Integrity of dilution

On occasion, the validated ULOQ for an assay is not sufficiently high to accommodate high concentration study samples that are anticipated to arise. It is possible to analyze such samples if it can be demonstrated that dilution of the high concentration samples does not invalidate the method. To assess whether such a a sample can be diluted with matrix for accurate quantitation within the range of the calibration curve, additional validation experiments are required. For this purpose QC samples, spiked at above the ULOQ concentration (the so-caUed above quantitation limit (AQL) QCs), are diluted with control matrix before sample preparation using the following procedure. 

Typically, a minimum of five individual dilutions of the AQL QC with control matrix are prepared using at least one dilution scheme. Dilutions may be made outside of the extraction tube/plate in separate tubes and aliquots assayed at the volume specified for the assay. Alternatively, aliquots smaller than that required by the assay can be transferred using a calibrated pipet into the extraction tube/plate and then diluted with control matrix to the volume required for the assay. The mean accuracy value of diluted AQL samples should be within 15 % of the nominal concentration value for each dilution scheme. The precision around the mean (% CV) should not exceed 15 % for each dilution scheme. If a given dilution scheme fails to meet acceptance criteria with no assignable cause for the failure, then the experiment may be repeated but it is recommended to use a 

In practice, if it is necessary to dilute samples during analysis, additional AQL QCs are added to the sample set (using the same dilutions as those used for the samples on that day) and the same type of acceptance criteria are used as for the other analytical QCs. If the AQL QCs fail, the entire sample set is not failed but the data from the diluted samples are rejected. 

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In applying current methods (Ref. 6, p. 161) we easily obtain the formulas that permit the calculation of heat integrals of dilution (1), in keeping with that expression. Since... 

Additional Components Analyte recovery (extraction efficiency) Stock stability Matrix stability Post process stability (extract) Integrity of dilution Carryover and contamination Matrix effects Incurred sample reproducibility Incurred sample stability... 

Figure Bl.11.9. Integrated 250 MHz H NMR spectrum of dilute propan-1-ol in dinrethylsulfoxide solvent. Here, the shift order parallels the chemical order. Arr expansion of the H2-I nrultiplet is included, as is the implicit frequency scale, also referenced here to TMS = 0.

The heat absorbed when unit mass of solute is dissolved in an infinite amount of solvent is the differential heat of solution for zero concentration, Lo, and this is evidently equal to the integral heat of solution for concentration s plus the integral heat of dilution for concentration s ... 

To calculate P at any other temperature we integrate Kirchhoff s equation for the heat of dilution ... 

In this process, the original solution is diluted by the addition of pure solvent, and hence, the enthalpy change is called an integral enthalpy of dilution. 

The enthalpy change for this process is an integral enthalpy of dilution for which we saw earlier that... 

FIG. 29 Integral heats of dilution for a solution of ammonium dodecane 1-sulfonate in water. 

Figure 3. Numerical integration of Equation E2 showing net oxidant [03-N0 ] yields from an initial [NMHCJq = SOOppb. A. Variation with the product reactivity parameter Q here a=)9=l and S=l. B. Variation with the dilution parameter S here a=)9=l, Q=l. When S is small, a nearly stoichiometric yield of oxidant=1000ppb is achieved at higher values of S, oxidant and reactants are diluted with less oxidant accumulation.

The purpose of in-use stability studies is to establish the period for which a product intended to be used on more than one occasion may be used after reconstitution or dilution or the withdrawal of the first dose from the container without adversely affecting the integrity of the product and with the product retaining acceptable quality characteristics. This type of test can be applied to any multiple use product (e.g., sterile products in multiple-use containers, powders or granules including those used to produce oral solutions or suspensions) but is likely to be of particular importance in the case of products that are manufactured with an inert headspace gas, for products containing antioxidants to protect an active ingredient that is liable to oxidative decomposition, and for products that contain a volatile antimicrobial preservative. 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

A graphical integration of the Gibbs-Duhem equation is not necessary if an analytical expression for the partial properties of mixing is known. Let us assume that we have a dilute solution that can be described using the activity coefficient at infinite dilution and the self-interaction coefficients introduced in eq. (3.64). 

By integration of this equation, the relationship between the concentration of the dissolved gas and pressure in dilute solution can be found... 

Although the potential to use Caco-2 cells to screen large numbers of formulations under carefully controlled experimental conditions appears attractive, the assumption that this model is suitable to evaluate drug formulations should not be made. In fact, the utility of Caco-2 cells in formulation evaluation is limited because these cells are sensitive to pharmaceutical excipients.112 In addition, the dilution of formulations into the simple buffer solutions used in permeability studies is likely to break the physical integrity of the... 

One method of overcoming this difficulty is as follows. Instead of setting the lower limit in the integration of Equation (17.33) at infinite dilution, let us use a temporary lower limit at a finite concentration X2. Thus, in place of Equation (17.34), we obtain... 

The data required to carry out such a calculation are the enthalpies of dilution as a function of molality at each temperature of interest. The integration would have to be carried out numerically. Enthalpy data for aqueous calcium chloride have been reported by Simonson, et al. [5]. 

Henry s law is obeyed by a solute in a certain temperamre range. Prove that An2. Ani. and the integral heat of dilution are zero within this range. Do not assume that Heiuy s-law constant is independent of temperamre generally, it is not. 

The enthalpies of dilution of BE were required to calculate the enthalpies of transfer (19). From these Integral enthalpies of dilution AHj.jj the relative apparent molar enthalpies were derived following the technique of Fortier et al (21). The values of AHjjj corresponding to the Initial and final molalities are given In Table 1 along with the parametric equation for. ... 

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