Allan H. Marcus

Multicompartment kinetic models for lead. I. Bone diffusion models for long-term retention

The long-term retention of lead in bone poses a number of difficulties for the usual multicompartment models. The use of diffusion models based on exchange of lead between blood in canaliculi and the crystalline bone of the osteon allows a linear compartmental approximation suitable for statistical estimation of kinetic parameters in peripheral compartments. The model is applied to lead retention by beagle dogs.

Multicompartment kinetic model for lead. III. Lead in blood plasma and erythrocytes

Multicompartment models have been fitted to experimental data on plasma lead and blood lead concentrations of subjects studied by P. E. deSilva (Brit. J. Ind. Med. 38, 209-217, 1981) and one subject studied by W.I. Manton and C.R. Malloy (Brit. J. Ind. Med. 40, 51-57, 1983). Nonlinear models for plasma lead vs blood lead in populations provide significantly better descriptions than does a linear model. Short-term kinetic data do not clearly resolve the precise nonlinear mechanism, however, Parameters of plasma and erythrocyte distribution in a single subject were significantly different on two occasions.

Sexual differences in the distribution and retention of organic and inorganic mercury in methyl mercury-treated rats

At 56 days of age, male and female Long-Evans rats received 1 mumole of 203Hg-labeled methyl mercuric chloride per kilogram sc and total, organic, and inorganic mercury contents and concentrations in tissues were determined for up to 98 days postdosing. Whole body clearance of mercury was faster in females than in males, and females attained higher peak percentages of the methyl mercury dose in kidney and brain than did males. Females had significantly higher mean percentages of the mercury dose present in the kidney and brain as organic or total mercury and in brain as inorganic mercury than did males. Males had significantly higher mean percentages of the dose present as organic or total mercury in pelt and whole body than did females. When expressed on a concentration basis, the only significant sexual difference was in the higher average concentration of organic mercury in the kidneys of females. When expressed on a tissue content basis, significant male-female differences in the kinetics (sex X time interactions) of organic mercury retention were found in kidney, brain, skeletal muscle, pelt, and whole body. Significant sex X time interactions in the concentrations of organic mercury were found in kidney, skeletal muscle, and whole body. Kinetics of retention and concentration of inorganic Hg in the pelt differed significantly for males and females. Discordance in degree of statistical significance of differences in mercury contents and concentrations reflected in part differences in relative body composition of males and females. Integrated exposures of tissues of males and females to organic or inorganic mercury were determined by fitting multiexponential retention functions to retention data. Differences in integrated exposure were estimated by the female-to-male ratio of areas under retention curves. Reconstruction of whole body organic and inorganic mercury burdens from constituent tissues indicated that integrated exposures of males and females to inorganic mercury were equal but females had a lower integrated exposure to organic mercury. Integrated exposure of liver to either form of mercury was about equal in males and females. However, the integrated exposure of the brain of females to inorganic mercury was 2.19 times that of males suggesting a sexual difference in accumulation or retention of inorganic mercury in the nervous system. These sexual differences in distribution and retention of organic and inorganic mercury after methyl mercury exposure may underlie reported sexual differences in sensitivity to the toxic effects of methyl mercury.

Omaha childhood blood lead and environmental lead: A linear total exposure model☆

The majority of experimental and population studies of blood lead (PbB) and environmental lead, including the Omaha study, have utilized the Goldsmith-Hexter log-log or power function model. Comparison was made of the log-log model and a linear model of total exposure to describe the Omaha Study of 1074 PbBs from children ages 1-18 years as related to air (PbA), soil (PbS), and housedust (PbHD) lead. The data fit of the linear model was statistically equivalent to the power model and the predicted curves were biologically more plausible. The linear model avoids the mathematical limitations of the power model which predicts PbB zero at PbA zero. From the Omaha data, this model, ln PbB = ln (beta 0 + B1 PbA + B2 PbS + beta 3 PbHD) predicts that PbB increases 1.92 micrograms/dl as PbA increases 1.0 microgram/m3. Since PbS and PbHD increase with PbA, however, the increases in total exposure predict a PbB increase of 4-5 micrograms/dl as PbA increases 1.0 microgram/m3.

Multicompartment kinetic models for lead: II. Linear kinetics and variable absorption in humans without excessive lead exposures

Multicompartment models with constant fractional transfer rates have been fitted to experimental data on lead metabolism in four subjects studied by M. B. Rabinowitz, G. W. Wetherill, and J. D. Kopple (Science 182, 725-727, 1973; Environ. Health Perspect. 7, 145-153, 1974; Arch. Environ. Health 31, 220-223, 1976; J. Clin. Invest. 58, 260-270, 1976; J. Lab. Clin. Med. 90, 238-248, 1977). Long-term retention is estimated for blood, soft tissue, cortical and trabecular bone pools, and for facial hair. The absorption of lead from diet is shown to change with time, but no evidence was found for other variable or nonlinear kinetic mechanisms of lead metabolism in humans without excessive lead exposure.

The body burden of lead: comparison of mathematical models for accumulation

Abstract Compartmental models for kinetic studies of lead metabolism can be generalized to include power function distributions of residence time of lead molecules in bone, as well as exponential distributions. The predicted long-term accumulation of lead is shown to differ by a factor of 1.3 among several proposed models. Satisfactory models will require at least two bone compartments with mixed power function and exponential distributions of residence time.

Compartmental models with spatial diffusion: estimation for bone-seeking tracers

Abstract A compartmentlike model is developed for tracers in which bone-volume diffusion plays an important role in body distribution (e.g. bone-volume-seeking metals). The model requires solution of an infinite eigensystem. Approximations are presented for cylindrical diffusion in canalicular territory. An application to lead metabolism in beagle dogs suggests that finite truncation of the system of equations provides an adequate approximation for routine use in computer programs for compartmental-parameter estimation. The model is consistent with both power-law and exponential mixture retention functions.

Multicompartment kinetic models for cadmium. I. Effects of zinc on cadmium retention in male mice.

Abstract A multicompartmental model was fitted to data on cadmium concentrations in male mice published by K. E. Shank, R. J. Vetter, and P. L. Ziemer (1977, Arch. Environ. Contam. Toxicol. 6 , 63–68 1977, Environ. Res. 13 , 209–214. The zinc treatment increased the rate of flow of cadmium from rapidly exchanging compartments to slowly exchanging compartments in blood and liver, and possibly increased the rate of release from the slowly exchanging liver compartment. Most other cadmium distribution processes were slowed by zinc treatment, including blood into liver, kidney, gastrointestinal tract, and pancreas, and back into blood from the liver, kidney, and pancreas. Many other processes were slowed less significantly. The rate of excretion processes was nearly unchanged.

Mathematical models for carboxyhemoglobin

Abstract This paper describes a non-linear model for blood COHb fraction as a function of a subjects activity level, individual physiological parameters, and individual time-variable exposure to carbon monoxide. The computer solution of the model fits data on smokers and non-smokers. The simpler models of Ott and Mage (1978) and Venkatram and Louch (1979) are shown to have the correct form in low-stress environments, but the simpler models do not allow assessment of health effects for sensitive or high-risk subpopulations. Their postulated constant time-scale of 2.49 h may lead to substantial underestimation of COHb buildup.

Compartmental models for trace metals in mammals.

Kinetic models for the distribution and elimination of certain trace metals in mammals allow evaluation of metal burdens in critical target organs under time-variables exposure patterns, and thus may assist in formulating exposure standards. The linear compartmental model is described and some of its implications for conceptual models of trace metal metabolism are developed. The model is then applied to data on multiple doses of cadmium in mice. Many trace metals do not follow simple linear kinetic models because exposure to more than one metal simultaneously often results in synergistic effects.