Abstract：A mathematical model based on Fick’s first law was established to describe the process of ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii. Acid hydrolization with hydrochloric acid promotes the conversion of arctiin to arctigenin in the arctiin-rich active pharmaceutical ingredient, and the hydrolyzed products were further examined to investigate the process setup. By considering the mechanism of the extraction process and experimental data, the effects of parameters including solvent to solid ratio, particle size of hydrolyzed samples, ethanol volume fraction, ultrasound power, extraction temperature and extraction time on concentration of arctigenin were analyzed in detail. The model was suitable for simulating the process of ultrasonic-assisted extraction of arctigenin. The simulation results of the model agree well with experimental data with the deviation below 13%, indicating that the mathematical model can provide valuable guidance for the extraction of arctigenin from acid hydrolyzed FructusArctii.
Keywords：FructusArctii; acid hydrolysis; ultrasonic-assisted extraction; arctigenin; mathematical model
FructusArctii (Niubangzi in Chinese), the dried fruits ofArctiumlappaL., is one of the most popular traditional medicinal plants in China, which is widely used in Chinese prescriptions to treat inflammation and infection for centuries[1-3]. The major active chemical ingredients in theArctiumlappaL. seeds are lignans and phenolic compounds[4-5]. A number of compounds have been separated and identified from FructusArctii, including arctiin, arctigenin, lappaol, matairesinol and diarctigenin[6]. Arctiin and arctigenin are the major lignan constituents[7-9]. Modern pharmacological studies have revealed that arctiin and arctigenin possess a variety of pharmacological properties and induce a number of important biological activities, such as anti-proliferative[10-11], anti-carcinogenesis[12], and anti-HIV properties[13-15]. So, in the process of chemical standardization of FructusArctii, the inherentarctiin and arctigenin are usually chosen as “marker compounds”[16-17]. However, various studies have been conducted to identify the main active constituent of FructusArctii. These results indicated that arctiin was rapidly transformed to arctigenin in the rat gastrointestinal tract in vivo[18-19], and arctigenin rather than arctiin acted as the major effective ingredient[8,14,20-23]. Therefore, it is necessary to improve the extraction yield of arctigenin fromArctiumlappaL. seeds for food and the pharmaceutical industry. From a literature review in brief, studies on the analysis of FructusArctii extracts revealed that the level of arctiin was significantly higher than that of arctigenin[5, 16-17, 24]. To obtain high amounts of arctigenin,ArctiumlappaL. seeds were hydrolyzed by hydrochloric acid before extraction, which was a simple and efficient way to promote the conversion of arctiin to arctigenin.
The traditional methods used to extract bioactive constitutes from natural materials are heating reflux, soxhlet and solvent extraction. However, these methods have some critical disadvantages such as a long extraction time, large consumption of solvent, poor product quality, energy consumption and very few adjustable parameters. Since the solvent extraction requires a high temperature, it is not suitable for thermo labile compounds. In recent years, a number of new methods have been developed and applied to overcome these limitations, such as accelerated solvent extraction[25], supercritical fluid extraction[26], the microwave-assisted method[27]and ultrasonic-assisted extraction (UAE). Among them, UAE is reported to be a more economical and efficient method to isolate bioactive compounds[28-29]with minimal harm to their bioactivity[30]. The acoustic cavitation of ultrasound in extraction improves the interaction between targeted compounds and the solvent, causing destruction of the cellular wall and facilitating the mass transfer of contents[31-33]. From extensive literature research, there are no reports on mathematical models describing the kinetics process of the ultrasonic-assisted extraction of arctigenin from hydrolyzed FructusArctii.
In this paper, on the basis of single factor experimental data and Fick’s first law, the corresponding solution to the mathematical model was established to simulate the process of ultrasonic-assisted extraction of arctigenin from hydrolyzed FructusArctii. The parameters including solvent to solid ratio, particle size of hydrolyzed samples, ethanol volume fraction, ultrasound power, extraction temperature and extraction time were taken into consideration in the model. The parameters of the model were estimated by single factor experiments.
1.1 Reagents and herbs
The fruits ofArctiumlappaL. were obtained from Nanjing Zelang Pharmaceutical Technology Co., Ltd., Jiangsu, China.ArctiumlappaL. seeds were ground to powder (mesh size 20-40, 40-60, 60-80, 80-100) using an electronic grinder and stored at 4 ℃ for use. The standard arctigenin was purchased from the National Institute for the Control of Pharmaceutical and Biological Products (Beijing, China, see Fig.1 for chemical structure). The methanol was chromatographically pure and all other reagents were analytically pure.
(a)
(b)
Fig.1 Chemical structures. (a) Arctiin; (b) Arctigenin
1.2 Sample pre-treatment
In order to convert arctiin to arctigenin, the powder of FructusArctii was hydrolyzed in 3% (weight percentage) hydrochloric acid for 6 h, and the ratio of ground materials to hydrochloric acid solution was about 1∶6. After hydrolysis, the mixture was filtrated and the residues were washed with a large amount of distilled water until the pH of the washing liquid was 7. Then, the hydrolyzed materials were dried at temperature of 50 ℃ for 24 h. The dried materials were kept at 4 ℃ without light until use.
1.3 Apparatus and instruments
The ultrasonic bath (DCTZ-2000E type, 40.0 kHz, Hongxianglong Co., Ltd., Beijing, China) was equipped with a stainless extraction vessel of 500 mL and a ultrasonic generator (maximum power 1 200 W). Circulating water was used to keep the solution’s temperature stable during the experiment. The analytical high-performance liquid chromatograph (10ATvp, Shimadzu, Japan) was equipped with a LC-10AT pump, a CTO-10AS column oven, a SCL-10A controller, a SPD-10A ultraviolet (UV) detector and a manual injector with a 20 μL sample loop. A CLASS-VP software package was used for data analysis.
1.4 Determination of arctigenin in the extract by HPLC
The concentration of arctigenin in the extracts was determined by HPLC. A ODS-2 Hypersil column (5 μm, 150 mm×4.6 mm) operating at 25 ℃ was applied to separate the arctigenin by isocratic elution with a mobile phase consisting of methanol: water (50∶55 in volume percentage)[1]at a flow rate of 0.5 mL/min. The detector was employed at a wavelength of 280 nm and the injection volume of filtered sample was 20 μL. The identification of arctigenin was carried out by comparing the retention time with the reference standard of arctigenin. Standard calibration curves applied to calculate the concentrations of arctigenin were generated by using seven standard dilutions ranging from 0.022 to 1.386 mg/mL. The regression line for arctigenin wasy=3.0×107x+406 489 (R2=0.999 7), whereyis the peak area (mAU) of arctigenin, andxis the concentration of standard solution (mg/mL).
1.5 Ultrasonic-assisted extraction
The extraction was performed in an ultrasound bath. A mixture of ethanol and water at different ratios was put into the stainless extraction vessel as the extraction solvent. When the temperature of the solvent reached a preset temperature and remained steady in the water bath, the dry hydrolyzed samples were macerated into the extraction vessel, following the immersion of an ultrasonic generator into the solvent at approximately 2 cm. Under the sets of designed ultrasonic conditions (ultrasonic power and time), the solvent-material slurry was extracted and then filtered. After each run, 1 mL of the extract solution was put into volumetric flask and diluted 10-fold with a mobile phase of high performance liquid chromatograph (HPLC). Then, the diluted solution was filtered through 0.22 μm nylon syringe membranes. 20 μL aliquot of filtrated solution was injected into the HPLC for analysis. The result was expressed as the extraction yield:
Y=
×100%
(1)
whereYis the extraction yield, %;Cis the measured concentration of arctigenin in injections, mg/mL;Vis the volume of extract solution, mL;Mis the mass of dry hydrolyzed samples, mg.
1.6 Experimental design
The parameters of single factor experiments are as follows:
1) The effect of solvent to solid ratio on the concentration of arctigenin was experimentally studied at the extraction temperature 313 K, ethanol volume fraction 50%, ultrasound power 400 W, extraction time 20 min and particle size 20 to 40 mesh;
2) The effect of the particle size on the concentration of arctigenin was experimentally studied at an extraction temperature 313 K, solvent to solid ratio 20 mL/g, ultrasound power 400 W and extraction time 20 min and ethanol volume fraction 50%;
3) The effect of the ethanol volume fraction on the concentration of arctigenin was experimentally studied at an extraction temperature 313 K, solvent to solid ratio 20 mL/g, ultrasound power 400 W, extraction time 20 min and particle size 20 to 40 mesh;
4) The effect of the ultrasound power on the concentration of arctigenin was experimentally studied at extraction temperature 313 K, ethanol volume fraction 50%, solvent to solid ratio 20 mL/g, extraction time 20 min and particle size 20 to 40 mesh;
5) The effect of the extraction temperature on the concentration of arctigenin was experimentally studied at a solvent to solid ratio 20 mL/g, ethanol volume fraction 50%, ultrasound power 400 W, and extraction time 20 min and particle size 20 to 40 mesh;
6) The effect of the extraction time on the concentration of arctigenin was experimentally studied at an extraction temperature 313 K, ethanol volume fraction 50%, solvent to solid ratio 20 mL/g, and ultrasound power 400 W and particle size 20 to 40 mesh.
During the process of liquid-solid extraction, the solute transforms from the solid phase to the liquid phase. The process is comprised of three steps[34]:
1) Extraction solvent permeates into the solid matrix;
2) Solute dissolves into solvent and then diffuses to the solid-liquid interface;
3) Solute is transformed from the solid-liquid interface to the liquid phase. The schematic diagram of the extraction process and the variation of solute concentrations in the solid phase and the liquid phase are illustrated in Fig.2.
(a) (b)Fig.2 Schematic diagram of solute concentrations variation in the process of liquid-solid extraction. (a) Schematic representation of liquid-solid interface; (b) Concentration variation as a function of the distance from the solid particle
By considering Fick’s first law, the following equation can be obtained:
=-DS
(2)
whereis the leaching rate of arctigenin, kg/s;Dis the diffusion coefficient of arctigenin in the liquid phase, m2/s;Sis the diffusion area, m2;is the concentration gradient of arctigenin from the surface of the hydrolyzed FructusArctii powder to the bulk of the solution, kg/m4; a negative sign indicates that arctigenin diffuses in the opposite direction of the concentration gradient.
During the process of ultrasonic extraction,Dis generally composed of the molecular diffusion coefficient and eddy diffusion coefficient; therefore, the diffusion coefficient can be proposed as follows:
D=DM+DE
(3)
whereDMis the molecular diffusion coefficient, m2/s;DEis the eddy diffusion coefficient, m2/s;
The molecular diffusion coefficientDMcan be described by the Arrhenius equation:
DM=Ae-E/(RT)
(4)
whereAis the transfer coefficient factor, m2/s;Eis the activation energy for the extraction, J/mol;Ris the universal gas constant, 8.314 J/(mol·K);Tis the extraction temperature, K.
During the process of extraction,Ais a function of concentration for concentrated solution, the following equation can be proposed[35]:
AM=D0Cn
(5)
whereD0is the intrinsic diffusion coefficient, m2/s;Cis the mass concentration of arctigenin, kg/m3;nis a constant. Since the diffusion coefficient decreases with the increase in distance,nis usually less than 0.
On the basis of predecessors’ study[36], the eddy diffusion coefficient is a function of ultrasound power and extraction temperature, which can be defined as
DE=k3ek1TPk2DM
(6)
wherek1,k2andk3are the influence parameters of the extraction temperature, ultrasound power and their interaction on the transfer coefficient, respectively;Pis the ultrasound power, W.
As the turbulence degree of extraction solution is greatly enhanced by ultrasonic waves, the effect of eddy diffusion is much larger than that of molecular diffusion, which meansD≈DE. According to Eqs.(3) to (6), the following equation can be obtained:
D=k3D0Pk2Cnek1T-E/(RT)
(7)
In general, the process of extraction is usually unstable, thus the concentration gradient of the solute is usually a function of space and time. Since a larger concentration gradient leads to a faster diffusion and a greater variation of concentration gradient with time, the following equation is proposed; which assumes that the change of concentration gradient with time is proportional to the concentration gradient[35]:
(8)
whereαis a proportionality constant. Since the concentration gradient decreases with the increase of solute concentration in solvent,αis usually less than 0. With the initial condition listed as follows, Eq.(8) can be integrated to obtain the following equation:
t=0, -=C0
-
=C0eαt
(9)
C0=acbek4T
(10)
whereC0is the arctigenin concentration on the solid-liquid interface, kg/m3;cis the ethanol volume fraction, %;b,k4andaare the influence parameters of ethanol volume fraction, extraction temperature and their interaction onC0, respectively
According to Eqs.(2), (7), (9) and (10) and definingW=VCandk=k1+k4, the following equation can be obtained:
=
(11)
whereWis the mass flux of arctigenin transferred across the diffusion layer, kg;Vis the total volume of extracts, m3.
During the process of ultrasonic-assisted extraction, the diffusion areaSand the mass of hydrolyzed FructusArctiiGcan be proposed as follows:
S=k′ωσ2
(12)
G=k″ωρsσ3
(13)
whereωis the granule number of granule number;σis the particle size of sample powders, μm;Gis the mass of hydrolyzed FructusArctii, g;ρsis the density of samples, g/m3;k′andk″ are both the proportionality constants related to the shape of particles of hydrolyzed samples.
For a certain quality of hydrolyzed FructusArctii powder, the ratio ofVtoGis proportional to the solvent to solid ratio. According to Eqs.(12) and (13) and definingk1=
, the following equation can be obtained:
=
(14)
whereλis the proportionality constant.
According to Eq.(14) and the initial conditiont=0,C=0, Eq.(11) can be integrated as
C1-n=
(15)
Eq.(15) is a mathematical model of ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii, which gives the relationship among the arctigenin concentrationCand ultrasonic powerP, extraction temperatureT, solvent to solid ratioq, ethanol volume fractionc, particle sizeσand extraction timet.
With the value ofβdefined, Eq.(15) can be transferred into the following equation:
β=
ln
(16)
lnC=β-
-
+
+
+
(17)
In Eq.(17),n,k1,k2,k3,k,λ,a,b,D0,α,EandRare all constants. The parametersn,k2,k,b,αandEcan be determined by single factor experiments and Eq.(17) can be rewritten as
lnC=φ1-
(18)
lnC=φ2-
(19)
lnC=φ3-
(20)
lnC=φ4-
(21)
lnC=φ5-
-
(22)
lnC=φ6-
(23)
whereφ1toφ6are the constant terms when only one factor is considered in the model. Then, substitutingn,k2,k,b,α,Eandφ1toφ6into Eq.(17) gives the corresponding values ofβ1toβ6which are then averaged to obtain the value ofβfor the mathematical model. The mean value of (1-n)k1k3λaD0/(-α) can be determined by the value ofβ.
3.1 Solution of the model
3.1.1 Single factor experiment of solvent to solid ratio
To obtain the value ofn, the values of all factors except the solvent to solid ratio are kept constant. Fig.3 shows the relationship between arctigenin concentration and solvent to solid ratio. The linear regression equation is shown as follows:
lnC=2.955 7-0.758 7lnq
=0.989 0
(24)
=0.758 7
(25)
=2.955 7
(26)
Fig.3 Relationship between arctigenin concentration and solvent to solid ratio
3.1.2 Single factor experiment of particle size
To obtain the value ofn, the values of all factors except particle size are kept constant. Fig.4 shows the relationship between the arctigenin concentration and particle size. The linear regression equation is given as
lnC=5.426 6-0.743 5lnσ
=0.998 5
(27)
=0.743 5
(28)
=5.426 6
(29)
Fig.4 Relationship between arctigenin concentration and particle size
3.1.3 Single factor experiment of ethanol volume fraction
To obtain the value ofb, the values of all factors except ethanol volume fraction are kept constant. Fig.5 shows the relationship between the arctigenin concentration and ethanol volume fraction. The linear regression equation is given as
lnC=1.852 1-1.773 0lnσ=0.995 0
(30)
=1.773 0
(31)
=1.852 1
(32)
Fig.5 Relationship between arctigenin concentration and ethanol volume fraction
3.1.4 Single factor experiment of ultrasound power
To obtain the value ofk2, the values of all factors except ultrasound power are kept constant. Fig.6 shows the relationship between arctigenin concentration and ultrasound power. The linear regression equation is given as
lnC=-0.541 0-0.195 3lnP=0.953 0
(33)
=0.195 3
(34)
=-0.514 0
(35)
Fig.6 Relationship between arctigenin concentration and ultrasound power
3.1.5 Single factor experiment of extraction tem-perature
To obtain the values ofkandE, the values of all factors except extraction temperature are kept constant. Fig.7 shows the relationship between the arctigenin concentration and extraction temperature. The linear regression equation is given as
lnC=516.975 9-0.815 9T-8.170 7×
(36)
=0.815 9
(37)
=8.170 7×104
(38)
β5-
-
+
+
+
=516.975 9
(39)
3.1.6 Single factor experiment of extraction time
To obtain the value ofα, the values of all factors except extraction time are kept constant. Fig.8 shows the relationship between the arctigenin concentration and extraction time. The linear regression equation is shown as follows:
lnC=0.754 8+0.751 1ln(1-e-0.120 7t)·
(40)
α=-0.120 7
(41)
β6--+++
(42)
Fig.7 Relationship between arctigenin concentration and extraction temperature
Fig.8 Relationship between arctigenin concentration and extraction time
The values ofn,b,k2,k,Eandαcan be calculated by Eqs.(25), (28), (31), (34), (37), (38) and (41):
n=-0.331 4,b=2.360 6,k2=0.260 0
k=-1.086 3,E=9.044 8×105,α=-0.120 7
(43)
Substituting Eq.(43) into Eqs.(26), (29), (32), (35), (39) and (42), respectively, the value ofβcan be obtained as 524.280 7, 524.227 3, 524.151 0, 524.195 7,
524.094 0 and 524.224 0. Substituting the mean value ofβ,nandαinto Eq.(16), the following expression can be obtained:
k1k3λaD0=e695.594 7
(44)
Combining Eqs.(43) and (44) with Eq.(15), the mathematical model of ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii is obtained:
(45)
wherePis the ultrasound power, W;cis the ethanol volume fraction, dimensionless;Tis the extraction temperature, K;tis the extraction time, min;qis the solvent to solid ratio, mL/g;σis the particle size of material, μm;Cis the arctigenin concentration in the extraction solvent, mg/mL.
3.2 Verification of the model
Further experiments are carried out under different conditions to verify the accuracy of the presented model (see Tab.1). Each experiment was repeated three times and the average values were used to measure the accuracy of the model. Fig.9 presents the resulting concentration level for arctigenin in the extract.
Fig.9 Verification of the mathematical model for ultrasonic-assisted extraction
Tab.1 Comparison between simulation and experimental data in verification experiment
RunT/Kt/minP/Wcq/(mL·g-1)σ/μmArctigeninconcentration/(mg·mL-1)SimulationdataExperimentaldataRelativeerror/%1308303000．6203243．60354．121512．572308305000．6403242．36562．29433．113308103000．8203244．68994．48014．684328103000．8403242．41502．67369．675328303000．8203245．20115．13211．346328105000．8203244．49104．38952．317318155000．7133247．66037．88352．838308305000．8203246．63086．50231．989308205000．6203243．78723．97604．7510328205000．8203245．46634．893811．7011328205000．8403243．24783．03886．8812301205000．7303242．36252．52496．4313318205000．5303242．70902．71190．1014318205000．7133248．16477．57117．8415318205000．7473243．15563．35746．0116318205000．7303244．40694．55143．17
From Tab.1, it can be seen that the relative error between the experimental data and simulation data is between 0.10% to 12.57%. Higher relative errors of above 10% are observed in Runs 1 and 10, most likely resulting from the inherent nonuniform character of FructusArctii as a natural product. Although there is still an error between simulating data and experimental data, the prediction tendency of the model shown in Fig.9 basically matches the experimental data. So, the process of ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii can be described appropriately by the mathematical model.
A mathematical model of ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii is established based on Fick’s first law and the model explains the relationship among arctigenin concentration and solvent to solid ratio, the particle size of samples, ethanol volume fraction, ultrasound power, extraction temperature and extraction time. The parameters of the model are estimated by single factor experiments. Although there is still an error between simulation data and experimental data, the prediction tendency of the mathematical model basically matches experimental data. The calculated data agrees well with the experimental data and the error is within an allowable range. Therefore, the process of ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii can be described appropriately by the model. Moreover, the mathematical model can also provide theoretical guidance for describing other similar extraction processes.
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References
摘要：基于Fick第一定律对超声提取牛蒡子酸水解产物中牛蒡苷元的过程建立了数学模型及其求解方法.采用盐酸对牛蒡子原药材进行酸水解,促使药材中含量较高的牛蒡子苷转化为苷元,然后以酸水解产物为原料,研究超声提取牛蒡苷元的工艺条件.在超声提取单元素实验中,着重考察了温度、时间、超声功率、乙醇浓度、液固比、原料粒径、占空比和提取溶剂8个因素对牛蒡苷元提取率及浸膏纯度的影响.将模拟结果与实验值进行比较,结果表明模型的计算值与实验值之间存在一定的误差,误差低于13%,但各因素对提取效果的影响规律与实验结果基本一致.
关键词：牛蒡子;酸水解;超声提取;牛蒡苷元;数学模型
中图分类号：R93
JournalofSoutheastUniversity(EnglishEdition) Vol．33，No．3，pp．370⁃376Sept．2017 ISSN1003—7985
DOI:10.3969/j.issn.1003-7985.2017.03.017
Foundationitems：The National Natural Science Foundation of China (No.21406272, 21676291), the Fundamental Research Funds for the Central Universities (No.2632017ZD01), Jiangsu Planned Projects for Postdoctoral Research Funds (No.1402060B).
Citation：Dai Lin, Zhang Yong, Hu Chi, et al. Mathematical modeling for ultrasonic-assisted extraction of arctigenin from acid hydrolyzed FructusArctii[J]．Journal of Southeast University (English Edition),2017,33(3):362-369．
DOI：10.3969/j.issn.1003-7985.2017.03.017.