Extraction of Protodioscin from Tribulus terrestris-Optimisation of Kinetics and Modeling

The aim of the present study was to establish the optimal conditions for protodioscin extraction from Tribulus terrestris plant and to investigate the possibilities of mathematical modeling of the process and calculation of the diffusion coefficients essential for the industrial scale-up and management of the extraction process. The kinetics of protodioscin extraction from Tribulus terrestris was experimentally studied at varying the solvent type (70% and 96% ethanol) and temperature (20°C, 30°C, 40°C). The optimal process conditions for these parameters were determined. The experimental results were mathematically modelled. Numerical solutions of the propsed in the study empirical model with constant and variable effective diffusivity in the solid phase, Deff, were obtained. The empirical model was based on comparative analyses with the Regular regime model solutions. It was established that the experimental data complied satisfactorily with the the resulting numerical solutions.


Introduction
T. terrestris is a well-patronized medicinal herb used individually as a single therapeutic agent, as a prime or subordinate component of many pharmaceutically active formulations and food supplements [1,2]. Тhe plant is found in compact fields in Bulgaria, Southern Europe and Central Asia. The whole herbaceous part contains saponins (triline, dioscin, grascillin, protodioscin, methylprotribescine, kukubasoponin) [3], flavonoids (rutin, astragaline, quercetin, kempferol, israminetin), sterols (sitosterol, campsterol), tannins, fatty oils and potassium salts [4]. It is found that in Bulgaria the content of furostanol saponins in the plant is 4 to 5 times higher as compared to that in plants from regions in China and India (Table 1), which except for protodioscin contain also protogracillin. According to a number of studies, spirostanol saponins accumulate mainly in the fruits, while furostanol -in the leaves [5][6][7]. Protodioscin is one of the most widely investigated furostanol saponins, which is believed to be metabolized in the human organism to dihydroepiandrosterone (DHEA) -the precursor of sex hormones. T. terrestris has been explored exhaustively for its phytochemical and pharmacological activities such as diuretic, aphrodisiac, antiurolithic, immunomodulatory, antihypertensive, antihyperlipidemic, antidiabetic, hepatoprotective, anticancer, anthelmintic, antibacterial [10], analgesic, and antiinflammatory [2,11,12]. A study revealed that the di-p-coumaroylquinic acid derivatives extracted from aerial parts of Tribulus terrestris L. possess potent antioxidant activity, thus they were considered as the major constituents contributing to the antioxidant effect of the plant [13].
The extraction process is dependent on a number of variables which can impact the extraction parameters and the yield. Therefore, a specific mathematical method, which can take into account the effect of every single variable on the overall process efficiency, is necessary [7,18]. Response surface methodology is a statistical approach, which has been widely established to improve the extraction process with a minimal input of experimental data. With its the help the influence of various conditions on the extraction procedure can be simulated, both individually and through their cumulative interactions, thereby giving dry lab values for optimization of wet lab procedures [18,19]. One of the commonly used empirical models was the Peleg's one for the description of moisture sorption curve which could be adopted during extraction processes [20][21][22]. A number of factors such as solvent composition, extraction time, solid-to-liquid ratio, pH, temperature, and particle size, might significantly influence the solid-liquid extraction processes [23]. The model trait is that it has only one adaptation parameter -the diffusion coefficient of the solute in the plant material, which depends on the solvent and plant material properties. Satisfactory agreement between the model results and the experimental data of the extraction of hydrophobic diterpene acids from sage leaves and hydrophilic flavonoids from common knotgrass herb was established [14].
The solid-liquid extraction of biologically-active substances from raw plant materials is almost ever limited by the mass transfer resistance inside the solid phase pores. The major factors that influence the rate of the diffusion process are quantitively expressed by the effective diffusivity and are represented in a concealed way by the experimental kinetics curve [24][25][26]. The Film theory model is able to describe the microwave-assisted extraction kinetics of flavonoid compounds from cocoa leaves under the effects of various operating parameters. Higher microwave heating power enhanced diffusivity, while greater solvent quantity to the feed ratio ensured lower mass transfer resistance and lead to improved equilibrium yield [27]. The combination of the experimental and process analytical data is used for the calculation of Deff using the methods of Standard function and Regular regime [28]. Recently, empirical models are widely preferred; however thermodynamics explanations have scarcely been presented. The base of its creation is the numerical analysis of the experimental data, their accurate description and simultaneous modelling of all studied extraction process parameters.
The aim of the present study was to establish the optimal conditions for protodioscin extraction from Tribulus terrestris plant and to investigate the possibilities of mathematical modeling of the process and calculation of the diffusion coefficients, essential for the industrial scale-up and management of the extraction process.

Materials and reagents
Tribulus terrestris was collected from compact deposits in Southern Bulgaria in 2017. The entire aboveground part (Herba) was used in the present study. Prior to extraction the plant material was dried in a thin-layer in an oven at temperature within the range T = 35-40°C. The physicochemical properties The standard pure substance protodioscin (P) (C51H84O22, CAS 55056-80-9, > 98%) was purchased from ChromaDex, USA. Acetonitrile (HPLC, 99.8%) and ethanol (HPLC, > 99.8%) were supplied by Sigma Aldrich.

Extraction design and conditions
Kinetics experiments of periodic extraction of Tribulus terrestris in a batch reactor were conducted. A number of experimental series were carried out at: solid/liquid ratio ξ = 0.02 m 3 kg -1 , temperature: 20°C, 30°C, 40°C and solvent concentrations: 70% and 96% ethanol. The agitation rate was n = 5 s -1 , at which the process is limited by internal diffusion (the external diffusion resistance is eliminated).

HPLC method for protodioscin analysis
Saponins are difficult to be isolated because of the accompanying organic and inorganic substances. In the present work, an HPLC method with ELSD (electronic light scattering) detector and protodioscin as a standard substance was applied. The chemical structure of the organic compound is presented in Figure 1.

Extraction Modelling
The calculation of Deff by non-stationary mass transfer was accomplished by two mathematical conceptsthe Regular regime and Standard function models, which were applied in the comparative estimation of the compliance between the analytical/numerical data for solid phase for the three "classical" shapes and the experimental results ( Table 3).
The methods applied are based on the analysis of the kinetics behavior of the studied system during the process of periodical solid-liquid extraction.

Results and discussions
The modeling of the experimental results was performed using the MatLAB 7.0 software environment. Appropriate functions for solving the mathematical model with constant and variable effective diffusion coefficient in the solid phase were developed.

Determination of Deff
The values of the constant effective diffusion coefficient, obtained by the Standard function method, at various working conditions are presented in Table 4.  A comparison between the Deff values obtained by both methods for the three working temperatures is graphically presented in Figure 3.  Figure 3 shows that the values obtained by the two methods are of the same order. In addition, the values obtained by the Standard function method can be considered as an average of these obtained by the Regular mode method. This is an indication of the accuracy of the obtained results.

Approximation of Deff
The numerical solutions of the model are obtained by discretization of the partial differential equation (1) and the boundary conditions. If the Standard function method is used (Deff = const.), the Deff value is applied directly to the model numeric scheme. If the Regular regime method, Deff ≠ const., is applied, then the number of the variable Deff values has to correspond to the number of the sampling points for discretization of the defined numerical network. The calculated Deff values presented in Table 5 are obtained on the basis of the experimental data. Thus, their number corresponds to the number of the experimental points, but not to the number of the discretized points of the numerical network. The latter defines the necessity of approximation of the data from Table 5 with an appropriate function, which could later be applied in the numerical scheme of the model. The application of the selected approximation function allows the calculation of the value of Deff for any point in the numerical network. Thus, the values of the effective diffusivity, obtained by the Regular regime model (Table 5), have to be approximated. Therefore, these values are hereinafter referred to as "experimental", on the basis of which non-linear regression was performed. As the effective diffusion coefficient depends on the a seven-parameter model and its parameters a, b, d, f, m, n and p can be calculated via multidimensional nonlinear regression of the Deff values obtained by the Regular regime method for all process conditions.
In the present study all experiments were carried out at a steady solid/liquid ratio ξ = 0.02 kg/m 3 . Thus, the effect of ξ was excluded and eq. (12) was reduced to a three-dimensional model, considering the influence of the concentration of the two-component mixed solvent, temperature and time on the Deff values change. In this respect, eq. (12) was transformed as follows: Equation (13) is also a seven-parameter one, but it does not include the modification of the solid/liquid ratio. To determine the parameters of this equation, multidimensional non-linear regression of the data for Deff in Table 5 has to be conducted. The regression analyses were performed by the inlinfit function of the Matlab program environment. The results obtained are presented in Table 6. Table 6. Values of the parameters in eq. (13) The values of Deff at various temperatures (Table 5) and their approximation by eq. (13) are graphically presented in Figure 4. The comparative analyses of the model and experimental curves in Figure 4 established significant compliance between the experimental results and model data, which is an indication that eq. (13) is suitable for approximation of the results obtained by the Regular regime method.

Numerical solutions of the mathematical model
The numerical solutions and experimental points of protodioscin extraction at 30 o C with different solvents are presented in Figure 5 as plots of c1 vs. time, τ.  (Table 5). Based on these data, it could be concluded that the results obtained at Deff ≠ const. described more precisely the experimental points. Analogous results were obtained for the mathematical modeling of the experimental series at all the other cited working conditions. Therefore, the concept of applying variable effective diffusivity for the performance of the numerical solution at the studied operating conditions was adopted. Figure 6 presents the experimental points and model data for protodisocin extraction with 70% and 96% EtOH solutions as solvents. Evidently, in both cases, satisfactory conformity between the experimental results and model data was established. However, the application of 70% EtOH as a solvent was more favourable due to the achievement of significantly higher yield of the target componentprotodioscin, .
The effect of temperature on the kinetics behavior of the studied system with 70% EtOH is presented in Figure 7.

Conclusions
The kinetics of protodioscine extraction from Tribulus terrestris with 70% and 96% EtOH as solvent at T 20°C, 30°C and 40°C was studied. The extraction of the target compound with 70% EtOH was more favourable due to the significantly higher yield achieved. Due to the molecular protodioscine structure, the presence of water in the extractant significantly increased the rate of extraction. A direct relationship between the temperature increase and the efficiency of the target compound extraction, at identical other operating conditions, was determined. The latter is explained by mass transfer intensification at higher temperature due to increased solubility of the target components in the solvent. On the other hand, the free flow of molecules in the liquid phase also increased, which facilitates the interaction between the solvent and the solid phase. However, extraction at high temperature is not always possible. Most valuable natural components are unstable at temperatures above 40-50°C, as they lose their bioactive properties. In addition, the increase in the process temperature is always associated with the use of extra energy, which makes production more expensive. The obtained experimental results show that the differences between the equilibrium concentrations of protodioscin at T 30 and 40℃ were very low. Consequently, at both temperatures at the end of the process, the amount of protodioscin extracted was almost the same. In this respect, extraction at 30℃ was proved as economically more advantageous.
The results obtained and the conclusions derived are indicative that the proposed empirical equation (2) is appropriate for the approximation of the experimental results of protodioscin extraction from Tribulus terrestris.