]. In our group, it was striking that the variation in glomerular volume derived from differences between patients rather than within patients. This is perhaps not surprising as the needle biopsy is likely to sample glomeruli at a similar depth within the cortex and generally from the lower pole. Such a sampling method cannot exclude the possibility of populations of larger or smaller glomeruli elsewhere within the kidney. However, similar criticisms may be made of any previously reported studies which have used needle biopsies. The effect of different embedding media has already been alluded to [18] but in contrast, use of 1% or 2.5% glutaraldehyde for fixation prior to resin embedding does not affect glomerular volume [23]. Consistency in methodology is essential within research protocols, from biopsy method to choice of embedding medium and care should be taken when making comparisons of results from different laboratories.

Interest in the relationships between structure and function is advancing in all aspects of renal disease and the renal biopsy is seen by some as a vital research tool [10,24]. In addition to the cross-sectional quantitative studies already mentioned [4,712,14,2023] renal biopsy analysis has been used prospectively to assess risk of disease progression [25] or the effect of interventions such as pancreatic transplantation [17], improved glycaemic control [26] and the ongoing study of anti-hypertensive treatment [15]. In order to understand structural–functional relationships within the glomerulus, knowledge of the reference glomerular volume is a fundamental requirement for estimation of such parameters as absolute filtration surface areas or absolute capillary lengths from measured surface or length density [7,8,10]. As these parameters are volume dependent, absolute values are necessary for valid comparisons between patients or treatment groups [6,17]. This implies the use of the Cavalieri method wherever possible to give an accurate reference volume measurement.

Measurement of glomerular volume is time-consuming and laborious whatever method is used. Although the present sectioning and counting regime is relatively labour intensive, it is straightforward and only requires the basic sectioning skills and standard equipment available to any laboratory. This efficient application of the Cavalieri principle to glomerular volume estimation could be used in conjunction with the more routine qualitative assessments of biopsy tissue, permitting widespread use of glomerular volume measurement both in the research and clinical setting. We would recommend this method for future studies of glomerular structure in diabetic and other glomerulopathies.

Acknowledgments

During the period of the study Dr J. M. MacLeod held the British Diabetic Association RD Lawrence Fellowship. Mrs K.E. White was funded by project grants from Merck, Sharp and Dohme Ltd and the British Diabetic Association. We are grateful to Mr Neil Hamilton for his assistance with computer hardware and software and to Dr Jens Nyengaard for his advice.

Notes

* ESPRIT Study Group Members (European Study of the Progression of Renal Disease in Type 1 Diabetes). (UK) University of Newcastle upon Tyne: Dr J. M. MacLeod, Mrs K. E. White, Dr L. Baines, Dr S. Marshall and Dr R. W. Bilous; Guy's Hospital, London: Dr K. Earle, Dr D. Barnes, Dr I. Abbs, Miss A. Collins and Prof. G. C. Viberti; Northern General Hospital, Sheffield: Dr A. M. El Nahas; Merck, Sharp and Dohme Ltd, Hoddesdon, Herts: Dr P. Robinson, Ms H. Tate and Dr R. Tomiak. (Italy) Instituto di Richerche Farmacologiche Mario Negri, Bergamo: Dr P. Ruggenenti, Dr F. Gaspari and Dr G. Remuzzi; Ospedale Casa Sollieva della Sofferenza, San Giovanni Rotondo: Dr S. de Cosmo, Dr S. Bacci, Dr M. D'Errico; Ospedale San Michele, Cagliari: Dr G Piras. Steering Committee: Dr R. W. Bilous, Dr G. Remuzzi, Dr P. Robinson, Prof G. C. Viberti.

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Received for publication: 17.11.98
Accepted in revised form: 15. 4.99