A physiologically based kinetic model for lead in children and adults.

A physiologically based model of lead kinetics in children and adults has been developed and tested. The premises on which the physiologically based model is founded are reviewed in this paper. Because 95% or more of the body burden of lead in adults is found in the bone, bone metabolism is central to the model. Bone volumes are expressed as functions of body weight. Bone formation and resorption rates are estimated from human studies of stable labeled calcium kinetics. Cortical and trabecular bone are modeled separately, with their surface-to-volume ratios taken into account. Standardized growth curves are used to relate body weight to age. Other model features such as organ volumes and physiologic functions are related to body weight based on measurements made in human subjects over a range of ages. Calibrations of the model to two human data sets are shown, and two applications to specific research questions are illustrated. A brief comparison of the structure of this model with that of the Leggett model, and a comparison of the output of this model with that of the integrated exposure uptake biokinetic model of the U.S. Environmental Protection Agency, are also included.

A physiologically based model of lead kinetics in children and adults has been developed and tested. Several publications detailing its development and applications have appeared (1)(2)(3). The purposes of this paper are to review the premises on which the physiologically based model is built, to outline its relationship to bone metabolism, to depict some of its representations of physiologic functions, and to illustrate two of its applications. Brief comparisons of this model with that of Leggett (4) and with the integrated exposure uptake biokinetic (IEUBK) model of the U.S. Environmental Protection Agency (U.S. EPA) (5) are also included.

Bone Physiology and Metabolism
Total bone is conventionally considered to be about 20% trabecular bone and 80% cortical bone (6,7). Although there actually exists a spectrum of bone compositions lying between prototypical cortical and prototypical trabecular bone, the traditional division into two bone types is a useful one for modeling purposes.
Bone near the center of long bones (the diaphyseal region of long bone) is typical of cortical bone. Figure 1 is a set of schematic drawings of growing and mature cortical long bone in dogs, based on microradiographs from Lee et al. (8). As the long bone grows (Figure IA, B), its diameter is enlarged by the deposition of concentric lamellae at the outer (periosteal) surface and the accompanying enlargement of its marrow cavity by active bone resorption at the inner (endosteal) surface. These processes are integral components of the modeling that shapes growing bone. Mature diaphyseal bone, on the other hand ( Figure  1C, D), no longer displays the ragged endosteal surface that indicates active bone resorption. Instead, mature cortical bone is constantly renewed through the process of remodeling, in which cavities are excavated in existing bone by the action of osteoclasts. Each of these cavities is gradually filled with new bone by the action of osteoblasts. The open channel remaining in the center, the haversian canal, carries a blood vessel. The unit containing the haversian canal and the surrounding bone nourished by its blood vessel is an osteon.
Portions of two osteons are shown enlarged in Figure 2. Formation of new osteons appears to proceed without regard for the boundaries of existing osteons. Bone is laid down in the new osteon in lamellae, beginning at the periphery and moving in. Between the lamellae are cavities, or lacunae, which contain bone cells called osteocytes. The osteocytes are nourished via canalicules that radiate from each lacuna, connecting the spaces between lamellae with the haversian canal. These canalicules are the smallest of the channels that supply bone tissue with nutrients.
Bone in the interior of the vertebrae is typical of trabecular bone ( Figure 3). Trabecular bone takes the form of narrow plates and struts having a much greater surface-to-volume ratio than cortical bone. Mature trabecular bone displays little or no osteonal remodeling activity. It is renewed by surface remodeling, which replaces and restructures it in response to a variety of factors including physical stresses. Loss of trabecular bone is largely responsible for the fragility of vertebral and hip bones in osteoporosis. Table 1 gives an overview of some of the important features of bone physiology from the standpoint of devising a model of bone metabolism. Surface-to-volume ratios in trabecular bone are 5 to 6 times those in cortical bone, whereas cortical bone volume is 4 times that of trabecular bone. These physical features of bone appear to be reasonably species independent. If bone remodeling activity were assumed to be proportional to total surface area, then from 55 to 60% of total mature bone remodeling activity would be assigned to trabecular bone.
Total mature bone remodeling activity, however, is markedly species dependent. Small animals like mice and rats, with relatively short lifespans, display little cortical bone remodeling activity as adults. Presumably the need to replace aging cortical bone in these species is less acute. Recent studies in humans and in cynomolgus monkeys suggest that bone turnover is comparable in these two species. Although a range of bone turnover rates is found in both cortical and trabecular bone, reflecting the range of bone structures as well as other regional differences, the ranges observed in the monkeys (9,10) are consistent with experimental estimates of total turnover in mature human bone (Table 1).
Bone turnover is usually expressed as the mass of calcium exchanged per unit time. Early histomorphometric studies linked bone lead metabolism to that of calcium. In 1933, in a series of experiments in which the localization of lead in bone was compared to that of calcium, it was observed that It was apparent that lead is always deposited where mobilizable calcium deposits are found. (11) A C B D Figure 1. Transverse sections of femur midshaft from a puppy (A,B) and a mature dog (C,D). Fully calcified bone is white in these drawings; less fully calcified bone is denoted by degrees of shading. Note in Figure  1D that as the new osteons are filled in by freshly apposed bone mineral, the haversian canals that carry the blood vessels become narrower. Because of the general orientation of the haversian canals, most of the channels are cut transversely, but some are cut longitudinally. Drawings based on microradiographs from Lee et al. (8).
The link was made more explicit by other investigators. After 11 days [of feeding lead to young guinea pigs], lead deposits [in the diaphysis of the femur] ... consisted of a broad subperiosteal zone, a narrow subendosteal zone, and broad zones around the vascular channels. [In addition,] . . . a fine radiating structure was visible, especially around distant lacunae. (12) In long bones of adult guinea pigs,.... the predominant deposit is now in the subperiosteal lamellar region. Cortical areas bordering on marrow space contain little lead. Haversian and Volkmann's canals are lined with lead. . . . Similarly, lead is present in bone cells and bone canaliculi. (12) The studies showed that lead was being deposited on bone surfaces in general, and on surfaces engaged in modeling and remodeling in particular: While in acute experimental lead poisoning lead is predominantly deposited in the subperiosteal zone and in the vicinity of the Haversian canals, the localization of normal lead in humans is strikingly different .... These patterns [of "normal" lead deposition] are so striking that the question of their origin asserts itself. It is likely that the answer is linked to bone remodeling. (13) Figure 3. The structure of trabecular bone. A network of connecting narrow plates and struts creates a bone mesh with a high surface-to-volume ratio. These early studies of lead distribution in bone, associating it with surface deposition and incorporation into forming bone, were more qualitative than quantitative. A third mechanism of uptake of lead into bone was defined more precisely in studies with uranium and radium isotopes and with isotopes of calcium itself. In one experiment, 233U was administered to young adult beagles and its distribution in bone was evaluated between 1 and 726 days later. In cortical bone, Initially uranium is seen on endosteal and periosteal surfaces and lining the Haversian canals. As a function of time postinjection, the intensity of the surface label decreases and the cortical bone volume acquires a diffuse, uniform deposit. (14) In trabecular bone, Low magnification images show the transition of an initially heterogeneous surface deposit at 1 day to a pattern in which the dense deposits are diminished as a function of time in number but not in intensity. Higher magniflcation emphasizes the heterogeneous character of the early deposits and a subsequent gradual redistribution from surfaces to bone volume. (14) This redistribution of bone volumeseeking elements, a group that includes lead, throughout bone can be visualized as a heteroionic exchange of the elements with calcium (or an exchange of calcium with calcium) within the bone crystal matrix. Thus, surface exchange, deposition with forming bone, and slow migration throughout bone have all been implicated as mechanisms by which lead can become incorporated into bone.

Construction of Physiologically Based Lead Kinetics Model
The physiologically based lead kinetic model (hereafter called the O'Flaherty model) has been developed as a series of levels. The model of bone structure and agedependent metabolism was designed first, then encapsulated by a model of age-related whole-body growth and metabolism. The behavior of lead within this shifting anatomic and physiologic framework was added next. Finally, an exposure module was constructed to try to capture the varieties of human lead exposure in as flexible a form as possible. The parameters associated with each of these levels were assigned values based on the best appropriate data sets from the relevant literature. In a few instances, these data sets were from experimental animals rather than humans, but human data were relied on whenever possible. Parameters assigned values at each level were not allowed to change at the next or subsequent levels. With each model addition, only the new parameters were examined and assigned values.
The O'Flaherty model is based on body weight. All tissue volumes and blood flow rates, as well as bone turnover rates, are linked to body weight by means of expressions that reproduce physiologic measurements. For example, Figure 4 illustrates the volumes of liver and kidney as functions of body weight from birth to maturity (15). The departure of the kidney weights from linearity around 1 year of age is probably real but has not been explicitly modeled. Figure 5 illustrates the body weight dependence of the glomerular filtration rate (15,16). These data, as shown, were fit with two straight line segments. The change in slope occurs around 1 year of age, when standard body weight is 11.7 kg, which is also the age at which the deviation of body weight dependence of kidney weight from linearity is observed ( Figure 4).
Some physiologic functions are different in males and females even after body weight has been taken into account. Figure  6 shows respiration rates for males and females as functions of body weight from birth to maturity (15). The data were fit with straight line segments, a single one for both males and females up to 1 year of age and separate line segments for males and females subsequent to that age. Body weight is defined by five constants, two for the early childhood phase of growth and three for the subsequent adolescent growth spurt and stabilization at mature adult weight. Figure 7 shows body weight as a function of age for the white American female. The five constants allow other growth curves to be defined; for example, growth curves for specific ethnic or cultural groups or even for individuals. Once the growth curve has been specified, the other anatomic and physiologic features of the model have been defined as well.
Bone turnover is central to the model. It is responsible for incorporation of lead from blood plasma into forming bone and for return of lead from bone to plasma as bone is resorbed. Figure 8 shows bone formation rate as a function of age. The data are from a number of calcium isotope uptake studies, which provide estimates of the rates of new bone accretion. Bone  Gender-specific differences in the age dependence of bone formation rate are to be expected around puberty, which girls generally experience earlier than boys. However, there are too few data points, particularly for girls, in this crucial age range ( Figure 8) to define gender-specific curves on an empirical basis. The curves shown are based on an arbitrary difference modeled in the age at which the growth rate begins to slow, set at 10 years for girls and 11 years for boys. It is expected that these cutoff values, as well as the maximum rates of new bone accretion during adolescence, may be revised as new information about the timing and magnitude of the changes in these very rapid rates of bone growth becomes available. Because total bone volume is defined as a function of body weight, the expression for bone formation rate can be combined with the expression for net bone volume to generate an expression for bone resorption rate as a function of age or body weight. The two expressions, for bone formation rate and bone resorption rate, determine the rates of incorporation of lead into forming bone and loss of lead with resorbing bone. In addition, lead is allowed to diffuse into and throughout cortical bone in the model. Mathematically, this diffusion is expressed as a diffusion radially outward from the canalicules. Diffusion is not included in the trabecular bone compartment. Because of the thinness of the trabeculae in human bone and in the bone of smaller animals, haversian systems with their constituent canalicules are not present. The bone is supplied with nutrients directly from the marrow space.
Running the model is straightforward. The model includes exposure modules that allow the user to design exposure scenarios and to specify lead concentrations in air, food, water, dust, and soil. and tissues, including cortical and trabecular bone, can be accessed and plotted directly or imported into other graphical or spreadsheet software. The chief limitation of the model in its present form is that it is deterministic: model output does not indude estimates of population distributions.
Extensions of the model to accommodate pregnancy and to incorporate the loss of bone that occurs with aging are planned.

Model Calibration
Two fits of the model to human data are illustrated in this section. It should be emphasized these are data set fits, in which parameters of the model were optimized during the fitting process. One example is for children, one for adults. Figure 9 illustrates a model fit to one of the longitudinal data sets from the Cincinnati Prospective Lead Study (19). The group of children whose blood lead concentrations are shown here is the upper quartile of a large group that was followed from birth for over 6 years. These data were used to design the model expressions for soil and dust ingestion rates, illustrated in Figure  10. Dust ingestion was assumed to begin around age 3 months, to peak at age 2 years, and to fall off rather rapidly thereafter. Soil ingestion, an outdoor exposure, was assumed to begin at around age 6 months, to peak at age 3 years, and then to fall off fairly slowly with age as the child presumably continues to play outdoors and perhaps to participate in outdoor sports.  (19). The year of birth was set at 1983 for this simulation, drinking water lead concentration at 0.005 mg/I, soil lead concentration at 4100 ppm (g/g), and dust lead concentration at 1200 ppm. These blood lead concentration data were used to design the soil and dust ingestion curves shown in Figure 10. The line is the resulting model simulation.
Environmental Health Perspectives * Vol 106, Supplement 6 * December 1998 Finearo 2 Fr::retionnn hanni fnrmqtinn rnto nc n fiinrtinn Together, these two curves for soil and dust ingestion generate the blood lead concentration curve shown in Figure 9, which displays a rather sharp peak at age 2 years. The maximum blood lead concentration at age 2 years was a consistent feature of all quartiles in the Cincinnati Prospective Lead Study. It should be noted that lead uptake from soil and dust is determined by both age-dependent intake and age-dependent fractional absorption from the gastrointestinal tract. The curves illustrated in Figure 10 are coupled with a reasonable but somewhat uncertain expression, derived from an incomplete database, for age-dependent fractional lead absorption, which had been calibrated prior to addition of the exposure module to the model. Figure 11 shows a simulation carried out in the course of general model calibration (2), for a 50-year-old male with workplace lead exposure superimposed on ambient exposure. The curve is made up of the end points of simulated 30-year exposures to a range of workplace air lead concentrations. The data points are from a study by Van de Vyver et al. (20) in which lead was assayed in ashed biopsy samples from the iliac crest of control and lead-exposed human subjects. As the simulated relationship is for a 30-year exposure, it would be expected to lie in the upper range of the experimental data, some of which would probably have represented shorter exposures. In addition, the simulation displays a degree of curvature that would not have been apparent from examination of the data alone but which nonetheless is entirely consistent with them. Age, years Figure 10. The modeled soil and dust ingestion rates. Together, these two curves generate the soil and dust contribution to the blood lead concentration curve shown in Figure 9.

Model Validation
Two examples of model validation will be given. These examples represent applications of the model to specific lead exposure issues without parameter adjustments. In both these examples, application of the model assisted in data resolution and interpretation. The first example uses an earlier model version for the rat (21,22). One of the chief uncertainties associated with lead modeling is the wide range of lead bioavailability from exogenous oral sources. Some of this variability is associated with the chemical and physical nature of the source itself, and some with the conditions under which exposure occurs. For example, fractional absorption is substantially greater in the fasting state than in the fed state (23). A number of bioavailability studies have been reported. In a standard experimental design, animals are fed lead in the form of concern, usually for about 30 days, after which the concentrations of lead in blood, liver, kidney, and bone are compared to those in animals given daily intravenous doses of a soluble lead salt for 30 days. An estimate of fractional lead absorption is obtained for each tissue examined at each dose.
The physiologically based rat lead kinetic model has been applied to one such dataset (24). In this study (25), male and female rats were fed for 30 days a diet formulated with one of eight different lead concentrations. The source of the lead was two mine waste-containing soils, one with 5 times the lead concentration of the other. An intravenous lead acetate group was included (26). Bone, liver, and blood lead concentrations were measured at the end of 20 40 Blood lead, ptg/di the 30-day exposure period. The model was fit to these data by optimizing the absorption rate constant for each group of rats at each dose level to achieve the best simultaneous fit to blood, liver, and bone lead concentrations. Thus, a single best estimate of fractional bioavailability was obtained from the three different tissue concentration measurements at each dose level ( Table 2). (Note that tissue concentrations were judged to be indistinguishable from background concentrations at several of the low dose levels.) Table 2 also gives the estimates of fractional bioavailability obtained by the conventional calculation, in which tissue concentrations were compared between oral and intravenous dose groups. As can be seen in the table, fractional bioavailability estimates vary widely, are tissue dependent, and display no apparent relationship to dose level. In addition, a disadvantage of this technique is that oral dose groups that generate tissue concentrations outside the range generated by intravenous dosing cannot be used in the calculations. Figure 12 demonstrates that fractional bioavailability estimated by application of the physiologically based model declines smoothly with dose from a high of 1.6% at the lowest dose to a low of 0.24% at the highest dose. Thus, the model integrates concentrations in different tissues into a single best estimate of fractional bioavailability at each dose, and by doing so reveals a clear-cut dose dependence of fractional bioavailability that was not previously apparent. The model can be applied at all dose rates at which tissue concentrations are distinguishable from background concentrations. In addition, because intravenous dose groups are not used, reliance on the model for estimation of fractional bioavailability reduces the number of animals required in a bioavailability study.
The second example application of the physiologically based lead model uses another version of the model. This version has been developed for the cynomolgus monkey, largely by scaling the human model to the body weight of the monkey. (The cynomolgus monkey skeleton is lighter in proportion to body weight than the human skeleton; actual data were used to model the monkey skeleton as a function of body weight in the scaled model.) This model version was applied to the results of a study in which adult female cynomolgus monkeys were administered stable lead isotopes sequentially, in order to label body stores of lead (almost exclusively Environmental Health Perspectives * Vol 106, Supplement 6 * December 998  bone lead) and thereby to distinguish between blood lead originating from past exposure and blood lead originating from current (dietary) lead (27). An observation made in this study was that on cessation of controlled lead exposure at the end of the isotope administration sequence, the blood concentrations of those lead isotopes administered earlier in the sequence, and therefore representative of endogenous lead, exhibited a transient but distinct rise, suggesting a shift to a new relationship between bone lead and blood lead ( Figure  13). The data shown in Figure 13 are for a single isotope mixture enriched in 204Pb. Administration of this isotope mix was begun on day 0 of the study and terminated on day 48. Lead exposure to other isotope mixes continued at an unchanged rate until exposure was terminated in this monkey on day 619 of the study. After day 619, total blood lead concentration, which is not shown, fell sharply from 40 to 45 pg/dl to 15 to 20 pg/dl. As illustrated in Figure 13, the model predicts the observed rise in endogenous blood lead at this time, with subsequent continuation of the steady concentration decline at the rate observed before cessation of lead exposure. This shift in blood lead concentration does not represent a change in lead kinetics related to the abrupt drop in exposure, as might be inferred from the data alone. The modelpredicted shift is caused by the nonlinearity of the relationship of red cell lead to plasma lead. Because lead is bound to a limited number of specific sites in the red cell, the capacity of the red cell to accommodate lead is limited. Although plasma lead is linearly related to exposure, red cell lead (and therefore blood lead) is not. At high blood lead concentrations, a larger fraction of total blood lead is present in the plasma than at low blood lead concentrations. Therefore, while plasma lead continues to decline smoothly after cessation of exposure in the situation modeled in Figure 13, readjustment of the equilibrium between plasma and red cell lead as total blood lead falls results in a shift in the plasma lead-blood lead relationship to a higher blood lead concentration for a given plasma lead concentration.

Comparison with the Leggett/ICRP Model
Another physiologically based lead kinetic model has been developed and published (4). It was presented and discussed at the workshop at which this paper was also presented (28). The Leggett/ICRP model is an expansion of an ICRP age-specific model of lead metabolism (17,18 Exchanges between a diffusible plasma compartment and tissues except bone are considered to be first order, but a nonlinear relationship between plasma and red cell is included. Tissue uptake and loss are defined in terms of age-dependent transfer half-times, which are assigned values by interpolation between sequential ages for six different age groups. The gastrointestinal tract is modeled as four anatomically based segments, with absorption occurring only from the small intestine and fractional absorption being age-dependent stepwise rather than continuously. Liver and kidney both consist of two subcompartments. Lead in blood interchanges among a diffusible fraction, a plasma-bound fraction, and the red cells. Plasma-bound lead is not diffusible. With time, a gradual age-dependent shift of plasma-diffusible lead to plasma-bound lead takes place. Extravascular fluid is also a component of the model. Excretion takes place not only in urine and feces but also in sweat, hair, skin, and nails. Most of these differences between the two models are not critical to model function, although the assignment of different parameter values could cause model outputs to be different for the same set of exposure conditions. The Leggett/ ICRP model has not been rigorously tested against datasets other than those on which it was based. [year]-dependent intake rates and applies an age-dependent fractional absorption to them), the forms of the two curves for uptake of lead from food and water cannot be made congruent (Figure 14). Similarly, because the same age-dependent fractional absorption from the gastrointestinal tract is applied in the O'Flaherty model to lead originating from soil and dust, the curves for uptake of lead from soil and dust do  Figure 15). Uptake of lead from air behaves in the same age-dependent fashion in the two models. Although it is greater in the O'Flaherty model than in the IEUBK model ( Figure 16), it is a very minor contributor to blood lead overall under these default conditions. Despite these qualitative and quantitative differences in lead uptake, the two models give predicted blood lead concentrations that are not greatly dissimilar (Figure 17). This is not unexpected, as both models were calibrated against the same types of data for blood lead concentrations in urban children. It is Age, years Age, years Age, years  Validation is the comparison of model predictions for particular situations with observations made under the same conditions holding all parameter values constant. Models designed to predict future events may never be fully validated. However, models such as these, which are designed to predict the behavior of a biological system or organism under a specified set of conditions, are capable of validation in that they can be shown to perform well (or not well) under a variety of different sets of conditions. If they do not perform adequately, then recalibration or, depending on the nature of the failure, model restructuring is in order. In a sense, then, calibration and validation are not entirely mutually independent exercises for models of this kind. Each process helps to inform the other. A validation failure may force model recalibration or redesign, whereas the process of calibration may pinpoint areas of uncertainty and suggest validation exercises specifically designed to examine model performance in these areas.