THE ANATOMICAL RECORD 232194-201 (1992)
Glomerular Number and Size in Relation to Age, Kidney Weight, and Body Surface in Normal Man J.R. NYENGAARD AND T.F. BENDTSEN Stereological Research Laboratory, University Institute of Pathology and 2nd. University Clinic of Internal Medicine, Institute of Experimental Clinical Research, Aarhus University, Denmark
ABSTRACT
The number and size of glomeruli in normal, mature human kidneys were estimated by a direct and unbiased stereological method, the fractionator. The number was 617,000 on average, and the mean size 6.0 M pm3. Both glomerular number and size showed significant negative correlation to age and significant positive correlation to kidney weight. Apparently, humans loose glomeruli with age. Body surface area correlated positively to kidney weight and total glomerular volume but not to number of glomeruli. Body surface area correlates significantly with metabolic rate (Robertson and Reid, Lancet, 1: 940-943, 1952). Thus, intraspecies adaptation of kidney filtration capacity to the metabolic demand is performed by changing the size of glomeruli, i.e., the number of glomeruli in individuals of a given species is independent of the metabolic rate.
In human adults, total metabolism declines significantly with age and rises proportionally with body surface area (BSA) (Robertson and Reid, 1952). Accordingly, renal function in terms of glomerular filtration rate (GFR) decreases with age and increases with BSA (Davies and Shock, 1950) in human adults, reflecting the different demand of the excretory function of the kidney. Waste products from metabolism are excreted mainly by filtration through the surface of the glomerular capillaries. The total filtration surface area of the glomerular capillaries is the product of the number of glomeruli, the mean glomerular volume, and the glomerular capillary surface area density. The variation of glomerular capillary surface area density among normal individuals is negligible. Variation of the filtration surface area is then essentially determined by variation of the total glomerular volume (the multiple of glomerular number and size) making total glomerular volume a useful indicator of total filtration surface area in normal man. The aim of the study was to determine whether a decline in metabolism and renal function with age corresponds to a decline in total filtration surface area, and, if so, whether such a decline is caused by fewer glomeruli or by smaller glomeruli. Also, this study attempted to analyze whether a relationship exists between BSA and total filtration surface area, and whether variation of total filtration surface area is related to variation of the glomerular number or the glomerular size. Enumeration of glomeruli has been performed for more than a century (Schweigger-Seidel, 18651,but so far no methods were available to generate a n unbiased estimate of the number of glomeruli in human kidneys (Bendtsen and Nyengaard, 1989). The fractionator (Gundersen, 1986) solves the problem as a design-based stereological sampling device independent of tissue deformation like swelling or shrinkage. An unbiased estimate of the number of glomeruli in a 0 1992 WILEY-LISS, INC.
practical way as described by Nyengaard and Bendtsen (1990) may for the first time answer the above-mentioned questions. MATERIALS
The kidneys were obtained from autopsy cases that showed no history of macroscopical kidney disease, congenital malformations, cachexia of any cause, or treatment with chemotherapy or regional X-rays. If patients were treated for hypertension or diagnosed as hypertensive during the final hospitalization andfor had abnormal kidney function (proteinuria, glucosuria, or increased S-creatinine), they were excluded, as were kidneys that later showed microscopic evidence of kidney disease. Only one kidney was chosen per cadaver; the choice of left or right was arbitrary, but essentially random. To improve the immersion fixation in formaldehyde, each kidney was split along the frontal plane into two halves. The kidneys were weighed after immersion fixation, and they were coded and blindly evaluated in the further processing. The results are based on a n equal number of men and women (Table I). METHODS
In this study a known fraction of a kidney was sampled and the glomeruli contained in the sample were counted. The total number of glomeruli in the kidney was estimated a s the inverse of the sampling fraction times the number of glomeruli in the sample. This
Received January 14, 1991; accepted September 3, 1991. Address reprint requests to J.R. Nyengaard, Stereological Research Laboratory, Bartholin Building, Aarhus University, DK-8000 Aarhus C. Denmark.
NUMBER AND SIZE OF HUMAN GLOMERULI
195
TABLE 1. Autopsy cases'
Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 31 32 33 34 35 36 37 Mean
cv
Age (years) 16 20 22 34 34 36 36 39 40 43 47 49 50 51 52 54 56 58 61 61 63 64 65 72 72 74 74 76 76 77 78 80 80 82 83 86 87 ~
Sex m f m f m f m m f m f f m m m m f f f m f m f f m f m m m f m m f f m f f
Height (cm) 171 166 170 159 179 173 173 177 163 167 155 168 178 174 171 166 179 164 159 163 148 172 172 165 171 161 169 164 167 165 173 176 143 151 168 162 155 166 0.05
BSA (m2) 1.71 1.58 2.26 1.47 1.95 1.76 2.00 1.90 1.60 1.71 1.56 1.54 1.97 2.28 1.86 1.76 1.86 1.56 1.49 1.65 1.34 1.88 1.72 1.82 1.69 1.67 1.72 1.45 1.87 1.63 1.54 1.90 1.24 1.56 1.58 1.54 1.40 1.70 0.13
Kidney weight (g) 95 104 147 137 155 199 167 159 107 145 138 181 196 206 171 187 132 113 123 119 102 117 114 122 190 123 145 99 147 100 109 80 99 91 124 88 91 131 0.26
Glom. number (lo3) 487 664 694 623 482 855 630 790 574 778 786 842 1,424 823 479 1056 645 667 391 737 562 567 500 539 626 554 608 561 763 413 608 331 393 428 675 551 522 617 0.25
5.87 5.17 7.54 6.91 8.97 7.04 6.63 7.31 3.89 6.39 5.78 5.55
Total glom.vo1. (cm3) 2.86 3.43 5.23 4.31 4.32 6.02 4.18 5.77 2.23 4.97 4.54 4.67
8.77 8.73 6.14 5.64 5.69 6.45 6.35 5.25 5.51 4.84 4.65 5.10 5.59 5.03 3.95 4.47 7.45 4.49 8.83 4.92 4.61 7.09 3.85 4.65 5.98 0.24
7.22 4.18 6.48 3.64 3.80 2.52 4.68 2.95 3.12 2.42 2.61 3.19 3.10 3.06 2.23 3.41 3.08 2.73 2.92 1.93 1.97 4.79 2.12 2.43 3.71 0.36
v( lom)
(10Q km3)
'Thirty-seven normal, adult autopsy cases are displayed with their age, sex, height, body surface area, kidney weight, glomerular number, mean glomerular volume, and total glomerular volume. Individual 13 is a n outlier with respect to the number of glomeruli: The estimate of the glomerular number deviates significantly from the group. We repeated the estimate, and the glomerular number was still significantly deviating. We concluded, that it did not come from the normal population and excluded it (Lentner, 1982, pp. 206-207). The mean results and coefficients of variation (CV) of height, body surface area, kidney weight, glomerular number, mean glomerular volume, and total glomerular volume of the remaining 36 normal human adults are shown.
study presents an unbiased sampling method combined with an unbiased counting method. The Fractionator-SamplingMethod
A kidney is arbitrarily cut in a number of pieces. A predetermined fraction of the pieces is sampled a t random, and the glomeruli in the sample are counted. The inverse of the sampling fraction times the number of glomeruli in the sample is then an unbiased estimate of the total number of glomeruli in the kidney. To reduce the variability of the unbiased estimate, the pieces are sectioned in roughly equal sizes and a sampling fraction is chosen, which assures the sampling of an adequate number of pieces. Variability is further reduced by making the sampling systematic, as demonstrated
in Figure 1, and by letting the sizes of the sampled slabs, in the initial sampling step, increase smoothly from the periphery towards the center in each kidney half. As long as any glomerulus in the kidney is sampled with equal probability determined a priori, the unbiasedness is not violated. A worked-out example follows. 1)Both kidney halves are cut exhaustively into 4-mm-thick slabs in the horizontal plane of the kidney. 2) A fourth of the slabs are sampled systematically, i.e., fi = 1/4. Among the first four slabs, the first slab is chosen using a random number (R) between one and four. Among the succeeding slabs every fourth is sampled. In the other kidney half, the first slab is chosen by R shifted by two (Fig. 1).3) Medulla is cut out from the sampled slabs, but a nar-
J.R. NYENGAARD AND T.F. BENDTSEN
196
Fig. 1. The initial sampling is performed, when the kidney has been cut into slabs. The first slab is sampled by means of a random number between 1 and 4, after which every fourth slab is sampled (indicated by crosses). The sampled slabs are cut into strips and every seventh strip is sampled similarly. The sampled strips are cut into blocks and every seventh block is sampled similarly. Thus the obtained sample contains 1/4.1/7.1/7 = ‘/I96 of the whole kidney and of all glomeruli.
ally sectioned on a LKB Historange microtome with a section thickness t of 15 pm. 9) Every eighth section is sampled systematically (f, = %). Until now 1/4.1/7.1/7.1/8 = %,568 of the renal cortex has been sampled. For every sampled section the succeeding section is collected as well, for the purpose of counting. The succeeding sections are called “look-up sections” in the following. 10) The sections are stained with PAS. 11)Two identical Zeiss light microscopes were placed side-by-side for viewing the sampled and the look-up sections simultaneously. Each microscope projects onto a table using a projection mirror in front of the monocular tube. A counting grid is placed on the projected field of vision of the sampling section. 12) The stage of the microscope with the sampling section is moved by a motor in predetermined, equidistant steps in two orthogonal directions. In this final sampling step, the counting grid covers a known fraction of the histological section, fa, called the areal fraction. The total grid area is 59,731 mm2 and the final linear magnification is x 115. Consequently, the area of the section covered by the grid (grid area) is 59,731/1~52mm2 = 4.52 mm2. The motor was adjusted to step 3.27 mm along the length of the slide and 3.05 mm orthogonal to the length. This means that the fraction of the section area covered by the grid that moved in predetermined steps is fa = 4.52/(3.z7.3.05) = 0.45. Finally, the total sampling fraction of the renal cortex is 0.45 . & = 1/3,484. The Disector-Counting Method
A glomerulus is counted if it appears in a sampled field of vision and is not present in the look-up section. This event appears only once per glomerulus in the section series (Sterio, 1984). Consequently, all glomeruli are sampled with a n equal, known a priori probability. The number of counted glomeruli is indicated by
\*
0
60
30
9 0 years
CQ-.
On the counting grid a point is placed arbitrarily. The point is used to estimate the fraction of tissue that may be used for glomerular counting CPJiP,. The total Fig. 2. The number of glomeruli per kidney declines significantly number of times the point hits the cortical area a t all is with age, 2P < 0.05; r = -0.35. Two possible explanations exist: Normal human beings may loose glomeruli with age, or more un- XPs. As described below, ZPf is the total number of likely, older human beings were born with fewer glomeruli than times the point hits tissue allowed for glomerular younger human beings. Apparently, the number of glomeruli starts to counting: a) Before counting every tissue block is foldecline about the age of 60 years. lowed through the series of sampled sections. The sections in the middle of the series, containing intact prorow rim of medulla is kept to assure that no glomeruli files of the tissue block, are circumscribed. Sections not are excised. 4) The sampled slabs are embedded in agar circumscribed have been cut too close to artificial surside by side in the original sequence. They are cut in faces and are excluded from glomerular counting and the sagittal plane of the kidney into 5 mm strips. 5) are used for estimation of ZP, only. b) Glomeruli interEvery seventh strip is sampled, i.e., f2 = %. The first sected by the artificial edges produced by the cutting in strip is chosen by means of a random number table. the sampling procedure or intersected by the margin of The next strip may be systematically sampled as de- the field of vision cannot be sampled, because their scribed under item (2). To reduce the variability fur- identity is ambigous or intersected glomeruli may have ther the “Modulus System” was used in this study (Fig. been lost. A glomerulus is counted if it is sampled in 2, Nyengaard and Bendtsen, 1990). 6) The sampled accordance with the unbiased two-dimensional samstrips are embedded side by side in agar in the original pling rule only if there is no artificial edges of the secsequence and are cut perpendicular to their length in tion within the guard area (Fig. 3, Nyengaard and 1.5 mm agar slices. These agar slices contain kidne Bendtsen, 1990; Gundersen 1977). Accordingly, a point blocks with maximal dimensions of 4.5.1.5 = 30 mmJ. hitting cortical tissue with a n artificial edge in the 7) Every seventh block is sampled (f3 = %). The sam- guard area is used only for estimation of CP,. The size pled blocks were chosen as described under item (5). of the guard area is decided in accordance with the The first block is always chosen by a random number maximal size of the glomeruli. table. 8) The sampled blocks are dehydrated, infilIn our example, total sampling fraction = %,484, ZP, trated, and embedded in plastic blocks, which are seri- = 125, ZP, = 215, and CQ- = 104: Age
197
NUMBER AND SIZE OF HUMAN GLOMERULI
The section thickness t, the grid area, CP,, and ZQ- are all explained above. When the stage of the microscope with the sampled section steps as described in item (121, the number of times cortex was hit by a point on the above-mentioned grid was counted CP(cor). Ten arbitrarily placed points on the grid hitting glomerular profiles, ZP(glom1, were also counted. The volume fraction of glomeruli in cortex then is
0
100
50
200 g
150
Kidney weight
Fig. 3. The number of glomeruli is significantly, positively correlated with kidney weight, 2P 0.05; r = 0.26). The BSA declines with age (2P < 0,05; r = -0.38); however, the positive correlation of BSA and kidney weight is significant, even after the effect of age is eliminated (2P
Glomerular Number and Size in Relation to Age, Kidney Weight, and Body Surface in Normal Man J.R. NYENGAARD AND T.F. BENDTSEN Stereological Research Laboratory, University Institute of Pathology and 2nd. University Clinic of Internal Medicine, Institute of Experimental Clinical Research, Aarhus University, Denmark
ABSTRACT
The number and size of glomeruli in normal, mature human kidneys were estimated by a direct and unbiased stereological method, the fractionator. The number was 617,000 on average, and the mean size 6.0 M pm3. Both glomerular number and size showed significant negative correlation to age and significant positive correlation to kidney weight. Apparently, humans loose glomeruli with age. Body surface area correlated positively to kidney weight and total glomerular volume but not to number of glomeruli. Body surface area correlates significantly with metabolic rate (Robertson and Reid, Lancet, 1: 940-943, 1952). Thus, intraspecies adaptation of kidney filtration capacity to the metabolic demand is performed by changing the size of glomeruli, i.e., the number of glomeruli in individuals of a given species is independent of the metabolic rate.
In human adults, total metabolism declines significantly with age and rises proportionally with body surface area (BSA) (Robertson and Reid, 1952). Accordingly, renal function in terms of glomerular filtration rate (GFR) decreases with age and increases with BSA (Davies and Shock, 1950) in human adults, reflecting the different demand of the excretory function of the kidney. Waste products from metabolism are excreted mainly by filtration through the surface of the glomerular capillaries. The total filtration surface area of the glomerular capillaries is the product of the number of glomeruli, the mean glomerular volume, and the glomerular capillary surface area density. The variation of glomerular capillary surface area density among normal individuals is negligible. Variation of the filtration surface area is then essentially determined by variation of the total glomerular volume (the multiple of glomerular number and size) making total glomerular volume a useful indicator of total filtration surface area in normal man. The aim of the study was to determine whether a decline in metabolism and renal function with age corresponds to a decline in total filtration surface area, and, if so, whether such a decline is caused by fewer glomeruli or by smaller glomeruli. Also, this study attempted to analyze whether a relationship exists between BSA and total filtration surface area, and whether variation of total filtration surface area is related to variation of the glomerular number or the glomerular size. Enumeration of glomeruli has been performed for more than a century (Schweigger-Seidel, 18651,but so far no methods were available to generate a n unbiased estimate of the number of glomeruli in human kidneys (Bendtsen and Nyengaard, 1989). The fractionator (Gundersen, 1986) solves the problem as a design-based stereological sampling device independent of tissue deformation like swelling or shrinkage. An unbiased estimate of the number of glomeruli in a 0 1992 WILEY-LISS, INC.
practical way as described by Nyengaard and Bendtsen (1990) may for the first time answer the above-mentioned questions. MATERIALS
The kidneys were obtained from autopsy cases that showed no history of macroscopical kidney disease, congenital malformations, cachexia of any cause, or treatment with chemotherapy or regional X-rays. If patients were treated for hypertension or diagnosed as hypertensive during the final hospitalization andfor had abnormal kidney function (proteinuria, glucosuria, or increased S-creatinine), they were excluded, as were kidneys that later showed microscopic evidence of kidney disease. Only one kidney was chosen per cadaver; the choice of left or right was arbitrary, but essentially random. To improve the immersion fixation in formaldehyde, each kidney was split along the frontal plane into two halves. The kidneys were weighed after immersion fixation, and they were coded and blindly evaluated in the further processing. The results are based on a n equal number of men and women (Table I). METHODS
In this study a known fraction of a kidney was sampled and the glomeruli contained in the sample were counted. The total number of glomeruli in the kidney was estimated a s the inverse of the sampling fraction times the number of glomeruli in the sample. This
Received January 14, 1991; accepted September 3, 1991. Address reprint requests to J.R. Nyengaard, Stereological Research Laboratory, Bartholin Building, Aarhus University, DK-8000 Aarhus C. Denmark.
NUMBER AND SIZE OF HUMAN GLOMERULI
195
TABLE 1. Autopsy cases'
Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 31 32 33 34 35 36 37 Mean
cv
Age (years) 16 20 22 34 34 36 36 39 40 43 47 49 50 51 52 54 56 58 61 61 63 64 65 72 72 74 74 76 76 77 78 80 80 82 83 86 87 ~
Sex m f m f m f m m f m f f m m m m f f f m f m f f m f m m m f m m f f m f f
Height (cm) 171 166 170 159 179 173 173 177 163 167 155 168 178 174 171 166 179 164 159 163 148 172 172 165 171 161 169 164 167 165 173 176 143 151 168 162 155 166 0.05
BSA (m2) 1.71 1.58 2.26 1.47 1.95 1.76 2.00 1.90 1.60 1.71 1.56 1.54 1.97 2.28 1.86 1.76 1.86 1.56 1.49 1.65 1.34 1.88 1.72 1.82 1.69 1.67 1.72 1.45 1.87 1.63 1.54 1.90 1.24 1.56 1.58 1.54 1.40 1.70 0.13
Kidney weight (g) 95 104 147 137 155 199 167 159 107 145 138 181 196 206 171 187 132 113 123 119 102 117 114 122 190 123 145 99 147 100 109 80 99 91 124 88 91 131 0.26
Glom. number (lo3) 487 664 694 623 482 855 630 790 574 778 786 842 1,424 823 479 1056 645 667 391 737 562 567 500 539 626 554 608 561 763 413 608 331 393 428 675 551 522 617 0.25
5.87 5.17 7.54 6.91 8.97 7.04 6.63 7.31 3.89 6.39 5.78 5.55
Total glom.vo1. (cm3) 2.86 3.43 5.23 4.31 4.32 6.02 4.18 5.77 2.23 4.97 4.54 4.67
8.77 8.73 6.14 5.64 5.69 6.45 6.35 5.25 5.51 4.84 4.65 5.10 5.59 5.03 3.95 4.47 7.45 4.49 8.83 4.92 4.61 7.09 3.85 4.65 5.98 0.24
7.22 4.18 6.48 3.64 3.80 2.52 4.68 2.95 3.12 2.42 2.61 3.19 3.10 3.06 2.23 3.41 3.08 2.73 2.92 1.93 1.97 4.79 2.12 2.43 3.71 0.36
v( lom)
(10Q km3)
'Thirty-seven normal, adult autopsy cases are displayed with their age, sex, height, body surface area, kidney weight, glomerular number, mean glomerular volume, and total glomerular volume. Individual 13 is a n outlier with respect to the number of glomeruli: The estimate of the glomerular number deviates significantly from the group. We repeated the estimate, and the glomerular number was still significantly deviating. We concluded, that it did not come from the normal population and excluded it (Lentner, 1982, pp. 206-207). The mean results and coefficients of variation (CV) of height, body surface area, kidney weight, glomerular number, mean glomerular volume, and total glomerular volume of the remaining 36 normal human adults are shown.
study presents an unbiased sampling method combined with an unbiased counting method. The Fractionator-SamplingMethod
A kidney is arbitrarily cut in a number of pieces. A predetermined fraction of the pieces is sampled a t random, and the glomeruli in the sample are counted. The inverse of the sampling fraction times the number of glomeruli in the sample is then an unbiased estimate of the total number of glomeruli in the kidney. To reduce the variability of the unbiased estimate, the pieces are sectioned in roughly equal sizes and a sampling fraction is chosen, which assures the sampling of an adequate number of pieces. Variability is further reduced by making the sampling systematic, as demonstrated
in Figure 1, and by letting the sizes of the sampled slabs, in the initial sampling step, increase smoothly from the periphery towards the center in each kidney half. As long as any glomerulus in the kidney is sampled with equal probability determined a priori, the unbiasedness is not violated. A worked-out example follows. 1)Both kidney halves are cut exhaustively into 4-mm-thick slabs in the horizontal plane of the kidney. 2) A fourth of the slabs are sampled systematically, i.e., fi = 1/4. Among the first four slabs, the first slab is chosen using a random number (R) between one and four. Among the succeeding slabs every fourth is sampled. In the other kidney half, the first slab is chosen by R shifted by two (Fig. 1).3) Medulla is cut out from the sampled slabs, but a nar-
J.R. NYENGAARD AND T.F. BENDTSEN
196
Fig. 1. The initial sampling is performed, when the kidney has been cut into slabs. The first slab is sampled by means of a random number between 1 and 4, after which every fourth slab is sampled (indicated by crosses). The sampled slabs are cut into strips and every seventh strip is sampled similarly. The sampled strips are cut into blocks and every seventh block is sampled similarly. Thus the obtained sample contains 1/4.1/7.1/7 = ‘/I96 of the whole kidney and of all glomeruli.
ally sectioned on a LKB Historange microtome with a section thickness t of 15 pm. 9) Every eighth section is sampled systematically (f, = %). Until now 1/4.1/7.1/7.1/8 = %,568 of the renal cortex has been sampled. For every sampled section the succeeding section is collected as well, for the purpose of counting. The succeeding sections are called “look-up sections” in the following. 10) The sections are stained with PAS. 11)Two identical Zeiss light microscopes were placed side-by-side for viewing the sampled and the look-up sections simultaneously. Each microscope projects onto a table using a projection mirror in front of the monocular tube. A counting grid is placed on the projected field of vision of the sampling section. 12) The stage of the microscope with the sampling section is moved by a motor in predetermined, equidistant steps in two orthogonal directions. In this final sampling step, the counting grid covers a known fraction of the histological section, fa, called the areal fraction. The total grid area is 59,731 mm2 and the final linear magnification is x 115. Consequently, the area of the section covered by the grid (grid area) is 59,731/1~52mm2 = 4.52 mm2. The motor was adjusted to step 3.27 mm along the length of the slide and 3.05 mm orthogonal to the length. This means that the fraction of the section area covered by the grid that moved in predetermined steps is fa = 4.52/(3.z7.3.05) = 0.45. Finally, the total sampling fraction of the renal cortex is 0.45 . & = 1/3,484. The Disector-Counting Method
A glomerulus is counted if it appears in a sampled field of vision and is not present in the look-up section. This event appears only once per glomerulus in the section series (Sterio, 1984). Consequently, all glomeruli are sampled with a n equal, known a priori probability. The number of counted glomeruli is indicated by
\*
0
60
30
9 0 years
CQ-.
On the counting grid a point is placed arbitrarily. The point is used to estimate the fraction of tissue that may be used for glomerular counting CPJiP,. The total Fig. 2. The number of glomeruli per kidney declines significantly number of times the point hits the cortical area a t all is with age, 2P < 0.05; r = -0.35. Two possible explanations exist: Normal human beings may loose glomeruli with age, or more un- XPs. As described below, ZPf is the total number of likely, older human beings were born with fewer glomeruli than times the point hits tissue allowed for glomerular younger human beings. Apparently, the number of glomeruli starts to counting: a) Before counting every tissue block is foldecline about the age of 60 years. lowed through the series of sampled sections. The sections in the middle of the series, containing intact prorow rim of medulla is kept to assure that no glomeruli files of the tissue block, are circumscribed. Sections not are excised. 4) The sampled slabs are embedded in agar circumscribed have been cut too close to artificial surside by side in the original sequence. They are cut in faces and are excluded from glomerular counting and the sagittal plane of the kidney into 5 mm strips. 5) are used for estimation of ZP, only. b) Glomeruli interEvery seventh strip is sampled, i.e., f2 = %. The first sected by the artificial edges produced by the cutting in strip is chosen by means of a random number table. the sampling procedure or intersected by the margin of The next strip may be systematically sampled as de- the field of vision cannot be sampled, because their scribed under item (2). To reduce the variability fur- identity is ambigous or intersected glomeruli may have ther the “Modulus System” was used in this study (Fig. been lost. A glomerulus is counted if it is sampled in 2, Nyengaard and Bendtsen, 1990). 6) The sampled accordance with the unbiased two-dimensional samstrips are embedded side by side in agar in the original pling rule only if there is no artificial edges of the secsequence and are cut perpendicular to their length in tion within the guard area (Fig. 3, Nyengaard and 1.5 mm agar slices. These agar slices contain kidne Bendtsen, 1990; Gundersen 1977). Accordingly, a point blocks with maximal dimensions of 4.5.1.5 = 30 mmJ. hitting cortical tissue with a n artificial edge in the 7) Every seventh block is sampled (f3 = %). The sam- guard area is used only for estimation of CP,. The size pled blocks were chosen as described under item (5). of the guard area is decided in accordance with the The first block is always chosen by a random number maximal size of the glomeruli. table. 8) The sampled blocks are dehydrated, infilIn our example, total sampling fraction = %,484, ZP, trated, and embedded in plastic blocks, which are seri- = 125, ZP, = 215, and CQ- = 104: Age
197
NUMBER AND SIZE OF HUMAN GLOMERULI
The section thickness t, the grid area, CP,, and ZQ- are all explained above. When the stage of the microscope with the sampled section steps as described in item (121, the number of times cortex was hit by a point on the above-mentioned grid was counted CP(cor). Ten arbitrarily placed points on the grid hitting glomerular profiles, ZP(glom1, were also counted. The volume fraction of glomeruli in cortex then is
0
100
50
200 g
150
Kidney weight
Fig. 3. The number of glomeruli is significantly, positively correlated with kidney weight, 2P 0.05; r = 0.26). The BSA declines with age (2P < 0,05; r = -0.38); however, the positive correlation of BSA and kidney weight is significant, even after the effect of age is eliminated (2P
