Modeling Normal Aging Bone Loss, with Consideration of Bone Loss in Osteoporosis

Ellen J. O'Flaherty

Department of Environmental Health, University of Cincinnati College of Medicine, 3223 Eden Avenue, Cincinnati, Ohio 45267-0056

Received March 17, 1999; accepted November 1, 1999


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A physiologically based model of normal bone loss in human aging is presented. The model is a modification of an existing physiologically based model of body and bone growth from birth to maturity. To account for loss of bone after peak bone mass is reached between ages 25 and 30 years, a slow first-order loss of bone is incorporated into the existing model. The rate constants for this first-order loss are the same for men and women but differ with the type of bone, being 3%/decade for cortical bone and 7–11%/decade for trabecular bone. In women, a 10-year period of more rapid loss of both cortical and trabecular bone is superimposed on the slow loss, beginning at the time of menopause. The superimposed loss occurs at the same relative rate in cortical and trabecular bone. Alterations in parameter values allow simulation of bone mass in osteoporotic men and women. The model is calibrated to quantitative estimates of cortical and trabecular bone mass as functions of age; in particular, to data sets of fractional vertebral bone volume as functions of age, and it is compared to the International Commission on Radiological Protection trend curves for skeletal mass in men and women to age 60. It is also applied to the question of whether loss of bone in women after menopause could create a hazard related to the return to blood of lead previously stored in bone. In agreement with observations made during 1976–1980, the model simulates an increase due to bone resorption of approximately 1 µg/dl in blood lead concentration in a postmenopausal (60-year-old) woman compared with a premenopausal (50-year-old) woman with typical lifetime ambient lead exposure.

Key Words: osteoporosis; bone lead; blood lead; aging.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Clinical osteoporosis, defined as bone (usually hip or spinal) fracture related to decreased bone density, is one of the most physically debilitating conditions associated with aging. In older people, the temporary immobilization associated with a hip or vertebral fracture often precipitates a period of reduced physical activity or permanent physical disability. As the United States' population becomes increasingly older, understanding and minimizing aging-related bone loss is increasingly becoming a national priority.

Bone loss with age is a natural phenomenon. Bone mass peaks around ages 25–30 years and declines gradually thereafter in both men and women (Exton-Smith et al., 1969Go; Firooznia et al., 1984aGo). The amount of bone in older people is determined by the peak bone mass, together with the rate of bone loss with age. Peak bone mass, in turn, is determined by many factors, including diet, particularly calcium nutrition; exercise; gender; and genetic makeup (Garn, 1972Go; Hamdy et al., 1994Go; Johnston and Slemenda, 1995Go; Stevenson et al., 1989Go). The rate of bone loss varies from individual to individual, but is broadly similar in women and men (Hansson et al., 1980) except for a five- to ten-year period of more rapid postmenopausal bone loss in women (Krølner et al., 1982; Meunier et al., 1973Go; Nilas and Christiansen, 1988Go; Smith et al., 1976Go; tepán et al., 1985Go) that affects both cortical and trabecular bone (Mazess, 1982Go). After this period of enhanced bone loss in postmenopausal women, the rate of loss reverts to the lower value observed in premenopausal women and in men (Mazess et al., 1987Go). This transient increase in bone loss rate in women, coupled with the typically smaller peak bone mass in women than in men, presumably accounts for the greater frequency of bone fractures among older women than among older men.

While absolute bone mass is most closely related to the likelihood of bone fracture in older people, the rate of bone loss presents another human health issue. Bone volume-seeking elements such as strontium, uranium, and lead are capable of accumulating to high concentrations in bone. Because of the mechanisms by which these elements enter and leave bone, they do not readily reach kinetic equilibrium between bone and blood, but accumulate steadily in bone as exposure persists. Lead is particularly noteworthy among the bone volume-seeking elements. It is widely disseminated in the environment, which represents a lifelong exposure source, and it has been present historically in many workplaces. Contemporary ambient exposure to lead is markedly lower than it was even 20 years ago, due largely to the removal of lead additives from gasoline and of lead solder from tin cans. However, those persons who are now 50 to 60 years old were exposed to much higher ambient levels of lead during their adolescence and early adulthood, and many may have experienced industrial exposures as well. The question has been raised whether the bone loss that accompanies aging may be associated with the return of biologically significant amounts of lead to the blood in persons who may be susceptible to effects of lead as a result of the aging process (Silbergeld et al., 1988Go).

It would be helpful to have a physiologically-based model structure that would facilitate prediction of lead kinetic behavior in later life based on the magnitude and pattern of lifetime lead exposure. A physiologically-based model of human lead kinetics from birth to adulthood has been developed, validated against human exposure data, and used in several interpretive and predictive applications (O'Flaherty, 1993Go, 1995Go, 1998Go). In this paper, that model is expanded to take into account aging-related bone loss and its predicted impact on blood lead concentration in older men and women.


    METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The general structure of the model is that of an existing physiologically based model of human lead kinetics from birth to maturity (O'Flaherty, 1993Go, 1995Go). The model incorporates uptake of lead by bone and its loss from bone by physiologic mechanisms related in part to the rates of bone formation and resorption, both of which are dependent on age. Bone mass is defined as a function of age and body weight (O'Flaherty, 1991bGo), and bone formation rate as a function of age (O'Flaherty, 1993Go, 1995Go). Bone resorption rate is calculated as that rate which, in combination with the bone formation rate, results in the appropriate net increase in bone mass or, in the young adult, in no net change in bone mass. The growth/maturity model has been calibrated and validated for human adult (O'Flaherty, 1993Go) and childhood (O'Flaherty, 1995Go) lead exposure. It does not account for net bone loss after peak bone mass has been reached in early adulthood.

The rate of bone formation and net rate of increase in bone mass together determine the rate of bone resorption in the growth/maturity model. However, from the point of view of modeling, any 2 of the 3 quantitative measures (bone formation rate, bone resorption rate, and bone mass) can formally determine the third. In the normal aging/osteoporosis model extension, bone formation rate and bone resorption rate are allowed to determine bone mass. Bone formation rate is assumed to remain constant at the level characteristic of young adults (Heaney and Whedon, 1958Go; Jowsey et al., 1965Go). The model is adapted to generate net bone loss by incorporating an unopposed small increase in bone resorption rate beginning at age 30 (TMAXAGE) for trabecular bone and at age 35 (CMAXAGE) for cortical bone (Mazess, 1982Go, 1987). In addition, a transient rise in bone resorption rate in women is incorporated beginning at the onset of menopause and terminating 10 years later.

The expressions for bone resorption rates CBRR and TBRR (liters/year) for cortical and trabecular bone in men after maximum bone mass has been achieved are

and

where CBRRMAX and TBRRMAX (liters/year) are the resorption rates of cortical and trabecular bone at the ages of maximum bone mass (CMAXAGE and TMAXAGE), CKLOSS and TKLOSS (1/year) are first-order rate constants, and CVBONE and TVBONE (liters) are the instantaneous volumes of cortical and trabecular bone. The corresponding expressions for bone resorption rate in women after maximum bone mass has been achieved are

and

where K1 (liters/year) and K2 (1/year) are constants, AGE is age in years, and MENO (default value = 55 years) is the age at which menopause begins. The complete model code, including growth to maturity as well as bone loss after maturity, is appended.

While there are differences among the rates of loss of mass from different bones, which vary from 2 to 13%/decade (summarized in Mazess, 1982), the rate of loss of cortical bone mass in both women and men is generally reported to be 3–5%/decade. The more variable rate of loss of trabecular bone mass is commonly reported to be 6–10%/decade with some reports as high as 13%/decade and no clear-cut difference between men and women (Mazess, 1982Go). Accordingly, the value of CKLOSS was set at 0.003/year for "average" cortical bone. The value of TKLOSS was set at 0.007/year for "average" trabecular bone, in both women and men. It was revised upward, to 0.011/year, in order to reproduce the data of Meunier et al. (1973) for the iliac crest, a particularly rapidly-turning-over bone region.

The values of K1, 0.01 liters/year, and K2, 0.3/year, in the modified model for women were determined by calibrating simulated trabecular bone volume to the cross-sectional age-dependent fractional bone volumes from Meunier et al. (1973). These investigators determined fractional bone volume histographically in sections taken from the iliac crest of 236 control subjects (150 males and 86 females) aged 15 to 96 years who had died violently and had been found at autopsy to have no macroscopic lesions. They included limited measurements of iliac crest bone volume in osteoporotic subjects. To simulate these data, it was assumed that peak bone mass in the osteoporotic groups was 66% of the values in normal subjects but that the rate of bone loss was the same as in normal aging.

The values of the four constants CKLOSS, TKLOSS, K1, and K2 were further examined by comparing simulated skeletal mass to skeletal mass in the International Commission on Radiological Protection (ICRP) model (ICRP, 1992). For this purpose, the weight of the skeleton WSKEL (kg) after age 30 was calculated as the maximum skeletal mass WSKELMAX (kg) at age 30 minus the combined losses of trabecular and cortical bone mass thereafter:

where CWLOSS is the loss in weight (kg) of cortical bone after age 35 and TWLOSS is the loss in weight (kg) of trabecular bone after age 30. This calculation assumes that marrow weight does not change as bone is lost. The absolute (arbitrarily normalized) skeletal weights in the ICRP model suggest average body weights for women of about 52.5 kg (6.8 kg skeletal wt/0.13 kg skeletal wt/kg body wt) and for men of about 74 kg (10.0 kg skeletal wt/0.135 kg skeletal wt/kg body wt). Accordingly, the parameters WCHILD and WADULT in the physiologically-based model (see the Appendix) were set to generate these adult body weights for men and women for this simulation.

In order to determine the predicted effect of increased bone resorption in later life on blood lead concentration, the lifetime lead exposure history of a woman born in 1918 (60 years old in 1978) and the lifetime lead exposure history of a woman born in 1928 (50 years old in 1978) were simulated. Air lead concentration was set at 1.25 µg/m3 prior to 1975, decreasing to 0.3 µg/m3 today; daily dietary lead intake at 200 µg/day prior to 1970, decreasing to 30 µg/day today; and drinking water lead at 5 µg/l. It was assumed that the women had had no excessive childhood lead exposure and no work-related lead exposure. The difference between the simulated blood lead concentration in the 50-year-old woman and the 60-year-old woman was compared with the cross-sectional blood lead concentrations recorded in pre- and postmenopausal women between 1976 and 1980 in the Second National Health and Nutrition Examination Survey (NHANESII) (National Center for Health Statistics, 1984Go) as they were analyzed by Silbergeld et al. (1988).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Figure 1Go displays "data points" for the age-related decline in iliac crest bone mass in normal female subjects, read from a statistically smoothed curve (Meunier et al., 1973Go), along with the simulation curve obtained with TKLOSS set at 0.011 year–1, K1 set at 0.01 liters/year, and K2 set at 0.3/year. Figure 2Go shows "data points" for the age-related decline in iliac crest bone mass in normal male subjects read from a statistically smoothed curve (Meunier et al., 1973Go), with the corresponding simulation curve with TKLOSS set to 0.011 year–1 and K1 set to 0. Note that the data suggest that the fraction of the iliac crest occupied by bone in females is substantially greater than that in males. The clarity of the observed transient postmenopausal iliac crest bone loss in females enables a precise setting of the constants K1 and K2, while the general rates of decline of trabecular bone volume in the iliac crest (Figs. 1 and 2GoGo) fix the modeled value of 11%/decade at this bone site, in both men and women. In addition to the Meunier et al. (1973) data, relied on for calibration of the constants K1 and K2, Figures 1 and 2GoGo show bone volume data from Aaron et al. (1987). These observations, which were not used in model calibration, were made by a comparable histographic technique using sections of the iliac crest. They are different from those of Meunier et al. (1973) up to about age 60 in both men and women (Figs. 1 and 2GoGo), but similar thereafter.



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FIG. 1. Age-related decline in iliac crest bone mass in normal females. The "data points" (circles) are taken from statistically smoothed curves in Meunier et al., 1973. The line is the simulation, adjusted by multiplying VBONE by 0.55 to bring it into line with the data, equivalent to the assumption that the iliac crest is 55% bone in females. These observations were used to calibrate the values of model parameters K1 and K2; see text for explanation. The value of TKLOSS was set to 0.011 da–1 for this simulation. Data from Aaron et al. (1987) (squares) are also shown.

 


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FIG. 2. Age-related decline in iliac crest bone mass in normal males. The "data points" (circles) are taken from statistically-smoothed curves in Meunier et al., 1973. The line is the simulation, adjusted by multiplying VBONE by 0.38 to bring it into line with the data, equivalent to the assumption that the iliac crest is 38% bone in males. The value of TKLOSS was set to 0.011 da–1 for this simulation. Data from Aaron et al. (1987) (squares) are also shown.

 
The limited data (Fig. 3Go) from osteoporotic subjects (Meunier et al., 1973Go) are consistent with the assumptions made for these simulations: that peak bone mass is low but that loss rates are normal in osteoporotic men and women.



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FIG. 3. Age-related decline in iliac crest bone mass in osteoporotic males and females. Data are from Meunier et al., 1973: males, squares; females, circles. The number of subjects represented by each data point is given in parentheses on the figure. The lines are the model simulations for males (– –) and females (—), assuming in each case that peak bone mass is only 66% that of normal subjects but that the rate of bone loss is the same as in normal subjects. TKLOSS was set to 0.011 year–1 for these simulations.

 
The modified bone model simulates the ICRP skeletal mass trend curve (ICRP 1992) well for both men and women (Fig. 4Go). The value of TKLOSS was set to 0.007 year–1 for this simulation, but in fact the correspondence would have been equally good with values of TKLOSS as large as 0.011 year–1. The rate of change of skeletal weight as modeled is not sufficiently sensitive to the contribution of trabecular bone that it can be used to discriminate among a range of reasonable values of TKLOSS. The ICRP noted that the spread about these trend curves was wide for both males and females, consistent with variability in rates of loss of both trabecular and cortical bone. It must also be acknowledged that the assumption made (in the absence of any data) in modeling these curves, that marrow mass is invariant as bone mass declines, is almost certainly not correct. Marrow mass might increase or decrease with loss of bone, depending on the bone structure at the site of loss.



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FIG. 4. Age-dependent skeletal mass in men and women. The "data" are read from the ICRP skeletal mass trend curves for men (squares) and women (circles) (ICRP, 1992), which are normalized to skeletal weights of 10 kg for adult males and 6.8 kg for adult females. The lines are the model simulations for males (– –) and females (—). See Methods for explanation of model calculations.

 
Using default lead exposures (see Methods), the model predicts a blood lead concentration of 17.6 µg/dl in the 50-year-old woman and 18.5 µg/dl in the 60-year-old woman in 1978. At and after 1978, modeled blood lead concentrations are decreasing, as environmental exposure decreased fairly sharply after this date. For example, in 1985 the 50-year-old women would be predicted to have a blood lead concentration of 13.1 µg/dl; the 60-year-old woman, a blood lead concentration of 14.4 µg/dl. Silbergeld et al. (1988) reported mean blood lead concentrations of 11.93 µg/dl in 293 premenopausal women and 12.96 µg/dl in 470 postmenopausal women based on data from the NHANESII study, which was concluded in 1980 (National Center for Health Statistics, 1984Go). Thus, the magnitude of the modeled increase in bone loss that occurs during the immediate postmenopausal period is in agreement with the observed magnitude of increase in blood lead concentration observed in postmenopausal women (Silbergeld et al., 1988Go), although either the model is overestimating blood lead concentrations after lifetime exposure or historical exposure was significantly lower than was assumed in the default values of the model exposure parameters. However, adjustment of exposure parameter values alone, in order to generate blood lead concentrations comparable to those observed in the NHANESII study, required unrealistic reductions in modeled ambient exposures (results not shown).


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Because bone-seeking elements have such long residence times in the human body, development of physiologically-based models of their kinetics dictates that the anatomic and physiologic features that form the basic structure of the model be defined as functions of age and/or body weight. This has been accomplished, for such physiologic functions as respiratory rate and glomerular filtration rate and for such anatomic measures as organ weights (or volumes), by reference to the pediatric and other literature. The anatomy and physiology of growth from birth to maturity is described fairly completely in the basic model. The only change associated with aging in the expanded model is bone loss. No other aging-related changes in physiologic or anatomic measures have been included in the modified model.

In addition to becoming incorporated into the mineral of forming bone and being returned to blood as bone is resorbed, lead in the model engages in a slow heteroionic exchange with calcium, described mathematically as radial diffusion outward from the canaliculi that perfuse the total cortical bone volume. These mechanisms were characterized and defined based on critical reviews of the literature relating to incorporation of isotopes of calcium and radioisotopes of calcium tracers like radium, strontium, and barium into bone (O'Flaherty, 1991aGo).

Loss of bone is a normal feature of human aging. In principle, net bone loss could occur either as the result of failure of normal bone formation or as the result of an increase in the rate of bone resorption coupled with a normal or reduced formation rate. In fact, it has been established that, in general, bone resorption rate increases with age while bone formation rate remains essentially constant after age 20–25 years (Heaney and Whedon, 1958Go; Jowsey et al., 1965Go). The curves for total skeletal weight as functions of age in men and women (ICRP, 1992) suggest establishment of maximum bone mass by age 20, with observable bone loss beginning about age 37. Some bone is actually lost before age 37, probably beginning as early as age 30 (Riggs et al., 1981Go).

The process of bone loss with aging is complex. Its rate depends on gender, hormonal status, calcium status, exercise, genetic makeup, and regional features of bone metabolism. Bone loss is not uniformly distributed throughout the skeleton. Many experimental studies of bone loss rates are limited to specific bone sites. Observations made in such studies are not directly applicable to a model of whole-body bone loss rate. However, one rough division of bone type is useful. The rate of loss of trabecular vertebral bone is distinctly more rapid than the rate of loss of predominantly cortical long bone (Meier et al., 1984Go). The difference in rates of trabecular and cortical bone loss is characteristic of both men (Meier et al., 1984Go) and women (Mazess, 1982Go). The transient acceleration in women in the rate of net bone loss in the immediate postmenopausal period is manifested in cortical bone (Nilas and Christiansen, 1988Go; Smith et al., 1976Go) as well as in trabecular bone in regions as distinct as the iliac crest, vertebra, and distal forearm (Krølner et al., 1982; Meunier et al., 1973Go; Nilas and Christiansen, 1988Go). Biochemical indices of bone remodeling confirm the occurrence of this transient increase in resorption following either natural or surgically induced menopause (Nilas and Christiansen, 1987Go; tepán et al., 1985Go, 1987).

The loss of bone in trabecular regions, both in women and in men, is largely an increase in trabecular spacing without significant reduction in the thickness of individual trabeculae, although thinning of trabeculae also occurs (Parfitt et al., 1983Go; Weinstein and Hutson, 1987Go). In the long bones, continuing subperiosteal apposition throughout life does not keep pace with the rate of loss from the endosteal surfaces (Garn, 1972Go). The marrow space enlarges and the thickness of the cortical shell decreases; at the same time, the bone becomes more porous (Jowsey et al., 1965Go; Thompson, 1980Go).

Most estimates of rates of bone loss are based on measurements at individual bone sites. Mazess (1982) summarized published loss rates to 1982. These were 3–5%/decade for cortical bone and 6–10%/decade for trabecular bone in predominantly Caucasian men and in women prior to about age 50, 9–12%/decade for cortical bone in the women after age 50, and up to 13%/decade for trabecular bone in the women after age 50. Net loss of bone from the entire skeleton is less frequently assessed. Nilas and Christiansen (1988) fit regression lines to measurements by dual photon absorptiometry of total body bone mineral in 141 women from 29–55 years old, estimating that the rate of mineral loss was 1%/decade at age 30 and 10%/decade at age 50 in premenopausal women, but 40%/decade shortly after the onset of menopause. The physiologically based model, with its current default settings for women, gives a total bone loss rate of 3–4%/decade at age 50, with a maximum rate at age 60 of 25%/decade with TKLOSS set to either 0.007 year–1 or 0.011 year–1. For trabecular bone alone, the simulated values are 5%/decade at age 50 and 60%/decade at age 60 with TKLOSS set to 0.007 year–1, or 9%/decade at age 50 and 63%/decade at age 60 with TKLOSS set to 0.011 year–1. It is apparent that a wide range of physiologically reasonable values of TKLOSS gives physiologically reasonable predictions of bone loss rates in women. While the model defines the postmenopausal interval of increased rate of bone loss rather sharply, in a population of women, both the range in age of onset of menopause and the range of individual increases in bone loss rates during the postmenopausal period would contribute to loss of distinctiveness of the postmenopausal period. The ICRP curve for women in Figure 4Go, for example, suggests earlier (than the default value of age 55) onset of menopause but does not extend beyond an age at which postmenopausal return to a slower bone-loss rate would be expected. Other composite data sets may have different characteristics, and other combinations of values of the 4 loss constants may be found to match other data sets better than the specific default combination used here. In particular, the range of values of bone diminution rates that determine the values of CKLOSS, TKLOSS, K1, and K2 is characteristic of a largely western Caucasian study group and may not be applicable to other racial and/or ethnic groups, as discussed below. In addition, although this particular data set did not require different values of CKLOSS and TKLOSS for men and women, and the majority of other studies (see the review in Mazess, 1982) lead to the same provisional conclusion, a few studies (for example, Riggs et al., 1981) suggest that such differences may exist. In any case, values of CKLOSS, TKLOSS, K1, and K2, while they can be estimated for defined population groups or subgroups having similar key bone metabolic characteristics, will in general not be known for individuals. Thus, these models simulate group kinetic behavior and can give only an approximate idea of bone loss rate in a specific individual. Entry into a simulation of the values of CKLOSS, TKLOSS, K1, and K2 at the extremes of their expected ranges can, however, serve to define an expected maximum or minimum rate of bone loss.

While the possibility of enhanced susceptibility to effects of lead in older people remains a postulate, whether prior lead exposure can result in elevated internal lead exposure in older people is an important contemporary question. The excellent agreement between the osteoporosis model prediction of blood lead concentration increase and the observed cross-sectional blood lead concentration increase between the ages of 50 and 60 in women (Silbergeld et al., 1988Go) suggests that the observed increase could in fact be entirely attributable to bone loss. However, its magnitude, about 1 µg/dl, is not large, even in these women who have had what would today be considered unacceptably high lifetime lead exposure. Lower lifetime lead exposure would, of course, be associated with lower bone lead-related increases in blood lead during and after menopause.

The fact that the predicted absolute values of blood lead concentration in these exposure scenarios are higher than the values observed in the NHANESII study (see Results) replicates a consistent disparity between predicted and observed values, which has become manifest with repeated exercise of the model in chronic exposure scenarios. As an example of one of these applications, the blood lead concentrations of a male researcher whose blood has been monitored at intervals since 1982 are shown in Figure 5Go, along with the model-predicted blood lead concentrations given typical ambient exposure conditions for the United States. The over-prediction is comparable to that observed for the NHANESII data. As noted above (see Results), realistic reductions in modeled ambient exposures do not correct this recurrently observed disparity. Physiologically plausible alterations in bone lead parameters also are not capable of correcting the defect, and in any case, the relationship between blood lead and bone lead concentrations has been reasonably well validated (O'Flaherty, 1993Go). However, a 25% increase in the modeled total plasma-lead clearance during adulthood brings prediction and observation into accord for the sequential series of blood-lead concentration measurements (Fig. 5Go). The same 25% increase in clearance (achieved by setting the constant C2 to 0.875 (see Appendix)) results in predicted blood-lead concentrations of 11.9 µg/dl in the 50-year-old woman and 12.7 µg/dl in the 60-year-old woman in 1978, compared with the NHANESII mean values (Silbergeld et al., 1988Go) of 11.93 µg/dl in premenopausal women and 12.96 µg/dl in postmenopausal women from 1976–1980. Thus, it appears possible that the tendency of the model to overpredict blood-lead concentrations may be associated with an underestimate of lead clearance. The adjusted plasma-lead clearance values are 15 liters/day for adult women and 18 liters/day for adult men, actually closer than previously to the midrange of the 7–50 liters/day reported by Chamberlain et al. (1978) and Manton and Cook (1984) for renal clearance alone.



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FIG. 5. Predicted and observed blood lead concentrations from 1982 to 1997 in an adult male without known excessive childhood lead exposure. The dotted curve is the simulation with default values. The solid curve is the simulation with a 25% increase in plasma lead clearance. See Discussion for details.

 
Older people exhibit a spectrum of bone mass, without a distinct separation between normal and osteoporotic bone. However, low bone mass is consistently associated with increased susceptibility to fracture (Cann et al., 1985Go; Firooznia et al., 1984bGo; Pødenphant et al., 1987Go). Particularly low bone mass in later life could originate from a low peak bone mass, from a greater than average rate of bone loss, or from both mechanisms acting together. Most studies of osteoporotic subjects have consisted largely of postmenopausal women, often over 60, when low bone mass begins to manifest itself in bone fragility (see, for example, Riggs et al., 1981, 1982; Seeman et al., 1988). It is not possible to determine from such data how the individuals arrived at their osteoporotic states. The trabecular bone volume data from osteoporotic subjects in Figure 3Go (Meunier et al., 1973Go) are cross-sectional, are limited to measurements in single subjects at the early ages, and cannot be taken as more than suggestive of longitudinal behavior. Krølner and Nielsen (1982) carried out a prospective study of lumbar spine bone mineral content in 3 groups of women: premenopausal, postmenopausal, and a group with spinal osteoporosis. The women were followed for from 10 to 30 years. The rate of loss of bone mineral content, 2–4%/year, was not significantly different in the premenopausal women after age 34, the postmenopausal women starting about 10 years after the onset of menopause, and the osteoporotic women, all of whom were late menopausal. This prospective study, taken together with cross-sectional studies (Cohn et al., 1974Go; Firooznia et al., 1984bGo), does not suggest that rates of bone loss are greatly different in normal and osteoporotic individuals, while low peak bone mass has long been known to be an important risk factor for osteoporosis (Garn et al., 1967Go).

Peak bone mass has both hereditary and environmental determinants (Pollitzer and Anderson, 1989Go). Twin and family studies suggest that as much as 50% of peak bone mass may be determined by polygenic loci (Johnston and Slemenda, 1995Go; Pollitzer and Anderson, 1989Go; Sowers et al., 1992Go). Distinct ethnic and racial differences in bone mass and susceptibility to the development of osteoporosis exist. In particular, African Americans have greater peak bone mass, higher cortical and trabecular bone density, and lower bone turnover than American whites. African American women also lose less bone in later years, both absolutely and relatively (Garn, 1972Go). These differences in bone metabolism are consistent with the difference in prevalence of clinical osteoporosis in black and white women. African American women have a much lower risk of hip fracture than white American women (Cummings et al., 1985Go). The differences in bone metabolism are also consistent with differences in postmenopausal/premenopausal blood lead concentrations between black and white women. Among the white women in the NHANESII study (National Center for Health Statistics, 1984Go), the postmenopausal increase in blood lead concentration was 14.7%; among the black women, it was 4.6% (Silbergeld et al., 1988Go). The expanded model could readily be calibrated to take into account group-specific features of bone kinetics such as differences in peak bone mass and rates of bone loss. Normative data for bone mass, bone density, and bone mineral content are being developed for different racial and ethnic groups, and for individuals of different sex and age (see, for example, Faulker et al., 1993; Mosekilde and Mosekilde, 1990; Palacios et al., 1993; Sugi-moto et al., 1994). Not only a variety of calibrations, but also expansion of the physiologically based model of human bone kinetics so that it applies to calcium as well as to those elements that mimic bone calcium kinetics in some respects would give the modified model even broader applicability to questions associated with human aging.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Model Code
PROGRAM: Physiologically-based Toxicokinetic Model: Lead in Humans

!Ellen J. O'Flaherty

!This version of the physiologically-based human lead kinetic model is

!written for ACSL (Advanced Continuous Simulation Language, MGA Software, 200 Baker

!Avenue, Concord, MA 01742–2100), Level 11.


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    NOTES
 
1 To whom correspondence should be addressed, from October to June, at 68 Rue Sully, 69006 Lyon, France, and from June to October at P.O. Box 1313, Pocasset, Massachusetts 02559-1313, USA. E-mail: eoflaherty{at}aol.com. Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Aaron, J. E., Makins, N. B., and Sagreiya, K. (1987). The microanatomy of trabecular bone loss in normal aging men and women. Clin. Orthoped. Rel. Res. 215, 260–271.

Cann, C. E., Genant, H. K., Kolb, F. O., and Ettinger, B. (1985). Quantitative computed tomography for prediction of vertebral fracture risk. Bone 6, 1–7.[ISI][Medline]

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