Isotopic methods mass-balance method

Stable-Isotope Mass-Balance Method. The equations presented in this section apply to groundwater-lake systems that are at hydrological and isotopic steady states. Equations that describe isotopic mass balances for non-steady-state systems and forms that pertain to the estimation of evaporation from lakes have been presented by other authors (13, 14). 

Reliable estimates of relative humidity are critical for use of the isotope mass-balance method however, humidity data are difficult to interpret and commonly not available for a specific study area. The index-lake method provides a means for checking the accuracy of these data and the validity of their use in isotope hydrology. The equation that describes the steady-state isotopic composition of a lake (35) is... 

Groundwater-inflow rates as calculated by the solute and isotope mass-balance methods for several northern Wisconsin lakes are listed in Table I. Dissolved calcium was used as the solute tracer because it is the constituent whose concentration differs the most between groundwater and precipitation, the two input components to be separated by the method. In addition, calcium is nearly conservative in the soft-water, moderately acidic to cir-cum-neutral lakes in northern Wisconsin. Results from the two methods agree relatively well, except for Crystal Lake, where groundwater-flow reversals are frequent. 

The isotope mass-balance method is not as useful for estimating groundwater-flow rates for groundwater-poor lakes as it is for lakes that receive substantial quantities of groundwater. Solute tracers, such as dissolved calcium, may be useful in assessing... 

A wide range of techniques are used to determine catabolic nitrate reduction rates. These include mass balance methods using input-outputs, acetylene inhibition techniques, dinitrogen production rates, nitrate consumption rates, nitrate pore water profiles, and stable isotope tracer techniques. The limitations and advantages of these methods are discussed by Seitzinger (1988) and Herbert (1999). 

Bowers and Taylor (1985) were the first to incorporate isotope fractionation into a reaction model. They used a modified version of EQ3/EQ6 (Wolery, 1979) to study the convection of hydrothermal fluids through the oceanic crust, along midocean ridges. Their calculation method is based on evaluating mass balance equations, as described in this chapter. 

Browne TR, Szabo GK, Ajami A, Wagner D (1993). Performance of human mass balance/metabolite identification studies using stable isotope (13C, 15N) labeling and continuous-flow isotope-ratio mass spectrometry as an alternative to radioactive labeling methods. J Clin Pharmacol 33 246-252... 

A holy grail for DON (and DOM in general) remains a rapid and portable method to quantitatively isolate and desalt a large dissolved sample (Bronk, 2002). Such a method would not only allow a wealth of diverse techniques to be brought to bear on the largest unknown fraction of DON, but would allow direct isotopic measurements and compound-specific mass balances. Examples of some approaches currently being explored to improve DON recovery on both small and large scales include homemade ion-retardation resins (Bronk, unpublished data), electrodialysis (Vetter et al, 2007), and use of nano-filtration membranes coupled to standard ultrafiltration approaches (McCarthy et al unpubhshed data). 

Nevertheless the rate equation depends on the mechanism of homoexchange. Different methods were in fact developed for the purpose of more fundamental and mechanistic studies [52,53,55,56,64-66]. On the other hand, the rate of isotopic heteroexchange may be accessed from the mass balance in O atoms during the experiments. Neglecting the O accumulation in metal particles, we get ... 

Systemic bioavailability is the product of fraction of dose absorbed (/a), fraction of dose escaping gut metabolism (/g), and fraction of dose escaping first-pass metabolism (F ). Permeability class is based upon /a, which may be estimated either in vivo or in vitro by direct measurement of mass transfer across human intestinal epithelium. In vivo methods include (i) mass balance studies using unlabeled, stable-isotope labeled, or a radiolabeled drug substance (ii) oral bioavailability using a reference intravenous dose or (iii) intestinal perfusion studies either in humans or an acceptable animal model. Suitable in vitro methods involve the use of either excised human/animal intestinal tissues or cultured epithelial monolayers. All of these methods are deemed appropriate for drugs whose absorption is controlled by passive mechanisms. 

Since there are no standards for flux determinations, as there are for chemical concentration measurements in water or sediments, evaluating their accuracy is difficult. One is forced to rely on comparison of different anal5dical approaches and modeling of nutrient and oxygen distributions to achieve a consensus. Of the different methods used to determine the organic carbon export presented in the following section, the first two (sediment traps and thorium isotope disequilibria) are used to evaluate the POC flux only. They must be combined with estimates of the DOC flux to achieve the total. The second two methods, molecular oxygen and carbon isotope mass balance, determine the sum of DOC and POC export. 

Here, 2 = l/8267(y )(= U/i/lnT), y equals the year of measurement, and x equals the year of sample formation or deposition (applied only when known by independent dating methods, for example, by the use of °Pb). This equation standardizes all A C values relative to the year ad 1950. In oceanography, A C is a convenient parameter because it is linear and can be used in isotopic mass balance calculations of the type shown in eqn [3]. 

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