JOURNAL OF HONE A N D MINERAL RESEARCH Volume 6, Numher 12, 1991 Mary Ann Liebert, Inc., Publishers
A New Method for Measuring Cancellous Bone Erosion Depth: Application to the Cellular Mechanisms of Bone Loss in Postmenopausal Osteoporosis MARTINE E. COHEN-SOLAL,'.' MEI-SHU SHIH,' MARK W. L U N D Y , ' and A. MICHAEL PARFITTI
ABSTRACT We have devised a new method for measurement of final depth of erosion in cancellous bone with an intraindividual precision of 4.3% and applied it to determine the mechanism of continuing reduction in trabecular thickness after menopause. Mean erosion depth (SD) was 40.8 (2.0) pm in 10 healthy postmenopausal women and 41.4 (2.1) pm in 10 age-matched patients with postmenopausal osteoporosis; the difference was not statistically significant. In contrast, wall thickness, using a method based on density differences between new and old bone, was 39.5 (2.0) pm in the normal subjects and 35.3 (2.0) pm in the patients with osteoporosis 0, < 0.0001). The balance per remodeling cycle (ABMU) was -1.34 (2.49) pm in the normal subjects and -6.11 (1.95) pm in the patients with osteoporosis. This difference was also highly significant (p < 0.001). Indirect estimations of erosion depth and ABMU, based on the fall in trabecular thickness from an assumed premenopausal value of 147 pm and the number of remodeling cycles accumulated since menopause, agreed closely with the measured values. Erosion depth measured by the Eriksen method also showed no significant difference between the two groups, but because the values were substantially higher ABMU was improbably high in both groups, did not differ significantly between groups, and was inconsistent with the observed difference in trabecular thickness. We conclude that (1) the more rapid continuing loss of cancellous bone in patients with postmenopausal osteoporosis than in age-matched control subjects is due entirely to a difference in wall thickness, not to a difference in erosion depth; and (2) defective recruitment and/or function of osteoblasts is the major cellular mechanism of trabecular thinning in patients with postmenopausal osteoporosis and probably also in normal subjects. We emphasize that these conclusions do not speak to the mechanism of complete removal of trabeculae in the early years after menopause.
INTRODUCTION has generated great interest these past few years because of its public health consequences. Methods of diagnosis have improved, but a fuller understanding of pathophysiologic mechanisms is crucial to develop new approaches to treatment. According to the quantum concept of bone remodeling,") all gains or losses of bone are the result of focal imbalance, during individual remodeling cycles, between the depth of a cavity
P
OSTMENOPACJSALOSTEOPOROSIS
eroded by a team of osteoclasts and the thickness of new bone deposited in the cavity by a team of osteoblasts. The summation of all such transactions determines the cumulative change in bone surface location, so that the rate of change also depends on how frequently new cycles are initiated. The purpose of histomorphometry is to provide in vivo information about these cellular mechanisms.(') A decline in wall thickness with aging and in osteoporosis is well e s t a b l i ~ h e d , ( ~but - ~ )much less information is available about erosion depth.
'Bone and Mincral Research Laboratory, Henry Ford Hospital, Detroit, Michigan. 'Present affiliation: Inserm Unite 18, Paris, France.
1331
1332
COHEN-SOLAL ET AL.
One method of measuring erosion depth is to count the number of lamellae that have been eroded adjacent to each cavity, since these are of relatively constant mean thickness.") Using this method, it was found that resorption but was increased in padepth tended to fall with tients with postmenopausal osteoporosis manifested by vertebral compression fractures. ( l o ) An alternative method was recently proposed in which the original location of the surface before the onset of resorption is reconstructed from the contours of the adjacent bone and both the mean depth and the maximum depth in each cavity determined by direct measurement,('l) but this method has not yet been applied to osteoporosis. In this study, we describe a new method of measuring erosion depth that has some features in common with each of the previous methods and present the results of applying this method to determine the mechanisms of continuing cancellous bone loss in postmenopausal osteopornsis.
SUBJECTS AND METHODS
using a computerized semiautomatic system phometry' (Bioquant System IV, R&M Biometrics, Nashville, TN); data from the cancellous surface only are reported. Tetracycline-based indices and wall width were measured on prestained sections, and other measurements were made on toluidine blue-stained sections. All distances were measured directly rather than indirectly.(I4' Calculations were performed as previously described,"') except that a correction was applied for the difference in length between the first and second labels.(Is) Data are expressed in three-di~ appropriate to conmensional terms using ~ / or 4 4 / as vert from the primary two-dimensional data.''4) Wall width was measured, at x 100 original magnification, from quiescent surfaces to the nearest line of sharp change in color from dark to pale green in the Villanueva prestained sections examined under ultraviolet light.'16) This method of demarcating the boundary of bone structural units has recently been validated by demonstrating that the change in color corresponds to a change in calcium content determined by scanning electron microscopy combined with x-ray microanalysis, and thus to a difference in age.(17'Sites of measurement were selected by random rotation of an eyepiece graticule containing 10 parallel lines to locate intersections, at which orthogonal intercept lengths were measured by digitization. On average, 21 sites (range 10-41) were measured in the normal subjects and 17 (6-27) in the patients. Erosion depth (E.De) was measured by two different methods. The first method was that proposed by Eriksen and colleagues,(1R)but without the assumption of a constant value for lamellae thickness (Lm.Th). All four available sections were used; there was no difference between the toluidine blue and prestained only sections, so that the data were pooled. The entire section was first examined at x 100 magnification. Measurement sites were randomly located as for wall width but including only intersections between graticule lines and surfaces covered by either preosteoblasts or osteoid, assumed to indicate that resorption had terminated at that location.(") For each cavity, the number of adjacent lamellae was counted, and in addition, the width of each individual lamella was measured at x 200 magnification and a mean lamellar width calculated for that cavity. Erosion depth was then calculated separately for each cavity:
A group of 10 healthy white postmenopausal women whose age [mean (standard deviation, SD)] was 60.7 ( 8 . 5 ) years served as controls; the mean years since menopause was 9.4 (range 3-19). They were recruited in response to a hospital newsletter or by word of mouth in accordance with a protocol approved by the institutional human rights committee. They were in good health, gave no history of any disease or drug exposure known to affect bone, were normal on physical examination, had normal indices of bone mineral metabolism, normal spinal radiographs, and normal values for forearm bone densitometry, and gave informed consent. Six of them had received calcium supplementation 1 &day for 3-4 months before the biopsy; in each an earlier biopsy had been obtained on the opposite side 1-2 years earlier, but the material remaining was insufficient for the present study. A group of 10 white postmenopausal women aged 60.8 (5.4) years underwent evaluation for osteoporosis. The mean years since menopause was 13.9 (range 2-24), not significantly different from the controls. Each had had at least one nontraumatic vertebral compression fracture. No other etiology was found, and they were receiving no medication interfering with bone metabolism, except that three were taking a calcium supE.De (pm) = Lm.Nb x Lm.Th (pm) plement of 500-1000 mg/day. The patients were younger (1) than usual, since they were selected to be age matched with the control subjects. Plasma calcium, inorganic phosphate, where Lm.Nb is lamellar number. For each subject, the alkaline phosphatase, and creatinine values were normal in mean of these individual values was used. O n the average, 8 sites suitable for measurement (4-13) were found in the all subjects. Transiliac bone biopsies were obtained in each subject normal subjects, and 5.4 (3-8) in the patients; these numafter in vivo double-tetracycline labeling. The samples bers d o not include an additional 1-5 sites in each subject were placed in 70% ethanol, prestained by the Villanueva in whom no measurement was possible. For measurement of erosion depth by the second method, embedded in polymethyl methacrylate, and sectioned with a Jung-K microtome.(I*)Two 5 pm consecutive method, only the toluidine blue sections were used. We sesections were obtained: the first was stained with toluidine lected only lacunae that fulfilled three criteria. First, they blue''3) and the second was prestained only. The block was were mainly covered by osteoid, to be certain that resorpreversed, and a second pair of sections was obtained from tion was complete over most of the lacunar surface. Secthe other side and the same procedure used for staining. ond, eroded lamellae were still visible at each extremity, so The first pair of sections was used for standard histomor- that although formation had begun it was still a long way
1333
EROSION DEPTH IN POSTMENOPAUSAL OSTEOPOROSIS from completion. Third, the new cement line, marking the furthest extent of erosion at any location, was clearly identifiable. For all such lacunae, a line joining the adjacent quiescent surfaces was drawn on the display screen by following the contours of the intact trabecular surface on either side (Fig. 1). Measurements were made at x 100 original magnification of orthogonal intercept length between this line and the closest cement line at intersections selected randomly by the same procedure. On the average, 33 intersections (20-54) from 9 (5-13) sites were selected in the normal subjects and 25 (13-36) intersections from 7.5 (5-10) sites in the patients. The number of sites was slightly larger than for the first method because of the difference in method of selection. The second method resembles the first with respect to including criteria for termination of resorption but differs from i t in applying these criteria to complete remodeling sites rather than to individual intersections. The method resembles that of Garrahan et al.("' in reconstructing the original surface location, but differs from it in applying this only to sites in which resorption has been completed, not where it is still in progress. To assess the reproducibility of the new method, all sets of slides were remeasured by the same observer after an interval of 1 month. T o interpret erosion depth, it is necessary to calculate activation frequency (Ac.f), representing the birth rate of
new remodeling sites. The total amount of bone formed can be regarded as the product of the average amount so that formed in each cycle and the number of BFR/BS (pm3/pm*/year)
=
Ac.f(year-') x W.Th (pm) (2)
where BFR/BS = bone formation r a t e h o n e surface. From which it follows that Ac.f(year-I) = BFR/BS (pm3/pm2/year)/W.Th (pm) (3) Several other indices of bone resorption werc then calculated from the erosion depth.(*.8.14'The erosion period (EP), including both resorption period and recersal period, is derived from the formation period (FP) and is given by EP (days) = ES x
0s FP (days)
(4)
where 0s = osteoid surface. The erosion rate (ER), exprcssed as movement of the erosion front perpendicular to the surface, averaged throughout the erosion period, is given by ER (pm/day) = E.De (pm)/EP (days)
(5)
The bone surface-based bone resorption rate (BRs.R/ BS) is the product of mean erosion depth and the probability that erosion will begin at any point on the surface in a
FIG. 1. Region of cancellous bone from a normal subject illustrating the method for measuring erosion depth. Note unfilled eroded surface at the right-hand margin of the cavity. The unlabeled arrows identify four representative sites for measuring the distance between the reconstructed surface and the cement line.
COHEN-SOLAL ET AL.
1334
defined time period. In a steady state, this probability is the same as Ac.f calculated from the formation indices, so that BRs.R/BS (pm3/pm2/year) = Ac.f(year-I) x E.De (pm) (6) The similarity in form between this and Eq. (2) should be noted. The bone volume-based resorption rate (BRs.R/ BV) is given by BRs.R/BV (%/year)
=
BRs.R/BS (pm3/~m2/year) (7) x BS/BV (mm2/mm3) x 100/1OOo
The bone balance at the basic multicellular unit (BMU) level (ABMU), which is the average outcome of each remodeling transaction, is given by ABMU (pm)
=
W.Th (pm) - E.De (pm)
(8)
The bone balance at the bone surface level is expressed as the average rate of movement of the surface toward or away from the midline of a trabecula and depends on the average change per cycle and the number of cycles completed in unit time, so that
of remodeling cycles accumulated since menopause (N.Cy), the mean value for Ac.f was multiplied by the mean value for years since menopause for each group. For measurements at multiple sites in a single subject, individual means, standard deviations, and coefficients of variation (CV = SD/mean x 100) were calculated and the individual means used for calculation of group means and SD. For each variable, differences between groups were tested by two-tailed unpaired Student's f-tests'21'; significance values were adjusted for the total number of comparisons. For selected pairs of variables, their relationship was assessed by linear regression analysis. The intraobserver precision of the second method was calculated as expressed as a percentage of the overall mean value,'*2) where D is the difference between paired measurements and n is the number of pairs (20). All calculations were performed using the CSS statistical package (Complete Statistical System, Statsoft Inc., Tulsa, OK).
m,
RESULTS
The results of standard histomorphometry are given in Table 1. The various indices of microstructure showed the expected differences between the two groups.(I.'O) The ABS (pm/year) = Ac.f (year'') x ABMU (pm) (9) greater than usual difference in trabecular thickness may = Ac.f (year'') x (W.Th - E.De) (pm) have resulted from the relatively low age, since the absolute difference between osteoporotic patients and ageAn alternative expression for this relationship, in terms matched control subjects declines with increasing age.") of primary measurements only, can be derived by combi- The difference in W.Th was smallest in magnitude (10%) nation with Eq. (3): but was most highly significant because of the greater precision of this measurement; the individual CV averaged ABS (pm/year) (10) about 25% and individual precision [standard error of the = BFR/BS (pm3/pm2/year) ( 1 - E.De/W.Th) mean, (SEM)/mean x 1001 about 6% and did not differ beThe bone balance at the bone surface level can also be ex- tween the groups. Bone formation rate and Ac.f were pressed as the rate of bone loss or gain per unit of bone lower in the osteoporotic patients than in the normal subjects to about the same extent as previously reported,") surface: but the differences were not statistically significant with ABV/BS (pm3/pm2/year) ( 1 1) these small samples. = (BFR/BS - BRs.R/BS) (pm3/pm2/year) There was no significant difference in lamellar width beThe bone balance at the bone volume level expresses bone tween the two groups, whether the unit of observation in lost per unit time as a fraction of the amount present, each subject was the individual lamella or the average for which is equivalent to a rate constant and is given by each cavity (Table 2). The values are about 16% lower than previously because we did not use the ABV/BV (%/year) (12) stereologic unfolding procedure originally devised for glo= ABS (p3/pm2/year BS/BV (mm2/mm') x 100/1OOo merular basement As others have ob= (BFR/BV - BRs.R/BV) (%/year) there was substantial variation in width between lamellae in each individual, with an average CV of about For comparison with the direct methods, ABMU and 35%. We also found somewhat more variation between inE.De were also estimated indirectly from a modified form dividuals, with a CV of about 7% in the normal subject of Eq. (9), relating total cumulative change in surface loca- and 11% in the patients compared to previous reports of tion to the cumulative number of cycles (N.Cy).(I9) about 5%.(7.18) There was no significant difference between the number of eroded lamellae in the two groups ABS (pm) = N.Cy x ABMU (pm) (13) (Table 2). Since there was also no difference in lamellar thickness, there was no difference in mean erosion depth T o obtain ABS for solving this equation, the mean value by the first (Eriksen) method (Table 3). There were also no for trabecular thickness in each group was subtracted from significant differences in any of the derived indices of rethe mean value for healthy premenopausal women of 147 sorption or bone balance based on this method. The intraindividual precision of the second (new) Fm(20)and the results divided by 2 to allow for bone loss on both sides of a trabecula. To estimate the total number method for measuring erosion depth was 4.3%; for com-
1335
EROSION DEPTH IN POSTMENOPAUSAL OSTEOPOROSIS TABLE1. SELECTED HISTOMORPHOMETRIC VARIABLES~
Variables Characterization of groups BV/TV, ’?lo Tb.Nb, mm-I Tb.Sp, pm O.Th, pm OS/BS, 070 Aj.AR, pm/day FP, days Further analysis Tb.Th, pm ES/BS, 070 W.Th, pm BFR/BS, pm3/pm’/year BFWBV, %/year Ac.f, year-‘ EP, days
Control
Osteoporosis
P
A New Method for Measuring Cancellous Bone Erosion Depth: Application to the Cellular Mechanisms of Bone Loss in Postmenopausal Osteoporosis MARTINE E. COHEN-SOLAL,'.' MEI-SHU SHIH,' MARK W. L U N D Y , ' and A. MICHAEL PARFITTI
ABSTRACT We have devised a new method for measurement of final depth of erosion in cancellous bone with an intraindividual precision of 4.3% and applied it to determine the mechanism of continuing reduction in trabecular thickness after menopause. Mean erosion depth (SD) was 40.8 (2.0) pm in 10 healthy postmenopausal women and 41.4 (2.1) pm in 10 age-matched patients with postmenopausal osteoporosis; the difference was not statistically significant. In contrast, wall thickness, using a method based on density differences between new and old bone, was 39.5 (2.0) pm in the normal subjects and 35.3 (2.0) pm in the patients with osteoporosis 0, < 0.0001). The balance per remodeling cycle (ABMU) was -1.34 (2.49) pm in the normal subjects and -6.11 (1.95) pm in the patients with osteoporosis. This difference was also highly significant (p < 0.001). Indirect estimations of erosion depth and ABMU, based on the fall in trabecular thickness from an assumed premenopausal value of 147 pm and the number of remodeling cycles accumulated since menopause, agreed closely with the measured values. Erosion depth measured by the Eriksen method also showed no significant difference between the two groups, but because the values were substantially higher ABMU was improbably high in both groups, did not differ significantly between groups, and was inconsistent with the observed difference in trabecular thickness. We conclude that (1) the more rapid continuing loss of cancellous bone in patients with postmenopausal osteoporosis than in age-matched control subjects is due entirely to a difference in wall thickness, not to a difference in erosion depth; and (2) defective recruitment and/or function of osteoblasts is the major cellular mechanism of trabecular thinning in patients with postmenopausal osteoporosis and probably also in normal subjects. We emphasize that these conclusions do not speak to the mechanism of complete removal of trabeculae in the early years after menopause.
INTRODUCTION has generated great interest these past few years because of its public health consequences. Methods of diagnosis have improved, but a fuller understanding of pathophysiologic mechanisms is crucial to develop new approaches to treatment. According to the quantum concept of bone remodeling,") all gains or losses of bone are the result of focal imbalance, during individual remodeling cycles, between the depth of a cavity
P
OSTMENOPACJSALOSTEOPOROSIS
eroded by a team of osteoclasts and the thickness of new bone deposited in the cavity by a team of osteoblasts. The summation of all such transactions determines the cumulative change in bone surface location, so that the rate of change also depends on how frequently new cycles are initiated. The purpose of histomorphometry is to provide in vivo information about these cellular mechanisms.(') A decline in wall thickness with aging and in osteoporosis is well e s t a b l i ~ h e d , ( ~but - ~ )much less information is available about erosion depth.
'Bone and Mincral Research Laboratory, Henry Ford Hospital, Detroit, Michigan. 'Present affiliation: Inserm Unite 18, Paris, France.
1331
1332
COHEN-SOLAL ET AL.
One method of measuring erosion depth is to count the number of lamellae that have been eroded adjacent to each cavity, since these are of relatively constant mean thickness.") Using this method, it was found that resorption but was increased in padepth tended to fall with tients with postmenopausal osteoporosis manifested by vertebral compression fractures. ( l o ) An alternative method was recently proposed in which the original location of the surface before the onset of resorption is reconstructed from the contours of the adjacent bone and both the mean depth and the maximum depth in each cavity determined by direct measurement,('l) but this method has not yet been applied to osteoporosis. In this study, we describe a new method of measuring erosion depth that has some features in common with each of the previous methods and present the results of applying this method to determine the mechanisms of continuing cancellous bone loss in postmenopausal osteopornsis.
SUBJECTS AND METHODS
using a computerized semiautomatic system phometry' (Bioquant System IV, R&M Biometrics, Nashville, TN); data from the cancellous surface only are reported. Tetracycline-based indices and wall width were measured on prestained sections, and other measurements were made on toluidine blue-stained sections. All distances were measured directly rather than indirectly.(I4' Calculations were performed as previously described,"') except that a correction was applied for the difference in length between the first and second labels.(Is) Data are expressed in three-di~ appropriate to conmensional terms using ~ / or 4 4 / as vert from the primary two-dimensional data.''4) Wall width was measured, at x 100 original magnification, from quiescent surfaces to the nearest line of sharp change in color from dark to pale green in the Villanueva prestained sections examined under ultraviolet light.'16) This method of demarcating the boundary of bone structural units has recently been validated by demonstrating that the change in color corresponds to a change in calcium content determined by scanning electron microscopy combined with x-ray microanalysis, and thus to a difference in age.(17'Sites of measurement were selected by random rotation of an eyepiece graticule containing 10 parallel lines to locate intersections, at which orthogonal intercept lengths were measured by digitization. On average, 21 sites (range 10-41) were measured in the normal subjects and 17 (6-27) in the patients. Erosion depth (E.De) was measured by two different methods. The first method was that proposed by Eriksen and colleagues,(1R)but without the assumption of a constant value for lamellae thickness (Lm.Th). All four available sections were used; there was no difference between the toluidine blue and prestained only sections, so that the data were pooled. The entire section was first examined at x 100 magnification. Measurement sites were randomly located as for wall width but including only intersections between graticule lines and surfaces covered by either preosteoblasts or osteoid, assumed to indicate that resorption had terminated at that location.(") For each cavity, the number of adjacent lamellae was counted, and in addition, the width of each individual lamella was measured at x 200 magnification and a mean lamellar width calculated for that cavity. Erosion depth was then calculated separately for each cavity:
A group of 10 healthy white postmenopausal women whose age [mean (standard deviation, SD)] was 60.7 ( 8 . 5 ) years served as controls; the mean years since menopause was 9.4 (range 3-19). They were recruited in response to a hospital newsletter or by word of mouth in accordance with a protocol approved by the institutional human rights committee. They were in good health, gave no history of any disease or drug exposure known to affect bone, were normal on physical examination, had normal indices of bone mineral metabolism, normal spinal radiographs, and normal values for forearm bone densitometry, and gave informed consent. Six of them had received calcium supplementation 1 &day for 3-4 months before the biopsy; in each an earlier biopsy had been obtained on the opposite side 1-2 years earlier, but the material remaining was insufficient for the present study. A group of 10 white postmenopausal women aged 60.8 (5.4) years underwent evaluation for osteoporosis. The mean years since menopause was 13.9 (range 2-24), not significantly different from the controls. Each had had at least one nontraumatic vertebral compression fracture. No other etiology was found, and they were receiving no medication interfering with bone metabolism, except that three were taking a calcium supE.De (pm) = Lm.Nb x Lm.Th (pm) plement of 500-1000 mg/day. The patients were younger (1) than usual, since they were selected to be age matched with the control subjects. Plasma calcium, inorganic phosphate, where Lm.Nb is lamellar number. For each subject, the alkaline phosphatase, and creatinine values were normal in mean of these individual values was used. O n the average, 8 sites suitable for measurement (4-13) were found in the all subjects. Transiliac bone biopsies were obtained in each subject normal subjects, and 5.4 (3-8) in the patients; these numafter in vivo double-tetracycline labeling. The samples bers d o not include an additional 1-5 sites in each subject were placed in 70% ethanol, prestained by the Villanueva in whom no measurement was possible. For measurement of erosion depth by the second method, embedded in polymethyl methacrylate, and sectioned with a Jung-K microtome.(I*)Two 5 pm consecutive method, only the toluidine blue sections were used. We sesections were obtained: the first was stained with toluidine lected only lacunae that fulfilled three criteria. First, they blue''3) and the second was prestained only. The block was were mainly covered by osteoid, to be certain that resorpreversed, and a second pair of sections was obtained from tion was complete over most of the lacunar surface. Secthe other side and the same procedure used for staining. ond, eroded lamellae were still visible at each extremity, so The first pair of sections was used for standard histomor- that although formation had begun it was still a long way
1333
EROSION DEPTH IN POSTMENOPAUSAL OSTEOPOROSIS from completion. Third, the new cement line, marking the furthest extent of erosion at any location, was clearly identifiable. For all such lacunae, a line joining the adjacent quiescent surfaces was drawn on the display screen by following the contours of the intact trabecular surface on either side (Fig. 1). Measurements were made at x 100 original magnification of orthogonal intercept length between this line and the closest cement line at intersections selected randomly by the same procedure. On the average, 33 intersections (20-54) from 9 (5-13) sites were selected in the normal subjects and 25 (13-36) intersections from 7.5 (5-10) sites in the patients. The number of sites was slightly larger than for the first method because of the difference in method of selection. The second method resembles the first with respect to including criteria for termination of resorption but differs from i t in applying these criteria to complete remodeling sites rather than to individual intersections. The method resembles that of Garrahan et al.("' in reconstructing the original surface location, but differs from it in applying this only to sites in which resorption has been completed, not where it is still in progress. To assess the reproducibility of the new method, all sets of slides were remeasured by the same observer after an interval of 1 month. T o interpret erosion depth, it is necessary to calculate activation frequency (Ac.f), representing the birth rate of
new remodeling sites. The total amount of bone formed can be regarded as the product of the average amount so that formed in each cycle and the number of BFR/BS (pm3/pm*/year)
=
Ac.f(year-') x W.Th (pm) (2)
where BFR/BS = bone formation r a t e h o n e surface. From which it follows that Ac.f(year-I) = BFR/BS (pm3/pm2/year)/W.Th (pm) (3) Several other indices of bone resorption werc then calculated from the erosion depth.(*.8.14'The erosion period (EP), including both resorption period and recersal period, is derived from the formation period (FP) and is given by EP (days) = ES x
0s FP (days)
(4)
where 0s = osteoid surface. The erosion rate (ER), exprcssed as movement of the erosion front perpendicular to the surface, averaged throughout the erosion period, is given by ER (pm/day) = E.De (pm)/EP (days)
(5)
The bone surface-based bone resorption rate (BRs.R/ BS) is the product of mean erosion depth and the probability that erosion will begin at any point on the surface in a
FIG. 1. Region of cancellous bone from a normal subject illustrating the method for measuring erosion depth. Note unfilled eroded surface at the right-hand margin of the cavity. The unlabeled arrows identify four representative sites for measuring the distance between the reconstructed surface and the cement line.
COHEN-SOLAL ET AL.
1334
defined time period. In a steady state, this probability is the same as Ac.f calculated from the formation indices, so that BRs.R/BS (pm3/pm2/year) = Ac.f(year-I) x E.De (pm) (6) The similarity in form between this and Eq. (2) should be noted. The bone volume-based resorption rate (BRs.R/ BV) is given by BRs.R/BV (%/year)
=
BRs.R/BS (pm3/~m2/year) (7) x BS/BV (mm2/mm3) x 100/1OOo
The bone balance at the basic multicellular unit (BMU) level (ABMU), which is the average outcome of each remodeling transaction, is given by ABMU (pm)
=
W.Th (pm) - E.De (pm)
(8)
The bone balance at the bone surface level is expressed as the average rate of movement of the surface toward or away from the midline of a trabecula and depends on the average change per cycle and the number of cycles completed in unit time, so that
of remodeling cycles accumulated since menopause (N.Cy), the mean value for Ac.f was multiplied by the mean value for years since menopause for each group. For measurements at multiple sites in a single subject, individual means, standard deviations, and coefficients of variation (CV = SD/mean x 100) were calculated and the individual means used for calculation of group means and SD. For each variable, differences between groups were tested by two-tailed unpaired Student's f-tests'21'; significance values were adjusted for the total number of comparisons. For selected pairs of variables, their relationship was assessed by linear regression analysis. The intraobserver precision of the second method was calculated as expressed as a percentage of the overall mean value,'*2) where D is the difference between paired measurements and n is the number of pairs (20). All calculations were performed using the CSS statistical package (Complete Statistical System, Statsoft Inc., Tulsa, OK).
m,
RESULTS
The results of standard histomorphometry are given in Table 1. The various indices of microstructure showed the expected differences between the two groups.(I.'O) The ABS (pm/year) = Ac.f (year'') x ABMU (pm) (9) greater than usual difference in trabecular thickness may = Ac.f (year'') x (W.Th - E.De) (pm) have resulted from the relatively low age, since the absolute difference between osteoporotic patients and ageAn alternative expression for this relationship, in terms matched control subjects declines with increasing age.") of primary measurements only, can be derived by combi- The difference in W.Th was smallest in magnitude (10%) nation with Eq. (3): but was most highly significant because of the greater precision of this measurement; the individual CV averaged ABS (pm/year) (10) about 25% and individual precision [standard error of the = BFR/BS (pm3/pm2/year) ( 1 - E.De/W.Th) mean, (SEM)/mean x 1001 about 6% and did not differ beThe bone balance at the bone surface level can also be ex- tween the groups. Bone formation rate and Ac.f were pressed as the rate of bone loss or gain per unit of bone lower in the osteoporotic patients than in the normal subjects to about the same extent as previously reported,") surface: but the differences were not statistically significant with ABV/BS (pm3/pm2/year) ( 1 1) these small samples. = (BFR/BS - BRs.R/BS) (pm3/pm2/year) There was no significant difference in lamellar width beThe bone balance at the bone volume level expresses bone tween the two groups, whether the unit of observation in lost per unit time as a fraction of the amount present, each subject was the individual lamella or the average for which is equivalent to a rate constant and is given by each cavity (Table 2). The values are about 16% lower than previously because we did not use the ABV/BV (%/year) (12) stereologic unfolding procedure originally devised for glo= ABS (p3/pm2/year BS/BV (mm2/mm') x 100/1OOo merular basement As others have ob= (BFR/BV - BRs.R/BV) (%/year) there was substantial variation in width between lamellae in each individual, with an average CV of about For comparison with the direct methods, ABMU and 35%. We also found somewhat more variation between inE.De were also estimated indirectly from a modified form dividuals, with a CV of about 7% in the normal subject of Eq. (9), relating total cumulative change in surface loca- and 11% in the patients compared to previous reports of tion to the cumulative number of cycles (N.Cy).(I9) about 5%.(7.18) There was no significant difference between the number of eroded lamellae in the two groups ABS (pm) = N.Cy x ABMU (pm) (13) (Table 2). Since there was also no difference in lamellar thickness, there was no difference in mean erosion depth T o obtain ABS for solving this equation, the mean value by the first (Eriksen) method (Table 3). There were also no for trabecular thickness in each group was subtracted from significant differences in any of the derived indices of rethe mean value for healthy premenopausal women of 147 sorption or bone balance based on this method. The intraindividual precision of the second (new) Fm(20)and the results divided by 2 to allow for bone loss on both sides of a trabecula. To estimate the total number method for measuring erosion depth was 4.3%; for com-
1335
EROSION DEPTH IN POSTMENOPAUSAL OSTEOPOROSIS TABLE1. SELECTED HISTOMORPHOMETRIC VARIABLES~
Variables Characterization of groups BV/TV, ’?lo Tb.Nb, mm-I Tb.Sp, pm O.Th, pm OS/BS, 070 Aj.AR, pm/day FP, days Further analysis Tb.Th, pm ES/BS, 070 W.Th, pm BFR/BS, pm3/pm’/year BFWBV, %/year Ac.f, year-‘ EP, days
Control
Osteoporosis
P
