Steady-state concentration, time

Figure A3.14.3. Example bifurcation diagrams, showing dependence of steady-state concentration in an open system on some experimental parameter such as residence time (inverse flow rate) (a) monotonic dependence (b) bistability (c) tristability (d) isola and (e) musliroom.

Once the steady-state concentration is known, the rate of dmg clearance determines how frequendy the dmg must be adininistered. Because most dmg elimination systems do not achieve saturation under therapeutic dosing regimens, clearance is independent of plasma concentration of the dmg. This first-order elimination of many dmgs means that a constant fraction of dmg is eliminated per unit time. In the simplest case, clearance can be deterrnined by the dose and the area under the curve (AUC) describing dmg concentration as a function of total time ... 

Theoretical volume of distribution (Vj) of a chemical is the volume in which the chemical would be distributed if its concentration were equal to a theoretical steady-state plasma concentration (Cq) at time zero. The volume of distribution is thus obtained quite similarly as the steady state concentration of a compound in the workroom air ... 

Chromium plating from hexavalent baths is carried out with insoluble lead-lead peroxide anodes, since chromium anodes would be insoluble (passive). There are three main anode reactions oxidation of water, reoxidation of Cr ions (or more probably complex polychromate compounds) produced at the cathode and gradual thickening of the PbOj film. The anode current density must balance the reduction and reoxidation of trivalent chromium so that the concentration reaches a steady state. From time to time the PbOj film is removed as it increases electrical resistance. 

If the entry of a molecule into the body were simply a temporally restricted absorption process, then a steady-state concentration would be achieved given enough time for complete absorption. However, what in fact is observed in drug pharmacokinetics is a complex curve reflecting absorption of the drug into the body and the diminution of the concentration that is absorbed back down to negligible levels. The reason for this complex pattern of rise and fall in... 

Anastrazole is a nonsteroidal, type H, aromatase inhibitor that is 200 times more potent than aminoglutethimide. It is eliminated primarily via hqDatic metabolism, has a terminal half life of 50 h with steady state concentrations achieved approximately 10 days with once daily dosing regimens. It is administered orally at a dose of 1 mg/day that achieves near maximal aromatase inhibition and hence estrogen suppression in breast cancer patients. No effect on adrenal steroidogenesis has been observed at up to ten times the daily recommended dose. When used in the metastatic setting, anastrozole has been shown... 

If a drug is given repetitively with a constant dose (D) and a constant administration interval (Tau) accumulation occurs until a steady-state concentration (Css) is obtained after 4.32 times the elimination half-life (/ss -4.32 Tl/2). 

A mechanical system, typified by a pendulum, can oscillate around a position of final equilibrium. Chemical systems cannot do so, because of the fundamental law of thermodynamics that at all times AG > 0 when the system is not at equilibrium. There is nonetheless the occasional chemical system in which intermediates oscillate in concentration during the course of the reaction. Products, too, are formed at oscillating rates. This striking phenomenon of oscillatory behavior can be shown to occur when there are dual sets of solutions to the steady-state equations. The full mathematical treatment of this phenomenon and of instability will not be given, but a simplified version will be presented. With two sets of steady-state concentrations for the intermediates, no sooner is one set established than the consequent other changes cause the system to pass quickly to the other set, and vice versa. In effect, this establishes a chemical feedback loop. 

Visually, of course, this occurs because the ratio [Ce4+]/tCe3+] is coupled to the steady-state concentration. This in turn can be made yet more visible for demonstration purposes by the addition of Fe(phen)3+/Fe(phen)2+. The feedback loop is controlled by [Br-]ss. At the same time [Br-] too is oscillating in inverse relation to HBr02, by virtue of a competition between those reactions that form Br- and those that conserve it. Some of these effects are shown in Fig. 8-1, which depicts various oscillations in [Ce4+]/fCe3+] and in [Br-]. This figure shows the results for experiments under two sets of conditions. It illustrates how the amplitude and the frequency of the oscillations depend on the concentrations. 

Let us compare these results with the predictions of the theory formulated by Lampe etal. (24) in terms of a steady-state concentration of collision complexes. This is a classical macroscopic treatment insofar as it makes no assumptions about the collision dynamics, but its postulate of collision complexes implies that v8 = vp/2 for the system treated above. Thus, its predictions might be expected to coincide with those of the collision-complex model. Figure 3 shows that this is not so the points calculated from the steady-state theory (Ref. 25, Equation 10) coincide exactly with the curve for which v8 = vv. The reason for this is that the steady-state treatment assumes a constant time available for reaction irrespective oC the number of reactions occurring in any one reaction... 

Because ATP hydrolysis on F-actin takes place with a delay following the incorporation of ATP-subunits, and because in the transient F-ATP state filaments are more stable than in the final F-ADP state, polymerization under conditions of sonication can be complete, within a time short enough for practically all subunits of the filaments to be F-ATP. At a later stage, as Pj is liberated, the F-ADP filament becomes less stable and loses ADP-subunits steadily. The G-ADP-actin liberated in solution is not immediately converted into easily polymerizable G-ATP-actin, because nucleotide exchange on G-actin is relatively slow, and is not able to polymerize by itself unless a high concentration (the critical concentration of ADP-actin) is reached. Therefore, G-ADP-actin accumulates in solution. A steady-state concentration of G-ADP-actin is established when the rate of depolymerization of ADP-actin (k [F]) is equal to the sum of the rates of disappearance of G-ADP-actin via nucleotide exchange and association to filament ends. [G-ADP]ss in this scheme is described by the following equation (Pantaloni et al., 1984) ... 

Consider a transition from Product I to Product II. The simplest case is just to add component C to the feed at the required steady-state concentration of c,>, = 9mol/m. The governing ODEs are solved subject to the initial condition that the reactor initially contains the steady-state composition corre-sponding to Product I. Figure 14.3 shows the leisurely response toward the new steady state. The dotted lines represent the specification limits for Product II. They allow any Q concentration between 7 and 9mol/m. The outlet composition enters the limits after 2.3 h. The specification for Product I allows 1 mol/m of Q to be present, but the rapid initial increase in the concentration of Q means that the limit is quickly exceeded. The total transition time is about 2h, during which some 1001 of off-specification material would be produced. 

The presentation in this paper concentrates on the use of large-scale numerical simulation in unraveling these questions for models of two-dimensional directional solidification in an imposed temperature gradient. The simplest models for transport and interfacial physics in these processes are presented in Section 2 along with a summary of the analytical results for the onset of the cellular instability. The finite-element analyses used in the numerical calculations are described in Section 3. Steady-state and time-dependent results for shallow cell near the onset of the instability are presented in Section 4. The issue of the presence of a fundamental mechanism for wavelength selection for deep cells is discussed in Section 5 in the context of calculations with varying spatial wavelength. 

Fig. 17.—The ratio of the radical concentration to its steady-state concentration as a function of the time during alternate dark and light periods of durations t and rt, respectively. Curve OABCD represents /ts = 1.5 and r = 3 curve OGH, with r = 3 and t/Ts = l/4i, approaches a condition of oscillation about an average radical concentration [M ] / [M ] = 1 /2.

This should be compared with the initial plasma concentration of 50 pg F which is obtained when the same dose D is injected as a single bolus. The final concentration Cp(x) is also still far from the steady-state concentration (72.2 pg 1" ), since the duration of infusion x is only equal to once the half-life time of the dmg t,/2 (60 min). 

In this special case when the time between dosings is equal to the half-life time of the drug, we can deduce that the minimum (steady-state) plasma concentration with repeated dosing is equal to the peak concentration, obtained from a single dose. Under this condition, the corresponding maximum (steady-state) concentration is twice as much as the minimum one. 

Continue to monitor AED serum trough concentrations approximately every 3 to 5 days until the AEDs have reached steady-state concentrations. Give additional loading doses or hold doses as needed to maintain trough concentrations in the patient s therapeutic range. Be sure to evaluate the time the sample was drawn to assure it is a trough level. 

This is the basic relationship of electrode kinetics including the concentration overpotential. Equations (5.4.40) and (5.4.41) are valid for both steady-state and time-dependent currents. 

From these data, aquatic fate models construct outputs delineating exposure, fate, and persistence of the compound. In general, exposure can be determined as a time-course of chemical concentrations, as ultimate (steady-state) concentration distributions, or as statistical summaries of computed time-series. Fate of chemicals may mean either the distribution of the chemical among subsystems (e.g., fraction captured by benthic sediments), or a fractionation among transformation processes. The latter data can be used in sensitivity analyses to determine relative needs for accuracy and precision in chemical measurements. Persistence of the compound can be estimated from the time constants of the response of the system to chemical loadings. 

Improvement in symptoms and laboratory abnormalities should occur within 4 to 8 weeks, at which time a tapering regimen to maintenance doses can be started. Dosage changes should be made on a monthly basis because the endogenously produced T4 will reach a new steady-state concentration in this interval. Typical daily maintenance doses are PTU 50 to 300 mg and MMI 5 to 30 mg. 

Study the effect of varying residence time r (by changing feed rate), feed concentration, and rate constants on reactor performance. This can be done using Parametric Runs to obtain plots of the steady state concentrations as final values versus the corresponding change in parameter. 

The residence time rCd = rH/aCd and the limiting concentration CinCd/aCd are divided by a factor of 30 relative to a non-reactive case, e.g., chlorine. Entrainment by sediments flushes the excess Cd 30 times faster and decreases Cd steady-state concentration 30 times relative to a sediment-free lake. [Pg.351]

Let us first calculate steady-state concentrations when all Na weathered from evaporites has been transported to the sea and all the parameters become time-invariant. At steady-state, fluxes between reservoirs must be equal... 

Phenols are rather common antimicrobial components of metalworking fluids however, their use in recent years has been declining (36). The inhibition of nitrosation by phenols has recently been reviewed (35). In general, phenolic compounds inhibit nitrosation by reacting with nitrite (phenol reacts with nitrite 10,0 0 0 times faster than with dimethylamine), but the intermediate nitrosophenolis unstable and enhances nitrosation. "The overall effect is dependent on the steady state concentration of the nitrosophenol and the relative degrees of retardation and enhancement exerted by the phenol and the nitrosophenol, respectively ( 35)". 

FIGURE 12.4. Plasma concentration versus time profile showing steady-state concentrations following multiple dosing. 

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