Optimization of Extraction Using Mathematical Models and Computation

Chapter 3

Optimization of Extraction Using Mathematical Models and Computation Anup K. Das*, Saikat Dewanjee† *

ADAMAS University, Kolkata, India, †Jadavpur University, Kolkata, India

Chapter Outline 3.1. Introduction 3.2. Fundamentals of Design of Experiments 3.2.1 Planning Phase 3.2.2 Designing Phase 3.3. DoE-Based Optimization of MAE Process

75 76 78 79 101

3.4. DoE-Based Optimization of Supercritical Fluid Extraction Process 3.5. DoE-Based Optimization of Accelerated Solvent Extraction Process 3.6. Conclusions References

101

101 104 106

3.1. INTRODUCTION Bioactive plant extracts, mainly from medicinal herbs, have been used to treat various ailments since time immemorial. Herbal drugs are used not only as a single component (monoherbal), but are also used simultaneously as a polyherbal formulation, which is a complex mixture of several herbs and chemical entities in a defined ratio (Budovsky et al., 2016). Developing a robust technique for isolation of bioactive principles from crude drugs encompasses multiple objectives under its canopy. Earlier, such type of tasks was performed through trial and error methods accompanied by prior working experience, knowledge, and wisdom of the operator. However, systematic optimization of the extraction process is essential for maintaining quality of any herbal product. Optimization of an extraction process involves utilization of a great degree of time, energy, and resources. By applying this technique, solution to any specific problem arising from process intensification could certainly be achieved apart from ensuring an optimum outcome. Extraction of phytochemicals is a multifactorial process that involves different mechanisms and unit operations Computational Phytochemistry. https://doi.org/10.1016/B978-0-12-812364-5.00003-1 © 2018 Elsevier Inc. All rights reserved.

75

76  Computational Phytochemistry

with high degree of variability. Such processes customarily comprise different parameters or variables, and as a result, the relationships between input parameters with final product quality are difficult to ascertain. Moreover, the task gets more difficult due to the complex chemical composition of phytochemicals biosynthesized by plants. Unfortunately, in most of the cases, the extraction and isolation of phyto-drugs are performed relying on prior experience of the operator and thus the effect(s) of various input factors on the product quality are not well-defined. Consequently, the attributes of final products often suffer from high variability. Therefore, a thorough understanding of the relationships between the input factors and product quality is essential for improving the extraction performance of phyto-drug offering desirable products with acceptable quality being generated for the end users. In this chapter, an overview on different facets pertaining to extraction techniques of botanicals that have been subjected to DoE is presented. Additionally, a general abridgement on different features of experimental design and the steps involved in its practice are also described.

3.2.  FUNDAMENTALS OF DESIGN OF EXPERIMENTS In any manufacturing processes, it is often interesting to explore the relationships between the main input factors and the output or quality characteristics. For example, in a phytochemical isolation operation, the nature of solvent, particle size of the crude drug, duration of extraction, and cycle of extraction can be treated as input factors and the yield of the product can be considered as an output characteristic. Process intensification in botanical extraction can be achieved when the relationship between final product, i.e. outcome (y), and all the sources of variation or input factors (x) in the manufacturing process are understood. The outcome (y) can be described as a function, which depends on the input factors, as represented in Fig. 3.1. This function can be described in different forms (‘black box’ representing negligible predictive power; ‘gray box’ representing moderate predictive power; or ‘white box’ representing total predictive power) to describe a process depending upon the degree of predictability (Acharya and Pandya, 2013). The outcome (y) is defined in Eq. (3.1) y = f ( x1 ,x2 ¼ xn ) 2

(3.1)

The crucial sources of variations (δ ), which may affect an isolation process, can be attributed to the followings: features of raw material (RM), viz. raw material sourcing, raw material handling prior to extraction, plant part used, adulteration in raw material, if any; extraction related factors (EF), e.g., temperature during extraction, energy consumed, etc.; machinery (MACH) used during extraction, e.g., Soxhlet, microwave, supercritical fluid extractor, ultrasound, etc.; scale (SC), e.g., preparative or analytical scale; environment factors (EVN), e.g., moisture level, humidity, temperature; human (HR) resource involved. Therefore, the total variation can be represented as shown in Eq. (3.2).

Optimization of Extraction Using Mathematical Models  Chapter | 3  77

Uncontrolled variables

(x1, x2......xn) Input factors

f

y

Output or product quality

Negligible predictive power

Moderate predictive power

Total predictive power

Black-box models

Grey-box models

White-box models

FIG. 3.1  Relationship between final outcome (y) and all the sources of variation or input factors (x) in the manufacturing process.

d 2 ( Total ) =d 2 ( RM ) + d 2 ( EF ) + d 2 ( MACH ) + d 2 (SC) + d 2 ( EVN ) + d 2 ( HR )

(3.2)

Thus, the goal of extraction process development is primarily to predict how variations in input factors (x) will influence the outcome (y), and secondarily, to regulate these factors to improve the final product quality. Therefore, the challenge before any herbal industry is to sort out which inputs variables or factors will affect the process. While analysing a process, designed experiments are often performed to evaluate which input factors have a substantial impact on the final outcome, and what level of those input factors should be applied to achieve a desired output. Thus, the objectives of a designed experiment may include the following: 1. To determine the factors that are most influential to the outcome (y). 2. To determine where to set the influential input factor (x) so that y remains near the desired nominal value with minimum variation. 3. To determine where to set the influential input factor (x) to control the variations, if any, due to uncontrolled variables. In general, the goal of the person conducting the experiment should be to determine the impact of these factors on the output response. The general method of planning and experimentation is called an experimental strategy. One of the

78  Computational Phytochemistry

common methods used by many scientists in manufacturing nowadays is OneVariable-At-a-Time (OVAT), where a single factor is varied keeping all other factors constant during the experiment. The success of such approach is dependent on luck, experience, and intuition of the experimenter. In addition, this approach requires heavy financial investments to get limited information about the outcome. Usually, such approach is unreliable, inefficient, ineffective, timeconsuming, and may show false-optimal conditions for the process. The main drawback of OVAT strategy is that it does not take into account any possible interactions between these factors. The interaction between factors is common, and if this happens, it results in undesirable outcome. Despite the drawbacks, an OVAT experiment is still in use. Such experiments are always less efficient than other methods which are based on statistical designs. Statistical methods play important roles in planning, conducting, analysing, and interpreting data from any experiment. When several variables influence a certain characteristic of a product, the best strategy is then to design an experiment so that valid, reliable, and sound conclusions can be drawn effectively, efficiently, and economically. In a designed experiment, the experimenter often makes an intentional change into the input factors and then determines the effect on the final outcome. It is important to note that not all factors affect outcome in the same way. Some factors may impact significantly on the output performance, while some other may have moderate impact, and some may not be effective at all. Therefore, the goal of a designed experiment is to understand the important factors and to determine the optimal level of performance of these factors to get an effective outcome. In order to draw an effective conclusion from the experiment, it is obligatory to amalgamate simple and powerful statistical methods. The success of any industrial designed experiment relies on well-defined planning, selecting an appropriate design, data analysis, and teamwork. Experimental design encompasses planning process, design, and analysis of experiments, so that effective and objective conclusions can be effectively drawn as shown in the Fig. 3.2.

3.2.1  Planning Phase The planning phase is made up of the following steps. 1. Problem identification—Clear understanding of the problem in hand helps to understand what needs to be done during manufacturing. The statement should contain measurable outcomes, which will add real value to the company economy-wise. Some issues related to manufacturing can be resolved using experimental methods including: new product development or improvement of the existing products; intensifying the existing process; improving product performance as per market demand. After determining the experimental outcome, a group can be formed. The team may include

Optimization of Extraction Using Mathematical Models  Chapter | 3  79

Planning Phase

Identify the Problem Response selection Selection of parameters

Designing phase

Screening designs (Factorial designs, OVAT) Optimizing designs (Response surface methodology)

Conducting phase

Planned experiments are carried out and the results are evaluated

Analysing phase

Here Interpretation done so that valid and sound conclusions can be derived.

FIG. 3.2  Different phases involved in Design of Experiment.

experts, process engineers, quality engineers, floor operator, and a nominee from the management. 2. Response or outcome selection—The choice of an appropriate response is critical for the success of any designed experiment. The response can essentially be a variable or an attribute. Variable responses such as duration of extraction, strength of the solvent used, particle size of the raw material, etc. generally provide more information than the attribute response such as good/bad, pass/fail, or yes/no. 3. Process parameter selection—The selection of process parameters should be performed immaculately after in-depth deliberation based on prior knowledge of the process, historical data, cause-and-effect analysis, and brainstorming session. This is an important step in the experiment designing. Screening experiments in the first phase of any experimental survey is a good practice to determine the most important design parameters or factors. In-depth discussion is present in the subsequent sections.

3.2.2  Designing Phase At this phase, one may select the most suitable design for the experiment. The size of the experiment depends on the factors to be studied and/or the number of interactions, the number of levels per factor, and the budget and resources used to carry out the experiment. Screening is used to lessen the number of process factors by identifying the significant ones that affect quality or process performance. This reduction helps to focus on the few important factors or the vital few from trivial many as shown in Fig. 3.3. It is a good practice to have the design ready before commencing the experiment. The design matrix usually shows all the settings of the factors at different levels and the order in which a particular experiment needs to be run. The purpose of screening design is to identify and to separate those factors that demand further investigation, i.e. towards optimization. The designing phase is generally divided into two segments—screening phase and optimization phase. While developing novel extraction strategies, two types of situations may arise, where the mediation of experimental design becomes necessary. First is to screen vital few factors that are expected to have a significant effect on the final outcome

80  Computational Phytochemistry

Sample: solvent

Particle size of drug

Solvent strength

Soaking time

5

Extraction time

6

7

8

Solvent concentration Extraction temp

Instrument power

4

Sample: solvent ratio

3

Solvent concentration

2

Extraction time

Instrument power

1

FIG. 3.3  A typical representation of screening steps to screen out the vital few from trivial many.

and is called screening phase. Second is the optimization phase to optimize systematically the selected significant factors for getting optimal solutions.

3.2.2.1  Screening Phase Initially, a screening is carried out to determine the factors and their interactions, which would have significant influence on the final outcome. Based on these findings, we can move towards optimization using those factors, which are significant during screening. Screening is performed employing simple design (OVAT methodology) and factorial design technique. The former is applied by testing one factor at a time instead of all at a time. Whereas, in the latter case, all the factors are tested simultaneously. If k factors are studied at two level [+1 (high level), −1(low level)], a factorial design will consist of 2k experiments as shown in Box 3.1 below. Let us consider a simple extraction example taking two factors, viz. Factor A (xA): microwave power (Watts) at high level [+1] and low level [−1]; Factor B (xB): extraction time (min) at high level [+1] and low level [−1]. If two factors are taken at two different levels, then it is required to carry out four experiments (22 = 4) for which four different outcomes (yield or extractive value) will be obtained. This means an outcome (y) can be described as a function based on experimental factors and, in a designed experiment, it is called Transfer function

Optimization of Extraction Using Mathematical Models  Chapter | 3  81

BOX 3.1  Number of experiments when k factors are studied at two levels Factors (k)

No. of Experiments (2k)

2

4

3

8

4

16

5

32

6

64

10

1024

BOX 3.2  A general matrix containing all the level combinations of Factor A (XA) Factor B (XB) XA

XB

XA × XB

−1 (LOW)

+1 (HIGH)

−1

+1 (HIGH)

−1 (LOW)

−1

−1 (LOW)

−1 (LOW)

+1

+1 (HIGH)

+1 (HIGH)

+1

(f) as mentioned earlier in Eq. (3.1). All the four experiments, which need to be conducted, can be represented in the form of a general matrix containing all the level combinations as shown in Box 3.2. Both the factors will be at their higher level (+1) and lower level (−1). From the matrix shown below, two types of effects can be deduced, main effects of the factors (XA, XB) and interaction effects of the factors (xA × xB) as depicted. The information, which can be deduced from this matrix, is that each column can be considered as vectors (Box  3.3) and each of these columns (XA, XB, xA × xB) is having four components, i.e. (−1, +1, −1, +1) apart from being linearly independent to each other. If product of two vectors (xA × xB) are taken and added up, then zero (0) will be obtained. Similarly, zero will also be obtained if we do summation of XA and XB columns as shown in Box 3.3. Therefore, it can be asserted that the columns are independent of each other. However, if we square (the concept of secondorder model) each components of XA, XB and xA × xB, and add them up, we will get some value, i.e. four (4) as shown in Box 3.3. Through this explanation, we are trying to understand the basic properties of the factors (XA and XB) and their coefficients, which will determine the progress of the process subsequently.

82  Computational Phytochemistry

BOX 3.3  Representation of XA, XB, XA × XB as column vectors

Column components

Column vectors

xA

xB

xA × xB

–1

+1

–1

+1

–1

–1

–1

–1

+1

+1

+1

+1

4

SUM

Σx = 0 A

4

SUM

1

4

SQUARE

Σ 1

x2A = 4 SQUARE

Σx = 0 B

4

SUM

1

4

Σ 1

x2B = 4 SQUARE

Σx × x = 0 A

B

1

4

Σx

2 ×x =4 A B

1

Coefficients are the effects of each factor. By interpreting the results, it would be possible to tell the factor or factor combination having more influence on the outcome. So, let us now look into the relationship of outcome (y) with XA and XB. Like XA, XB and xA × xB, the outcome (y) can have up to four components as we are conducting four experiments. Therefore, we will be able to fit a curve or find a relationship, which can support only four parameters in this context. The simplest relationship, which could be thought of, is a linear relationship. Now the outcome (y) can be represented as shown in Eq. (3.3). y = b 0 + b A X A + b B X B + b AB X A X B (3.3) β0 = Intercept (mean of XA and XB). βA = coefficients of factor XA. βB = coefficients of factor XB. βAB = coefficients of interaction factor (XAXB). The above equation represents a linear relationship between y and factors XA, XB and their interaction (xA × xB). The next step is to find out the coefficient values of each factor and the intercept. Let us take an example of a microwaveassisted botanical extraction process, where the yield is represented as y (mg/kg of raw material), microwave power (Watts) as XA; extraction time (min) as XB. Here a number of factors can be taken, but to keep the things simple, we have taken two factors only. Let us specify the high values and the low values for each of the factors as shown in Box 3.4 below.

Optimization of Extraction Using Mathematical Models  Chapter | 3  83

BOX 3.4  Representation of high values and low values for factors XA, XB Factor A (xA): instrumental power (W) Factor B (xB): extraction time (min)

High (+1), 50 W

Low (–1), 10 W

High (+1), 10 min

Low (–1), 5 min

xA

xB

y(yield)

Y = b0 + bAXA + bBXB + bABXA XB

–1

+1

1.5 y1

1.5 = b0 – bA + bB – bAB

Eq.(1)

1.5 = b0 – bA + bB – bAB

+1

–1

8.2 y2

8.2 = b0 + bA – bB – bAB

Eq.(2)

8.2 = b0 + bA – bB – bAB

–1

2.0 y3

2.0 = b0 – bA – bB + bAB

Eq.(3)

2.0 = b0 – bA – bB – bAB

+1

3.5 y4

3.5 = b0 + bA + bB + bAB

Eq.(4)

3.5 = b0 + bA + bB + bAB

–1 +1

If l take (–) minus of Eq.1 and Eq.3

Add all the 4 equations

15.2 = 4b0

3.8 = b0

– 1.5 = – b0 + bA – bB + bAB 8.2 = b0 + bA – bB – bAB – 2.0 = – b0 + bA + bB – bAB 3.5 = b0 + bA + bB + bAB 8.2 = 4bA

2.05 = bA

Like wise by solving the matrix we can get the values of all the coefficients. b0 = 3.8, bA = 2.05, bB = – 1.3, bAB = – 1.05 • Coefficients are the effects of each parameters on the final outcome (yield). • Larger the coefficient value, the larger will be the influence of the factors on the final outcome

Using the matrix as shown in Box 3.4, we can now write four equations using the linear relationship. If we perform four experiments, then we will get four outcomes, y (i.e. yield values for example y1 = 1.5, y2 = 8.2, y3 = 2.0, y4 = 3.5) as shown Box 3.4. By solving these four equations, we can get the values of β0, βA, βB, and βAB which are +3.8, + 2.05, −1.3, −1.05, respectively. It is known that larger the value of coefficient, the larger is the influence of the factor on the final outcome. When we are looking for some general idea regarding the process in hand, we can apply first order polynomial model as shown in Eq. (3.2). This model only tells about the current factor settings, but does not give any information about the zone of optimization. In order to gain some knowledge about the optimum zone, it is necessary to introduce a square term, as mentioned earlier. The preferred model is a quadratic (second order) model. The various types of screening designs generally used in herbal extraction are presented hereunder. Full Factorial Design (2k) In a Full factorial design (FFD), the effect of all the factors and their interactions on the outcome (s) is investigated. A common experimental design is one, where all input factors are set at two levels each. These levels are termed high and low or +1 and −1, respectively. A design with all possible high/low groupings of all the input factors is termed as a full factorial design in two levels. If there are k factors, each at 2 levels, a full factorial design will be of 2k runs as mentioned earlier.

84  Computational Phytochemistry 6 8 2 5

4

X3 7

X1 1 X2 3 FIG. 3.4  Representation of a 23 design as a cube.

As shown in Box  3.1, when the number of factors is more than five, a full ­factorial design requires a large number of experimental runs and is not effective. Therefore, a fractional factorial design or a Plackett-Burman design (PBD) is a better choice for five or more factors and is discussed in next section. When a full factorial design for three input factors, each at two levels, is considered (23 design), it will have eight runs. Graphically, we can denote the 23 design by a cube shown in Fig. 3.4. The arrows show the direction of increase of the factors. The numbers 1 through 8 at the corners of the design box represent the Standard Order of runs (Fig. 3.4). In tabular form, this design can be represented as shown in Table 3.1. The column on the left hand side of Table 3.1, which numbers up to 8, is called the Standard Run Order. These numbers are also depicted in Fig. 3.4. For example, run number 8th is made at the high setting of all three factors. Fractional Factorial Design (2k−p) Simply, it can be considered as a half of a full factorial design. Fractional factorial designs offer a reduced number of experiments without losing a lot of information. Let us put some observation values (y1---y8) in Table 3.2 and try to deduce why we do not need all eight runs. The right-most column of the Table  3.2 lists y1 through y8 to indicate the outcomes measured for the experimental runs when listed in standard order. For example, y1 is the response observed when the three factors were all run at their ‘low’ setting (−1). The numbers placed in the ‘y’ column will be used to calculate the main effects of the factors. From the entries in Table 3.2, it is possible to compute all ‘effects’ such as main effects, first-order interaction effects, etc. For example, to compute the main effect estimate c1 of factor X1, it is necessary

Optimization of Extraction Using Mathematical Models  Chapter | 3  85

TABLE 3.1  A 23 Two-Level, Full Factorial Design Table Showing Runs in ‘Standard Order’ Run

Pattern

X1

X2

X3

1

−

−

−

−1

−1

−1

2

+

−

−

+1

−1

−1

3

−

+

−

−1

+1

−1

4

+

+

−

+1

+1

−1

5

−

−

+

−1

−1

+1

6

+

−

+

+1

−1

+1

7

−

+

+

−1

+1

+1

8

+

+

+

+1

+1

+1

TABLE 3.2  A 23 Two-Level, Full Factorial Design Table Showing Runs in Standard Order Plus Observations (y) Run

Pattern

X1

X2

X3

y

1

−

−

−

−1

−1

−1

y1 = 43

2

+

−

−

+1

−1

−1

y2 = 73

3

−

+

−

−1

+1

−1

y3 = 51

4

+

+

−

+1

+1

−1

y4 = 67

5

−

−

+

−1

−1

+1

y5 = 67

6

+

−

+

+1

−1

+1

y6 = 61

7

−

+

+

−1

+1

+1

y7 = 69

8

+

+

+

+1

+1

+1

y8 = 63

to compute the average response at all runs with X1 at the high setting (+1), namely (1/4)(y2+y4+y6+y8), minus the average response of all runs with X1 set at low, namely (1/4)(y1+y3+y5+y7). That is, c1 = (1 / 4 ) ( y2 + y4 + y6 + y8 ) - (1 / 4 ) ( y1 + y3 + y5 + y7 ) = (1 / 4 ) ( 73 + 67 + 61 + 63 ) - (1 / 4 ) ( 43 + 51 + 67 + 69 ) = 8.5

86  Computational Phytochemistry 6 8 2 5

4

X3 7

X1 1 X2 3 FIG. 3.5  Representation of unshaded corners of the design cube.

Suppose we do not have enough resources in hand to perform eight runs, is it still possible to estimate the main effect for X1? The answer is yes. For example, suppose we select only the four light (unshaded) corners of the design cube as shown in Fig. 3.5. Using these four runs (1, 4, 6, and 7), we can still compute c1 as follows: c1 = (1 / 2 ) ( y4 + y6 ) - (1 / 2 ) ( y1 + y7 ) = (1 / 2 ) ( 67 + 61) - (1 / 2 ) ( 43 + 69 ) = 8 In either case, it is possible to obtain a value for the main effects (c1) of X1 and for other factors as well without losing much information. In both the cases, the value of main effects (c1) of X1 is close to 8. Plackett-Burman Design PBD is a particular type of fractional factorial design, which assumes that the interactions can be completely ignored and the main effects can be calculated with a reduced number of experiments. Various factors (n) can be screened in an ‘n + 1’ run PBD. A distinctive feature is that the sample size is a multiple of four, rather than a power of two (4k observations with k = 1, 2…n). PBD is used to investigate n − 1 factor in ‘n’ experiments proposing experimental designs for more than seven factors and especially for n × 4 experiments, i.e. 8, 12, 16, 20, etc. These are suitable for studying up to 7, 11, 15, 19, etc. factors. Such designs are also known as saturated designs, which allow an efficient separation of main effects and interaction effects. An example of PBD with 12 runs and 11 factors is presented in Table 3.3. A case study carried out by Das et al. (2013) using PBD for screening of factors, which significantly helps towards achieving an effective, rapid, and

Trial

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

Response

1

+

−

+

+

+

−

−

−

+

−

−

y1

2

+

−

+

+

+

−

−

−

+

−

+

y2

3

−

+

+

+

−

−

−

+

−

+

+

y3

4

+

+

+

−

−

−

+

−

+

+

−

y4

5

+

+

−

−

−

+

−

+

+

−

+

y5

6

+

−

−

−

+

+

+

−

+

+

y6

7

−

−

−

+

−

+

+

+

+

y7

8

−

−

+

−

+

+

+

+

+

−

y8

9

−

+

−

+

+

−

+

+

+

−

−

y9

10

+

−

+

+

−

+

+

+

−

−

−

y10

11

−

+

+

−

+

+

+

−

−

−

+

y11

12

−

−

−

−

−

−

−

−

−

−

−

y12

+

Optimization of Extraction Using Mathematical Models  Chapter | 3  87

TABLE 3.3  An Example of a 12-Run Plackett-Burman Design

88  Computational Phytochemistry

e­ nvironmentally friendly microwave-assisted extraction (MAE) strategy for the industrial scale-up of lupeol using response surface methodology (RSM), is presented here. Initially, a PBD matrix as shown in Table  3.4 was used to determine the most significant extraction factors among microwave power, irradiation time, and particle size, solvent: sample ratio, different solvent strength, and soaking time. Apart from this, five dummy factors were used to estimate the experimental error in a design (Vander et al., 1995). The corresponding outcomes of 12 experiments are shown in Table 3.4. The adequacy of the model was calculated, and the variables showing statistically significant effects were screened via regression analysis (Table  3.5). Among six extraction parameters (microwave power, irradiation/extraction time, solvent composition, particle size, solvent: sample/loading ratio, and soaking time) studied, three parameters (microwave power, irradiation/extraction time, and solvent: sample ratio) had significant influence on lupeol extraction as evidenced from the chart (Fig. 3.6) by their P values (P < 0.05, significant at 5% level) obtained from regression analysis. The coefficient of determination (R2) of the model was found to be 0.923, which indicates the model could explain up to 92.39% variation of the data. Among the six factors tested, it was found that microwave power, irradiation time, and solvent-sample ratio had a significant effect on lupeol extraction (P < 0.05). These three factors were later used for optimization (Das et al., 2013). Taguchi Design A full factorial design (FFD) determines all possible combinations of a given set of experimental factors. Since most industrial experiments often involve many factors, the FFD results in a large number of experimental runs. To reduce the number of experiments without losing significant information, only a small portion from all the possibilities is selected. The technique of selecting a fewer number of experiments, which provide adequate information, is called fractional factorial experiments. Even though this approach is well-known, there is no general guideline for applying it. Taguchi has built a general design guide for fractional factorial experiments covering many applications (Rao et  al., 2004, 2008; Rosa et  al., 2008). Taguchi method uses a special set of arrays called orthogonal arrays, which advocate minimum number of experiments with maximum information about all the factors that affect the outcome. The core of the orthogonal array method emphasizes on choosing the level of the input factors for each experiment. An orthogonal array is a type of experiment where the columns for the factors are ‘orthogonal’ to one another, i.e. independent to each other. Although there are many standard orthogonal arrays available, each of these arrays is meant for a specific number of independent design factor and their levels. For example, if we conduct an experiment to understand the influence of four factors at three levels (level 1: −1; level 2: 0; level 3: +1), the L9 orthogonal

TABLE 3.4  Initial Level of the Extraction Factors for Extraction of Lupeol From Ficus racemosa Leaves by Using Plackett-Burman Design Extraction Factors

Low Level (−)

High Level (+)

X1

Microwave power

20% W

50% W

X2

Irradiation time

1 min

3 min

X3

Solvent: Sample/loading ratio

5:1 mL/g

15:1 mL/g

X4

Particle size

20 mesh

40 mesh

X5

Methanol conc.

50% v/v

100% v/v

X6

Pre-leaching/soaking time

5 min

10 min

Yield of lupeol using the different levels of factors of Plackett-Burman design Expt

X1

X2

X3

X4

X5

X6

Lupeol yield (μg/g)

1

20

1

15

20

100

10

15.87

2

20

1

5

40

50

10

15.48

3

50

1

15

40

100

5

16.48

4

20

1

5

20

50

5

15.52

5

20

3

5

40

100

5

15.95

6

20

3

15

20

100

10

15.89

7

50

3

15

20

50

5

16.65 Continued

Optimization of Extraction Using Mathematical Models  Chapter | 3  89

Code

Expt

X1

X2

X3

X4

X5

X6

Lupeol yield (μg/g)

8

50

3

5

40

100

10

16.31

9

50

3

5

20

50

10

16.34

10

50

1

5

20

100

5

15.79

11

20

3

15

40

50

5

16.1

12

50

1

15

40

50

10

16.32

X1 = Microwave power %; X2 = Irradiation time; X3 = Solvent:sample ratio; X4 = Particle size; X5 = Methanol conc.; and X6 = Pre-leaching/soaking time.

90  Computational Phytochemistry

TABLE 3.4  Initial Level of the Extraction Factors for Extraction of Lupeol From Ficus racemosa Leaves by Using Plackett-Burman Design—cont’d

TABLE 3.5  ANOVA and Regression Analysis of Plackett-Burman Design Data for the Prediction of Significant Extraction Factors ANOVA Table Sum of Squares [Partial]

Mean Squares [Partial]

F Ratio

P Value

Inference

Model

6

1.3975

0.2329

10.1241

0.0112

Significant

Main effects

6

1.3975

0.2329

10.1241

0.0112

Significant

Residual

5

0.115

0.023

Lack of fit

5

0.115

0.023

Total

11

1.5126

Regression Information Term

Effect

Intercept

Coefficient

Standard Error

Low CI

High CI

T Value

16.0583

0.0438

15.9701

16.1466

366.745

X1

0.5133

0.2567

0.0438

0.1684

0.3449

5.8618

X2

0.2967

0.1483

0.0438

0.0601

0.2366

3.3877

X3

0.32

0.16

0.0438

0.0718

0.2482

3.6541

X4

0.0967

0.0483

0.0438

−0.0399

0.1366

1.1039

X5

−0.02

−0.01

0.0438

−0.0982

0.0782

−0.2284

X6

−0.0467

−0.0233

0.0438

−0.1116

0.0649

−0.5329

R2 value of the model is 92.39% with R2 (adj) = 83.27%. Microwave power%, irradiation time (min) and solvent:sample (mL/g) were significant (P < 0.05).

Optimization of Extraction Using Mathematical Models  Chapter | 3  91

Source of Variation

Degrees of Freedom

92  Computational Phytochemistry Pareto Chart 5.86

A

Bonferroni Limit 4.88191

4.40 C

B

2.93 t-Value Limit 2.57058

1.47

D F

E

0.00 1

2

3

4

5

6

7

8

9

10

11

X1: Rank X2: t-Value of |Effect|

FIG. 3.6  Pareto plot chart showing significant parameters during screening.

array may be the right choice. The L9 orthogonal array is used to understand the effects of four factors, each with three levels. This array assumes that neither of the two factors interacts. Table 3.6 shows a typical L9 (34) orthogonal array set up. Nine experiments could be conducted, each based on a combination of the level values shown in this table. For example, to perform the third experiment, the factor 1 at level 1 (−1), factor 2 at level 3 (+1), factor 3 at level 3 (+1), and factor 4 at level 3 (+1) must be kept as it is. The orthogonal array has the following characteristics, which have the ability to reduce the number of experiments to be conducted. 1. Vertical column under each factor of Table 3.6 has a special combination of level. All the level settings appear for an equal number of times. In case of factor 4 (X4), level 1, level 2, and level 3 appear thrice. This is referred to as the balancing property. 2. All the level values of factors are used for conducting the experiments. 3. The sequence of level for each factor must not be changed. This suggests that one cannot conduct experiment number 1 with factor 1 at level 2 and experiment 4 with factor 1 at level 1 setup. The reason for this is that the arrangement of each factor column is mutually orthogonal to each other, i.e. the inner product of vectors will turn out to be zero. The above 3 levels are designated as −1, 0, 1 for level 1, level 2, level 3, respectively. Hence, the inner product of factor 1 and factor 4 would be

(( -1 - 1) + ( -1 0 ) + ( -1 1)) + (( 0 1) + ( 0 - 1) + ( 0 0 )) + ((1 0 ) + (1 1) + (1 - 1)) = 0 *

*

*

*

*

*

*

*

*

Experiment

Factor 1

Factor 2

Factor 3

Factor 4

y

1

Level 1 (−1)

Level 1 (−1)

Level 1 (−1)

Level 1 (−1)

y1

2

Level 1 (−1)

Level 2 (0)

Level 2 (0)

Level 2 (0)

y2

3

Level 1 (−1)

Level 3 (+1)

Level 3 (+1)

Level 3 (+1)

y3

4

Level 2 (0)

Level 1 (−1)

Level 2 (0)

Level 3 (+1)

y4

5

Level 2 (0)

Level 2 (0)

Level 3 (+1)

Level 1 (−1)

y5

6

Level 2 (0)

Level 3 (+1)

Level 1 (−1)

Level 2 (0)

y6

7

Level 3 (+1)

Level 1 (−1)

Level 3 (+1)

Level 2 (0)

y7

8

Level 3 (+1)

Level 2 (0)

Level 1 (−1)

Level 3 (+1)

y8

9

Level 3 (+1)

Level 3 (+1)

Level 2 (0)

Level 1 (−1)

y9

Optimization of Extraction Using Mathematical Models  Chapter | 3  93

TABLE 3.6  Layout of L9 Orthogonal Arrays

94  Computational Phytochemistry

3.2.2.2  Optimization Phase Experimental design is applied during optimization of various factors for the development of several analytical strategies encompassing liquid extraction, sample digestion, and chromatographic methods. Here a brief explanation of the different strategies related to modern extraction technique of botanicals that have been subjected to experimental design will be reviewed in particular. A detailed study of the various factors and outcomes involved in the optimization process is also presented. In connection to this, it has been observed that the number of research papers referenced by Science Direct with search term ‘extraction’, ‘optimization’ and ‘response surface methodology’ have seen an increasing trend in the past decade (Fig. 3.7). There have been numerous articles published on application of experimental design with novel extraction technologies of botanicals as depicted in the following Figs. 3.8–3.11 given below. In optimization phase, the most significant factor (s) obtained from screening or from previous experience is/are examined extensively to determine the optimum condition. In any extraction process, many extraction factors and their interactions are known to affect the final outcome of the process or reaction. When this is expected, a special type of optimization technique referred as response surface methodology (RSM) is an effective tool for the optimization process. In addition, RSM has been successfully applied to various optimization procedures in the extraction process and in drug research. In RSM, the approximate relationship between response and multifactor is modelled as a polynomial equation obtained by regression analysis. The equation is called a response surface and is graphically represented as a contour map for analysing the desired response or result. Number of papers published using search term Extraction, Optimization and Response Surface Methodology since 2000-2017 2500

1959

2000

No of papers

1563 1400

1500

1491

1277 1034 910

1000

500

284 196 223 239 0

427 346 398

517

620 672

774

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Year

FIG. 3.7  Number of research papers referenced by science direct with search term ‘extraction’, ‘optimization’ and ‘response surface methodology’ from 2000 to 2017.

Optimization of Extraction Using Mathematical Models  Chapter | 3  95

Number of papers published using search term Microwave assisted extraction and Response Surface Methodology since 2000-2017 400 350

334 296

No of papers

300

275

250

209

219

200

143

150 100 50 0

49

52

58

73 52

88 66

96

158

111 92

64

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Year

FIG. 3.8  Number of research papers referenced by science direct with search term ‘microwaveassisted extraction’, and ‘response surface methodology’ from 2000 to 2017.

Number of papers published using search term Ultrasound assisted extraction and Response Surface Methodology since 2000 - 2017 350 323 303

300

282

250

No of papers

212 200

188 147

150 123

75 50 23 0

105

94

100

35

46

60

74

81

86

34

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Year

FIG. 3.9  Number of research papers referenced by science direct with search term ‘ultrasoundassisted extraction’, and ‘response surface methodology’ from 2000 to 2017.

96  Computational Phytochemistry

Number of papers published using search term Supercritical fluid assisted extraction and Response Surface Methodology since 2000 - 2017 350

323 303

300

282

No of papers

250 212 188

200 147

150

123 94

100 50 0

105

75 23

35

46

74

60

86

81

34

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Year

FIG. 3.10  Number of research papers referenced by science direct with search term ‘supercritical fluid-assisted extraction’, and ‘response surface methodology’ from 2000 to 2017.

Number of papers published using search term Accelerated solvent extraction and Response Surface Methodology since 2000 - 2017 434

450 400

377 341

350

No of papers

400

312

300 243

250 202

200 150 100

67

71

85

93

108

145

131

166

167

174

98

50 0

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Year

FIG. 3.11  Number of research papers referenced by science direct with search term ‘accelerated solvent extraction’, and ‘response surface methodology’ from 2000 to 2017.

Terminologies We Need to Know The following nine terminologies are associated with optimization phase and need to be clearly understood. 1. Experimental design: A statistical technique encompassing planning, analysing, conducting, and interpreting data obtained from experiments. 2. Response: Outcome of an experiment, which needs to be quantified or observed. Examples: Yield of the targeted analyte, retention time, etc.

Optimization of Extraction Using Mathematical Models  Chapter | 3  97

3. Factor/parameter/predictor: An entity, which controls an outcome. These are inputs that the experimenter manipulates to cause the output to change conditionally. They can be set and reset at different levels depending on the needs and conditions that affect the experiment. 4. Level of a factor: It signifies value of a factor that is prescribed in an experimental design. Designs are named by the number of levels chosen for a factor, e.g., two-level, three-level design. Examples: extraction temperature: 20°C (low level, −1), 25°C (mid-level, 0), 30°C (high level, +1); extraction time: 1 min (low level, −1), 3 min (mid-level, 0), 5 min (high level, +1), ­microwave power: 20 W (low level, −1), 40 W (mid-level, 0), 60 W (high level, +1). 5. Randomization: While designing and running an experiment, there are several factors in the form of external disturbances (commonly known as noise factors), which may influence the output of the experiment. For example, variations in the quality of the raw material due to seasonal change, variations in the temperature, humidity, and atmospheric pressure and their effects on the overall extraction yield, operator errors, and power fluctuations may influence the final outcome and such factors are difficult to control. Randomization is one of the methods to remove or reduce such errors occurring due to uncontrollable factors. Randomization actually helps in averaging out the effects of the external disturbances if present in the process. 6. Replication: Replication means repetitions of an entire experiment or a portion of it, under more than one operating condition. It helps to obtain an estimate of the experimental errors and to understand and estimate more specifically about the factors and their interaction. 7. Blocking: It is a mode to eliminate the effects of external disturbances and in the process improves the efficiency of experimental design. External disturbances cause batch-to-batch variation, inter-day and intra-day variation, shift-to-shift variation, etc. The primary aim is to arrange similar experiments runs into one group, so that the whole group becomes a homogeneous unit. For example, an experimenter wants to improve the percentage yield of a drug through MAE. Four factors are considered for the initial experiment trials, which might have some impact on the extraction yield. It is decided to study each factor at two-level setting (i.e. a low value and a high value). Eight experimental trials are chosen by the experimenter, but only four trials are possible to run per day. Here, each day can be treated as a separate block. 8. Response surface: Relationship of a response to values of one or more factors is response surface. The surface is usually a plot in two or three dimensions of the function that is fitted to the experimental data. Response surface methodology (RSM) is used to describe the use of experimental designs that give response surfaces from which information about the experimental system is deduced (Skartland et al., 2011).

98  Computational Phytochemistry

9. Model: An equation that communicates between responses with the factors under investigation. Here the outcome can be denoted as a function based on the experimental factors, i.e. y = f ( x ) + e for one parameter ( x ) y = f ( x1 ,x2 ¼ xn ) + e for two parameters ( x1 ,x2 ,x3 ) The function f(x) denotes a good relationship between the factors and the responses (y) with residuals (ε) and is depicted through polynomial equation. Three different models are shown below. Linear model: This is the simplest polynomial model that contains only linear terms and describes only the linear relationships between the factors and the responses. A linear model with two factors x1, x2 are expressed as: k

Y = b0 + åbi X i + e

(3.4)

i =1

or

Y = b0 + b1 x1 + b2 x2 + e where, Y is the outcome, bi the regression coefficients, b0 is model intercept, i is the factor number (1…k), and Xi is the independent factor. Interaction (second order) model: This model contains an additional term that describes interactions between different factors, if any. It is denoted as: k -1

k

k

(3.5) Y = b0 + åbi X i + å å bij X i X j + e i =1 i =1 j = i +1 or Y = b0 + b1 x1 + b2 x2 + b12 x1 x2 + e



b0, bi, bii, and bij are the regression coefficient for intercept, linear, quadratic, and interaction terms, respectively, and Xi, and Xj are extraction factors. Both the linear and second-order models are used for screening studies and robustness tests. Quadratic model: To determine the optimum value, quadratic terms need to be introduced in the model. It helps to identify non-linear relationships between the factors and responses. This model can be represented as below: k

k

i =1

i =1

k -1

k

Y = b0 + åbi X i + åbii Xi 2 + å å bij Xi X j + e or

(3.6)

i =1 j = i +1

Y = b0 + b1 x1 + b2 x 2 + b11 x1 2 + b22 x 2 2 + b12 x1 x 2 + e Effects: This is often regarded as the coefficient of the factors as discussed earlier. Main effect: It denotes the coefficient of the terms in the first order of a factor.

Optimization of Extraction Using Mathematical Models  Chapter | 3  99

Interaction effect: This is the coefficient of the products of linear terms. Quadratic effect: It denotes the coefficient of the square of the linear terms. Sequential Nature of Response Surface Methodology Phase 0: At first, some ideas are generated concerning which factors or parameters are likely to be important in response surface study. It is usually called a screening experiment. The objective of factor screening is to reduce the list of candidate parameters to a relatively few so that subsequent experiments will be more efficient and require fewer runs or tests. The purpose of this phase is the identification of the important independent parameters. Phase 1: Here the objective is to determine the current settings of the factors, which will result in a response value close to the optimum region. If the current settings or levels of the independent parameters are not consistent with optimum performance, then the experimenter must determine a set of adjustments to the process parameters that will move the process towards the optimum. This phase of RSM uses the first-order model without interaction and the technique is called the method of steepest ascent (descent). Phase 2: It begins generally when the process approaches near the optimum. Here at this point, an experimenter wants a model, which will accurately approximate the actual or true response function. As the true response surface usually exhibits curvature near the optimum, a second-order model must be used. These experiments are usually performed within some region of the input factors called the region of interest. Optimization Designs Sometimes simple linear and interaction models are not adequate to provide a vivid picture about the process. For example, suppose that the outputs are product loss or extraction yield, and the goal is to minimize loss and maximize the yield. If these entities are in the interior of the region in which the experiment is to be conducted, we need a mathematical model that can represent curvature so that it has a local optimum. The simplest model is the quadratic model as shown in Eq. (3.6), which contains linear terms for all factors, squared terms for all factors, and products of all pairs of factors. Response surface designs are generally used for fitting quadratic models. One such design is the full factorial design having three levels for each input factors. It is not really an acceptable design in most cases because it has too many runs than that are necessary to fit the model. The central composite designs and Box-Behnken designs are the two most common designs generally used in response surface modeling. In these types of designs, the factors take on three or five distinct levels, but not all combinations of these values appear in the design. Central composite design (CCD): Central composite designs are a special type of response surface designs that can fit a full quadratic model.

100  Computational Phytochemistry

CCD contains an embedded factorial or fractional factorial design with centre points that is augmented with a group of star or axial points. Using the axial points is an efficient way to determine the coefficients of a second-degree polynomial for the variables (Breyfogle, 1992). A CCD can be denoted as a cube having corners, which represents product of the levels [−1, 1], a star or axial points along the axes at or outside the cube (helps to calculate curvature), and a centre point at the origin as shown in Fig. 3.12. Box-Behnken design (BBD): Like the central composite design, the box design is able to adapt to the full quadratic model of the response surface design (Manohar et al., 2013). BBD does not contain any embedded factorial or fractional factor designs like CCD. In this design, the treatment combinations are at the midpoints of the edges of the cube and at the centre as shown in Fig. 3.13. BBD is a rotatable design and needs three levels for each factor. BBD should be considered for experiments with greater than two factors, and when it is anticipated that the optimum is known to lie in the middle of the factor ranges.

Factorial design with center point

Axial points

Central composite design

FIG. 3.12  A graphical representation of central composite design. (+1, +1, +1)

(–1, +1, +1) (–1, +1, –1)

(+1, +1, –1) (0, 0, 0)

(–1, –1, +1)

(+1, –1, +1)

C

(+1, –1, –1)

(–1, –1, –1) A

FIG. 3.13  A graphical representation of Box-Behnken design.

B

Optimization of Extraction Using Mathematical Models  Chapter | 3  101

3.3.  DOE-BASED OPTIMIZATION OF MAE PROCESS Both screening and optimization designs have been applied in MAE of phytochemicals. A concise report on the use of various experimental designs in MAE of phytochemicals is presented in Table 3.7.

3.4.  DOE-BASED OPTIMIZATION OF SUPERCRITICAL FLUID EXTRACTION PROCESS The optimization of the supercritical fluid extraction (SFE) process is a complex process, when compared with other extraction techniques due to factors such as extraction time, pressure, temperature, flow rate, tapping technique, and supercritical fluid composition. In addition to a large number of input factors, each factor may have a significant effect on the extraction efficiency. Therefore, establishing an optimal setting is a very important and time-consuming process. Different types of experimental designs have been used to determine the effect that numerous factors have on the process, including temperature, pressure, pre-treatment of sample, extraction time, fluid flow rate, and addition of modifier. Table 3.8 lists reports of SFE using experimental design for screening and optimization.

3.5.  DOE-BASED OPTIMIZATION OF ACCELERATED SOLVENT EXTRACTION PROCESS One way to improve the extraction rate of bioactive compounds from food matrices is to use accelerated solvent extraction (ASE) (Sarker and Nahar, 2012). The technique uses high pressure, allowing the user to extract at a temperature above the boiling point of the solvent. This increases the solubility and mass transfer rate of the analyte, resulting in a better recovery of the target compound than conventional solid-liquid extraction techniques. The high temperature used in ASE also reduces the viscosity and surface tension of the solvent. This means that it is easier to enter into the sample matrix area, eventually improving the extraction rate. In this way, ASE uses a combination of high temperatures and pressures to provide a faster extraction process that requires a small amount of solvent. ASE typically requires a smaller amount of organic solvent than conventional methods and can therefore be considered a green extraction technique. So far, ASE has been primarily used at the analytical level for quantitative recovery of target analytes. For example, ASE has been used to optimize the use of methanol as an organic solvent to extract polyphenols from apple analysis. This technique has shown potential as a green extraction method to obtain crude extracts with useful biological properties. For example, ASE was used to optimize the extraction of antioxidants from microalgae, anthocyanins from dried red grape skin, antioxidants from rosemary, and vitamin E-rich oil was isolated from grape seeds using ASE. Various scientific findings on the use of various experimental designs in ASE of botanicals are listed in Table 3.9.

Analyte

Experimental Design

Factors/Levels

Withanolides from roots of Withania somnifera

Taguchi design with 4 factors

Microwave power (20%, 60%, and100%) Temperature (40°C, 50°C, and 60°C) Time (1, 2, and 4 min) Sieve number (22, 44, and 60)

Puerarin from Radix puerariae

PBD with 8 factors

Solvent: material ratio (20:1–30:1 mL/g) Mean particle size (0.15–0.25 mm) Ultrasound (without-with) Solvent type (ethanol-methanol) Solvent conc. (40%–60%) Microwave power (100–300 W) Extraction time (40–80s) Extraction cycle (1–3)

Polysaccharides from Stigma maydis using microwave energy

PBD with 6 factors

Temperature (30–100 °C) Liquid – solid ratio (20–100 ml/g) Microwave power (300–700 W) Time (5–30 min) Particle size (20−100) Origin of material (siping-nongan)

Lpeol extraction from Ficus racemosa leaves

PBD with 6 factors

Microwave power (20% W of 700—50% W of 700) Irradiation time (1–3 min) Solvent: sample ratio (5:1–15: 1 mL/g) Particle size (20–40 mesh) Methanol conc. (50%–100% v/v) Pre-leaching time (5–10 min)

Screening designs used

102  Computational Phytochemistry

TABLE 3.7  Selected Literature on the Use of Experimental Designs in Microwave-Assisted Extraction of Botanicals (Das et al., 2014)

Triterpenoid extraction from Actinidia deliciosa roots

Ethanol conc. (30%–90%) Extraction time (10–50 min) Liquid–solid ratio (5–25 mL/g) Microwave power (200–600 W)

Method

Analyte

Designs

Phenolics from pomegranate peel

Phenolic compounds

CCD

Phenolics from broccoli

Total phenolics

CCD

Extraction from milk thistle seeds

Silymarin

CCD

Extraction from ginseng

Saponin

CCD

Color pigments from Rubiaceae plants

Alizarin, Purpurin

CCD

Polysaccharides from Catathelasma ventricosum fruiting

Polysaccharides

BBD

Phenolics from hawthorn fruit

Polyphenols

BBD

Extraction from Capsicum frutescens L.

Capsaicin

BBD

Phenolics from apple pomace

Polyphenols

BBD

Optimization design used

Optimization of Extraction Using Mathematical Models  Chapter | 3  103

FFD with 4 factors

104  Computational Phytochemistry

TABLE 3.8  Selected Literature Instances on the Use of Various Experimental Designs in Supercritical Fluid Extraction of Botanicals (Das et al., 2014) Method

Analyte

Designs (Factors/Level)

Taguchi design

Pressure (bar) (150–250) Temperature (°C) (40–60) CO2 Flowrate (g/min) (10−20)

Extraction from the flower of borage (Borago officinalis L.)

Fatty acids and essential oils

CCD

Extraction from Ginkgo biloba L. leaves

Ginkgo biloba extraction yield

BBD

Extraction from Artemisia annua L.

Artemisinin

CCD

Extraction from Brassica napus L.

Rapeseed Oil

BBD

Extraction from Maydis stigma

Flavonoids

BBD

Extraction from Herba moslae

Essential Oil

BBD

Extraction from Spirulina platensis

Antioxidant profiling

BBD

Extraction from Asian pear

Arbutin

BBD

Extraction from Apricot pomace

β-carotene

CCD

Extraction from Lepidium apetalum

Seed oil

CCD

Screening design used Extraction from Nigella sativa seeds and its bioactive compound, thymoquinone Optimization design used

3.6. CONCLUSIONS The DoE approach provides an effective experimental strategy towards obtaining bioactive substances in industrial-scale and promotes scientific exploitation of potent bioactives. This strategy helps to conduct experiments with reduced number of trials without losing vital system information with added advantages of saving time and power consumption apart from evaluating the important interactions between multiple parameters involved. It also helps to perform

Method

Analyte

Designs (Factors/Level)

Oleuropein content

PBD

Extraction from jabuticaba skins

Phenolic compounds

FFD

Extraction from olive leaves

Oleuropein content

CCD

Extraction from Fructus Schisandrae

Schizandrin, schisandrol B, deoxyschizandrin and schisandrin B

BBD

Extraction from Rosemary, Marjoram, and Oregano

Antioxidant compounds

CCD

Extraction from Piper gaudichaudianum Kunth leaves

Nerolidol, palmitic acid, phytol, stearic acid, squalene, vitamin E, stigmasterol and β-sitosterol

FFD

Extraction from Cynanchumbungei

4-Hydroxyacetophenone, baishouwubenzophenone, and 2,4-dihydroxyacetophenone

BBD

Extraction from potato peel

Caffeic acid content

BBD

Extraction from lemongrass

Oleoresin

CCD

Screening design used Extraction from olive leaves Optimization design used

Optimization of Extraction Using Mathematical Models  Chapter | 3  105

TABLE 3.9  Selected Literature Instances on the Use of Experimental Designs in ASE of Botanicals (Das et al., 2014)

106  Computational Phytochemistry

e­ xperiments with less number of trials without losing important information, with additional advantages of saving time and power, apart from assessing the important interactions between multiple factors involved. This concept not only reduces development and manufacturing cycle times, but also the costs incurred during the extraction process as well.

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