Distribution transport rates

Distribution Transport Rate 215 10.9.3 Plasma Concentration versus Time... 

The distribution transport rate (r is ) is a measure of how quickly drug molecules are exchanged between the plasma and the tissues. A rapid distribution transport rate causes the plasma and tissues to come quickly into equilibrium with each other, whereas a slower rate will cause a prolonged approach to equilibrium. As with the rate of absorption, different types of PK modeling approaches can be employed to approximate distribution rates. In the case of distribution there are essentially two types of models, instantaneous distribution and first-order distribution. The difference between the two types of models is in the number of compartments used to represent the drug disposition in the body. 

Scale-Up Principles. Key factors affecting scale-up of reactor performance are nature of reaction zones, specific reaction rates, and mass- and heat-transport rates to and from reaction sites. Where considerable uncertainties exist or large quantities of products are needed for market evaluations, intermediate-sized demonstration units between pilot and industrial plants are usehil. Matching overall fluid flow characteristics within the reactor might determine the operative criteria. Ideally, the smaller reactor acts as a volume segment of the larger one. Elow distributions are not markedly influenced by... 

The transport rate of mercury flowing from the land to the oceans in rivers has been increased by a factor of about three by human activity. While the increased rate is still relatively less important than the total transport of Hg through the atmosphere, it can represent a significant stress on the exposed organisms, particularly since the increased flux is unevenly distributed. That is, human activity has created local environments where the transport of mercury or its concentration in a river or estuary is many tens of times higher than background levels. 

Toigerson T, Tnrekian KK, Turekian VC, Tanaka N, DeAngelo E, O Donnell J (1996) ""Ra distribution in surface and deep water of Long Island Sound Sources and horizontal transport rates. Cont Shelf Res 16 1545-1559... 

Because the amounts and density of these transporters vary along the gastrointestinal tract, it is necessary to introduce a correction factor for the varying transport rates in the different luminal and enterocyte compartments. Due to the lack of experimental data for the regional distribution, and Michaelis-Menten constants for each drug in Table 18.2, we fitted an intrinsic (concentration-independent) transport rate for each drug to closely approximate the experimental %HIA. This... 

The distribution of Hg within seepage lakes is a net result of the processes that control Hg transport between the atmosphere, water column, seston, sediments, and groundwater. This discussion focuses on the processes that control the exchange of Hg between the sediments and lake water. We first present data on spatial and temporal concentrations in the water column, sediments, pore water, and groundwater. These data set the context for a subsequent discussion of the chemical and physical processes responsible for the transport of mercury across the sediment-water interface and are necessary for assessing transport rates. 

The external factors comprise the nature of the membrane, the substrate concentration in the aqueous phase and any other external species that may participate in the process. They may strongly influence the transport rates via the phase distribution equilibria and diffusion rates. When a neutral ligand is employed to carry an ion pair by complexing either the cation or the anion, the coextracted uncomplexed counterion will affect the rate by modifying the phase distribution of the substrate. The case of a cationic complex and a counteranion is illustrated schematically in Figure 10 (centre). 

In addition to specific carrier features, a number of external factors may also have marked effects on transport rates. The nature of the membrane phase (in particular for liquid or supported liquid [6.10b] membranes) influences the distribution equilibria as well as the stability and selectivity of the complex in the membrane and the cation exchange rates at the interfaces. The nature of the coextracted anion affects transport via a (cationic complex-anion) pair (Fig. 10) simply by modifying the amount of salt extracted into the membrane this amount decreases with higher hydration energy and lower lipophilicity of the anion (for example, chloride compared with picrate). The concentration of salt in the aqueous phase will, of course, affect the amount extracted into the membrane and therefore the transport rates (for illustrations of these effects see for instance [6.1]). 

Several investigators have used radioactive tracer methods to determine diffusion rates. Bangham et al. (32) and Papahadjopoulos and Watkins (33) studied transport rates of radioactive Na+, K+, and Cl" from small particles or vesicles of lamellar liquid crystal to an aqueous solution in which the particles were dispersed. Liquid crystalline phases of several different phospholipids and phospholipid mixtures were used. Because of uncertainties regarding particle geometry and size distribution, diffusion coefficients could not be calculated. Information was obtained, however, showing that the transport rates of K+ and Cl" in a given liquid crystal could differ by as much as a factor of 100. Moreover, relative transport rates of K+ and Cl" were quite different for different phospholipids. The authors considered that ions had to diffuse across platelike micelles to reach the aqueous phase. 

The explanation of the pharmacokinetics or toxicokinetics involved in absorption, distribution, and elimination processes is a highly specialized branch of toxicology, and is beyond the scope of this chapter. However, here we introduce a few basic concepts that are related to the several transport rate processes that we described earlier in this chapter. Toxicokinetics is an extension of pharmacokinetics in that these studies are conducted at higher doses than pharmacokinetic studies and the principles of pharmacokinetics are applied to xenobiotics. In addition these studies are essential to provide information on the fate of the xenobiotic following exposure by a define route. This information is essential if one is to adequately interpret the dose-response relationship in the risk assessment process. In recent years these toxicokinetic data from laboratory animals have started to be utilized in physiologically based pharmacokinetic (PBPK) models to help extrapolations to low-dose exposures in humans. The ultimate aim in all of these analyses is to provide an estimate of tissue concentrations at the target site associated with the toxicity. 

In the physiological sense, one can divide the body into compartments that represent discrete parts of the whole-blood, liver, urine, and so on, or use a mathematical model describing the process as a composite that pools together parts of tissues involved in distribution and bioactivation. Usually pharmacokinetic compartments have no anatomical or physiological identity they represent all locations within the body that have similar characteristics relative to the transport rates of the particular toxicant. Simple first-order kinetics is usually accepted to describe individual... 

PK modeling can take the form of relatively simple models that treat the body as one or two compartments. The compartments have no precise physiologic meaning but provide sites into which a chemical can be distributed and from which a chemical can be excreted. Transport rates into (absorption and redistribution) and out of (excretion) these compartments can simulate the buildup of chemical concentration, achievement of a steady state (uptake and elimination rates are balanced), and washout of a chemical from tissues. The one- and two-compartment models typically use first-order linear rate constants for chemical disposition. That means that such processes as absorption, hepatic metabolism, and renal excretion are assumed to be directly related to chemical concentration without the possibility of saturation. Such models constitute the classical approach to PK analysis of therapeutic drugs (Dvorchik and Vesell 1976) and have also been used in selected cases for environmental chemicals (such as hydrazine, dioxins and methyl mercury) (Stem 1997 Lorber and Phillips 2002). As described below, these models can be used to relate biomonitoring results to exposure dose under some circumstances. 

Modeling of H F contactors is in most papers based on a simple diffusion resistance in series approach. In many systems with reactive extractants (carriers) it could be of importance to take into account the kinetics of extraction and stripping reactions that can influence the overall transport rate, as discussed in refs. [30,46], A simple shortcut method for the design and simulation of two-phase HF contactors in MBSE and MBSS with the concentration dependent overall mass-transfer and distribution coefficients taking into account also reaction kinetics in L/L interfaces has been suggested [47]. 

Next let us show how one can compute the proteasome output if the transport rates are given. In our model we assume that the proteasome has a single channel for the entry of the substrate with two cleavage centers present at the same distance from the ends, yielding in a symmetric structure as confirmed by experimental studies of its structure. In reality a proteasome has six cleavage sites spatially distributed around its central channel. However, due to the geometry of its locations, we believe that a translocated protein meets only two of them. Whether the strand is indeed transported or cleaved at a particular position is a stochastic process with certain probabilities (see Fig. 14.5). 

This equation should be fulfilled at least in one point for x + D > 0. To note y is here the rate of cleavage. Hence, there are no limitations for its value. Eq. (22) shows that the condition for obtaining a maximum when we have a single cleavage center is independent of the actual form of the transport rate function, but is rather dependent on its slope. This would suggest that it is possible to obtain a peak in the length distribution even when the transport rate function is monotonically decreasing, and indeed that is what we find from our numerical simulations. 

Fig. 14.6 (a) Monotonously decreasing transport rate function v(x) = v (x). The vertical lines show the location of the point where the condition for the maximum in the length distribution (Eq. 22) holds and the location of the cleavage centre. The parameters are D = 15 and y = 0.001. 

Fig. 14.8 The case of nonmonotonous transport rate function 1 1. v, shown by a solid line in (a,e,h). From top to bottom different location of the cleavage centre D = 3, 15, 32 (shown the vertical line) with respect to two points where the condition of maximum holds (shown vertical lines) (b,f,i) the corresponding length distributions for the...

Next, we analyze the case when the cleavage centre D = 15 is between two points where the derivative is equal to — y, and hence the maximum condition can be fulfilled in one point (see Fig. 14.8e). As predicted by theory and confirmed by numerics, the length distribution has a maximum in this case (see Fig. 14.8f). It is noteworthy that the theory in this case works sufficiently also in the case when the cleavage products do not disappear immediately (see Fig. 14.8g). If we believe in the nonmonotonous transport rate function hypothesis [50], this case seems to be the most adequate for protein degradation by the proteasome. In the last case, the cleavage centre is so deep in the proteasome, D = 32, that the maximum condition can be fulfilled nowhere. As expected, the length distribution has no maxima in all cases computed for this relation between the transport function and the geometry of the proteasome. 

Truck transportation rates for anhydrous ammonia are relatively high because of liability insurance rates and the need to use specialized equipment. Distribution is further complicated by attempts to restrict the movement of ammonia in some jurisdictions. In 1990, the U.S. Department of Transportation classified anhydrous ammonia as a non-flammable gas and required shipments to be marked with the words inhalation hazard. International shipments are required to carry the inhalation hazard and poison gas markings57. 

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