Variability of formulations

There has been some attention recently in the literature to tests to compare variability of formulations as well as comparing means. (See, for example, Dragalln et cd. (2003), and Grieve (1998).) A technical difficulty, which has to be dealt with in examining the variances, arises from the correlation of measurements taken on the same individual. 

Figure 4.52. Coefficients of variation that reflect both tablet to tablet and analytical variability. For formulation B, particularly strengths 2 and 3, the drop in CV with higher cumulative release (a - b) is marked, cf. Fig, 4.50. When the dissolution rate is high, individual differences dominate, while towards the end analytical uncertainty is all that remains. The very low CVs obtained with strength 3 of formulation A ( 0.7-0.8%, data offset by +10% for clarity) are indicative of the analytical uncertainty. Because content uniformity is harder to achieve the lower the drug-to-excipient ratio, this pattern is not unexpected.

For the RF system, the development was not as far advanced. There were still difficulties in making acceptable-quality foams, and significant factors and ranges had not been determined. There was also no clear indication of the relative importance of formulation and process variables. For these reasons, it was considered appropriate to execute a screening experiment to identify key variables. 

The process of formulation for any of the above is generically the same, beginning with some form of product specification and ending with one or more formulations that meet the requirements. Correct choice of additives or excipients is paramount in the provision of efficacy, stability, and safety. For instance, the excipients may be chemically or physically incompatible with the drug or they may exhibit batchwise variability to such an extent that at the extremes of their specification they may cause failure in achieving the desired drug release profile. In addition, some excipients, especially those that are hydroscopic, may be contraindicated if the formulation is to be manufactured in tropical countries. Flence formulators must work in a design space that is multidimensional in nature and virtually impossible to conceptualize. 

Often these design criteria involve competitive requirements. What is best for meeting one criterion may be counterproductive in meeting another. For example, certain excipients such as the hydrophobic stearate lubricants are important for efficient manufacture, yet they have the potential to retard the release of drug from an immediate-release formulation. The design of a dosage form thus frequently requires the optimization of formulation and process variables in a way that best meets all design criteria. 

All piroxicam batches were manufactured in compliance with Good Manufacturing Practices, and three formulations having fast, moderate, and slow dissolution were chosen for comparison to a lot of the innovator s product in a human bioavailability study [100]. The resulting pharmacokinetic data provided still another opportunity to examine the effects of formulation variables. To explore the relationship between the in vitro dissolution of piroxicam from these capsules and in vivo absorption, Polli [ 102] used the following previously described [145] deconvolution-based model ... 

Fig. 25 Response surfaces for the effect of formulation variables on percent of piroxicam dissolving from capsules in 10 minutes. (From Ref. 100.)...

ND Eddington, M Ashraf, LL Augsburger, JL Leslie, MJ Fossler, LJ Lesko, VP Shah, GS Rekhi. Identification of formulation and manufacturing variables that influence in vitro dissolution and in vivo bioavailability of propranolol hydrochloride tablets. Pharm Dev Tech 3(4) 535-547, 1998. 

One of the most difficult parenteral dosage forms to formulate is a suspension. It requires a delicate balance of variables to formulate a product that is easily resuspended and can be ejected through an 18-to 21-gauge needle through its shelf life. To achieve these properties it is necessary to select and carefully maintain particle size distribution, zeta potential, and rheological properties, as well as the manufacturing steps that control wettability and surface tension. The requirements for, limitations in, and differences between the design of injectable suspensions and other suspensions have been previously summarized [17b, 18,19]. 

B. Lueckel, B. Helk, D. Bodmer, and H. Leuenberger, Effect of formulation and process variables on the aggregation of freeze dried interleukin-6 (IL-6) after lyophilization and storage, Pharm. Dev. Technol., 3, 337 (1998). 

Thus, the design of a batch reactor can be based on the optimization of a temporal superstructure. Given a simulation model with a mathematical formulation, the next step is to determine the optimal values for the control variables of a batch reaction system. 

The model equations in Section II,A have been formulated to describe the energy and mass transfer processes occurring in two-phase tubular systems. The accuracy of these model equations in representing the physical processes depends on the parameters of the equations being correctly evaluated. Constitutive equations that relate each of the parameters to the physical properties, system properties, and dependent variables of the system are discussed in the following sections. 

In their formulation, Ierapetritou and Floudas (1998), separated task and unit events by assigning corresponding binary variables to tasks, wv (i,p), and units, yv (i,p), respectively. This led to an overall number of binary variables of P(Nt+Nj), where P is the number of time points, whilst N, and Nj are the numbers of tasks... 

Representation requires that the designer of a typical evolutionary computation algorithm (EA) formulates one inadaptable blueprint for the solution of some problem, then present the variables of that blueprint in a form that is amenable to manipulation by the genetic operators of the EA. Fitness evaluation, on the other hand, has limited GA in two distinct ways (1) it has limited environmental feedback to the confines of a formula or algorithm, which reflects accurately and exclusively the quality of the complete candidate solution from the perspective of the human designer. In addition, (2) fitness evaluation has proven to be the most computationally costly part of a typical EA. Note that elaborate developmental mappings actually increase that computational cost. However, our interest here lies in the limiting effects of representation. 

The ingredients of formulating optimization problems include a mathematical model of the system, an objective function that quantifies a criterion to be extremized, variables that can serve as decisions, and, optionally, inequality constraints on the system. When represented in algebraic form, the general formulation of discrete/continu-ous optimization problems can be written as the following mixed integer optimization problem ... 

The approach taken here is to employ standard materials characterization tests to measure the materials properties of the granulated product. With this information, the mechanism of attrition, i.e., breakage versus erosion, is determined. The rate of attrition can then be related, semi-empirically, to material properties of the formulation and the operating variables of the process, such as bed depth and fluidizing velocity. 

Widespread medicinal use of colloidal bismuth subcitrate (CBS) has prompted extensive studies of bismuth compounds involving the citrate anion. Bismuth citrate is essentially insoluble in water, but a dramatic increase in solubility with increasing pH has been exploited as a bio-ready source of soluble bismuth, a material referred to as CBS. Formulation of these solutions is complicated by the variability of the bismuth anion stoichiometry, the presence of potassium and/ or ammonium cations, the susceptibility of bismuth to oxygenation to Bi=0, and the incorporation of water in isolated solids. Consequently, a variety of formulas are classified in the literature as CBS. Solids isolated from various, often ill-defined combinations of bismuth citrate, citric acid, potassium hydroxide, or ammonium hydroxide have been assigned formulas on the basis of elemental analysis data or by determination of water and ammonia content, but are of low significance in the absence of complementary data other than thermal analysis (163), infrared spectroscopy (163), or NMR spectroscopy (164). In this context, the Merck index lists the chemical formula of CBS as KgfNHJaBieOafOHMCeHsCbh in the 11th edition (165), but in the most recent edition provides a less precise name, tripotassium dicitrato bismuthate (166). 

According to Zeleznik and Gordon, tempers became so heated that a panel convened in 1959 to discuss equilibrium computation had to be split in two. Both sides seemed to have lost sight of the fact that the equilibrium constant is a mathematical expression of minimized free energy. As noted by Smith and Missen (1982), the working equations of Brinkley (1947) and White et al. (1958) are suspiciously similar. As well, the complexity of either type of formulation depends largely on the choice of components and independent variables, as described in Chapter 3. 

The WATS model is formulated in deterministic terms. However, an extension to include simple Monte-Carlo stochastic simulation is possible, taking into consideration a measured variability of the process parameters. 

You can see that the model for a realistic process can become extremely complex what is important to remember is that steps 1 and 3 in Table 1.1 provide an organized framework for identifying all of the variables and formulating the objective function, equality constraints, and inequality constraints. After this is done, you need not eliminate redundant variables or equations. The computer software can usually handle redundant relations (but not inconsistent ones). 

From the discussion so far, it is clear that the mapping to a system of noninteracting particles under the action of suitable effective potentials provides an efficient means for the calculation of the density and current density variables of the actual system of interacting electrons. The question that often arises is whether there are effective ways to obtain other properties of the interacting system from the calculation of the noninteracting model system. Examples of such properties are the one-particle reduced density matrix, response functions, etc. An excellent overview of response theory within TDDFT has been provided by Casida [15] and also more recently by van Leeuwen [17]. A recent formulation of density matrix-based TD density functional response theory has been provided by Furche [22]. 

Early optimism about the possibility of in vitro-in vivo correlation was tempered by the need for a performance test that would yield reproducible results (10). Even though not necessarily correlated to bioavailability, dissolution requirements were seen as useful in controlling variables in formulation or processing. Thus, from the start, sources of variability in the results were seen as factors to be minimized in any proposed compendial method. 

Comparing only the results at low pH, one would expect both formulations to perform equally in the clinic. However, as would be expected from the dissolution profiles at both pH values, formulation B produced far less variability of absorption in the clinical studies and was also better absorbed than formulation A. This example illustrates clearly the value of the hypochlorhydic model for screening formulations prior to taking them into the clinic. 

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