Design space formulation

Definition 5.1.1 Given a sequencing graph G, V, E,8) and resource types T, a resource allocation is the mapping a T — from the set of resource 

Given a resource allocation a, a resource binding for a sequencing graph G, is an assignment of shareable operations V to specific instances of the allocated 

A partial binding can be defined for more than one allocation, where it is assumed that the number of resources required by the partial binding is satisfied by these allocations. This leads to the concept of compatible bindings, defined below. 

Definition 5.1.3 A complete binding is compatible with a partial binding 

In other words, a compatible binding can be derived fix)m a given partial binding by mapping all hardware-unbound vertices to resource instances. Obviously, 

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An important aspect of the design space formulation is that it is a com-... 

An important aspect of the design space formulation is that it is a complete charactmzation of the entire set of possible design tradeoffs for a given allocation of resources. This formulation allows partial binding information to be uniformly incorporated, where the partial binding is used to limit the design... 

With the design space formulated as a set of resource bindings for a given resource allocation, Hebe explores the design space to find a favorable implementation with respect to a particular design goal, such as minimal area ot minimal latency. Any valid implementation must satisfy both resource and timing constraints. 

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. 

Pharmaceutical formulation and process development should provide sufficient information and knowledge to understand and support establishment of the design space, specifications, and manufacturing control. The design space of QbD is defined as the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality.6 Because multiple variables in formulation and process can be encountered, it is important to use an effective methodology to define the design space. 

Formulation Optimization. Formula optimization follows the selection of a formulation composition from the preliminary screening work. Formulation optimization focuses on determining the optimal level of each excipient to enable definition of a design space for each individual excipient. A proper DOE study is an effective and efficient way of defining the excipient levels and aiding in the selection of the optimal formulation. Factors in an optimization DOE study may include ... 

The proportion of saccharose was allowed to vary, so that the tablets would be of constant mass. The design space thus becomes a parallelogram, each side of the parallelogram representing the replacement of saccharose by another excipient. As the saccharose is a filler, completing the formulation to 100%, the proportions of sorbitol and the citric acid/bicarbonate mixture may be set independently of one another at any selected value, and may thus be considered as independent variables. The tablet formula is summarised in table 3.6, and the levels are given in table 3.7. 

The method is also useful where a number replications of each experiment is required for reasons of precison, for example, in vivo experiments on formulations. The "best" experiments are thus replicated more times than those less well placed in the design space. 

This constraint, in the case of mixture-amount problems where the proportion of active substance is allowed to vary, is one which is particularly relevant to pharmaceutical formulation. We take a formulation where the percentage of drug substance is between 5 and 50%. This variation is compensated for by a change in the percentage of diluent (for simplicity we assume a single diluent). The tablet mass is varied from 100 to 200 mg, so the design space is square as shown in figure 9.28c (broken lines). 

Figure 10.2 Factor and design space for formulation of a modified release tablet,...

Once the individual limits of each component are known, the design space for the experiment may be defined. For 3 components it may be determined graphically. For more than 3 or 4 components the McLean-Anderson algorithm (6) is used. Experiments must then be selected within the design space. As examples we take the solubility of a drug in a ternary mixture where the constraints give rise to a non-simplex design space and the formulation of a sustained release tablet, with 4 variable components. 

Figure 10.7 Design space for hydrophilic tablet formulation.

Table 10.10 Vertices of the Design Space for Formulation of a Hydrophilic Matrix Tablet... 

A NLP optimisation problem can be viewed as the minimisation of an objective function F(d,x) in a design space d subject to equality c(x)a.n inequality g(x) constraints. Mathematically, the formulation is ... 

O. Khatib. Op ational Space Formulation in the Analysis, Design, and Control of Manipulators. In Preprints 3rd Int. Symp. Robotics Research, pages 103-110,1985. 

The Q8 guideline emphasises the importance of understanding the formulation and the method of preparation, as well as preparation process control that is based on scientific data and risk analysis of the preparation process (see also Chap. 21). Identification of all relevant sources of variability will result in a window (the design space) for all adjustable parameters (particle size, pH, mixing time, etc.). Practically, the QbD approach will lead to a robust formulation and preparation process that is stUl flexible enough to adapt to necessary modifications. Detailed documentation of the development research will help limiting time- and resourceintensive follow-up studies in order to explain process deviations or applying process modifications. 

For pharmacy preparations, the process of standardisation of an individual formulation can be seen as defining its design space. This design space should be large enough to enable different pharmacies to prepare a product following the formulation and according to the requirements. Ways to perform that task are ... 

Fig. 3.5 Design space consideration during development of the hot-melt extrusion (HME) formulation...

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