Surface compartment model

The surface compartment model (SCM)14,15, which is a theory of ion transport focused on ionic process in electrical double layers at membrane protein surfaces, can explain these phenomena. The steady state physical properties of the discrete surface compartments are calculated from electrical double layer theory. 

To study the effects of electrochemical properties on passive ion transport processes, we developed a model that focuses on ionic processes at membrane and channel surfaces (14). The surface compartment model (SCM) is based on a Helmholtz electrical double layer, where the enhanced concentration of counterions and the depletion of co-ions at charged surfaces is described by straight line gradients. Treatment of the electrical double layer as a compartment greatly simplifies the calculation of ion transport. 

Rituximab is a monoclonal antibody to the CD20 receptor expressed on the surface of B lymphocytes the presence of the antibody is determined during flow cytometry of the tumor cells. Cell death results from antibody-dependent cellular cytotoxicity. The pharmacokinetics of rituximab are best described by a two-compartment model, with a terminal half-life of 76 hours after the first infusion and a terminal half-life of 205 hours after the fourth dose.36 Rituximab has shown clinical activity in the treatment of B-cell lymphomas that are CD20+. Side effects include hypersensitivity reactions, hypotension, fevers, chills, rash, headache, and mild nausea and vomiting. 

For a better idea of the toxicity of VOCs, we can look more closely at some studies of TCE (Bogen et al., 1998). In vitro uptake of C-14-labeled trichloroethylene (TCE) from dilute (similar to 5-ppb) aqueous solutions into human surgical skirt was measured using accelerator mass spectrometry (AMS). The AMS data obtained positively correlate with (p approximate to 0) and vary significantly nonlinearly with (p = 0.0094) exposure duration. These data are inconsistent (p approximate to 0) with predictions made for TCE by a proposed EPA dermal exposure model, even when uncertainties in its recommended parameter values for TCE are considered but are consistent (p = 0.17) with a 1-compartment model for exposed skin-surface. This study illustrates the power of AMS to facilitate analyses of contaminant biodistribution and uptake kinetics at very low environmental concentrations. Eurther studies could correlate this with toxicity. 

Surface water half-life for all processes, except for dilution t,/2 = 0.5 h in stream, eutrophic lake and pond and t,/2 = 600 h in oligotrophic lake, based on transformation and transport of quinoline predicted by the one-compartment model (Smith et al. 1978) ... 

Surface water t,/, = 0.55 h in river, t,/, = 12 h in pond and eutrophic lake, and L, = 2400 h in oligotrophic lake for a point source continuously discharging 1.0 pg/mL predicted by one compartment model for all processes including dilution (Smith et al. 1978 quoted, Howard 1989) ... 

FIGURE 30.2 Two-compartment model for peritoneal pharmacokinetics. Drug administered via a catheter is placed in the peritoneal cavity with a distribution volume of VpQ, yielding concentrations within the peritoneum of Cpc- Subsequent transfer betw een the peritoneum and the body compartment is mediated by diffusion with a permeability coefficient—surface area product of PA. CLp is the elimination clearance from the body. Plasma drug concentrations (Cp ) and systemic toxicity are minimized because the distribution volume of the body compartment (Vd) is much greater than VpQ and because CLp prevents complete equilibration of concentrations in the tw o compartments. (Adapted from Dedrick RL et al. Cancer Treat Rep 1978 62 1-11.)... 

This last observation deserves further consideration. Because any molecule exhibits a measurable volume, the parameter V is expected to be the most important variable in the MLR (Table 15.1) in comparison with other parameters, especially those representing specific interactions, properties that some of the solutes in the set might lack. If a three-compartment model can be invoked for the micelle structure (inner core, interface, and surface) as opposed to the Hartley model ( oil droplet, hydrophobic core encased by a hydrophilic region), remarkable differences in cavitation energy between the aqueous bulk and the micelle interface as well as between the aqueous bulk and the micelle inner core are anticipated. Thus, the parameter V coefficient in the MLR with the entire set of solutes is expected to be prominent as well. More importantly, the parameter V coefficient reflects an average behavior, that is, it is indicative of cavitation energy differences between a given micelle... 

Figure 3.1 Surface plot of residual sum of squares (SSE) for data shown to the right of the figure fit to a 1-compartment model with intravenous administration. The volume of distribution was varied from 0 to 100 L and clearance was varied from 2 to 60 L/h.

Equations 46 have been directly derived from the full model in [19]. On the other hand, they are almost identical with the relations obtained from the so-called two-compartment model (the only difference is that the numerical coefficient is a little bit lower). The two-compartment model was first developed for sensors with receptors placed on small spheres [23]. In [24-26] it was adapted for the SPR flow cell and in [ 18] it was approved and verified by comparison of munerical results with those obtained from the full model. The two-compartment model approximates the analyte distribution in the vicinity of the receptors by considering two distinct regions. The first is a thin layer around the active receptor zone of effective thickness fiiayer> and the second is the remaining volume with the analyte concentration equal to the injected one, i.e., a. While the analyte concentration in the bulk is constant (within a given compartment), analyte transport to the inner compartment is controlled by diffusion. The actual analyte concentration at the sensor surface is then given by the difference between the diffusion flow and the consump-tion/production of the analyte via interaction with receptors. For the simple pseudo first-order interaction model we obtain ... 

Kinetic studies have demonstrated that uptake of compounds into leaves is best represented by a two-compartment process a rapid distribution into the outer leaf surface, followed by a slower diffusion into the interior of the leaf. This is illustrated by studies of the uptake of DDE in spmce needles." A 10-year old spruce tree was placed in a chamber and exposed to air containing 50 ng m of DDE. It can be seen from Eigure 3.25 that DDE concentration increased more rapidly in a soluble cuticular lipid fraction than in the needle remaining after extraction. The former was obtained by extraction with dichloromethane and was considered to be representative of the lipophylic needle surface. Note that introducing the tree into the exposure chamber reduced the concentration of the DDE in the air. When the tree was transferred to a clearance chamber , DDE was lost rapidly from the extracted lipid fraction and only slowly from the remaining needle. A two-compartment model has been developed to simulate DDE uptake and release. Based on this response, if needles were to be used for monitoring, it is important to recognize that one portion of the needle reacts within hours to atmospheric concentrations, whereas the needle as a whole could take months to achieve some steady state. 

To better define the role of blood flow in dermal pharmacokinetics, Williams et al. (1990) represented the skin vasculature as a three-compartment model with a fourth compartment for the skin surface (Figure 13.5). They then examined hypothetical changes in the absorption profile of the organophosphate pesticide malathion in the IPPSF fitted to the model as shown in Figure 13.6 (Rivirae and Williams, 1992). The amounts of solute in each compartment of this model are described by the following expressions (Equation 13.6 to Equation 13.9) (Williams etal., 1990) ... 

A six compartments model representing the pharmacokinetics of dust movement within the alveolar area of the lungs and lymph nodes was proposed by Smith (1985) including free particles and two macrophage departments on the alveolar surfaces, temporary and encapsulation particles in the interstitial area, and particles in lymph nodes. Seven processes control the quantities of particles in each of the three areas ... 

EXAIR is a mesoscale atmospheric transport model, EXWAT a transport model for surface water bodies, EXSOL a multilayer soil model for the upper soil zone. EXATM is a compartment model for the transport of globally dispersed substances in the troposphere and stratosphere. 

In the following sections, different surface complexation models will be introduced. General aspects and specific models will be discussed. The components of surface complexation theory will be presented, as well as some recent developments covering, for example, the use of equations for the diffuse part of the electrical double layer for electrolyte concentrations, for which the traditional Gouy-Chapman equation is not recommended or a generalization of Smit s compartment model [6] for situations in which the traditional models are at a loss. 

This multi-compartment model was used by Kocher to calculate collective committed dose equivalent versus time following the release of 1 Ci of to each of several compartments. Of interest here is the conclusion that the long term (> 10 year) collective doses are essentially the same whether the is released to the atmosphere (over land or water), to the surface soil compartments, or the mixed ocean layer. 

In order to be realistic, environmental models must contain multiple phases, and are often referred to as multiphasic, or multimedia compartment models. Being so requires interfaces that separate the phases and media. These interfaces can be real or idealized (i.e., imaginary). Two-dimensional interface planes are assumed to exist between the air-water, water-sediment, and soil-air phases or media. In reality, chemical transport across the air-water interphase plane involves a true phase change. The watery interface plane at the water-bed sediment junction and airy interface plane at the soil-air junction are only separated by imaginary planer surfaces. Nevertheless, due to the dramatic changes that typically occur within the fluid and the associated media fluid dynamics on either interface side, different transport processes occur on opposite sides, typically. Therefore it is also practical to define an interfacial compartment for such imaginary and idealized interface situations. The interfacial compartment concept for multimedia, interphase chemical transport is based on the following ideas ... 

FIGURE 8.7 This graph compares the concentration change (where C(0)is the concentration at the soil surface) versus normalized depth zjz of the compartment-model solution and analytical solution for the case where soil properties are assumed uniform. (Adapted from McKone, T. E. Bennet, D. H. 2003. Environmental Science Technology, 35(14) 2123-2132.)... 

The two-compartment model was developed to describe reactions on a surface affected by a diffusion mass transfer of an analyte from a solution to the surface. In this model, the zero flow velocity at the surface is taken into account through a (hypothetical) tmstirred layer with the thickness deptending on a volumetric sample flow rate v and the geometry of the flow channel (i.e., on its depth h, length L, and width w). Diffusion rate km of analyte molecules through the unstirred layer to and from the surface can he expressed as... 

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