Distribution between compartments

This section proposes the use of a semi-Markov model with Erlang- and phase-type retention-time distributions as a generic model for the kinetics of systems with inhomogeneous, poorly stirred compartments. These distributions are justified heuristically on the basis of their shape characteristics. The overall objective is to find nonexponential retention-time distributions that adequately describe the flow within a compartment (or pool). These distributions are then combined into a more mechanistic (or physiologically based) model that describes the pattern of drug distribution between compartments. The new semi-Markov model provides a generalized compartmental analysis that can be applied to compartments that are not well stirred. 

Both extracellular fluid (ECF) and intracellular fluid (ICF) contain electrolytes, a general term applied to bicarbonate and inorganic anions and cations. The electrolytes are unevenly distributed between compartments Na and Cl are the major electrolytes in the ECF (plasma and interstitial fluid), and and phosphates such as HP04 are the major electrolytes in cells (Table 4.1) This distribution is maintained principally by energy-requiring transporters that pump Na out of cells in exchange for (see Chapter 10). 

This compartment contains about one-third of total body water and is distributed between the plasma and interstitial compartments. The extracellular fluid is a delivery system. It brings to the cells nutrients (eg, glucose, fatty acids, amino acids), oxygen, various ions and trace minerals, and a variety of regulatory molecules (hormones) that coordinate the functions of widely separated cells. Extracellular fluid removes COj, waste... 

It is useful to factor out Ca (f) and solve the differential equation in terms of just C[)(t). This can be done by taking into account the mass balance, which requires that the total amount of sample be preserved, and be distributed between the donor and the acceptor compartments (disregarding the membrane for now). At t 0, all the solute is in the donor compartment, which amounts to VpCp 0) moles. At time t, the sample distributes between two compartments ... 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

The evaluative fugacity model equations and levels have been presented earlier (1, 2, 3). The level I model gives distribution at equilibrium of a fixed amount of chemical. Level II gives the equilibrium distribution of a steady emission balanced by an equal reaction (and/or advection) rate and the average residence time or persistence. Level III gives the non-equilibrium steady state distribution in which emissions are into specified compartments and transfer rates between compartments may be restricted. Level IV is essentially the same as level III except that emissions vary with time and a set of simultaneous differential equations must be solved numerically (instead of algebraically). 

The distribution of the annual emissions of PCDD/F in the atmosphere of the F.MFP region in 2001 as compared with their distribution between different environmental compartments by the end of the calculated period is presented in Figure 7. Only 1 % of the annual PCDD/F emissions remains in the atmosphere about 56% are deposited to other media. However, the distribution between media after a long time period is not directly determined by PCDD/Fs depositions in 2001. To a great extent it results from their long-term accumulation in the environment (1970-2001). For example, the annual contribution of PCDD/Fs total emissions to soil is about 47%. However, after a long time period the most part of the total PCDD/Fs content in the environment (about 95%) accumulated in soil due to relatively low degradation rates for this medium. Thus, soil is the main medium-accumulator of PCDD/Fs. 

Sorption plays a significant role in the environmental fate and effects of compounds released into the aquatic environment, largely determining their distribution between different environmental compartments. Apart from affecting the mobility, and therefore the potential of a surfactant to reach groundwater and surface water, sorption can affect its toxicity and biodegradation by influencing bioavailability. This process is especially relevant for surfactants, since their molecular structure presents a pronounced tendency to sorb onto interfaces. 

Some of the results obtained by differential centrifugation showed enzyme distribution between different cell fractions which were difficult to interpret. Enzymes like carbamoyl phosphate synthase or isocitrate dehydrogenase were found both in mitochondria and in the soluble fraction of the cell. This led to detailed kinetic studies with purified enzymes which indicated there might be populations of enzymes with slightly different properties (isozymes) catalyzing similar reactions in different compartments or in different cell types. Variations in kinetic behavior appeared to tailor the enzyme appropriately to the particular compartment or cell where the reaction took place. 

Clearance (Cl) and volumes of distribution (VD) are fundamental concepts in pharmacokinetics. Clearance is defined as the volume of plasma or blood cleared of the drug per unit time, and has the dimensions of volume per unit time (e.g. mL-min-1 or L-h-1). An alternative, and theoretically more useful, definition is the rate of drug elimination per unit drug concentration, and equals the product of the elimination constant and the volume of the compartment. The clearance from the central compartment is thus VVklO. Since e0=l, at t=0 equation 1 reduces to C(0)=A+B+C, which is the initial concentration in VI. Hence, Vl=Dose/(A+B-i-C). The clearance between compartments in one direction must equal the clearance in the reverse direction, i.e. Vl.K12=V2-k21 and VVkl3=V3-k31. This enables us to calculate V2 and V3. 

The alkalinity produced at the sediment-water interface by sulfate reduction will be distributed between the water column and sediment compartments in proportion to their alkalinity deficit. At the end of acidification in LRL, both the water column and the sediments (expressed in terms of excess cations in the water) had initial alkalinity deficits of 50 me-quiv/m3, and therefore generated alkalinity was assumed to be distributed equally. In other words, for every 2 mequiv of alkalinity produced, 1 mequiv contributes to water-column alkalinity and 1 mequiv to sediment alkalinity. 

Atmospheric POPs are distributed between the gas and particulate phases and, as mentioned above, the distribution rates are temperature-dependent [35]. However, other atmospheric processes such as photochemical oxidation and deposition are also relevant for the ultimate value of POPs in the air compartment (Fig. 7). 

Fast exchange, maintaining the singlet-oxygen equilibrium distribution between both compartments. The singlet oxygen will follow, in the... 

Although both models could be valid theoretically, Model 18 does not constitute a significant benefit over Model 7 in terms of AIC (Akaike Criteria) and SBC (Schwarz s Bayesian Criteria). In principle, any model should be practical and as simple as possible. UM-203 has its target within the central compartment, i.e., the platelets. Therefore, one could visualize the compound distributing between two compartments within the blood, i.e., plasma and platelets. For this reason, Model 7 was selected for further analyses. The final parameters from Model 7 are listed in Table 3. 

The input required by multimedia fate models includes properties of the chemicals (such as distribution over compartments air, water, and soil or sediment), properties of the environment or landscape receiving the contaminants, and emission patterns and mode of entry of chemicals into the environment (OECD 2004) (Figure 1.1). Fenner et al. (2005) compared the outcome of 9 multimedia fate models by applying them to a set of 3175 hypothetical chemicals covering a range of 25 half-life combinations (in water, air, or soil or sediment) and 127 combinations of partition coefficients (air-water (/<", ), Kov/, and Koa). Results show great similarities between the model outputs for Pov predictions, but less for LRTR Pov and, to a lesser extent,... 

The half-life of M-MT is dependent on the binding affinity of thionein for different metal ions. For instance, upon oxidation, Cu-MT forms insoluble polymers which are biologically unavailable and are eventually eliminated via biliary secretion. In contrast, thionein has lower affinity for Zn, making it more easily released from the protein and rendering the ion available for cellular processes. Furthermore, the rate of degradation may be influenced by differences in metal distribution between MT isoforms. It has been determined that MT degradation can occur in lysosomal and nonlysosomal (cytosolic) compartments. 

---