Application of Mathematical Models in Drug Release Kinetics of Lagerstroemia Speciosa Extract-Phospholipid Complex

Patel Anar J.1*, Singh R. P.2, Patel Vaibhav3, Goswami Shambaditya2

1Associate Professor, Sal Institute of Pharmacy, Opp. Science City, Ahmedabad 380061, Gujarat, India.

2NIMS Institute of Pharmacy, Jaipur, Rajasthan, India.

3Anand Pharmacy College, Gujarat, India.

*Corresponding Author E-mail: anar.patel0@gmail.com

ABSTRACT:

The aim of present work is to govern and scrutinize the kinetics of drug release from the complex by employing various mathematical models. A study was done with Lagerstroemia speciosa extract-phospholipid complex, 50 mg/200mg by employing anticipation precipitation technique using soya lecithin and cholesterol as complex forming polymer. In-vitro drug release profile was carried out in phosphate buffer saline, pH 7.4  (900mL) using USP dissolution apparatus II (Paddle) at 50 RPM at an extended time period of 0.5, 0.75, 1, 1.5, 2, 2.5, 3 and 4 hours. The drug release data was obtained, quantitatively correlated and interpreted with various mathematical models viz. Zero order model, first order model, Higuchi model and Korsmeyer-Peppas model and evaluated to understand the kinetics of drug release. The criterion for the most suitable model was based on the high degree of coefficient of correlation of drug release profile was best fitted with Korsmeyer-Peppas model and follows drug release kinetics which is diffusion controlled.

KEYWORDS: Lagerstroemia speciosa extract-phospholipid complex; Diffusion; Coefficient of correlation; Kinetics of drug release.

INTRODUCTION:

Dissolution1

When solid particles come in contact with the GI tract, a saturated layer of drug solution is created very quickly in the surface of particles in the liquid immediately surrounding them (called the diffusion layer). (1)  Dissolution is a process in which a solid substance solubilises in a given solvent i.e., mass transfer from solid surface to the liquid phase.

Theories of drug dissolution: Several theories have been proposed to explain drug dissolution. Some of the important ones are:2,3

Diffusion layer model/ film theory: This model considers that a layer of liquid, H cm thickness, close to the solid surface remains stagnant as the bulk liquid passes over the surface with a particular speed.

The rate of dissolution is carried out by the diffusion of the solid molecules from the stagnant liquid film to the bulk liquid according to Fick’s first law:

J=- Df dc/dx

Where J is the amount of substance passing perpendicularly through a unit surface area per time, Df is the diffusion coefficient and dc/dx, is the concentration gradient. After a time t, the concentration between the limit of the stagnant liquid layer and the bulk liquid becomes Ct.

·       Danckwert model/penetration or surface renewal theory: This model considers that there is formation of macroscopic packets of solvent which attaches at the solid /liquid interface in a diffusion manner. Hence at the interface, the packet is able to absorb solute according to the laws of diffusion which is to be replaced by a new packet of solvent. This surface renewal process is related to the rate of transfer of solute and finally to the rate of dissolution.

·       Interfacial barrier model/ double barrier or limited salvation theory: In this model, it can be considered that the interaction at the solid/liquid interface is not spontaneous due to a high activation free energy barrier which is to be surrounded before the solid can dissolve. Thus, the dissolution mechanism is almost same as in diffusion layer model, with the concentration at the limit of the stagnant layer of liquid becoming Ct after time t. The rate of diffusion in the stagnant layer is relatively fast in comparison with the presence of the energy barrier, hence it becomes rate limiting in the dissolution process.

Application of drug release data on mathematical models: Various mathematical models are employed to understand drug release kinetics which is explained below. 4-7

Zero order model4: According to the principles of pharmacokinetics, drug release from the dosage form can be represented by the equation:

C0-Ct =K0t

Ct is the amount of drug released at time t,

C0 is the initial concentration of drug at time t=0, K0 is the zero-order rate constant.

Hence to study the drug release kinetics data obtained from in-vitro dissolution study is plotted against time i.e., cumulative drug release Vs. time.

Hence the slope of the above plot gives the zero-order rate constant and the correlation coefficient of the above plot will give the information whether the drug release follows zero order kinetics or not.

First order model5: The release of drug which follows first order kinetics can be represented by the equation

DC/dt=-K1C

K1 is the first order rate constant, expressed in time-1 or per hour.

Hence it can be defined as that first order process is the one whose rate is directly proportional to the concentration of drug undergoing reaction i.e., greater the concentration faster the reaction. Hence, it follows linear kinetics.

Hence to study the drug release kinetics data obtained from in-vitro dissolution study is plotted against time i.e., log % of drug remaining vs. time and the slope of the plot gives the first order rate constant.

Higuchi model6: The release of a drug from a drug delivery system (DDS) involves both dissolution and diffusion.

Mt/M = KH t1/2

Where, Mt = Amount of medication discharged in time t,

M∞ = Amount of medication discharged at limitless time,

KH = Higuchi discharge rate consistent communicating structure variable of framework.

The data obtained were plotted as cumulative percentage drug release versus square root of time. Hence if the correlation coefficient is higher for the above plot then we can interpret that the prime mechanism of drug release is diffusion controlled release mechanism.

Korsmeyer-peppas mode7:

Once it has been ascertained that the prime mechanism of drug release is diffusion controlled from Higuchi plot then it comes the release of drug follows which type of diffusion.

Korsmeyer and Peppas put forth a simple relationship which described the drug release from a polymeric system follow which type of dissolution and an equation as:

Mt/M∞=Kkptn

Mt/M∞ is a fraction of drug released at time t,

Log (Mt/M∞)=log Kkp + nlog t,

Mt is the amount of drug released in time t,

M∞ is the amount of drug released after time ∞,

n is the diffusional exponent or drug release exponent,

Kkp is the Korsmeyer release rate constant.

To study release kinetics a graph is plotted between log cumulative % drug release log (Mt/M) Vs. log time (log t).

Formulation of Lagerstroemia speciosa extract phosphatydil choline complex, 50mg/200mg8,9

The phytosome technology creates intermolecular bonding between individual polyphenol molecules and one or more molecules of the phospholipids, phosphatidyl choline (PC)8 Phytosomes are produced by a process whereby the standardized plant extract or its constituents are bound to phospholipids, mainly phosphatidylcholine producing a lipid compatible molecular complex. This phytophospholipid complex (phytosome) resembles a little cell. A Phytosome is generally more bioavailable than a simple herbal extract due to its enhanced capacity to cross the lipid-rich biomembranes and reach circulation and thus exhibits better pharmacokinetic and pharmacodynamics profile than conventional herbal extracts.10-13

Lagerstroemia speciosa (Lythraceae, commonly known as Banaba, pride of India) is a medicinal plant that grows in the Philippines, China, India and Southeast Asia. Major constituents of Lagerstroemia speciosa leaves include lagertannin, Lagerstroemia speciosa, ellagic acid, lagerstroemin, etc. Traditionally, the whole plant and specifically leaves are used to treat diabetes and hyperglycemia (elevated blood sugar).The hypoglycemic (blood sugar lowering) effect of Banaba extract is reported to be similar to that of insulin which induces glucose transport from the blood into body cells. This effect is attributed to the various active chemical constituents present like corosolic acid and larger tannins14

Corosolic acid is a naturally occurring pentacyclic triterpene, 2 alpha-hydroxy ursolic acid. It displays a potential anti-diabetic activity, anti-inflammation, and antihypertension properties. It has been found out that Lagerstroemia speciosa has poor bioavailability and pharmacokinetic profile in dosage form like dry powder extracts, tablets, soft gelatin capsules etc. in comparison to the banaba extract.14

To detour this, our aim is to separately formulate such nanoparticulate formulations to enhance solubility, efficacy and bioavailibility of Lagerstroemia speciosa. In the present study, an attempt was made to design phytosomal complex and its release profile was interpreted with various mathematical models.13,15-21

MATERIAL AND METHODS:

Soya Lecithin was procured as gift sample from Indena pvt. Ltd., Germany. Chitosan was purchased from Himedia Laboratories Pvt Ltd, Mumbai. Methanol and water was of HPLC grade. All the other reagents and solvents were of the highest purity commercially available.

Preparation of Extract for Lagerstroemia speciosa:

Dried leaf powder of Banaba (100g) was refluxed in round base jar with half litre of aqueous alocohol (90%) for 2 hr and filtered. The process was repeated thrice till extract obtained was colourless. The extracts were pooled and concentrated under reduced pressure totally to yield reddish brown residue. Percentage yield of fractions was calculated.

Preparation of Phytosomes by antisolvent precipitation method:22-25

The specific amounts of plant extract and soya lecithin were refluxed with acetone at a temperature 50 – 60oC for 2 h. The mixture was concentrated to obtain the precipitate which was filtered and collected. The dried precipitate of phytosome complex was placed in amber colored glass bottle and stored in refrigerator.

Evaluation of trial batch for working method selection:26-30

Selection of working method was done on the basis of minimum particle size and better entrapment efficiency for preparation of Phytosomes.

A full factorial design was used to study the effect of Independent variables on the dependent variables. Independent and dependent variable are given in Table 1, Table 2.

Table 1: Independent and dependent variables

 Independent Variables Cholesterol concentration, Soya lecithin concentration Dependent Variables Particle size, entrapment efficiency and invitro release Levels Low, Medium and High Constraints Particle size and maximum Entrapment efficiency

Design Expert 11.0.4.0 (Trial Version Stat-Ease, Inc, USA) was used for the analysis of effect of each variable on the designated response i.e. particle size, span value and entrapment efficiency. ANOVA was used to study the statistical significance.

### Entrapment efficiency:

Entrapment efficiency of phytosomes was determined by centrifugation method. Phytosome was weakened with methanol and afterward centrifuged at 10,000rpm for half hour at - 4oC utilizing rapid cooling rotator machine. Supernatant was gathered and measure of free concentrate was controlled by UV noticeable spectrophotometer at 366nm for L. speciosa extricate. Entanglement proficiency was determined by following equation:

[Total amt. of drug – amt. of free drug]

------------------------------------------------------ × 100

Total amt. of drug

Table 2: Formula used for formulation of Phytosome complex (50 mg /200 mg):

 Batches Extract (g) Soya lecithin (X1) (g) Cholesterol (X2) (g) Temperature (oC) Methanol (ml) DCM (ml) Hexane (ml) F1 5 5 1 40 20 10 20 F2 5 10 4 40 20 10 20 F3 5 7.5 1 40 20 10 20 F4 5 5 2.5 40 20 10 20 F5 5 10 2.5 40 20 10 20 F6 5 7.5 2.5 40 20 10 20 F7 5 5 4 40 20 10 20 F8 5 10 1 40 20 10 20 F9 5 7.5 4 40 20 10 20

### Mean Particle Size and Size Distribution:

PCS using Zetasizer Nano ZS90 was utilized to decide molecule size and size distribution. 20µl phytosomal suspension was placed in glass cuvette and customized estimation mode with five runs was picked. Normal molecule size (z-normal) and size appropriation of arranged phytosomes was determined from auto relationship capacity of power of light dissipated from particles expecting round kind of particles. All estimations were finished in triplicate and performed at 25oC. Molecule size dispersion was communicated by length esteem. Length is proportion of width of size dispersion. Littler range esteem demonstrates slender size dispersion.

Span = [D (90%) - D (10%)]/ [D (50%)]

Where D (90), D (10) and D (50) are equivalent volume diameter at 90, 10 and 50% cumulative volume respectively.

### Visualization:

Perception of phytosomes was practiced by using examining electron microscopy. Filtering electron microscopy has been used to choose molecule size gauge appointment and surface morphology of complex. Tests were falter secured with gold/palladium for 120 s at 14 mA under argon air for assistant electron emissive SEM (Hitachi-S 3400N) and looked for morphology at voltage of 15.0 kV.

### Zeta Potential:

Zeta potential is most crucial boundary for physical dependability of phytosomes. Higher electrostatic aversion between particles more is soundness. Zeta expected estimation of upgraded phytosome was finished by utilizing zeta sizer Nano ZS90 (Malvern Instruments Ltd., Malvern, UK). Test was weakened to 10ml with water, 5ml of this weakened example was moved to cuvette and hence Zeta potential was measured.

Dissolution profile of Lagerstroemia speciosa extract-phospholipid complex:

In vitro release was measured using dialysis method. Formulation was dispersed in release medium (phosphate buffered saline (PBS), pH 7.4 to form a suspension. The suspension was filled in a USP Dissolution apparatus II (Paddel, Himedia, Mumbai, India) at 50RPM, its both ends were tied. It was then suspended in a glass vial containing 10 ml of release medium. The vial was shaken horizontally using water bath shaker at 37°C. In vitro drug release was assessed by intermittently sampling the release medium at predetermined time intervals of 0.5, 0.75, 1, 1.5, 2, 2.5 3 and 4 hrs. The medium was replaced with fresh medium to maintain sink condition. The amount of extract released in each sample was determined using a calibration plot; the reported values are average of three replicates (n= 3). Results of in vitro drug release studies obtained are shown graphically with application of different models.

RESULTS AND DISCUSSION:

Evaluation of Lagerstroemia speciosa extract phosphatidyl complex:

An optimized formulation was selected based on the set criteria i.e. minimum particle size and maximum entrapment efficiency. (Table 3)

Table 3: Particle size and entrapment efficiency of various batches of complex

 Batch Soya lecithin (g) (X1) Cholesterol (g) (X2) Particle size (nm) (Y1) Entrapment efficiency (%) (Y3) F1 05 01 142 ± 00.41 45.50 ± 01.30 F2 10 04 197 ± 01.47 52.70 ± 00.87 F3 07.50 01 222 ± 01.50 58.70 ± 00.37 F4 05 02.50 257 ± 02.32 63.51 ± 01.51 F5 10 02.50 296 ±0 0.51 82.45 ± 01.65 F6 07.50 02.50 313 ± 01.37 77.32 ± 01.41 F7 05 04 342 ± 01.02 79.58 ± 01.50 F8 10 01 398 ± 00.57 73.34 ± 01.96 F9 07.50 04 455 ± 00.33 76.60 ± 01.80

Since the desired goal of the concern phytosomal formulations was to obtained particle size below 300 nm and maximum entrapment efficiency, thereby F5 with particle size 296 nm and entrapment efficiency 82.45 % and Zeta potential - 19.35 mv was optimized.

Visualisation:

SEM of enhanced definition is appeared (Figure 4). Molecule size was seen as 295 nm for L. speciosa.

Figure 4. SEM of optimized formulation

Application of drug release data on mathematical models:

The zero order model of Lagerstroemia speciosa extract phosphatydil complex, 50 mg/200 mg with cumulative % of drug release against time (Figure 5) describes that drug release of corosolic acid from the complex does not follow perfectly the principle of zero order release kinetics, though it is slightly approaching (r2=0. 9736).

The First Order model was applied in the release profile of complex with log cumulative % of drug release against time (Figure 5) describes that drug release of corosolic acid from the complex does not follow the principle of first order release kinetics as there is lower value of coefficient of correlation (r2=0.9729).

Higuchi model, Cumulative % drug release vs. Square root time (Figure 5) represents that drug release of corosolic acid from complex is not closest to trend line or regression line. (r2= 0.9767). We can interpret that the prime mechanism of drug release is diffusion controlled release mechanism.

Korsmeyer – peppas model was applied in the release profile of corosolic acid complex, (Figure 5) the slope of the plot was constructed which described that the release exponent or dissolution the exponent found to be higher than 0.99 which implies that the drug release from the system follow Dissolution release profile.

Figure 5. Graphical comparison between all Pharmacokinetic models

The optimized formulation from different batches were compared with the Lagerstroemia speciosa extract alone. (Figure 6)

Figure 6: %Drug release Comparison between Optimized Formulation and Extract

From the figure, the slope of the plot was constructed which described that the release exponent or the diffusion exponent found to be higher than (r2 = 0.9983) with complex in comparison to extract alone (r2 = 0.9904) which implies that the drug release from the complex follow dissolution release profile.31-34

Comparison between four models:

The in-vitro drug release profile was applied in different mathematical models and was interpreted in the form of graphical presentation and evaluated by correlation coefficient (r2) represented in Table 4.

Table 4: Results of different models in terms of r2, slope and intercept.

 Model Name r2 Slope Intercept Zero Order 0.9736 0.897 0.0133 First Order 0.9729 0.0043 2.0002 Higuchi Model 0.9767 0.9388 -0.0333 Korsmeyer-Peppas Model 0.9985 0.0924 0.1147

The highest degree of correlation coefficient determines the suitable mathematical model that follows drug release kinetics35. From the above comparison, it was found that Korsmeyer-Peppas power model showed higher degree of correlation coefficient (r2) than other models. Hence, drug release profile of Lagerstroemia speciosa extract – phosphatydil choline complex, 50 mg/200mg follows dissolution mechanism. Also, the model Higuchi model states the type of diffusion, which was evaluated by value, n which is higher than 0.9767 which implies that the drug release from the system follow Super case II transport.32

CONCLUSION:

Mathematical models play a vital role in the interpretation of mechanism of drug release from a complex of Lagerstroemia speciosa extract– phosphatydil choline 50mg/200mg were manufactured in this research paper showed an extended release profile with the polymers Soya Lecithin and Cholesterol. The drug release was found to be best fitted by Korsmeyer-Peppas power model (r2=0.9985) which implies that release of drug from complex was found to be time dependent process and diffusion controlled. Also, the model Higuchi Square root law equation states the type of diffusion, which was evaluated by value, n (Release exponent) which is higher than 0.9767 which implies that the drug release from the system follow Super case II transport.

CONFLICTS OF INTERESTS:

There are no conflicts of interests.

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Received on 28.10.2020            Modified on 24.04.2021

Accepted on 12.07.2021           © RJPT All right reserved

Research J. Pharm.and Tech 2022; 15(3):1257-1262.

DOI: 10.52711/0974-360X.2022.00210