Materials
Medium viscosity sodium alginate powder (viscosity of 2% solution, 25 °C ≈ 3500 cps, Sigma-Aldrich, London), calcium chloride dihydrate (Merck, Germany), theophylline anhydrous with a purity ≥ 99% (Sigma-Aldrich Chemicals Ltd, USA) were used. All other chemicals used were of analytical grade and were procured locally.
Methods
Preparation of drug-loaded calcium alginate nanoparticles
THP-loaded calcium alginate (Ca-ALG) was synthesized by an ionotropic gelation technique by following a previously reported procedure with slight modification [30, 31]. Aqueous sodium alginate solution (1 %, w/v) was mixed together with honey (added as surfactant and stabilizer). THP was dispersed in the solution at the ratio of 20% (w/w) (compared to the weight of Ca-ALG). Aqueous calcium chloride solution (1 %, w/v) was added drop-wise into this solution with constant stirring by a magnetic stirrer. This homogenized mixture was sonicated for 5 min. Nanoparticles were collected via centrifugation at 3500 rpm for 5 min, washed, and finally dried under vacuum.
Swelling studies
The swelling nature of nanoparticles was established by a tea bag technique [32, 33]. A known quantity of dried sample (Wd) was taken in a pre-weighed tea bag (mixed cellulose ester (MCE) membrane of 25 nm pore size, Millipore) and permitted to swell in a solution of 0.1 M phosphate buffer of pH 7.4 for a particular duration. The swollen samples were withdrawn and weighed instantly after evacuating the excess liquid from the surface with a filter paper (Ws). The swelling percentage was computed using Eq. (1). Each swelling study was performed three times and the average value obtained.
$$ S=\left[\frac{Ws- Wd}{Wd}\right]\times 100 $$
(1)
In vitro drug release studies
In vitro drug release studies were carried out in 0.1 M phosphate buffer, pH 7.4, as per the United States Pharmacopoeia standard (37 °C, 100 rpm) [34]. THP concentration was detected using a UV–Vis spectrophotometer (PerkinElmer Lambda Bio 40) at 286 nm [27]. All experiments were conducted in triplicate.
Mathematical analysis
Release mechanism
Upon contact with simulated fluids, the matrix swells and drug release from the swollen matrix is governed by
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1.
Advective transport of drug
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2.
Molecular diffusion
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3.
Hydrodynamic dispersion within the system
Model assumptions
To derive the governing equation of transport, the following assumptions are made regarding drug release from the alginate matrix system.
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1.
Upon contact with release medium, hydrodynamic dispersion occurs.
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2.
Matrix swelling is isotropic, ideal, and uniform throughout the device.
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3.
Perfect sink conditions were kept throughout the study.
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4.
The dispersion of the drug is uniform within the polymer matrix.
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5.
No mass loss takes place during the entire process.
It was assumed that the drug diffuses out of the domain in only one dimension. Therefore, the drug transport process in the entire system can be portrayed by the one-dimensional equation. The governing transport equation of drug release in the system is derived based on the principle of conservation of mass for an element in the system and is given as
$$ \frac{\partial C}{\partial t}=D\frac{\partial^2C}{{\partial x}^2}-v\frac{\partial C}{\partial x} $$
(2)
where C is the concentration of drug in the system (M L−3), D is the hydrodynamic dispersion coefficient (L2 T−1), ν is the average velocity (L T−1), t is time, and x is the distance along the axis. The drug diffusion coefficient D can be found experimentally by the reported method [35,36,37]. Although the velocity may be varying with respect to space and time, in this work the velocity across the entire system is assumed constant and equal to its vertically averaged magnitude. Figure 1 represents the schematic of the drug-loaded spherical calcium alginate nanoparticles (Ca-ALG NP) for mathematical analysis.
The initial and boundary conditions to the problem can be stated as follows:
Initially, the drug concentration at the surface of the matrix is supposed to be equal to zero.
$$ C\left(0,\kern0.5em {t}_1\right)={C}_{\mathrm{max}} $$
(4)
$$ C\left(x,{t}_1\right)=0 $$
(5)
$$ C\left(x,{t}_{\infty}\right)={C}_{max} $$
(6)
Equation (4) corresponds to the inlet boundary condition, which represents the concentration of the drug at the point of release. Equation (5) represents the outlet boundary condition in the system and Eq. (6) implies that after a particular time maximum drug release is achieved and it remains constant in the system.
Numerical model
The source code of the numerical model for simulating the drug release was written in MATLAB. The drug transport equations were discretized using a fully implicit numerical scheme of a finite difference method. An upwind implicit scheme was utilized for discretizing the advection part in Eq. (2) whereas a fully implicit scheme was used for discretizing the diffusion part in Eq. (2). Thomas algorithm was employed for solving the resulting set of simultaneous linear algebraic equations. The continuity of fluxes at the drug-matrix interface was ensured by iterating the solution at each time step. A uniform grid size was selected along the axis; finer grids were selected in the matrix whereas relatively larger grid sizes were adopted in the medium. The concentration flux transfer through the drug-matrix interface was accurately modelled by keeping a relatively small grid size at the interface. The validation of the numerical model was done by comparing the numerical model results with the experimentally obtained values.