The estimation of the rates of lead exchange between body compartments of smelter employees

Abstract

The overwhelming proportion of the mass of lead (Pb) is stored in bone and the residence time of Pb in bone is much longer than that in other tissues. Hence, in a metabolic model that we used to solve the differential equations governing the transfer of lead between body compartments, three main compartments are involved: blood (as a transfer compartment), cortical bone (tibia), and trabecular bone (calcaneus). There is a bidirectional connection between blood and the other two compartments. A grid search chi-squared minimization method was used to estimate the initial values of lead transfer rate values from tibia (λTB) and calcaneus (λCB) to blood of 209 smelter employees whose bone lead measurements are available from 1994, 1999, and 2008, and their blood lead level from 1967 onwards (depending on exposure history from once per month to once per year), and then the initial values of kinematic parameters were used to develop multivariate models in order to express λTB and λCB as a function of employment time, age, body lead contents and their interaction. We observed a significant decrease in the transfer rate of lead from bone to blood with increasing body lead contents. The model was tested by calculating the bone lead concentration in 1999 and 2008, and by comparing those values with the measured ones. A good agreement was found between the calculated and measured tibia/calcaneus lead values. Also, we found that the transfer rate of lead from tibia to blood can be expressed solely as a function of cumulative blood lead index.

Propagation of lead in the human body

“…This is because the majority of lead settles where calcium deposits are found [17]. Similar to established models such as [5], here we separate the bones into two separate compartments because the transfer rates between blood and the two bone types are reported to be significantly different [4]. As Figure 2 illustrates, the tougher cortical bone has a lower transfer rate to the blood than the spongier trabecular bone when the amount of lead in the bone is less than 50 mg; otherwise, the rates are comparable.…”

“…However, data in [4] shows that the transfer rates from the bone back to the blood do depend upon the levels of lead (see Figure 2). These rates are estimated from measurements of lead content in the various compartments.…”

“…The ODE model is a functionally standard compartment model ( [4,20]), but we include nonlinearity in our analysis to account for the change in transfer rates as the amount of lead in the body increases [4]. We demonstrate that the nonlinear interactions affect:…”

“…The linear equations will have P C,B = P T,B = P B,O = 0. We note that the model proposed is symbolically identical to the one in [4]. However, while [4] uses this approach to carry out optimization and parameter estimation based on experimental data, our goals are to examine the steady states of the system in the case of linear and nonlinear reaction rates as well as the amount of lead variation in each compartment with time.…”

“…However, the exchange rates become comparable once each bone segment contains roughly 50 mg of lead. For the values of k B,T and k B,C we used the average in the range of values provided in [4]. Given the absence of data for transfer of lead from blood to outside the body, we arbitrarily chose P B,O = 0.005 in our simulations.…”