Estimation of Glomerular Podocyte Number: A Selection of Valid Methods

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1 Estimation of Glomerular Podoyte Number: A Seletion of Valid Methods Kevin V. Lemley,* John F. Bertram, Susanne B. Niholas, and Kathryn White *Division of Nephrology, Children s Hospital Los Angeles, Los Angeles, California; Department of Pediatris, University of Southern California Kek Shool of Mediine, Los Angeles, California; Department of Anatomy and Developmental Biology, Shool of Biomedial Sienes, Faulty of Mediine, Nursing and Health Sienes, Monash University, Melbourne, Australia; Morphometry and Stereology Laboratory, Department of Researh, Charles Drew University of Mediine and Siene, Los Angeles, California; Divisions of Nephrology and Endorinology, David Geffen Shool of Mediine at University of California Los Angeles, Los Angeles, California; and EM Researh Servies, Faulty of Medial Sienes, Newastle University, Newastle upon Tyne, United Kingdom ABSTRACT The podoyte depletion hypothesis has emerged as an important unifying onept in glomerular pathology. The estimation of podoyte number is therefore often a ritial omponent of studies of progressive renal diseases. Despite this, there is little uniformity in the biomedial literature with regard to the methods used to estimate this important parameter. Here we review a seletion of valid methods for estimating podoyte number: exhaustive enumeration method, Weibel and Gomez method, disetor/cavalieri ombination, disetor/frationator ombination, and thik-and-thin setion method. We propose the use of the disetor/frationator method for studies in whih ontrolled setioning of tissue is feasible, reserving the Weibel and Gomez method for studies based on arhival or routine pathology material. J Am So Nephrol 24: , doi: /ASN Podoytes play a key role in the preservation of normal glomerular struture and funtion. 1 Podoyte loss has been assoiated with progression of glomerular diseases both in humans 2,3 and in experimental models of glomerular injury. 4 6 The assessment of podoyte number in human renal biopsy samples and in kidney speimens from animal models may therefore be a pivotal omponent of studies of the pathogenesis and treatment of glomerular disease. Despite this, there is little uniformity in the biomedial literature with regard to the methods used for estimating podoyte number either in experimental models or linial biopsy speimens. As a result, estimates of podoyte number an vary widely between studies, making meaningful omparisons diffiult. The glomerulus and the ells within it are three-dimensional objets. Quantitative assessment of these strutures, on the other hand, has traditionally involved measurements on two-dimensional images from histologi setions. Stereology is a body of mathematial/statistial theory and methods wherein threedimensional harateristis of objets are estimated from lower-dimensional images of those objets. Although stereology is a well developed field, as with other forms of statistially based reasoning, its results an sometimes seem ounterintuitive. At the same time, apparently ommon-sense approahes to the estimation of quantitative strutural variables, suh as podoyte number, often lak stereologi validity and, as a result, introdue biologi unertainty. In this review we desribe five methods for estimating podoyte number, examine their assumptions and limitations, and indiate some of the irumstanes under whih they may represent appropriate approahes. These methods oupy a range of inreasingly general assumptions and orresponding hanges in methodologi design. The main body of this paper provides an overview and motivation for these five methods (the Supplemental Material desribes the methodswithworkedexamplesin more detail). We also present one example of a ommonly used but invalid method and illustrate its shortomings. A BRIEF INTRODUCTION TO STEREOLOGY Stereology is the mathematial/statistial analysis of the struture of three-dimensional objets based on lower-dimensional samples of those objets. 7 9 Its unavoidable use of quite simple equations is often Published online ahead of print. Publiation date available at. Correspondene: Dr. Kevin V. Lemley, Division of Nephrology, MS#40, Children s Hospital Los Angeles, 4650 Sunset Boulevard, Los Angeles, CA klemley@hla.us.edu Copyright 2013 by the Amerian Soiety of Nephrology J Am So Nephrol 24: , 2013 ISSN : /

2 intimidating for biomedial investigators, whih may explain the ontinued use of invalid, apparently ommon-sense approahes to quantifying strutural measures suh as podoyte number. However, although the underlying mathematis may seem daunting, stereology as a tool is simple to use. It is essentially based on sampling and ounting. A ertain resistane to learning and using more ompliated quantitative methods is understandable. However, it would be of great benefit for the researh ommunity to embrae the same type of transition in sophistiation that was heralded 30 years ago regarding the use of statistis in mediine with the seminal paper by Stanton Glantz 10 on statistial errors in the medial literature. That paper demonstrated a remarkably high frequeny of basi statistial errors in artiles appearing even in premier biomedial journals and introdued new standards for evaluating and reporting statistial results in the medial literature. The diffiulty of making suh a transition should not be underestimated, however, inasmuh as ommon sense and probability seem so often to be at odds. 11 In stereologi studies of the kidney, typial samples onsist of histologi setions through an entire kidney (as in animal studies) or from a kidney biopsy (as in linial studies). In lassi stereology, measures of the feature of interest (podoyte number) are expressed relative to a referene volume (glomerular volume). In general, ell number is estimated by ell nulear number beause this is a well defined feature of the ell. These lassi measures are thus densities, whih represent a ratio analogous to the ommon meaning of density as mass per unit volume. In this ase, though, the quantity in the numerator may represent any spatial variable suh as volume, area, length, or number. One of the simplest and oldest stereologi priniples is that of Delesse (1847), who demonstrated that frational volume or volume density of a mineral in rok (V V, shorthand for volume of mineral per unit volume of rok) may be estimated without bias from the frational area of the mineral phase in a ut fae (setion) of the rok (A A, area of mineral phase per unit ross-setional area of rok). Here is a ase in whih the ommon sense and the stereologi approahes learly oinide. All stereologi methods depend on representative sampling of the referene spae (the whole kidney, biopsy speimen, or glomerulus). The existene of differenes in variability at the different levels of the sampling proess means that for any given problem there is an optimal partitioning of effort at the different sampling levels to minimize the total variane of the measurement relative to the time and effort invested, a priniple sometimes desribed as Do more less well. 12 Although biologi variation between individuals is often the major soure of total variane, the exat interand intraindividual varianes of the measured variables are in general not known before the study is onduted. After appropriate unbiased sampling of the tissue, there is a fundamental dihotomy in the subsequent stereologi method between model-based methods and design-based methods. MODEL-BASED METHODS The earliest stereologi methods for partile ounting (in stereology, partiles are defined as disrete three-dimensional objets, suh as ell nulei, glomeruli, or other objets) were model-based methods performed on single setions. The model struture, expressed in terms of geometri probability, is the set of assumptions made about the geometri features of the partiles in question, suh as the assumptions that glomerular tufts are spherial, podoytes are uniformly distributed throughout glomeruli, or podoyte nulei have a speifi shape. To the degree that these assumptions reflet the atual state of affairs, mathematial relationships an be derived relating average values for features measured in the two-dimensional images of setions through the referene spae to the desired quantitative strutural features of the three-dimensional partiles. To the degree that the assumptions systematially deviate from the atual state of affairs, however, the estimates obtained will be biased. For example, with respet to partile numerial density (number per volume), the likelihood of sampling a partile with a single setion through the referene volume is not simply a funtion of the overall partile density in spae but also of the size, shape, and orientation of the partile. This neessitates the introdution of orretion fators into the general partile density estimation equation. The simplest suh equation (desribed by Wiksell in 1925) is N V =N A / D, where N V is the partile numeri density (number of partiles per unit volume), N A is the profile numeri density (number of partile profiles per unit setion area), and D is the average aliper diameter of the partiles. The average aliper diameter is the average over all partile orientations of the maximum extent of the partile between two parallel planes (alipers; Figure 1). More omplex forms of estimation equations, suh as that of Weibel and Gomez, 13 ontain terms expliitly refleting partile shape and variation in Figure 1. The aliper diameter is the distane D between parallel tangent lines (just touhing the objet) in any given diretion. Note that D will differ depending on the orientation of the tangent lines. The probability of hitting a partile with a single setion through a referene spae is proportional not only to the density of partiles in the spae, but to the size of the partile and the thikness of the setion. The partile size is quantified by the mean aliper diameter, D, whih is the average over all partile orientations of the maximum extent of the partile between two parallel planes (alipers) Journal of the Amerian Soiety of Nephrology J Am So Nephrol 24: , 2013

3 BRIEF REVIEW partile size (see Supplemental Material). It is important to note these methods estimate partile density (N V )and not absolute partile number (N). Estimation of the latter also requires estimation of the referene volume. For example, estimation of total glomerular podoyte number (N pod,glom )requires an additional estimate of average glomerular volume (V glom ). The following equation represents stereologi estimation of the total number of podoytes per glomerulus N = N V 3 V: N pod;glom ¼ N Vpod;glom 3V glom where N pod,glom is the number of podoytes per glomerulus, N Vpod,glom is the number of podoytes per unit glomerular volume, and V glom is average glomerular volume. DESIGN-BASED (UNBIASED) METHODS Design-based (unbiased) stereologi methods were developed as a response to the limitations inherent in modelbased methods, in partiular the bias in sampling introdued by the use of single setions and the diffiulty of establishing values for the model (geometri) variables in biologi speimens. The urrent gold standard for design-based partile number estimation is the disetor. 14 As originally desribed, the physial disetor is based on the new appearane of a partile between two physial tissue setions with known separation, implying that the leading point of the partile first ourred within the volume ontained between the setions. As long as the speifi partile an be identified as present or absent in the two setions, the event of its appearane between the setions is independent of its size or shape and the partile an be unambiguously and uniquely attributed to the volume element in whih it first appeared (Figure 2). The disetor so desribed involves two physial tissue setions (alled the referene and look-up setions). An optial version of the disetor has also been desribed. 15 In this ase, optial setions Figure 2. The physial disetor is based on the new appearane of a partile between two physial tissue setions with known separation implying that the leading point of the partile first ourred within the volume ontained between the setions. As long as the speifi partile an be identified as present or absent in the two setions, the event of its appearane between the setions is independent of its size or shape and the partile an be unambiguously and uniquely attributed to the volume element in whih it first appeared. The disetor so desribed involves two physial tissue setions (alled the look-up, here A, and referene setion, here B). Notie that in the referene setion (B) there are seven appearanes of podoyte nulei (blue) not present in the look-up setion (A). When ounting ell nulei with physial disetors, setion pairs (A, B) are used to ount appearing and disappearing nulei. In this example, 1-mm onfoal optial images separated by 4 mm are used. Paraffin setions from a human glomerulus were stained for Wilms tumor 1 (WT-1) antigen to loalize podoytes (green ytoplasm), von Willebrand fator (vwf) to loalize endothelial ells (red ytoplasm), and DAPI for all nulei (blue). Nulei present in the lookup setion (A) that were not present in the referene setion (B) were ounted (white arrows, two nulei). Then, those nulei present in the referene setion (B) but not in the look-up setion (A) were ounted (asterisks, seven nulei). from bright-field or onfoal mirosopy are used to ount partiles at a unique foal point (e.g., when they are first observed) (Figure 3). Like the above-mentioned modelbased methods, the disetor by itself doesnotestimatetheabsolutenumberof partiles but rather the numeri density of partiles within a referene volume (N V ). Estimation of absolute podoyte number (N pod,glom ) thus requires multiplying this density by the average glomerular volume. Alternatively, the disetor an be ombined with a hierarhial sampling sheme known as the frationator to estimate the number of partiles diretly. This also overomes the effets of tehnial artifats, suh as setion ompression and tissue shrinkage, 16,17 as well as the need for preise estimation of the separation of the tissue setions. Moreover, it is not neessary to estimate glomerular volume when estimating podoyte number using the disetor/ frationator ombination. Using the frationator, 17 systemati subsampling of an entire glomerulus or population of entire glomeruli allows an absolute quantity of interest to be determined in a defined fration of glomerular tissue. Multipliation of the measured quantity by the inverse of the sampling fration gives the absolute value for the individual glomerulus or an average glomerulus in the population (see Supplemental Material). Another way to ompensate for the effets of partile size and shape on the likelihood of that partile being sampled by a single setion was desribed by Loud and olleagues 18 in 1978 and traed by them to Aberrombie in This approah uses the fat that for the same atual partile numerial density (N V ), the number of partile profiles per unit J Am So Nephrol 24: , 2013 Estimating Podoyte Number 1195

4 version of this method based on two different setion thiknesses has been reintrodued reently under the name thik-and-thin setion method. 19 COMPARING MODEL-BASED AND DESIGN-BASED METHODS Figure 3. When ell nulei are ounted with optial disetors, nulei are ounted at a unique moment (e.g., when they first ome into fous). In this figure, 14-mm paraffin setions were immunofluoresently stained for Wilms tumor 1 (WT-1) to identify podoytes (green ytoplasm), von Willebrand fator (vwf) to identify endothelial ells (red ytoplasm), and DAPI for all nulei (blue). Eah paraffin setion was then optially setioned using onfoal mirosopy at 1-mm intervals; six optial setions (A F) are shown. Nulei in fous in A were not ounted beause they did not ome into fous. Nulei that ame into fous in setions B F are indiated by asterisks. The presene of WT-1 and vwf identified whih of the ounted ells were podoytes (three ells) and whih were endothelial ells (seven ells). area of setion (N A ) inreases not only with partile aliper diameter (D) but also with setion thikness t (when t is non-negligible ompared with D): N A = N V (D + t) (Figure 4). It an be shown that for varying setion thiknesses, the slope of the regression line of the setion thikness t on N A is equal to 1/N V.A There have been few head-to-head omparisons of model-based and designbased methods to problems of ounting in the kidney Basgen et al. 21 found that in estimating the number of ells (not just podoytes) in the mouse glomerulus, the estimate obtained using the disetor/frationator was not signifiantly different from that derived from omplete enumeration on serial setions, whereas the Weibel and Gomez method yielded an estimate on average about 10% higher than the atual number. Of note, the Weibel and Gomez method showed a onsiderably greater oeffiient of determination (R 2 )than the disetor method and a regressionline slope of approximately 1, illustrating the fat that a method may be haraterized by both bias and high preision. White and Bilous, 22 on the other hand, found that in 32 renal biopsy speimens from patients with type 1 diabetes and 10 biopsy speimens from ontrols, the Weibel and Gomez method gave results similar to those of the disetor/frationator method as long as the Weibel and Gomez method was performed on eletron mirosopi images. In those images, setion thikness was negligible ompared with the diameter of podoyte nulei. When setion thiknesses of different methods are not omparable, large disparities in podoyte number estimates may be expeted. 23 Clearly, additional head-to-head omparisons of podoyte ounting methods are needed, espeially in studies omplemented by the gold standard method of omplete enumeration by omplete serial setioning of the glomerulus. It would also be of value to establish shape and size distributions of podoyte nulei in different speies and disease states. Suh data ould help set limits on 1196 Journal of the Amerian Soiety of Nephrology J Am So Nephrol 24: , 2013

5 BRIEF REVIEW also be a soure of bias, at least in the Weibel and Gomez method. 26 Figure 4. The number of partile profiles per setion area (N A )isafuntionnotonlyoftheir density in the referene volume (N V ) but also of their size (aliper diameter, D) and the setion thikness (t): N A =N V 3 (D + t). Notie that the thiker setion (right) ontains more intersetion profiles. the auray and appliability of the Weibel and Gomez method. It is ertainly possible that an effiient and preise method with a small bias may be adequate for identifying large differenes in podoyte number between groups. If, in fat, the methodologi bias is the same in eah experimental group, the statistial evaluation of group differenes may even be failitated with a more preise, biased method ompared with a less preise, unbiased method. In that ase, problems arising from bias would arise mostly in omparing different studies if they use different methods. Of ourse, the foregoing approah requires establishing that bias is the same in the various estimates. Establishing this an take longer than performing the study using an unbiased method in the first plae. We therefore strongly reommend the latter approah whenever possible. In addition to onsiderations of robustness, auray, and preision (reproduibility), other harateristis by whih estimation methods may be judged inlude operational effiieny (time invested per measurement and therebyost), perentage of the overall experimental time spent on measurements, equipment requirements for the measurements, and the nature of the material to whih the method is applied. Routine linial material, not surprisingly, presents rather severe limitations to any method requiring systemati sampling. Hene, different methods for the estimation of podoyte number may be appropriate depending on the tissue and the laboratory resoures available and the need for auray and effiieny. Five valid methods urrently in use are briefly desribed below. Please see more detailed desriptions of these methods with worked examples in the Supplemental Material. ADDITIONAL CONSIDERATIONS Estimating Mean Glomerular Volume Other than the exhaustive enumeration and the disetor/frationator methods, the preeding methods must all be used in onjuntion with an estimate of average glomerular volume (V glom )orindividual glomerular volume in order to derive the total number of podoytes per average glomerulus or per individual glomerulus (N pod,glom ). This an easily be performed using the Cavalieri priniple, 24,25 whih provides an unbiased estimate of V glom. Division of the volume density of glomeruli by the numeri density of glomeruli also provides an unbiased estimate of V glom. 8 Tissue Proessing If tissue used for N Vpod,glom and V glom estimates is proessed differently (e.g., resin-embedded for the former and paraffin-embedded for the latter), differenes in tissue shrinkage between these proessing methods an lead to signifiant errors in the estimate of total podoyte number. Nonuniform Distribution of Podoytes A nonuniform distribution of podoyte nulei through the glomerular tuft may Podoyte Identifiation For the methods desribed, unambiguous identifiation of podoyte nulei is essential. Other than exhaustive enumeration and optial disetor approahes, these methods require that podoyte nulear profiles an be unambiguously identified in single setions. 9 This is not easy in routine histologi preparations. Therefore, either a very well perfusion-fixed speimen with thin setions and good staining of the glomerular basement membrane must be used, or speifi immunostaining (e.g., with antibody against WT-1; see Figures 2 and 3) 19 is needed to identify the podoyte nulei. Staining of podoytes for light mirosopy using anti WT-1 antibodies may not detet dedifferentiated podoytes, whih are present in some diseases. 19 Identifying podoyte nulei with eletron mirosopy is generally straightforward but time-onsuming. Binuleate Podoytes All five methods outlined later are based on equating the number of podoytes with the number of podoyte nulei. Binuleate podoytes have been desribed in human biopsy material, 27 although their frequeny appears to be low. Dupliated nulei would easily be attributed to a single podoyte in the exhaustive enumeration method and would probably present no signifiant diffiulties to the other methods if images of suffiient resolution were used. Counting Podoytes in Biopsy Speimens Clinial biopsy speimens may be arhival or of limited volume, effetively exluding the possibility of using podoyte ounting methods requiring multiple setions. From the preeding desriptions, it is lear that the Weibel and Gomez method (based on single setions) may be the only feasible option in these ases. Studies based on linial biopsies would need to be speifially designed to aommodate the use of J Am So Nephrol 24: , 2013 Estimating Podoyte Number 1197

6 design-based methods and are likely to exeed the apabilities of any but researh-oriented pathology servies. The disetor or thik-and-thin setion methods may be optimal for studies in whih whole kidneys are available (largely animal models), espeially if the former is used in onjuntion with the frationator. AN EXAMPLE OF AN INVALID METHOD One example of a ommonly used but invalidmethodofestimationofpodoyte number should be mentioned. The number of podoyte nulear profiles observed in a single glomerular tuft ross-setion is often reported as glomerular podoyte number. Thisisthe ultimate ommon-sense approah to estimating podoyte number just ount the podoytes. But, of ourse, this approah provides information only on the number of podoyte nulear fragmentsseeninasetionthroughtheglomerulus and does not provide reliable information on the number of podoytes in the whole glomerulus. In addition, ompared with the Weibel and Gomez method as a gold standard, this approah an be shown to have low preision. 26 It is subjet to several soures of bias. There are often glomerular size hanges as a result of natural or experimental renal disease for whih this approah does not aount. If the volume of the glomerular tuft inreases, for example, and the total number of podoytes in the glomerulus remains unhanged, then the number of hits of podoyte nulei in single setions will derease (Figure 5). So, to use this approah even omparatively it would be neessary to verify that average glomerular volume does not differ between groups. In addition, if truly random setions through glomeruli are used, there will be a very high variane in the number of nulear hits. If only the large, entral setions are evaluated (to redue this effet), a bias will be introdued beause of the nonuniform distribution of podoytes in the tuft. Figure 5. Changes in the referene spae affet podoyte density. This illustrates one soure of error in assessing glomerular podoyte number by ounting the number of podoyte nulear hits per glomerular ross setion. If the glomerular volume inreases, the hanes of a single setion interseting a podoyte nuleus will derease even if the total number of podoytes is unhanged. These two referene spaes (A and B) ontain the same number of partiles (podoyte nulei). Beause of the larger size of B, single setions through it ontain fewer partile profiles per setion than setions through spae A. In this ase, setion 1 intersets 3 partiles in A and 1 partile in B. Setion 2 intersets 2 partiles in A and 1 partile in B. CONCLUSIONS In light of these onsiderations, we propose that all researh studies reporting podoyte number use one of the five methods desribed below and that partiular attention should be paid to satisfying the assumptions of the method used. The Weibel and Gomez method is probably the only pratiable method for studies based on routine pathology speimens. The disetor-frationator ombination is likely the best method to use in experimental irumstanes in whih whole kidneys are available. It is imperative that appropriate stereologi expertise be obtained in the review of submitted manusripts onerning suh studies in order to assure the methodologi and biologi validity of the reported results. CONCISE METHODS All five methods desribed below an be used to estimate the total number of podoytes in individual glomeruli (Table 1). With the exeption of the exhaustive enumeration method 21,28 (use of whih is limited by prohibitive time onstraints), all an be used to estimate total podoyte number per average glomerulus. 1. Exhaustive Enumeration Method The Basi Idea Serial setioning is performed through the entire referene volume (in this ase, a glomerulus). Podoyte nulei are uniquely identified by their appearane in the serial setions. No sampling at the level of the glomerulus is required (i.e., every podoyte in the glomerulus is ounted). Prinipal Measurements The number of podoyte nulei uniquely identified in the setions. Assumptions of the Method Ability to serially setion through the whole glomerulus. Ability to identify podoyte nulei. Ability to identify profiles as representing the same podoyte nuleus in adjaent setions. Advantages over Alternative Methods Total podoyte number diretly determined for a given glomerulus Journal of the Amerian Soiety of Nephrology J Am So Nephrol 24: , 2013

7 BRIEF REVIEW Table 1. Overview of five methods Method Setioning Parameter Estimated Exhaustive enumeration Weibel and Gomez Serial setions Podoyte number per glomerulus (N pod,glom ) Single setions. Does not require knowledge of setion thikness Podoyte numerial density (NVpod,glom) Multipliation by Vglom provides Npod,glom Disetor/ Cavalieri ombination Pairs of physial or optial setions Podoyte number per glomerulus (N pod,glom ) Disetor/ frationator ombination Thik-and-thin setion method Pairs of physial setions or optial setions; does not require knowledge of setion thikness Multiple setions Podoyte number per glomerulus (N pod,glom ) Podoyte numerial density (NVpod,glom, number per glomerular volume) +, little time required to ++++, very time onsuming. Requires Complete Glomerulus? Assumptions Affeted by Sample Proessing? Unambiguous Identifiation of Podoyte Nulei Required? Time Consuming? Yes None No Yes ++++ Yes for individual glomeruli; no for average glomerular estimates Uniform distribution of podoytes in the glomerulus; size and shape of podoyte nulei known Only if glomerular volume (Vglom) is estimated from tissue proessed in a different manner Yes None Only if glomerular volume (Vglom) is estimated from tissue proessed in a different manner Yes for individual glomeruli; no for average glomerular estimates Yes (best by eletron mirosopy; light mirosopy may require speifi staining) Yes; use of multiple setions aids identifiation None No Yes; use of multiple setions aids identifiation +/++ (verifiation of model parameters would add signifiantly to time required) for average glomerulus estimates +++ for individual glomerular estimates No None Yes, if glomerular volume (Vglom) is estimated from tissue proessed in a different manner Yes (using speifi stains for light mirosopy) +++ J Am So Nephrol 24: , 2013 Estimating Podoyte Number 1199

8 No sampling error at the level of the glomerulus. Not affeted by hanges in tissue dimensions due to proessing. Adjaent setions an be used to help identify podoyte nulei. Disadvantages Compared with Alternative Methods Time onsuming. Only omplete glomeruli an be analyzed. Beause of the time-onsuming nature of the tehnique, unlikely to be used to estimate podoyte number per average glomerulus. 2. Weibel and Gomez Method The Basi Idea The number of podoyte nulei per unit volume of glomerulus (N Vpod,glom )anbe estimated from the number of podoyte nulear profiles per unit area of setioned glomerulus (N Apod,glom ) and the nulear areal fration (A Apod,glom) in a single setion through the glomerulus. Allowane must be made for the shape of the podoyte nulei and their variation in size. Prinipal Measurements The number of profiles of podoyte nulei (hits) per unit setion area of glomerulus (N Apod,glom ) and the areal fration of the referene (glomerular) area made up by these nulear profiles (A Apod,glom ). Multipliation of N Vpod,glom by glomerular volume (V glom, estimated for example using the Cavalieri priniple 8 ) provides an estimate of the total number of podoytes in the average glomerulus. Assumptions of the Method Podoyte nulei are uniformly distributed through the glomerulus. Podoyte nulear profiles an be unambiguously identified (even small profiles) in single setions. Podoyte nulei have idential known shapes, random orientations, and known size variation. Setion thikness is (muh) smaller than the mean aliper diameter (D) of podoyte nulei. Advantages over Alternative Methods Can be performed on single setions. Does not require knowledge of setion thikness. Does not require omplete glomeruli. Disadvantages Compared with Alternative Methods Requires signifiant effort to verify model assumptions (shape and size distribution of podoyte nulei) in eah experimental group. In most instanes requires eletron mirosopi images to derease bias due to setion thikness. 22 Also requires estimation of V glom to obtain N pod,glom. 3. Disetor/Cavalieri Combination The Basi Idea Podoyte nulei are ounted with physial disetors (whih use pairs of physial setions; Figure 2) or optial disetors (whih use optial setions; Figure 3). Podoyte nulei are ounted at a unique point (e.g., when they are sampled by the referene setion but not the look-up setion, when they are first seen, when they disappear, when they first ome into fous). Prinipal Measurements Obtain physial or optial setions a known distane apart from a random loation within the glomerulus. Count podoyte nulei using either physial or optial disetors. Measure the area of the glomerular profile in the referene setion. Determine the separation of the setions (the height of the disetor). Multipliation of podoyte numerial density (N Vpod,glom ) by glomerular volume (V glom, estimated using the Cavalieri priniple 8 ) provides an unbiased estimate of the number of podoytes in the glomerulus. Assumptions of the Method Podoyte nulear profiles an be reognized and unambiguously assigned as being from the same nuleus in adjaent setions (physial or optial). Mean aliper diameter ( D) of podoyte nulei is greater than the distane between setions (most nulei are hit twie in the paired setions). Advantages over Alternative Methods No assumptions of the shape, orientation, or size of podoyte nulei are required. Disadvantages Compared with Alternative Methods Time required to obtain two physial setions a known distane apart (annot rely on mirotome settings 19 ) or obtain optial setions. Time required to ompare presene or absene of speifi podoyte nulei in referene and look-up setions. Requires omplete setioning of glomeruli (for V glom ). 4. Disetor/Frationator Combination The Basi Idea Count podoytes using physial or optial disetors (see above) Journal of the Amerian Soiety of Nephrology J Am So Nephrol 24: , 2013

9 BRIEF REVIEW By knowing the fration of glomerular tissue analyzed (for either a single glomerulus or a population of glomeruli), one an use simple algebra to alulate the total number of podoytes in that individual glomerulus or in an average glomerulus. Prinipal Measurements Count podoyte nulei using physial disetors or optial disetors. Keep trak of the sampling frations used. Assumptions of the Method Podoyte nulear profiles an be reognized and unambiguously assigned as being from the same nuleus in adjaent setions (physial or optial). The fration of tissue used to ount podoytes is known. Advantages over Alternative Methods No assumptions of the shape, orientation, or size of podoyte nulei are required. Tehnial artifats, suh as setion ompression and tissue shrinkage, do not influene estimates. Knowledge of setion thikness is not required. Not neessary to estimate glomerular volume. Does not require omplete setioning of glomeruli to obtain average values (i.e., number of podoytes per average glomerulus). Disadvantages Compared with Alternative Methods Time required to obtain two setions a known distane apart (annot rely on mirotome settings 19 ) or obtain optial setions. Time required to ompare presene or absene of speifi podoyte nulei in referene and look-up setions. Requires omplete setioning of glomeruli to obtain podoyte numbers for individual glomeruli. 5. Thik-and-Thin Setion Method The Basi Idea Obtain multiple setions with two or more different speified thiknesses from random loations within the glomerulus. The number of podoyte nulei per unit glomerular volume (N Vpod,glom ) an be estimated from the inverse of the slope of the straight line formed by plotting setion thikness t (y axis) against the areal density of podoyte nulear profiles, N Apod,glom (x axis). Prinipal Measurements The number of podoyte nulear profiles per unit area of glomerular setion (N Apod,glom ) for setions of two or more known thiknesses. Assumptions of the Method Podoyte nulei an be unambiguously identified in any single setion. Advantages over Alternative Methods No assumptions about the shape, orientation, size or size distribution of podoyte nulei are required. Unlike the disetor, setions are not paired, and nulear profiles in different setions do not have to be reoniled. Does not require a omplete glomerulus to obtain average glomerular values (i.e., number of podoytes per average glomerulus). Disadvantages Compared with Alternative Methods Time needed to ut setions of at least two different thiknesses. Need to aurately determine the thiknesses of the setions. Requires omplete setioning of glomeruli (for V glom ) for estimation of podoyte number in individual glomeruli. DISCLOSURES None REFERENCES 1. Kriz W, Gretz N, Lemley KV: Progression of glomerular diseases: Is the podoyte the ulprit? Kidney Int 54: , Pagtalunan ME, Miller PL, Jumping-Eagle S, Nelson RG, Myers BD, Rennke HG, Coplon NS, Sun L, Meyer TW: Podoyte loss and progressive glomerular injury in type II diabetes. JClinInvest99: , Lemley KV, Lafayette RA, Safai M, Derby G, Blouh K, Squarer A, Myers BD: Podoytopenia and disease severity in IgA nephropathy. Kidney Int 61: , Matsusaka T, Xin J, Niwa S, Kobayashi K, Akatsuka A, Hashizume H, Wang Q-C, Pastan I, Fogo AB, Ihikawa I: Geneti engineering of glomerular slerosis in the mouse via ontrol of onset and severity of podoytespeifi injury. JAmSoNephrol16: , Wharram BL, Goyal M, Wiggins JE, Sanden SK, Hussain S, Filipiak WE, Saunders TL, Dysko RC, Kohno K, Holzman LB, Wiggins RC: Podoyte depletion auses glomeruloslerosis: Diphtheria toxin-indued podoyte depletion in rats expressing human diphtheria toxin reeptor transgene. JAmSo Nephrol 16: , Fukuda A, Wikman LT, Venkatareddy MP, Sato Y, Chowdhury MA, Wang SQ, Shedden KA, Dysko RC, Wiggins JE, Wiggins RC: Angiotensin II-dependent persistent podoyte loss from destabilized glomeruli auses progression of end stage kidney disease. Kidney Int 81: 40 55, Weibel ER: Pratial Methods for Biologial Morphometry, Stereologial Methods, Vol. 1, London, Aademi Press, 1979, pp Bertram JF: Analyzing renal glomeruli with the new stereology. Int Rev Cytol 161: , Nyengaard JR: Stereologi methods and their appliation in kidney researh. JAmSo Nephrol 10: , Glantz SA: Biostatistis: How to detet, orret and prevent errors in the medial literature. Cirulation 61: 1 7, Rosenhouse J: The Monty Hall Problem: the remarkable story of math s most ontentious brain teaser, New York, Oxford University Press, 2009 J Am So Nephrol 24: , 2013 Estimating Podoyte Number 1201

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