Introduction
Some calculations will not get easy solutions in one step or immediately or by placing the values in one formula, so in that type of cases we pave the way towards different optimization methods for getting the solution. And this optimization is not that much easy in finding the solutions why because at the end we have to give a perfect conclusion. If we fail there means the entire batch will get fails. This optimization is easy in finding the solution but at the same time it is difficult to conclude also.
Definition: The term optimization has been derived from optimize, that means to make as perfect, functional or effective as possible. In pharmacy, the word optimized was earlier used to suggest that a product has been improved to obtain the desired objectives of a development scientist, in pharmaceutical preparations or pharmaceutical processes; optimization is a technique of searching the best composition or experimental conditions.
Previously new formulations are formulated by changing the dosage forms, doses, quantities of excipients or excipients directly. In some cases by changing one single or separate factor at a time while maintaining the others constant which is known as changing one variable at a time or one factor at a time. In some other cases by changing the physicochemical properties we used to modify the formulation. With these types of techniques there are so many disadvantages. They are mainly it is time consuming, wastage of the excipients, wastage of funds, too expensive, will form errors, incompatible with each other and form interactions etc. So to overcome these problems a new solution is introduced new advanced technique i.e., optimization technique which involves organized, efficient and systematic experimental design.
The main objectives of these optimization techniques are to concerned in maintaining the quality, economy and safety of the industry. The consequence of optimizing a pharmaceutical product involves in the innovating different important variables involved, competent way of formulating the product, improving the stability and usefulness of quality specification in the formulation [7]. These type of studies done mainly during the research studies or in developing of a new product to encounter the problems in an efficient manner. To obtain the relevant information random sampling should be done.
Different terminology used in Experimental design:
Variables
These are the measurements or values that are characteristics of the data. There are two types of variables, dependent and independent variables. Formulation and process variables are directly controlled by the formulator, these include ingredients. Dependent or secondary variables are the responses of in-progress material or the resulting drug delivery system; it is the result of independent variables.
Factor
The factor is an assigned variable like concentration, temperature, lubricating agent, drug-polymer ratio, polymer-polymer ratio etc. A factor can be qualitative or quantitative. A quantitative factor has a numerical value to it e. g., concentration (1%, 2% so on), a drug to polymer ratio (1:1, 1:2 etc). Qualitative factors are the factors, which are no numerical, e. g., Polymer grades, humidity condition, type of equipment etc, these are discrete in nature. The factor is Assigned and Independent variable that affects the product or output of the process. It is an assigned quantitative and qualitatively as follows:
Quantitative: A numerical factor is assigned to it. Example: Concentration-1%, 2%, 3% etc.
Qualitative: These are non-numerical. Example-Polymer grade, humidity condition etc.
Level: The levels of a factor are values or designation assigned to the factor, e. g., concentration (factor) 1% will be one level, while 2% will be another level. Two different plasticizers are levels of grade factor. Usually, levels are indicated as low, middle or high level. Normally for ease of calculation, the numeric and discrete levels are converted to-1 (low level) and+1 (high level). The general formula for this conversion is X — the average of the two levels Level =Half the difference of levels Where ‘X’ is the numeric value.
Response: Response is mostly interpreted as the outcome of an experiment. It is the effect, which we are going to evaluate i.e., disintegration time, duration of buoyancy, thickness, etc. It is an outcome of the experiment.
Response surface: Response surface representing the relationship between the independent variables X1 and X2 and the dependent variable Y.
Run or trials: Experiments conducted according to the selected experimental designs.
Screening: To sort out something from.
Contour Plot: Geometric illustration of a response obtained by plotting one independent variable against another, while holding the magnitude of response and other variables as constant.
Interaction: It is also similar to the term effect, which gives the overall effect of two or more variables (factors) of a response. For example, the combined effect of lubricant (factor) and glidant (factor) on hardness (response) of a tablet. From the optimization, we can draw a conclusion about Effect of a factor on a response i.e., change in dissolution rate as the drug to polymer ratio changes. The relationship between various factors and response, those are a quantitative change of a response as we change the factors and its levels. The contribution effect i.e., whether two factors are contributing additively or antagonistically for a response, e. g., any relationship between the concentration of lubricant and glidant on the hardness of the tablet or flow property of the granules. It gives the overall effect of two or more variables means lack of summation of factor effects.
Effect: The effect of a factor is the change in response caused by varying the levels of the factor. This describes the relationship between factors and levels.
Multiple Linear Regression Analysis: The technique which expresses mathematically in form of the quadratic equation the linear relationship between a various independent variable and the dependent variable (Response).
Orthogonality: When the effect is due to the main factor of interest and no interaction.
Confounding: Lack of Orthogonality is termed as confounding or aliasing.
Resolution: Measurement of the degree of confounding.
Effect: The effect of a factor is the change in response caused by varying the levels of the factor. This describes the relationship between factors and levels
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Optimization parameters
The optimization parameters are generally divided into two types:
- Problem type and
- Variables.
1. Problem type
The problem type of parameters again grouped into:
- Constrained type: In this restrictions placed on the system by means of physical limitations or perhaps by simply practical based. This can be explained by taking hardness of tablet and its disintegrating time in less than 15 min.
- Unconstrained type: In unconstrained type, there are no restrictions placed on the system by means of physical limitations or perhaps by simply practical based. But in pharmaceuticals, there is always a limitation of a means of a physical limitation or perhaps by simply practically the formulator wishes to place or must place on a system.
Variables
There are several variables in pharmaceutical formulation and processing but generally, variables can be classified into:
- Independent variables: These are directly under the control of formulation scientist.
Example: mixing time.
- Dependent variables: these are not directly under the control of formulation scientist. Example: Homogeneity of mixed granules.
Experimental designs (ED)
Experimental design is a statistical design that prescribes or advises a set of combination of variables. These variables play an important role in the Experimental design. In this the process is divided into 2 screens. Coming to the first screen the process variables are screened to determine which variables are important to our research like Disintegration time, dissolution time, type of excipients etc. The second screen is the optimization; here in this step we can select the best optimized variables for the method. Not only this but also it will changes the concentrations of excipients and elaborates the changes which will affect the properties of the mixture. Experimental designs are selected based on the levels, interactions, designs chosen and the interaction between each and other. By using all the data we can determine the relationship between the factors (Xs) affecting a process and the output of that process (Ys). Finally we should conclude the experimental design in a valid and objective manner by collecting all the data.
There are different types of ED, out of those which one is suitable for our study we have to select.
Factorial designs
It is initially used in the 19th century by John Bennet Lawes and Joseph Henry Gilbert. By using this we can determine the interactions between different levels and factors etc. In this type of experiments all the levels of a one factor is combined with all levels of the other factor. So based on the results obtained we can conclude the number of trials required. These are usually based upon first-degree mathematical models. Whenever we are conducting these experiments the design of choice should be perfect then only the result will be efficient.
Fractional factorial design
Fractional factorial design is commonly used for screening of factor. Less number of runs will be done in this so it has low resolution. So these are economical in conducting number of experiments i.e., reduction in the number of experiments.
Full factorial design (FFD)
Dimensional factor space at the corner of the design space is the main concept of this type of design. Factorial designs (FD) are used when different effects, different conditions and different levels and different factors are included with their interactions. The simplest one is the 2 factorial design, in which two factors are measured each at two levels, leads to four experiments. And these are placed in 2-dimensional factor space at the corners of a rectangle. In the case of 3 factors, each at two levels results in eight experiments which are placed at the corners of an orthogonal cube on a 3-dimensional space. The number of experiments is given by 2, where ‘n’ is the number of factors.
Plackett-burman designs (Hadamard designs)
Plackett-Burman designs (PBD) are special two-level FFDs used when the factors are in high number. For example if we want to study the effect of 7 factors then we have to show four dummy factors. Not only this but also it is used for the screening of factors. Bu using Pareto chart and half normal plot the interpretations of results in FFD, PBD and taguchi design (TD) are drawn which prove to be effective screening designs.
Central composite design (Box-Wilson design)
This Central composite design design was developed by Box and Wilson. It is quite popular in response surface optimization during pharmaceutical product development. It mainly consists of +2k Factorial design or Fractional factorial design and that is considered as the advantages of factorial design or fractional factorial design or the star design. It is frequently used for nonlinear responses which require second-order models. A two-factor CCD is equal to a 32 FD with the rectangular experimental domain.
Box-behnken designs (BBD)
This design is inexpensive and efficient because it requires less number of trials i.e., it requires only three levels for each factor (-l, 0 and+1). It is subjecting 15 experiments run with three factors at three levels.
Taguchi design (TD)
It is a method which gives superior performance in the development of products or processes which refers the experimental design as 'off-line quality control. It has another advantage of screening of factors which provides 8 experimental runs for 7 factors.
Mixture design (MD)
Mixture deign mainly stand for the quantity of each substance present i.e., in pharmaceutical formulations with multiple excipients, the individuality of the finished product do not depend on the quantity of each substance but they depend on their proportions. The sum of all proportions should be unity and he fraction should never exceeds 1.
Screening designs (SD)
These are used for developing the quality of formulation especially which shows linear responses.
Response surface designs (RSD)
These are used when we requisite exact image of response, estimating interaction and even quadratic effects. It supports not only nonlinear and quadratic response but also capable of detecting curvatures.
Star design
The star design is simply a 22 factorial design rotated over 45 ° angle in the space. To this a center point is added which replicates to estimate experimental error. In star design, 2k Factorial designs are rotated over 45 ° in (k-i) direction in k-dimensional space with a replicated center point. K indicates the number of factors in the design. This results in 2k+R experiments, where R indicates the replicate of the center point.
Box design (BD)
Box Design is used when the number of factors are increased in high in number its completely opposite to central composite design. . The design is called an orthogonal balanced incomplete block design. It will divide into a set of incomplete blocks in which every effect is not placed in every block but every effect is measured as an equal number of times with a unbiased division over the different blocks.
Doehiert hexagon or uniform shell design (USD)
This design is introduced by Doehiert which projects uniform shell designs (USD. It initiates with an equilateral triangle. It will give a good basis for interpolation and a major disadvantage is the numbers of levels are not same for all factors. The design may be initiates with one side of the hexagon parallel to the most significant axis.
Simplex lattice design (SLD)
These designs are used to determine the interior and the boundaries of the simplex. The number of factors included in the design determines its dimensions. Based on the model postulated the pattern of design points in the factor space and their number depend on the degree (the term of the highest order) are selected. The points are which are included distributed in a correct way over the factor space forms a lattice.
Extreme vertices design (EVD)
In this design it will not allows the whole factor space for accessing. Specific points only allow for giving the useful responses which is extremely seen in formulation studies. In this design, observations are made mainly at 3 points i.e., at the corners of the bounded design space, at the middle of the edges and at the center of the design space. These are not only used for the mixture composition but also used in combination with factorial designs.
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