Steady state concentration, time needed

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. 

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. 

Also bioaccumulating substances may in some situations call for a higher assessment factor. If accumulation is likely, the toxicity studies need to be of sufficient length to cover the accumulation period (e.g., the time to reach a steady-state concentration). If there is limited information on these aspects, it has to be considered to which extent this lack of information should affect the assessment factor. 

By setting the input function, I(t), in the differential equations on p. 28 to a constant rather than zero the equations can be solved to yield the disposition function for an intravenous infusion. With a fixed rate infusion, the plasma concentration will gradually increase towards a steady state concentration, CSS. Since CSS is constant, the amount of drug entering the body via the infusion at steady state must equal that being eliminated, (i.e. the clearance). Thus the infusion rate, R, e.g. mg min-1, needed to reach CSS is R=CSS.CI. It will take approximately 4 to 5 terminal half-lives to reach 95% CSS. Note that if the infusion rate is doubled CSS will also double, but the time taken to reach CSS remains the same, i.e. it is independent of the infusion rate (Figure 2.6). 

In concluding, let us comment on the time needed to attain the steady state after establishing the surface activities. Two transient processes having different relaxation times occur I) the steady state vacancy concentration profile builds up and 2) the component demixing profile builds up until eventually the system becomes truly stationary. Even if the vacancies have attained a (quasi-) steady state, their drift flux is not stationary until the demixing profile has also reached its steady state. This time dependence of the vacancy drift is responsible for the difficulties that arise when the transient transport problem must be solved explicitly, see, for example, [G. Petot-Er-vas, et al. (1992)]. 

In a typical case, only two large clusters of the particles of A and B type survive in the system [88, 89]. The steady-state concentration takes a value corresponding to the time needed for the creation of a cluster of such a size. This characteristic time is given by the relation Sd/2td/2 (a M/2 where M is the full volume (number of sites) of the fractal considered. According to equation (7.3.7), at large times one gets... 

If all cells are recycled back into the fermenter, the cell concentration will increase continuously with time and a steady state will never be reached. Therefore, to operate a CSTF with recycling in a steady-state mode, we need to have a bleeding stream, as shown in Figure 6.19. The material balance for cells in the fermenter with a cell recycling unit is... 

Since an important feature of Biicherer-Bergs hydantoin formation is that the process can only work for a-aminonitriles without substituent on the amino group, it follows that one compound of the equilibrium mixture formed from an aldehyde, ammonia, and cyanide is selectively reacted through an irreversible process leaving N-alkylated aminonitriles or imino-dinitriles unreacted. However, the difficulty with this process is that CAAs and hydantoins are poorly reactive towards hydrolysis and need long periods of time to be converted into free AAs. But, CAAs may also have per se a prebi-otic importance in activation pathways towards polypeptides (see Sect. 3.3.7). CAAs can also be synthesized by reaction of free amino acids with cyanic acid/cyanate (a likely prebiotic compound [50]). In the presence of a steady-state concentration of either cyanate or urea in aqueous medium, CAAs are at equilibrium with A A [51]. 

Note A faster rate of infusion does not change the time needed to achieve steady state only the steady-state concentration, Css, changes. 

A loading dose is an initial dose of drug that is administered at a dose rate higher than that normally used. A loading dose is used when the time needed to reach steady-state concentrations (i.e. about three to five half-lives) is long relative to the need for treatment. It rapidly increases plasma concentrations so that steady-state concentrations are approached more rapidly. 

However when only the steady-state concentration profiles and the process performance of an SMB are required, the use of the model SSM-1 is recommended because it requires a much shorter computing time and allows the separate, easy adjustment of the adsorption isotherm when needed. 

The method of false transients converts a steady-state problem into a time-dependent problem. Equations 4.1 govern the steady-state performance of a CSTR. How does a reactor reach the steady state There must be a startup transient that eventually evolves into the steady state, and a simulation of that transient will also evolve to the steady state. The simulation need not be physically exact. Any startup trajectory that is mathematically convenient can be used even if it does not duplicate the actual startup. It is in this sense that the transient can be false. Suppose at time f = 0 the reactor is instantaneously filled with fluid of initial concentrations ao, bo, — The initial concentrations are usually set equal to the inlet concentrations, ai , , but other values can be used. The simulation begins with gin set to its steady-state value. For constant-density cases, gout is set to the same value, and V is constant. The variable-density case is treated in Section 4.3. 

At 80 km, T — 200 K, at which 1.4 X 10 cm molecule s. The exponential term in (3.64) is <0.01 for r > 1.8 X 10 s (50 h). Thus the time needed for O to establish a steady-state concentration is much longer than that over which the solar intensity varies, and O is never in steady state at this altitude in the atmosphere. The reason why, at this altitude, 0( D) achieves a steady state and O does not, is based on the relative rates of the removal reactions. That for 0( D) is sufficiently fast that for O is too slow to keep up with the formation step. In the lower regions of the atmosphere, where the pressure is large, and hence the concentration of third bodies, M, is large, removal reactions for both O and 0( D) are, under all conditions, sufficiently fast that steady states are rapidly established for both species. 

Because the for theophylline is approximately 8 h in nonsmoking adults, meaningful steady-state serum concentrations cannot be obtained until approximately 24 to 48 h after initiation or change of therapy i.e., approximately 3.3 to 5 times the assumed t,/2 in the treated patient is needed for achieving 90% and >95% of steady-state concentrations, respectively. Corresponding adjustments to this time period have to be made if ty2 is known to be increased or decreased in other patient subpopulations. 

This is a very useful expression for the time lag. All it needs is the concentration distribution at steady state. Thus by measuring the time lag experimentally (the LHS of eq. 12.3-12), the RHS can be evaluated to yield information about the diffusion coefficient. Let us proceed this one step further. Substituting the steady state concentration distribution given in eq. (12.3-3) into the above equation and then carrying out the integration by parts will give the following expression for the time lag written completely in terms of the diffusion coefficient function ... 

Given the postulated reaction scheme, the net rate of reaction often takes a simple form when it is expressed in terms of the concentration of the intermediate. Such an expression is algebraically correct, and is the form one needs so as to propose and interpret the mechanism. This form is, however, usually not useful for the analysis of the concentration-time curves. In such an expression the reaction rate is given in terms of the concentration of the intermediate, which is generally unknown at the outset. To eliminate the concentration term for the intermediate, one may enlist certain approximations, such as the steady-state approximation. This particular method is applicable when the intermediate remains at trace levels. 

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