Immunologically restricted patients exhibit a pronounced inflammation and inadequate response to hypoxia in fracture hematomas.

For patients who are known to have an impaired immune system, bone healing is often impaired. Therefore, it has been suggested that an effectively functioning immune system will have an influence on the quality of bone healing. Here, we demonstrate that cells within the fracture hematoma of immunologically restricted patients (1) exhibit a disturbed osteogenic differentiation (normal SPP1 but diminished RUNX2 expression), (2) show a strong inflammatory reaction (high IL8 and CXCR4), and (3) react on local hypoxia (high expression of HIF1A) but with inadequate target gene responses (diminished LDHA and PGK1 expression). Thus, it is already within the early inflammatory phase of fracture healing that the local gene expression in fracture hematomas of immunologically restricted patients points toward a critical regeneration.

Concordance between in vitro and in vivo dosimetry in the proinflammatory effects of low-toxicity, low-solubility particles: the key role of the proximal alveolar region.

We previously demonstrated the importance of the surface area burden as the key dose metric in the elicitation of inflammation in rat lungs by low-solubility, low-toxicity particles (LSLTP). We have now explored the dosimetry of LSLTP in vitro using epithelial cell interleukin (IL)-8 gene expression as a surrogate for potential of particles to cause inflammation. The proximal alveolar region (PAR) of the lung has been identified as a key site for the retention of respirable particles, as it receives high deposition but has slow clearance compared to the larger airways. For these reasons, a few days after exposure to particles the residual dose is concentrated in the PAR region. Re-expressing our rat lung data as particle surface area burden per unit of PAR surface area we obtained a threshold value for onset of inflammation of 1 cm(2)/cm(2). We carried out dose responses in vitro for onset of IL-8 gene expression with the same particles as we had used in vivo. When we expressed the in vitro dose as surface area dose per unit A549cell culture surface area, we obtained a threshold of 1 cm(2)/cm(2). This concordance between proinflammatory effects in vivo (PMN in BAL) and in vitro (epithelial IL-8 gene expression) confirms and supports the utility of the particle surface area metric and the importance of the PAR. These studies also open the way for future in vitro approaches to studying proinflammatory effects of a range of toxic particles based on sound dosimetry that complements animal use in particle toxicology.

Lung dosimetry and risk assessment of nanoparticles: evaluating and extending current models in rats and humans.

Risk assessment of occupational exposure to nanomaterials is needed. Human data are limited, but quantitative data are available from rodent studies. To use these data in risk assessment, a scientifically reasonable approach for extrapolating the rodent data to humans is required. One approach is allometric adjustment for species differences in the relationship between airborne exposure and internal dose. Another approach is lung dosimetry modeling, which provides a biologically-based, mechanistic method to extrapolate doses from animals to humans. However, current mass-based lung dosimetry models may not fully account for differences in the clearance and translocation of nanoparticles. In this article, key steps in quantitative risk assessment are illustrated, using dose-response data in rats chronically exposed to either fine or ultrafine titanium dioxide (TiO2), carbon black (CB), or diesel exhaust particulate (DEP). The rat-based estimates of the working lifetime airborne concentrations associated with 0.1% excess risk of lung cancer are approximately 0.07 to 0.3 mg/m3 for ultrafine TiO2, CB, or DEP, and 0.7 to 1.3 mg/m3 for fine TiO2. Comparison of observed versus model-predicted lung burdens in rats shows that the dosimetry models predict reasonably well the retained mass lung burdens of fine or ultrafine poorly soluble particles in rats exposed by chronic inhalation. Additional model validation is needed for nanoparticles of varying characteristics, as well as extension of these models to include particle translocation to organs beyond the lungs. Such analyses would provide improved prediction of nanoparticle dose for risk assessment.

The London Underground: dust and hazards to health.

AIMS: To assess hazards associated with exposure to dust in the London Underground railway and to provide an informed opinion on the risks to workers and the travelling public of exposure to tunnel dust. METHODS: Concentrations of dust, as mass (PM2.5) and particle number, were measured at different underground stations and in train cabs; its size and composition were analysed; likely maximal exposures of staff and passengers were estimated; and in vitro toxicological testing of sample dusts in comparison with other dusts was performed. RESULTS: Concentrations on station platforms were 270-480 microg/m3 PM2.5 and 14,000-29,000 particles/cm3. Cab concentrations over a shift averaged 130-200 microg/m3 and 17,000-23,000 particles/cm3. The dust comprised by mass approximately 67% iron oxide, 1-2% quartz, and traces of other metals, the residue being volatile matter. The finest particles are drawn underground from the surface while the coarser dust is generated by interaction of brakes, wheels, and rails. Taking account of durations of exposure, drivers and station staff would have maximum exposures of about 200 microg/m3 over eight hours; the occupational exposure standard for welding fume, as iron oxide, is 5 mg/m3 over an eight hour shift. Toxicology showed the dust to have cytotoxic and inflammatory potential at high doses, consistent with its composition largely of iron oxide. DISCUSSION: It is unjustifiable to compare PM2.5 exposure underground with that on the surface, since the adverse effects of iron oxide and combustion generated particles differ. Concentrations of ultrafine particles are lower and of coarser (PM2.5) particles higher underground than on the surface. The concentrations underground are well below allowable workplace concentrations for iron oxide and unlikely to represent a significant cumulative risk to the health of workers or commuters.

Modeling the retention and clearance of manmade vitreous fibers in the rat lung.

A mathematical model describing the dissolution and disintegration of long fibers and the clearance of short fibers is developed. For short fiber clearance, the model is based on previous modeling of the retention and clearance of particles, and most model parameters are taken from that particulate model. In addition to modeling the disappearance of long fibers, the present study includes a quantitative measure of goodness of fit of the model to observed data. Data from chronic inhalation experiments with insulation glass wools (MMVF10 and MMVF11) and rockwool (MMVF21) were provided for this study. These data comprised lung burdens at 10 time points at each of 3 concentrations for each fiber in inhalation experiments lasting up to 104 wk. At the two higher concentrations, the model had to take into account the effects of lung burden on macrophage-mediated clearance. The modeling shows that the overload dependence appears remarkably similar to that for low-toxicity particles in that the critical volumetric lung burden is similar to that for low toxicity dust. The model describes overload as leading to alveolar sequestration of short fibers or particles, and the estimated rate of alveolar sequestration for MMVF10 was similar to that for particles, but the estimated rate was lower for the other two fibers. Two alternative hypotheses to describe the process of the disappearance of longer fibers were tested by assessing their effect on a quantitative measure of fit of model predictions to the lung-burden data. These tests indicated that (a) dissolution leading to disintegration of long fibers into shorter fibers gave a much better fit than the alternative assumption that dissolution would leave only nonfibrous residue and (b) the relative rates of disintegration of the fibers in the lung appear to be directly dependent on their rates of in vitro dissolution and their diameters.

Biological and statistical approaches to predicting human lung cancer risk from silica.

Chronic inflammation is a key step in the pathogenesis of particle-elicited fibrosis and lung cancer in rats, and possibly in humans. In this study, we compute the excess risk estimates for lung cancer in humans with occupational exposure to crystalline silica, using both rat and human data, and using both a threshold approach and linear models. From a toxicokinetic/dynamic model fit to lung burden and pulmonary response data from a subchronic inhalation study in rats, we estimated the minimum critical quartz lung burden (Mcrit) associated with reduced pulmonary clearance and increased neutrophilic inflammation. A chronic study in rats was also used to predict the human excess risk of lung cancer at various quartz burdens, including mean Mcrit (0.39 mg/g lung). We used a human kinetic lung model to link the equivalent lung burdens to external exposures in humans. We then computed the excess risk of lung cancer at these external exposures, using data of workers exposed to respirable crystalline silica and using Poisson regression and lifetable analyses. Finally, we compared the lung cancer excess risks estimated from male rat and human data. We found that the rat-based linear model estimates were approximately three times higher than those based on human data (e.g., 2.8% in rats vs. 0.9-1% in humans, at mean Mcrit lung burden or associated mean working lifetime exposure of 0.036 mg/m3). Accounting for variability and uncertainty resulted in 100-1000 times lower estimates of human critical lung burden and airborne exposure. This study illustrates that assumptions about the relevant biological mechanism, animal model, and statistical approach can all influence the magnitude of lung cancer risk estimates in humans exposed to crystalline silica.

A biomathematical model of particle clearance and retention in the lungs of coal miners. II. Evaluation of variability and uncertainty.

The objective of this study is to investigate the sources of variability and uncertainty in a previously developed human lung dosimetry model. That three-compartment model describes the retention and clearance kinetics of respirable particles in the gas-exchange region of the lungs. It was calibrated using exposure histories and lung dust burden data in U.S. coal miners. A multivariate parameter estimation and optimization method was developed for fitting the dosimetry model to these human data. Models with various assumptions about overloading of alveolar clearance and interstitialization (sequestration) of particles were evaluated. Variability in the estimated clearance rate coefficients was assessed empirically by fitting the model to groups' and to each miner's data. Distributions of lung and lymph node particle burdens were computed at working lifetime exposures, using the variability in the estimated individual clearance rate coefficients. These findings confirm those of the earlier analysis; i.e., the best-fitting exposure-dose model to these data has substantial interstitialization/sequestration of particles and no dose-dependent decline in alveolar clearance. Among miners with different characteristics for smoking, disease, and race, the group median estimated alveolar clearance rate coefficients varied by a factor of approximately 4. Adjustment for these group differences provided some improvement in the dosimetry model fit to all miners (up to 25% reduction in MSE), although unexplained interindividual differences made up the largest source of variability. The predicted mean lung and lymph node particle burdens at age 75 after exposure to respirable coal mine dust at 2 mg/m(2) for a 45-year working lifetime were 12 g (5th and 95th percentiles, 3.0-26 g) and 1.9 g (0.26-5.3), respectively. This study provides quantitative information on variability in particle retention and clearance kinetics in humans. It is useful for risk assessment by providing estimated lung dust burdens associated with occupational exposure to respirable particles.

Methodological issues of using observational human data in lung dosimetry models for particulates.

INTRODUCTION: The use of human data to calibrate and validate a physiologically based pharmacokinetic (PBPK) model has the clear advantage of pertaining to the species of interest, namely humans. A challenge in using these data is their often sparse, heterogeneous nature, which may require special methods. Approaches for evaluating sources of variability and uncertainty in a human lung dosimetry model are described in this study. METHODS: A multivariate optimization procedure was used to fit a dosimetry model to data of 131 U.S. coal miners. These data include workplace exposures and end-of-life particle burdens in the lungs and hilar lymph nodes. Uncertainty in model structure was investigated by fitting various model forms for particle clearance and sequestration of particles in the lung interstitium. A sensitivity analysis was performed to determine which model parameters had the most influence on model output. Distributions of clearance parameters were estimated by fitting the model to each individual's data, and this information was used to predict inter-individual differences in lung particle burdens at given exposures. The influence of smoking history, race and pulmonary fibrosis on the individual's estimated clearance parameters was also evaluated. RESULTS: The model structure that provided the best fit to these coal miner data includes a first-order interstitialization process and no dose-dependent decline in alveolar clearance. The parameter that had the largest influence on model output is fractional deposition. Race and fibrosis severity category were statistically significant predictors of individual's estimated alveolar clearance rate coefficients (P < 0.03 and P < 0.01-0.06, respectively), but smoking history (ever, never) was not (P < 0.4). Adjustments for these group differences provided some improvement in the dosimetry model fit (up to 25% reduction in the mean squared error), although unexplained inter-individual differences made up the largest source of variability. Lung burdens were inversely associated with the miners' estimated clearance parameters, e.g. individuals with slower estimated clearance had higher observed lung burdens. CONCLUSIONS: The methods described in this study were used to examine issues of uncertainty in the model structure and variability of the miners' estimated clearance parameters. Estimated individual clearance had a large influence on predicted lung burden, which would also affect disease risk. These findings are useful for risk assessment, by providing estimates of the distribution of lung burdens expected under given exposure conditions.

Inhalation of poorly soluble particles. I. Differences in inflammatory response and clearance during exposure.

Results from animal studies have indicated some uncertainties over the validity of a single general occupational control limit for all types of "particulates (insoluble) not otherwise classified" (PNOC) (ACGIH, 2000). Therefore, to examine the extent to which a given control limit may be valid for nontoxic dusts with different physical characteristics, this study compared the pulmonary effects in rats of inhalation exposure to two poorly soluble dusts of similar density and with relatively low toxicity: titanium dioxide and barium sulfate. The objectives were to compare the dusts in (a) their buildup and clearance in the lungs during inhalation; (b) their transfer to lymph nodes; (c) the changes, with time, in the lavageable cell population; and (d) the pathological change from histology. The exposure aerosol concentrations were selected to achieve similar mass and volume lung burdens for both dusts and to attain "overload" over the common exposure periods of about 4 mo and 7 mo. Despite obtaining similar lung burdens for both dusts, there was significantly more translocation of TiO(2) to the hilar lymph nodes than with BaSO(4). It was also found that clearance of TiO(2) was retarded whereas clearance of BaSO(4) was not. Trends in these data were clarified by the use of a simple model of particle clearance. Retardation of particle clearance and translocation to the lymph nodes are markers of the condition known as "overload" in which the alveolar macrophage-based clearance of particles from the deep lung is impaired. In addition, bronchoalveolar lavage showed that TiO(2) caused significantly more recruitment of inflammatory neutrophils to lungs than BaSO(4). These differences between the dusts were not due to differences in toxicity, solubility, or lung deposition. The explanation that the different responses are due to the different particle size distributions of the two dust types is examined in a companion paper (Tran et al., this issue).

Inhalation of poorly soluble particles. II. Influence Of particle surface area on inflammation and clearance.

In this article the volumetric overload hypothesis, which predicts the impairment of clearance of particles deposited in the lung in terms of particle volume, is reevaluated. The degree to which simple expressions of retained lung burden explain pulmonary responses to overload was investigated using data from a series of chronic inhalation experiments on rats with two poorly soluble dusts, titanium dioxide and barium sulfate. The results indicated that the difference between the dusts in the level of inflammation and translocation to the lymph nodes could be explained most simply when the lung burden was expressed as total particle surface area. The shape of the statistical relationship for both lung responses indicated the presence of a threshold at approximately 200-300 cm(2) of lung burden. On the basis of this and other similar results, a hypothesis regarding a generic mechanism for the impairment of clearance and associated lung responses is proposed for such "low-toxicity" dusts.

Mathematical Modeling to Predict the Responses to Poorly Soluble Particles in Rat Lungs.

Rat inhalation experiments with titanium dioxide (TiO2) and barium sulfate (BaSO4), at concentrations calculated to produce similar volumetric lung burden for both dusts, showed overload with TIO2 but not for BaSO4 "Overload," occurring in rats exposed to "low-toxicity" dusts at high concentrations, is characterized by a rapid deterioration in clearance and onset of inflammation. Impairment of alveolar macrophage (AM) mediated clearance, dust translocation to the lymph nodes, and neutrophil (PMN) recruitment for both dusts were better predicted by the lung burden expressed as surface area rather than mass or volume. A mathematical model describing the translocation (in terms of particulate mass) of inhaled particles in various physiologically based pulmonary compartments was used to calculate pulmonary clearance when effective and also when impairment by overload leads to increased dust translocation to the lymph nodes. Our objectives were: (I) to modify this model to include the influence of particle surface area on clearance and interstitialization; (2) to extend the model to describe the PMN recruitment; and (3) to use the model to estimate the highest exposure level such that overload would be avoided in a chronic inhalation experiment with rats. In extrapolating down to no-overload concentrations, due account was taken of the observed interanimal variation (assuming this variation was mainly due to differences in inhaled dose). For TiO2 and BaSO4, with the given size distributions, the predicted concentrations at which 95% of the animals were expected to avoid overload were 3 mg m(-3) and 7.5 mg m(-3), respectively. The general quantitative relationships on the role of particle surface area and on the estimation of the no-overload level have important implications for setting standards for poorly soluble particles.

Evaluation of Particle Clearance and Retention Kinetics in the Lungs of U.S. Coal Miners.

Rodent studies are frequently used to assess risk in humans, yet it is not known whether the overloading of lung clearance, as observed in rodents, occurs in humans, or whether overloading is related to particle-related lung diseases in humans. The objective of this study is to develop a biologically based mathematical model to describe the retention and clearance of respirable coal mine dust in the lungs of humans. A human dosimetric lung model was developed that includes alveolar, interstitial, and hilar lymph-node compartments. The model describes the particle mass transfer kinetics among these compartments and clearance via the tracheobronchi. The model was calibrated using data in U.S. coal miners, including individual working lifetime exposure histories and lung and lymph-node particle burdens. The model fit to the human data was evaluated using a least-squared error criterion. The end-of-life lung dust burdens of all coal miners in this study were substantially greater than expected from a simple, linear first-order model with effective clearance, yet their lung and lymph-node dust burdens were lower than expected from the rodent-based overload model, particularly at higher exposures. The best fitting model included a predominant first-order interstitial compartment, in which the particles are essentially sequestered (with very slow clearance to the lymph nodes), and a first-order alveolar clearance compartment with either no dose-dependent decline (overloading) or much less than expected from the rodent studies. These findings are consistent with the findings from magnetopneumography studies of clearance in retired miners and from studies of particle retention patterns in rodents and primates. This human dosimetric lung model is useful for evaluating the kinetic differences of particle retention in humans and rodents, and for evaluating the lung closes in humans given different exposure scenarios.

Mathematical modeling of the retention and clearance of low-toxicity particles in the lung.

A mathematical model has been formulated to describe the mechanisms that determine the retention or clearance of insoluble inhaled particles in the rat lung. The hypotheses underlying the model are described-for example, the phagocytosis of free particles by macrophages, the transport of particles in macrophages from the alveolar region, the effect of the life cycle of macrophages leading to the eventual release of phagocytosed particles, the effect of lung burden on the macrophage activity, the transport of particles into the interstitium, the role of interstitial macrophages, the formation of granulomata, and transport of interstitialized particles to the thoracic lymph nodes. With these hypotheses, the fate of particles is described mechanistically via the cellular response of the lung. The mathematical model expresses these particle transitions as differential equations quantifying the transport of particles from one compartment to another, where the compartments represent the alveolar surface, the alveolar macrophages, overloaded alveolar macrophages, the interstitium, interstitial macrophages, and the thoracic lymph nodes. A companion article describes the application of the model to a data set from rats exposed to a low-toxicity dust at several concentrations and for a range of exposure times.

Exploration of the mechanisms of retention and clearance of low-toxicity particles in the rat lung using a mathematical model.

A mathematical model of the mechanisms of clearance or retention of inhaled particles in rat lungs is used to explore the extent to which a hypothesized sequence of events (including phagocytosis, macrophage-mediated clearance, transfer into the interstitium, transfer to lymph nodes, and overloading of the defense mechanisms) can account for data from a series of inhalation experiments with a low-toxicity, insoluble dust-titanium dioxide, TiO(2). These data include mean lung burdens and mean lymph-node burdens in groups of rats exposed to concentrations of 1, 10, 30, 50, and 90 mg m(-3), with exposure periods for as long as 2 yr (at 10 mg m(-3)), up to 7 mo at 50 mg m(-3), and 3.5 mo at 1 and 30 mg m(-3). The estimation of the parameters in the model is based mainly on information from other experimental studies or prior modeling. Values within the biologically plausible range were evaluated for the main parameters by inspection of predictions in comparison with data from the lowest concentration experiments. The suitability of the selected values was then confirmed by comparison of model predictions with data from the higher concentration experiments (at 30, 50, and 90 mg m(-3)). During inhalation, clearance rates are affected by translocation of dust and by overloading. The characterization of overload appears to describe these experiments well. Comparison with the effect of lung burden reported for other types of particles supports the hypothesis that overload is more dependent on the volume rather than the mass of the particles.

Tumor necrosis factor genetic polymorphisms correlate with infections after liver transplantation. NEMC TNF Study Group. New England Medical Center Tumor Necrosis Factor.

Tumor necrosis factor-alpha (TNF-alpha) is a pro-inflammatory mediator of the immune response to allogenic and infectious stimuli. Non-immunosuppressed individuals possessing a NcoI restriction enzyme site in the TNF gene locus produce less TNF-alpha in vitro and in vivo compared with individuals lacking this restriction site. We performed polymerase chain reaction amplification and restriction enzyme fragment length analysis of the TNF locus from 86 liver transplant recipients to determine if presence of the NcoI site is associated with the frequency of rejection or infection, time to rejection or infection, and patient and graft survival. We controlled for recipient primary diagnosis, age, sex, United Network for Organ Sharing status, year of transplant, type of immunosuppression, use of anti-lymphocyte agents, and graft ischemia time. Fifty-six recipients possessed the NcoI+/low TNF-alpha genotype and 30 were NcoI-/high TNF-alpha genotype. In the first year after transplant, there were no significant differences in the frequency, or time to first rejections or the overall number of rejection episodes between the two genotypes. NcoI+/low TNF-alpha genotype recipients had significantly more infections (1.52 vs. 0.87, P=0.014). In a linear regression, multivariate model controlling for all marginally significant variables, the NcoI+/low TNF-alpha genotype was still associated with significantly more infections (P=0.0031). Patient and graft survival were equal for the two groups. One implication of this study, in individuals genetically predetermined to be low TNF-alpha producers, is that additional inhibition of TNF-alpha production by routine immunosuppression may be excessive, rendering these individuals less able to respond to infectious stimuli. These patients may benefit from lower doses or withdrawal of corticosteroids.

Physiologically based pharmacokinetic analysis of the concentration-dependent metabolism of halothane.

1. Previous studies with the halothane analogue and chlorofluorocarbon replacement 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123) have shown that there are concentration-dependent, sex-specific differences in the rate of uptake during inhalation exposure in rat. Since it is well established that there are sex-specific differences in the control of enzyme activity in drug metabolism, male and female rats were exposed by inhalation to halothane concentrations ranging from 500 to 4000 ppm. 2. A physiologically based pharmacokinetic model describing the concentration-dependent reduction in uptake and metabolism of halothane in male and female rats was developed. The in vivo metabolic rate constants obtained were: for male rats, Km = 0.4 mg litre-1 (2.03 mumol litre-1) and Vmaxc = 9.2 mg kg1 h-1 (46.6 mumol kg1 h-1); for female rats, Km = 0.4 mg litre-1 (2.03 mumol litre-1) and Vmaxc = 10.2 mg kg-1 h-1 (51.7 mumol kg-1 h-1). 3. An equation describing the concentration-dependent decrease of hepatic metabolism of halothane successfully simulated the gas-uptake data. Simulation of cumulative urinary excretion of the major metabolite, trifluoroacetic acid, required introduction of a proportionality constant to limit the extent of reduction of halothane metabolism to 20% of the amount of enzyme activity. Good simulation of urinary excretion data was achieved, which was interpreted to indicate that, when only 20% of the enzyme is inactivated, the rate of enzyme resynthesis was adequate to replenish enzyme activity within 24 h. 4. A rapidly reversible, non-biological inactivation mechanism called "physical toxicity' is discussed as a possible explanation of concentration-dependent gas uptake.

Evidence of overload, dissolution and breakage of MMVF10 fibres in the RCC chronic inhalation study.

This paper describes (i) the evidence revealing the biological mechanisms underlying data from inhalation experiments at the Research and Consulting Company (RCC) (HESTERBERG et al. 1993); and (ii) the quantitative evaluation of the kinetic rates of these mechanisms using a mathematical model developed at the Institute of Occupational Medicine (IOM) (TRAN et al. 1994).

Mathematical model of phagocytosis and inflammation after the inhalation of quartz at different concentrations.

A mathematical model was developed with several distinctive features to represent the various processes leading to silicosis. It assures the phagocytosis of quartz by the resident alveolar macrophages. It then models the necrosis of macrophages caused by the ingestion of quartz particles and the subsequent release of these clusters onto alveolar surfaces. The inflammatory recruitment of alveolar macrophages and neutrophils in response to the cell necrosis caused by the ingestion of quartz particles is described in a functional form and is included in the model. The model also describes the pathological and other biological reactions to quartz particles in the interstitium. Specifically, once the quartz particles arrive at the interstitium, they can be phagocytozed by interstitial macrophages. The pathological interaction between quartz and interstitial macrophages may lead to quartz particles being sequestered in silicotic nodules, and also cleared to the efferent lymph nodes.

Prediction of responses in milk constituents to changes in the nutrition of dairy cows.

Milk quotas, based on an average fat content, severely limit milk production on UK farms. Predictions of the time-course of lactation are incorporated into most computerized herd management programs but these models take no account of food inputs, body weight change or milk composition. Dynamic models are generally used to simulate metabolic pathways and, as such, have little direct relevance to commercial milk production. Dynamic models can be converted to an adaptive-predictive model that partitions food energy into milk and non-milk constituents. This paper reports the development of an adaptive-predictive model to partition food into milk and non-milk components. Additional functions further partition milk energy into the principal constituents, fat, protein and lactose.