Optimization of extraction conditions for polyphenols from the stem bark of Funtumia elastica (Funtum) utilizing response surface methodology

Background: The recovery of phenolic compounds is seen as an arduous task because phenolic compounds are available as free aglycones, as sugar or ester conjugates, or as polymers with several monomeric components. Furthermore, phenolic compounds do not disperse evenly and may be connected to cell walls, carbohydrates, or proteins. This study looks at the optimization of factors that affect the efficiency for the extraction of phenolic compounds from the stem-bark of Funtumia elastica. Methods: Five independent variables (solvent concentration, time, the temperature, solid-liquid ratio, and pH) of the extraction process were selected. Single factor analysis as well as the response surface method was used to evaluate the impact of the selected factors on the total phenolic content. The effect of the extraction factors on the phenolic content was statistically significant (p <0.05). For the response surface method, a five/factor, five/level central composite design used, and a fitted second-order polynomial regression model equation was used to show how the extraction parameters affected the total phenolic recovery. Results: The predicted value (R² of 0.5917) agreed with the adjusted value (R² of 0.7707). The residuals for response predictions were less than 5%. The optimal factors for the extraction were ethanol concentration of 75.99% v/v, extraction time of 193.86 minutes, temperature of 63.66°C, pH of 5.62, and solid-liquid ratio of 1:21.12 g/mL. Actual overall content of the phenolic compounds was validated at 82.83 ± 3.335 mg gallic acid equivalent (GAE) /g weight of extract, which agreed with the predicted response of 89.467 mg GAE/g of the dried extract under the optimal factors. Conclusions: The rich phenolic content of stem-bark of Funtumia elastica points to its potential as a functional medicinal product to alleviate diseases caused by oxidative stress such as asthma, breathing disorders, inflammation, and cardiovascular diseases.


Introduction
Phenolic compounds are naturally produced in plants for UV radiation protection, attracting pollinators and preventing microbial infections, etc. 1 . These compounds act as natural antioxidants and are directly involved in lipid peroxidation and anti-carcinogenesis. The existence of diverse polyphenols acting as antioxidants facilitates the entrapment of free radicals spawned from various metabolic processes, thereby inhibiting the initiation of any cancerous cells 2 . They also exhibit anti-inflammatory, antimicrobial, cardio-protective, and antiaging activities 3,4 . Several reports have indicated a strong positive correlation between the total phenolic content (TPC) and the antioxidant activity of dietary and medicinal plants 5,6 .
Phenolic compounds from Funtumia elastica could be obtained using various conventional extraction methods-solid-liquid extraction by maceration, decoction, stirring, shaking 7-9 , using ethanol and water as their main solvents 10,11 . Other modern methods include microwave-assisted, ultrasonic 12 , soxhlet, heat reflux 11 , and ultrahigh-pressure 13 extractions. Despite the advantages of these modern extraction techniques, they are expensive to operate and ultrasound energy greater than 20kHz during ultrasound-assisted extraction may damage active phytochemicals 14 . Moreover, thermal degradation and oxidation of compounds 15 are found in microwave-assisted extraction on account of the additional cycles of extraction and the fact that it is limited to small phenolic molecules 14 .
Maceration is an easy and inexpensive extraction technique that utilizes simple equipment 16 . Skilled operation is not needed compared to other modern techniques, and it ensures energy economy. This method is suitable and ideal for less soluble substances that require a prolonged interaction with the extraction solvent. Polyphenols are usually extracted using ethanol, methanol, or ethyl acetate as solvents 17 . Ethanol with water is also widely used for extracting phenolics 18 and are commonly used by indigenous societies as their main solvents. During the maceration process, the efficiency of the extraction is attributed to numerous independent variables, such as the type of solvent, solvent concentration, temperature, pH, time of extraction, and the solid-liquid ratio 19 . There is an interaction between these variables, which affects the efficiency of the extraction 20 .
According to the one-factor-per-time (OFAT) method, all variables except one are kept constant at any point in time during the process 21 . However, this technique is often met with numerous obstacles including: requiring a huge number of experimental runs; proving to be inefficient and unreliable in giving optimal factors; and the inability to study the interactions between the factors or factors affecting the process or product 22 .
It is therefore imperative to assess the interaction between the independent variables. One of the appropriate techniques is to use the response surface method (RSM) as a tool to optimize the factors that affect extraction efficacy as well as to obtain maximum recovery of the compounds of interest [23][24][25] . The central-composite-design (CCD) of the response-surface-method is known to be useful for the optimization of extraction parameters of bioactive compounds 26 .
The purpose of the study was to evaluate the effects of the investigated factors (ethanol concentration, extraction time, extraction temperature, solvent pH, and solid-liquid ratio) on the TPC of the hydroethanolic extract of stem bark of Funtumia elastica (Preuss) Stapf, a proven medicinal plant, and to optimize the extraction factors of the polyphenols further using CCD.

Plant materials used
The stem barks of F. elastica from the tropical rain forest in the Asante Akim Municipality were collected by scraping them from intact mature trees. They were authenticated by a botanist at the Department of Herbal Medicine, KNUST. The samples were cleaned, chopped into pieces, and dried on plastic sheets under shade. The dried samples were milled using a pulverizer mill and kept in zip-locked bags and stored in the fridge at 4 o C.

Reagents
All chemicals and reagents used were of analytical grade. Folin-Ciocalteu, gallic acid, ethanol, and sodium carbonate were all obtained from Sigma-Aldrich.

Maceration extraction
From the dry powdered sample, 10.00 g was extracted with a hydroethanolic solution in 250 to 500 mL screw-capped Erlenmeyer conical flasks. The extraction was conducted using a temperature-controlled water bath (Grant JBN12, Grant Instruments Ltd, Cambridge, UK). The extraction conditions were set according to the experimental design. All the extractions were carried out in replicates.

Determination of TPC
The TPC of the plant extracts was measured spectrophotometrically using the Folin-Ciocalteu method previously reported 27 . Briefly, an amount of 0.5 mL of each solution of the different extracts (500-1000 µg/mL) was measured into test tubes, and 2.5 mL of Folin-Ciocalteu reagent added to each. 2 mL of aqueous sodium carbonate solution (75 mg/mL) was added to each and kept on a water bath at 50°C for 10 mins. The absorbance was read at 760 nm using a microplate reader (Synergy H1 TM Microplate Spectrophotometer, Thermo Fisher Scientific, Osaka, Japan). The gallic acid solutions were taken through the same procedure and used to plot a calibration curve of absorbance against log concentration (µg/mL). The total phenolic content was expressed as mg gallic acid equivalent (GAE) per gram of extract.

Experimental design
The experimental procedure of the study was group into two parts; a single-factor analysis and optimization using RSM. To determine a suitable range of  factors, single-factor analysis was conducted using solvent  concentration (20, 40, 60, 80 and 96% v/v), time for extraction (60, 120, 180, 240, and 300 minutes), extraction temperature (25, 35, 45, 55, and 65°C), pH (2.5, 5.5, 7, 9, and 12), and solid-liquid ratio (1:10, 1:20, 1:30, 1:40, and 1:50 g/mL). One independent variable was varied according to the set range whilst keeping the others constant. Based on the results obtained, all the five independent variables had significant influence on the extraction efficiency and were subsequently selected for the RSM design.

RSM.
This study deployed a five-factor, five-level CCD model (-2.378, -1, 0, +1, +2.378) to examine the optimum conditions for the dependent variable or response; total polyphenolic content maximization. The design comprised 50 randomized runs with 32 factorial points, 10 axial points, and eight replicates as the center points. The center points were repeated eight times to ascertain the statistical parameters of the proposed models. The five independent variables with their related actual and coded values are shown in Table 1. The range of each level were ethanol concentration (46.22 -93.78% (v/v), temperature (45 -65°C), time (138.65 -281.35 minutes), pH (3.10 -11.41) and solid-liquid ratio (1:13.11 -1:36.89 w/ v). The data from the experiment were analyzed by multiple regression fitted to the following second-order polynomial equation: where X i and X j represent the independent variables. β o , β i , β ii and β ij (i≠j) represent the coefficient of regression for the intercept (constant), linear, quadratic, and interaction terms, respectively. Design-Expert Software 11.0.0 (Stat-Ease, Minneapolis, MN, USA) was used to build the model, calculate the predicted values, and plot the three-dimensional graphs. Other tools such as Scilab, OpenDino and JMP statistical software could also be used.
Validation of the optimized model For validation of the optimized extraction parameters, six different experimental setups were employed for a trial extraction process. The average results (value) obtained from the trial extraction was compared with the predicted values.

Statistical analysis
The significance of the model and equation terms was investigated by determining the analysis of variance (ANOVA) with a 95% confidence interval. The statistical parameters; the sum of squares (SS), degrees of freedom (df), mean squares (MS), p-values, and F-values were employed. The model terms were deemed statistically significant if p <0.05. The quality of the regression model was shown using the coefficient of determination (R 2 ). To express the quality of the regression model, the R 2 , adjusted correlation coefficient (Adj-R 2 ), predicted correlation coefficient (Pred-R 2 ), and the significance of the model were tested using F-test.
In this study, all the experiments were performed in triplicate, and the results were expressed as mean value ± standard deviation (SD). The statistical analysis was carried out using Excel 2019 (Microsoft, Redmond, WA, USA) and Design-Expert version 11.0.0. Other tools such as Scilab, OpenDino and JMP statistical software could also be used. Multiple comparisons were carried out by ANOVA plus the posthoc Tukey test. p <0.05 was defined as statistical significance.

Results and discussion
Effect of single factor analysis of the TPC The impact of ethanol concentration, extraction time, temperature, solid-liquid ratio, and pH on the TPC from F. elastica stem bark is shown in Figure 1a-e.

Effect of the ethanol concentration.
The effect of the concentration of ethanol, ranging from 20% to 96% v/v, on the TPC is illustrated in Figure 1a. The extraction was conducted at a solid-liquid ratio of 1:20, temperature of 35°C, time of 180 mins, and extraction pH of 7.00. The recovery increased with an increased ethanol concentration and reached a maximum at 60% ethanol (79.062 ± 0.691 mg GAE/g of dried extract, p <0.05) until it showed a declining tendency from 60 to 96% v/v 28 . As a result, a range of 60-80% v/v was chosen for the optimization experiment.
An ethanol:water mixture was used as the solvent for this study. Compared with other solvents, ethanol is a relatively Effect of extraction time. The effects of the different extraction times on TPC of the extract was investigated in the range of 60 to 300 minutes. The other independent variables that were kept constant were the maximum 60% ethanol concentration from the first analysis, 35°C temperature, pH of 7, and a solid-liquid ratio of 1:20 g/mL. The impact of different extraction times on the TPC was seen in Figure 1b, which shows an increase in the TPC as the extraction time increased to 240 minutes. The maximum TPC recovery was observed at 240 minutes as 67.219 ± 0.642 mg GAE/g of dried extract for F. elastica. There was, however, a decline in TPC from 240 to 300 minutes. Thus, a range of 180 to 240 minutes was chosen for the optimization process. Glycine max L. TPC gradually increased from 5.4 to 12.8mg GAE/g of dried extract as the time increased from 15 to 60 minutes. However, from 60 to 150 minutes, the TPC remained unchanged at around 12.7 mg GAE/g of dried extract. 35 . Fick's second law of diffusion could explain this phenomenon by stating that an equilibrium was established between the solute and the extraction solvent 36 . As a result, when the time was prolonged, it did not significantly impact the TPC extraction 35 . One of the essential independent variables in solid-liquid extraction is time due to its impact on the analyte's solubility and mass transfer which is associated with the compound's structure and molecular weight. Prolonged extraction time may lead to oxidation, epimerization, and degradation of the metabolites of interest 37 . This was observed in our study, as shown in Figure 1b.
Effect of extraction temperature. The influence of the extraction temperature on TPC recovery is shown in Figure 1c. A significant (p <0.05) impact on the phenolic content of the extract was observed when varying the temperature from 25°C, 35°C, 45°C, 55°C, 65°C while keeping the other independent factors constant, with the solid:liquid ratio at 1:20 g/mL, ethanol concentration at 60%, extraction time at 240 minutes based on the previous study and pH at 7.00. The highest peak was seen at 45°C for F. elastica (85.84± 2.16 mg GAE/g of dried extract), and the TPC started to decline when the temperature was further increased. Consequently, a temperature range of 45-65°C was chosen for the optimization study.
An increase in temperature significantly increases the mass diffusivity 38 , which increases the rate at which the solute diffuses into the solvent.
In addition, other reports 39 emphasize that high extraction temperatures increase the mass transport of phenolic compounds and even reduce solvent viscosity and surface tension, thereby promoting phenolic compound extraction. The heating may, in turn, soften plant tissues, which weakens the phenol-polysaccharide and other phenol interactions and foster the migration or leaching of phytochemicals like flavonols into the solvent 40  Theoretically, the solid-liquid ratio significantly affects the extraction kinetics of the bioactive compounds due to its effect on the concentration gradient between the solute and the solvent at the surface of the raw material 47 . Many authors have reported a strong positive correlation between the TPC and solid-liquid ratio. A study conducted varied the solid-liquid ratio from 1:04 to 1:10 and observed a gradual increase in TPC from 1:04 to 1:06 but achieved equilibrium beyond 1:06 to 1:10 35 . This could be explained by an increase in concentration gradient as more solvent is added. However, the addition of ethanol will stop promoting TPC yield when the content of polyphenols in the material is depleted 35 .
Wang et al. (2020) also demonstrated the influence of solid-liquid ratio on the yield of the polysaccharides from Bletilla ochracea Schltr. The yield was improved when the solid-liquid ratio (1:10-1:30 g/mL) was increased and the optimum value for 1:30 g/mL was reached when temperature and time were set to 80°C min. and 90 minutes. The yield, however, showed a decreasing tendency between 1:30-1:50 g/mL 48 .
Another author determined the factors influencing the extraction of polyphenols from olive leaves. Three solid-liquid ratios (1:20 g/mL, 1:25 g/mL and 1:30 g/mL) were considered. The results of the study showed that the solid-liquid ratio affected the overall phenol levels significantly. The higher solvent-to-solid ratio (1:30 g/mL) achieved the highest TPC (24.5 mg caffeic acid/g of dry matter) 32 .
In general, a higher solid-liquid ratio could cause a greater concentration difference, which will in turn increase the diffusion of components into solvents and accelerate mass transfer 49 .
Effect of extraction pH. The influence of pH, which ranged from 2.5 to 12, was evaluated using a 60% ethanol solution, a solid-liquid ratio of 1:20 and temperature of 45 o C, and time for extraction was 240 minutes, as shown in Figure 1e. The TPC of F. elastica peaked at a pH of 7.00 (110.119 ± 0.200 mg GAE/g of dried extract, p <0.05). There was a decline in TPC as the pH increased from 9.00 to 12.00. The decrease could be due to the degradation of the phenolics or lower extraction under basic conditions. The TPC of Ocimum sanctum methanolic leaf extract was investigated under different pH conditions, and the highest TPC was observed at a pH of 7.20 50 . Our results were consistent with the maximum TPC of 7.20 reported in literature.
The antioxidant capacity and radical scavenging ability of many phenolic compounds are based on the number and positions of the hydroxyl groups and the methoxy substituents in molecules 51 . Changes in pH, like temperature conditions, can modify the phenolic compounds' chemical structure and thus the antioxidant activity of the compounds.
The antioxidant properties are pH-dependent, as changes in pKa values are consistent with changes in hydroxyl ionization or other functional groups of the phenolic compounds 20 .
Modeling of the total phenolic recovery using RSM-CCD A RSM-CCD with five independent variables and five levels was applied to evaluate the impact of vital extraction variables, including the concentration of ethanol (X 1 ), extraction time (X 2 ), extraction temperature (X 3 ), pH (X 4 ) and solid-liquid ratio (X 5 ), on TPC recovery of F. elastica.
The experimental design, experimental values, and predicted values of the 50 runs are shown in Table 2 for both plants. The TPC value ranged from 2.14821 to 124.391 mg GAE/g of dried extract for F. elastica.
Fitting the model. The data were investigated by multiple regression fitting and second-order quadratic polynomial regression model equations based on the coded values. These were automatically generated by the Design-Expert software. The equations communicate the relationship between the value of the response and the five independent factors, as shown in Table 3. The equation in terms of coded factors can be used to make predictions about the response for given levels of   Factor coding is Coded.

Sum of squares is Type III -Partial.
The F-value of 9.24 implied the model was significant. There was only a 0.01% chance that an F-value this large could occur due to noise. The P-values less than 0.0500 indicated that model terms were significant. In this case, X 2 , X 3 , X 1 X 4 , X 3 X 4 , X 4( ², X 5) ² were significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there were many insignificant model terms (not counting those required to support hierarchy), model reduction might be needed to improve the model. The lower lack of fit F-value of 0.95 implied the lack of fit was not significant relative to the pure error. There was a 57.65% chance that a lack of fit F-value this large could occur due to noise. Non-significant lack of fit demonstrates the model fits. The low lack of fit F-value and the high p-value indicated the reliability of the model that was generated.
Fit statistics. The predicted R) ² of 0.5917 was in reasonable agreement with the adjusted R² of 0.7707; i.e., the difference mathematical model. Furthermore, the residuals for the response predictions are less than 5%. Therefore, a suitable model was suggested for characterizing the effects of extraction conditions for total phenolic recovery of F. elastica based on the results of the model adequacy diagnostic plots.
Optimization of the extraction conditions. The perturbation plot shows the effect of all the factors on a single plot. The perturbation plot (Figure 3) indicates the impact of all the independent factors on the TPC at the center. The response is plotted by changing only one factor over its range while holding all the other factors constant. A variable with a steep slope or curvature indicates the sensitivity of the response to it, and a relatively flat line shows insensitivity to change in that particular factor 55 .
It can be observed that TPC increased as time (B) and temperature (C) were increased, while an increase in ethanol concentration (A) resulted in a decrease in TPC content. The effect of a reduction in solid-liquid ratio on TPC is minimal. By evaluating the slope patterns, it was observed that pH and solid-liquid ratio did not have a linear impact compared was less than 0.2. The adequate precision measured the signal-to-noise ratio. A ratio greater than 4 was deemed desirable, which implied an adequate signal and that the model could be used to navigate the design. The higher the adequate precision the more suitable the model for optimization 52 . In this study, the ratio of 12.620 indicated an adequate signal. This model could therefore be used to navigate the design space (Table 5).
The terms that were not statistically significant were excluded from the second-order polynomial to improve the model's predictability. The coefficients of regression indicated that some of the linear terms had a positive effect on the response ( Table 6). The interaction terms between ethanol concentration and solid-liquid ratio, extraction time and temperature, extraction time and solid-liquid ratio, and pH and solid-liquid ratio had a positive impact on the response. The linear term, temperature, had the biggest effect on the response followed by extraction time and pH.
Diagnostic plots are illustrated in Figure 2a The Cook's distance values are shown in Figure 2b. There were no outliers in the given experimental dataset, which meant that Cook's distances were less than the limit of 1.0. The plot of residuals against predicted values and against the run number is displayed in Figure 2c and d. The data points show unidentifiable patterns in these plots as they randomly fall on both sides of 0. These results specify the independence of the residuals from one another, their random distribution, and constant variance 54 .
The plot of predicted versus actual values shown in Figure 2e presents data points that lie close to the straight line, indicating an adequate agreement between the actual data from the experiment and the predicted data from the  to the other three factors. From the plot, pH has a strong effect on TPC recovery.
Exposure to severe acidic and alkaline conditions could result in oxidation and epimerization of the phenols.

Analysis of the surface plots.
The interaction of two of the five variables and their effect on TPC recovery while the rest of the three variables were kept constant is illustrated in the three-dimensional RSM plot. (Figure 4a-j).
The interactive effect of extraction time and ethanol concentration whilst fixing pH, temperature, and the solid-liquid ratio at a constant level was investigated in Figure 4a. The interaction between temperature and ethanol concentration is depicted in Figure 4b. A similar linear effect is observed concerning temperature and caused an increase in the TPC. A temperature increase utilizing lower ethanol concentrations led to higher TPC values 57 .
In Figure 4c, the interactive effect between pH level and ethanol concentration is displayed in the 3D plots. A similar effect of ethanol concentration on the value of the response was observed. The TPC recovery increased as ethanol concentration ranged between 60-70% v/v. As for the pH, the TPC value gradually increased as the pH was rising. When the pH exceeded 8.2, the TPC value slightly decreased. Thus, the pH had a slight quadratic trend. The highest recovery of 94.182 mg GAE/g of dried extract was recorded at a pH of 8.16 and ethanol concentration of 60% v/v. Roselló-Soto et al.
(2019) described the influence of pH and ethanol concentration on obtaining phenolics from the by-products of tiger nuts via conventional extraction methods using an ethanol: water mixture using RSM. The phenolic content was strongly affected by ethanol concentration (p = 0.0007). However, pH did not show a great influence on the phenolic extraction (p = 0.7961) 58 .
The impact of solid-liquid ratio and ethanol concentration on the TPC is illustrated in the response surface 3D plot in Figure 4d, at a constant pH of 7.25, extraction time of 210 minutes, and temperature of 55°C. The TPC was less affected by the solid-liquid ratio and increased by decreasing the ethanol concentration. The maximum TPC of 91.7257 mg GAE/g of dried extract was observed at 60% ethanol concentration and 1:22.8 g/ml solid-liquid ratio. Gavrilović et al. (2018) reported the interaction between ethanol concentration and solid-liquid ratio as having a major impact on TPC recovery from the leaves of Juglans nigra. According to their results, TPC levels increased accordingly with an ethanol concentration ranging from 0 to 50% v/v, above which a decline in TPC levels was observed. The TPC yield also increased with an increase in solid-liquid ratio. Ethanol concentration and solid-liquid ratio were deemed to be one of the major parameters that affected ultrasound-assisted extraction 59 . Figure 4e illustrates the effect of the interaction between extraction temperature and extraction time on the TPC. Both variables showed a linear effect on the response. At a temperature of 55°C, and a time of 210 minutes, the total phenolic recovery was 88.0548 mg GAE/g of dried extract, and the optimal TPC content of 106.081 mg GAE/g of dried extract occurred at 65°C and 240 minutes. Zulkifli et al. (2020) reported the interaction between the time of extraction and temperature on TPC recovery of Hylocereus polyrhizus seed extract by setting the solvent concentration at 70% v/v. The team observed that TPC recovery efficacy was enhanced as temperature and time were concurrently increased 60 . Kaleem et al. (2019) also investigated the effect of time and temperature on total polyphenolic extraction whilst keeping the solvent concentration fixed at 50% v/v. The TPC of the extract rose with increasing extraction time. However, after some time, the TPC level declined because phenolic compounds exposed to higher temperatures are destroyed over a longer period 61 .
The interaction between extraction time and pH while keeping the other variables fixed is shown in Figure 4f. The increase in extraction time caused a similar influence in increasing the TPC value. The response gradually increased when the pH increased within a certain range. When the pH exceeded about 7.38, the TPC began to decrease slightly. At a pH of 7.38 and time of 239.8 minutes, the TPC was 95.7678 mg GAE/g of dried extract.
In a study by Skrypnik and Novikova (2020), the optimal yield of total phenolics was seen in the midpoint at a pH of 4 and the levels of total phenolic compounds analyzed in the extracts of apple pomace-based non-ionic emulsifiers was increased when time for extraction was increased from 40 minutes to 65 minutes, yet declined gradually when the time period was increased further 20 .
The influence of extraction time and solid-liquid ratio on TPC is also illustrated in the response surface at constant ethanol concentration (70% v/v), extraction temperature (55°C), and pH of 7.25 (Figure 4g). It revealed that the TPC was less affected by the solid-liquid ratio and increased with time when the other factors were kept constant at the center point. The maximum TPC content was found to be 96.6589 mg GAE/g of dried extract at an extraction time of 240 minutes and a solid-liquid ratio of 1:25 g/mL. The relationship between TPC and the interaction between the independent variables i.e., solid-liquid ratio and extraction time, was previously shown by Andres et al. (2020). It was found that the optimal TPC levels occurred within the range of 10-13 g/mL. Time of extraction didn't have significant impact on the TPC 62 .
The impact of temperature and pH on the response whilst keeping other factors fixed at the midpoint is shown in Figure 4h. The temperature has a positive linear effect on the TPC. The TPC gradually increased when the pH increased to a certain extent and when the pH exceeded about 7.20, there was a slight decrement in the TPC value. The optimum TPC recovery of 104.441 mg GAE/g of dried extract was at a temperature of 65°C and pH of 7.20.
An interactive effect between pH and temperature was reported by Roselló-Soto et al. (2019) using RSM. They reported an optimum TPC level at a pH of 7 and a temperature of 37°C at a constant ethanol concentration 58 .
The three-dimensional response surface plot illustration of the interaction between temperature and solid-liquid ratio is shown in Figure 4i. The TPC increased at higher extraction temperatures and was less affected by the change in solid-liquid ratio at constant pH (7.25), time (210 minutes), and ethanol concentration (70% v/v). At a temperature of 57.5°C and solid-liquid ratio of 1:23 g/mL , the TPC was 92.93 mg GAE/g of dried extract, and the optimal TPC of 104.958 mg GAE/g of dried extract occurred at 65°C and a 1:22.6 solid-liquid ratio. The impact of the interactions between solid-liquid ratio and temperature has been investigated by Radojkovic et al. (2013) for optimization of total phenolic yield from mulberry extracts employing RSM. From their 3D plots, the TPC increased with increasing temperature to about 65°C, after which subsequent temperature increase didn't cause any significant change in TPC. The author also observed a significant increase in TPC as solid-liquid ratio was increased, reaching a maximum at about 1: 20 g/mL. Further increase in the solid-liquid ratio did not yield any significant impacts on TPC levels, however. The TPC levels of mulberry extracts varied from 18.63 to 52.43 mg of GAE/g of dried extract 63 .
The responses observed for the effect of the interaction between pH and the solid-liquid ratio at a fixed ethanol concentration of 70% v/v, temperature of 55°C, and time of 210 minutes indicated that solid-liquid ratio has less effect on ensuring maximum TPC (Figure 4j). For example, at a pH of 7.36 and solid-liquid ratio of 1: 23.18, the TPC was 88.463 mg GAE/g of dried extract.
In the optimization of anthocyanin extraction, 3D plots displayed a steeper change in pH in comparison to the solid-liquid ratio, signifying pH has a greater impact, which is consistent with our results 64 .

Determination of optimal conditions and validation of model
For the verification of the model's accuracy for optimal yield prediction, actual experiments were performed using the optimal extraction conditions. The values were very close to the predicted values, which indicated the reliability of the optimization accomplished in the research. The quadratic polynomial regression model that was generated gave the optimal extraction conditions with a desirability of 1.000.
Desirability functional values lie between 0 and 1. The value 0 is ascribed when the variables give an undesirable response, whereas the value 1 parallels the optimal functioning for the studied variable 65,66 . The optimal conditions for extracting total phenols from F. elastica hydroethanolic extracts were as follows; ethanol concentration 75.98% v/v, extraction time of 193.9 minutes, temperature of 63.66°C, pH of 5.63, and solid-liquid ratio of 1:25.12. At these optimal conditions, the TPC was 89.467 mg GAE/g of dried extract (Table 7).
To verify the model's capability to accurately predict the actual value, six replicates of verification experiments were undertaken and the outcome was 82.83 ± 3.335 mg GAE/g of dried extract, which was very close to the predicted value.

Conclusions
The extraction of polyphenols from the most active extract, the ethanolic extract of F. elastica was undertaken in this study. The extraction was performed via maceration, and the relationship between the total phenolic recovery and experimental variables, which included ethanol concentration, extraction time, extraction temperature, solid-liquid ratio, and pH, was considered. A multiple single-factor analysis was performed.  Open Peer Review independent variables constant). The Folin-Ciocalteu reagent was used to determine the total phenolic content extracted. Optimal ranges found for each independent variable were then combined using the central-composite-design of the response surface method (RSM) to determine the best overall extraction conditions (i.e., conditions where each independent variable is optimal). For the verification of the model's accuracy actual experiments were performed using the predicted optimal extraction conditions. The actual values of extracted phenolic compounds were very close to the predicted values, which indicates the reliability of the optimization accomplished in the research. Thus, the conditions reported herein are very useful for extracting phenolic compounds from Funtumia elastica and this study provides a blueprint for designing extraction protocols from other natural sources in the future (for phenolic compounds or otherwise).
Overall, the results are well organized, and the significance of the results are well supported by statistical analysis (F-test, P-values, ANOVA, etc.). The statistical analysis of each independent variable and of the overall extraction conditions adds considerable confidence to the optimization procedure and its results. The authors also provide a thorough analysis of their results, comparing them to previous reports from other groups. This level of critical analysis adds more confidence to the work and in the results obtained from the study.

If applicable, is the statistical analysis and its interpretation appropriate? Yes
Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes areas, for the protection and well being of humans, animals, crops and the environment.
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