Uptake Models

Marschner H. Mineral Nutrition of Higher Plants, Academic Press, London, 1995. S. A. Barber and J. H. Cushman, Nitrogen uptake model for agricultural crops, Moiieling Waste Water Renovation—Land Treatment (I. Iskander, ed.), Wiley In-terScience, New York, 1981. pp. 382-404. 

Bones and teeth, however, are primary archaeological materials and are common to many archaeological sites. Bones bearing cut marks from stone tools are a clear proxy for human occupation of a site, and in the study of human evolution, hominid remains provide the primary archive material. Hence, many attempts have been made to directly date bones and teeth using the U-series method. Unlike calcite, however, bones and teeth are open systems. Living bone, for example, contains a few parts per billion (ppb) of Uranium, but archaeological bone may contain 1-100 parts per million (ppm) of Uranium, taken up from the burial environment. Implicit in the calculation of a date from °Th/U or Pa/ U is a model for this Uranium uptake, and the reliability of a U-series date is dependent on the validity of this uptake model. 

EU and LU are not the only uptake models that have been proposed. More mathematically sophisticated models have been developed (e.g., Szabo and Rosholt 1969 Hille 1979 Chen and Yuan 1988), in some cases using both the U and U decay chains (see Ivanovich 1982 Millard and Pike 1999 for summaries). While there have been some apparently successful applications of these models, none have been found to be universally applicable, and the search for a reliable method of U-series dating of bones and teeth continues. In the last decade or so, two important new approaches to the modeling of U uptake in bones and in teeth have been developed. These are discussed in detail below. 

The previously proposed uptake models were mathematical assumptions and had no physical or chemical basis. Millard and Hedges, on the other hand, considered the chemistry of bone-uranium interactions. With the D-A model, they proposed that U was diffusing into bone as uranyl complexes, and adsorbing to the large surface area presented by the bone mineral hydroxyapatite (Millard and Hedges 1996). Laboratory experiments showed a partition coefficient between uranyl and hydroxyapatite under oxic conditions of 10" -10, demonstrating U uptake in the U state without the need for reduction by protein decay products as proposed by Rae and Ivanovich (1986). 

There are a few developments on the horizon that will increase our ability to date bones and teeth reliability. Both y- and a-spectrometric methods can measure Pa/ U and °Th/U and concordance between dates calculated using the two can provide a measure of reliability. However, the discordance between the two is not very sensitive to different uptake regimes, and it is difficult to resolve, for example, bones that have undergone EU from those that have undergone LU with the analytical errors commonly encountered in measurements by y- and a-spectrometry. On the other hand, it has been shown recently that TIMS can measure both isotopic ratios with a precision usually better than 1% (Edwards et al. 1997). TIMS measurements of Pa/ U and °Th/U have yet to be routinely applied to dating fossil remains, but in the future, concordance between the two decay series will provide further evidence of the validity of a particular uptake model to a particular sample. 

The criticisms of these results centre on the provenance of the dated faunal material, and the U uptake models employed by Swisher III et al.(1996). In a reply to the paper, Grun and Thome (1997) suggest the river terrace where the material was found had been reworked many times, mixing older with younger material, and that the state of preservation between the hominid remains and the faunal remains was sufficiently different to suggest they had fossilized in a different environment. In addition, they doubt whether the U uptake models employed are appropriate. In the future, direct dating of the hominid remains themselves will address the first problem, a more sophisticated U uptake model would be required to address the second. 

We now repeat the derivation of the steady-state heat transport limited moisture uptake model for the system described by VanCampen et al. [17], The experimental geometry is shown in Figure 9, and the coordinate system of choice is spherical. It will be assumed that only conduction and radiation contribute significantly to heat transport (convective heat transport is negligible), and since radiative flux is assumed to be independent of position, the steady-state solution for the temperature profile is derived as if it were a pure conductive heat transport problem. We have already solved this problem in Section m.B, and the derivation is summarized below. At steady state we have already shown (in spherical coordinates) that... 

The moisture uptake models we have discussed have been concerned with pure components. The deliquescing material could be a drug substance or an excipient material. In pharmaceuticals, however, mixtures of materials are also important. One possible situation involves mixing nondeliquescing and deliquescing materials that are formed into a porous tablet or powder blend. The obvious question is, Do the models for pure components apply to porous heterogeneous materials For pure components we have assumed that the mass and heat limiting transport... 

Jin, H. et al. (2009) Size-dependent cellular uptake and expulsion of single-walled carbon nanotubes single particletracking and a generic uptake model for nanoparticles. ACS Nano, 3 (1), 149-158. 

Figure 1. Outline of the uptake model showing the spherical diffusion of species M through the medium towards two different sites where adsorption is followed by internalisation. The radius of the organism is taken as ro...

As seen in Figure 7, the surface concentration attains a maximum, overshooting the steady-state concentration value. It has been shown theoretically [35] that the maximum appears for any combination of parameters values. Experimental evidence of the appearance of transient uptake rate maxima (which might be totally or partially related to the maximum predicted by the present uptake model) has already been reported [36-39]. 

Theoretical Uptake Model Membrane-Controlled Uptake... 

Box 3.1 Example of the Calculation of Sampling Rates from a PRC-Derived Sampling Rate, Using the Empirical Uptake Model (Eqs. 3.33 and 3.35)... 

Bouldin DR. 1989. A multiple ion uptake model. Journal of Soil Science 40 309-319. 

The shape and length of the wave that propagates in the bed is related to the mathematical form of the uptake rate expression that is substituted into the last term in Eq. (9.10). Equation (9.15) is the pde describing diffusion of an adsorbate from the gas phase into the adsorbent This is but one of many diffusion based uptake models that might be substituted into the uptake rate term of Eq. (9.9) or (9.10). 

The Henry s law constant in water was used in the McJilton et al. uptake model to determine the equilibrium concentration of ozone and sulfur dioxide at the surface of a simulated mucus film along the airways in Weibel s symmetric model.It is also used to determine the concentration of absorbed gas at the surface of the mucus when the pollutant gas undergoes a homogeneous or heterogeneous chemical reaction within the mucus layer. 

The major weakness is the requirement of nonreactivity of gases in the mucous layer. Very weakly reactive gases may be treated as nonreactive. However, the uptake of ozone, which is known to decompose in water and is expected to react rapidly with biopolymers and other organic molecules in the mucus layer, is probably underestimated in the upper airways and overestimated in the terminal airways of their model. Thus, their model represents a worst-case estimate of dosage of ozone to the terminal airways, which are unprotected by mucous. Too little is known of the chemical and physical properties of the mucus layer, and there is great uncertainty in the values of the diffusivity of ozone or other gases to be used in the liquid phase of gas uptake models. 

An improved gas-uptake model should incorporate the features of the DuBois and Rogers model and the McJilton et al. model. As shown in Figure 7-2 the model for gas uptake in the airways should include separate layers for mucous-serous fluid epithelial tissue and blood. Development of such a model awaits reliable data and methods for predicting the coefficient of diffusion of pollutant gases in tissue and information on the rates of local perfusion of blood and lymph in the bronchial epithelium. Experimental data from humans and animals on the rate of sulfur dioxide absorption in blood could be used to make improved estimates of the tissue-diffusion coefficients in vivo. 

McJilton, C., J. Thielke, and R. Frank. Ozone uptake model for the respiratory system. Paper Presented at the American Industrial Hygiene Association Conference, San Francisco, California, May 14-19, 1972. 10 pp. 

Determination of FxAbs of Ca based on the femur uptake model 48-h after feeding... 

Barber, M.C. (2008) Dietary uptake models used for modeling the bioaccumulation of organic contaminants in fish. Environ. Toxicol. Chem., 23 (4), 755-777. 

The radial diffusion model can be approximated by a linear uptake model of the form ... 

Test of the Uptake Model Based on the Assumption That Diffusion within the Particle is Rate Controlling. As discussed earlier, the plots of molybdenum and tellurium oxide vapor uptake data vs. diameters and diameters squared of the clay loam particles gave inconclusive evidence as to whether the rate-controlling step was a slow rate of reaction at the surfaces of the particles or a slow rate of diffusion of the condensed vapor into the particles. 

Test of Uptake Model Based on a Slow Surface Reaction Combined with Diffusion within the Particle. Since the simple diffusion model is inadequate to describe the uptake behavior of the molybdenum and tellurium oxide vapors by the clay loam particles, a more complex model is required, in which the effects of a slow surface reaction and of diffusion of the condensed vapor into the particle are combined. Consider the condensation of a vapor at the surface of a substrate (of any geometry) and the passage by diffusion of the condensed vapor through a thin surface layer into the body of the substrate. The change in concentration of solute per unit volume in the surface layer caused by vapor condensa-... 

Hydrolysis of N205 on sulfuric acid represents a very efficient channel for nitrogen deactivation. Measurements using large 100-pm droplet trains [75,96] and submicron sulfuric acid aerosols [73,77] indicate high uptake probalilities (y = 0.1), without strong dependence on f SO, concentration or temperature. The data were fitted into an uptake model [96], Uptake coefficients over on water-ice (y = 0.02), SAT ((y = 0.006) and NAT (y= 0.0003) are much suppressed [86,90]. 

Kv is not a constant and may vary by several orders of magnitude. It is affected by element properties and both solid phase and pore water characteristics. Knowledge of the relationship between soil characteristics and Kp values enables the calculation of the distribution of heavy metals over the solid phase and pore water for different soils. When coupled to an uptake model for metals by biota that are directly or indirectly exposed via the pore water, the relationships for predicting Kp values may be used to predict metal uptake for these organisms on the basis of the metal concentration in the solid phase and some selected soil properties. The latter should, like the total concentrations, be easily determinable. 

The most simplistic oxygen uptake model is one that treats the cells collectively as uniform black boxes requiring oxygen for cell growth (dX/dt), maintenance (where m is the specific maintenance uptake rate), and product formation (dP/dt), i.e.,... 

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