# Gellan Gum/Laponite Beads for the Modified Release of Drugs: Experimental and Modeling Study of Gastrointestinal Release

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}concentrations suitable for obtaining stable and spherical particles. GG beads were formed, through ionotropic gelation technique, with and without the presence of the synthetic clay laponite. The resultant beads were analyzed for dimensions (before and after freeze-drying), morphological aspects and ability to swell in different media miming biological fluids, namely SGF (Simulated Gastric Fluid, HCl 0.1 M) and SIF (Simulated Intestinal Fluid, phosphate buffer, 0.044 M, pH 7.4). The swelling degree was lower in SGF than in SIF and further reduced in the presence of laponite. The GG and GG-layered silicate composite beads were loaded with two model drugs having different molecular weight, namely theophylline and cyanocobalamin (vitamin B12) and subjected to in-vitro release studies in SGF and SIF. The presence of laponite in the bead formulation increased the drug entrapment efficiency and slowed-down the release kinetics of both drugs in the gastric environment. A moving-boundary swelling model with “diffuse” glassy-rubbery interface was proposed in order to describe the swelling behavior of porous freeze-dried beads. Consistently with the swelling model adopted, two moving-boundary drug release models were developed to interpret release data from highly porous beads of different drugs: drug molecules, e.g., theophylline, that exhibit a typical Fickian behavior of release curves and drugs, such as vitamin B12, whose release curves are affected by the physical/chemical interaction of the drug with the polymer/clay complex. Theoretical results support the experimental observations, thus confirming that laponite may be an effective additive for fabricating sustained drug delivery systems.

## 1. Introduction

_{0.7}[(Si

_{8}Mg

_{5.5}Li

_{0.3})O

_{20}(OH)

_{4}]

_{0.7}is a synthetic clay composed of a layered structure (30–25 nm diameter, 1 nm thickness) that has been used to synthesize a wide range of nano-composite hydrogels [21,22,23]. Specifically, laponite (LAPO) nanoparticles can be uniformly dispersed within the polymeric matrix where they self-arrange and act as both filler and cross-linker during gel formation [24,25].

_{2}) concentrations suitable for obtaining stable and spherical particles. Under optimized experimental conditions, laponite was uniformly dispersed in the polymeric solution allowing the formation of nano-composite GG beads with reduced mesh size. In order to investigate how the morphology, swelling and the release properties of the nano-composite hydrogels were affected by the laponite, beads were loaded with two model drugs having different molecular weights and release studies were performed in simulated gastric fluid (SGF) and in simulated intestinal one (SIF). Mathematical models for swelling and drug release from these highly porous beads were proposed. Reliable values of drug diffusion coefficients in different release media were obtained.

## 2. Materials and Methods

#### 2.1. Chemicals

^{TM}) were purchased from Sigma Aldrich Company (Darmstadt, Germany), and calcium chloride hydrate, potassium dihydrogen phosphate and sodium hydroxide from Carlo Erba Reagents S.r.l (Milan, Italy). We used bidistilled water from Carlo Erba Reagents S.r.l. for the HPLC analysis. For sample preparation and all the other analyses, we used demineralized water produced with a Pharma20 equipment, Culligan Italiana S.p.A (Bologna, Italy). Laponite XLG was a gift of Rockwood Additives Ltd. (Moosburg, Germany).

#### 2.2. Rheological Measurements

#### 2.3. Beads Preparation

_{2}(0.3% w/w), thus following the same procedure adopted for beads without laponite.

#### 2.4. Determination of Swelling Degree

#### 2.5. Preparation of Drug Loaded Beads

#### 2.6. Drug Entrapment Efficiency

#### 2.7. In Vitro Release Studies

_{res}of SIF or SGF, warmed to 37 °C in a water bath and stirred continuously at 200 rpm. At defined times, from 1 to 240 min, 1 mL of solution was withdrawn and replaced with 1 mL of fresh solution. Different volumes V

_{res}= 50, 75, 100, 150, 175 mL were considered in order to investigate the influence of the release volume V

_{res}on release curves. See Section 4.5.1 for a discussion on the role of V

_{res}.

_{res}(t

_{w}

^{i}) [mg/mL] at withdrawal times t

_{w}

^{i}[min] and as fraction of drug released up to time t

_{w}

^{i}with respect to the total amount of drug loaded in the beads. The experiments were carried out in triplicate with each value reported representing the mean ± SD.

#### 2.8. Statistics

## 3. Mathematical Modeling of Swelling and Drug release of Highly Porous Beads

#### 3.1. Swelling Modeling

_{r}

^{s}(φ) is the swelling velocity v

_{r}

^{s}(φ) = D

_{s}(φ)∂φ/∂r and D

_{s}(φ) is the solvent diffusion coefficient, that can be assumed constant or a function of the solvent volume fraction φ.

_{0}for 0 ≤ r ≤ R

_{0}, where R

_{0}is the initial radius of the dry particle, φ

_{eq}is the volume fraction at equilibrium and φ

_{G}is the threshold volume fraction to initiate swelling.

_{s}

^{sg}is the solvent diffusivity in the swollen gel, assumed constant for φ > φ

_{G}, and β is a parameter controlling the decay of the diffusivity in the glassy core. The larger the porosity, the smaller β, the greater the ability of the solvent to penetrate in the glassy core.

_{eq}, for increasing times, as obtained from the numerical solution of the swelling model Equations (6)–(9), for two different values of β, namely β = 2 (Figure 2A) and β = 8 (Figure 2B).

_{G}, thus exhibiting a very sharp interface, typical of a non-porous particle. On the contrary, for β = 2 (porous particle) concentration profiles exhibit a smoother behavior for φ < φ

_{G}because of solvent penetration in the glassy region.

_{s}

^{sg}, β and φ

_{eq}can be obtained by comparing model predictions with experimental data for the temporal evolution and asymptotic value of the swelling degree S(t)

_{s}and ρ

_{b}are the solvent and the freeze-dried bead densities, respectively.

#### 3.2. Drug Release Modeling of No-Interacting Drugs

_{d}(r,t), initially loaded in the glassy core, reads as

_{r}

^{s}(φ) is the point wise swelling velocity and D

_{d}(φ) = D

_{d}

^{sg}(φ)f(φ) is the drug diffusivity, modeled exactly as the solvent diffusivity D

_{s}(φ). Indeed, D

_{d}

^{sg}is the drug diffusion coefficient in the swollen gel, assumed constant for φ > φ

_{G}, and f(φ) is the same function adopted to describe solvent penetration in the glassy core, Equation (7). Consistently with the solvent penetration model adopted, drug diffusion is allowed in the glassy core through the pore network, and the parameter β controlling diffusivity decay in the glassy core is assumed the same for the solvent and the drug.

_{res}(t), entering the boundary condition at the rubbery-solvent interface, represents the drug concentration in the reservoir in which the beads are immersed for release, with volume V

_{res}, assumed perfectly mixed. C

_{res}(t) evolves in time according to the macroscopic balance equation accounting for drug release from swelling beads and withdrawals, modeled as an instantaneous depletion of drug concentration in the reservoir

_{beads}is the total number of swelling/releasing beads, V

_{w}is the withdrawal volume, t

_{w}

^{i}is the time of the i-th withdrawal and N

_{W}

^{t}is the number of withdrawals from time zero to current time t. The simplifying assumption of perfect sink condition is therefore replaced by the more accurate expression Equation (13) for C

_{res}(t) that, in the limit for V

_{res}/V

_{beads}→ ∞, permits to recover the perfect sink condition C

_{res}(t) = 0. Equations (11)–(13) for drug transport must be solved together with Equations (6)–(9) for solvent diffusion.

_{d}−C

_{res})/(c

_{d}

^{0}−C

_{res}) for increasing times as obtained by choosing β = 2 (porous particle) and β = 8 (non-porous particle) for both D

_{s}(φ) and D

_{d}(φ). We observe that, for β = 2 (porous particle), the drug can smoothly diffuse out of the glassy core through the pore network while, for β = 8 (non-porous particle), drug concentration profiles exhibit a jump at the sharp glassy-rubber interface.

_{d}

^{sg}entering the drug release model is obtained by direct comparison of model predictions for C

_{res}(t) with experimental data for withdrawal drug concentrations C

_{w}

^{i}= C

_{res}(t

_{w}

^{i}) or by direct comparison of model predictions with experimental data of the integral release curve

_{res}(∞) is the asymptotic concentration in the reservoir and N

_{W}is the total number of withdrawals made during the entire release experiment.

#### 3.3. Drug Release Modeling of Interacting Drugs

_{d}(φ), the same adopted in Section 3.2 for non-interacting drugs.

_{b}and c

_{d}the drug concentrations in the bounded and free (gel-solvent) phases, respectively. Drug concentration c

_{b}(r,t) evolves in space and time according to the transport equation for the clay-polymer complex during the swelling process

_{b}

_{→g}= k

_{bg}(φ) c

_{b}, induced by solvent penetration and modeled, according to the solvent diffusion model Equation (7), as k

_{bg}(φ) = k

_{bg}

^{sg}f(φ) where k

_{bg}

^{sg}[1/s] is the transfer rate coefficient in the swollen gel, assumed constant for φ > φ

_{G}. Correspondingly, the transport equation for drug molecules in the free (gel) phase c

_{d}(r,t) reads as

_{res}(t).

_{bg}

^{sg}represents the characteristic time for the irreversible transfer of a drug molecule from the bounded to the free (gel) phase. This characteristic time t

_{bg}= 1/k

_{bg}

^{sg}can be compared to the characteristic drug diffusion time t

_{D}= R

_{0}

^{2}/D

_{d}

^{sg}by introducing the Thiele modulus Φ

^{2}= t

_{D}/t

_{bg}= k

_{bg}

^{sg}R

_{0}

^{2}/D

_{d}

^{sg}to identify the rate-controlling step.

_{d}

^{sg}, and k

_{bg}

^{sg}and is obtained by direct comparison of model predictions with experimental data for withdrawal drug concentrations C

_{res}(t

_{w}

^{i}) and for the integral release curves M

_{t}/M

_{∞}.

#### 3.4. Numerical Issues

^{−4}and absolute tolerance 10

^{−7}. The number of finite elements is 10

^{4}with a non-uniform mesh. Smaller elements were located close to the boundary r = S(t) in order to accurately compute concentration gradients controlling the velocity of the moving front.

## 4. Results and Discussion

#### 4.1. Rheological Measurements

#### 4.2. Beads Preparation

_{2}solutions at different concentrations in order to evaluate the effect of the cross-linking agent on the properties of the resulting beads.

^{2+}of 1:5, 1:7.5, 1:10 and 1:15 mol:mol were investigated. Regular and spherical beads were obtained with GG concentration 1.5% w/w for 1:5 and 1:10 GG:Ca

^{2+}molar ratios, corresponding to CaCl

_{2}concentrations of 0.3% w/w and 0.6% w/w, respectively. Concentrations of CaCl

_{2}< 0.3% w/w have not produced stable and spherical beads. GG solution 1.0% w/w gave irregular beads even for higher GG:Ca

^{2+}molar ratios 1:7 and 1:15. Based on these results, concentrations of GG below 1% w/w were not further investigated and the GG concentration of 1.5% w/w with CaCl

_{2}concentrations of 0.3% w/w and 0.6% w/w were adopted because these concentrations did not cause clogging of the syringe needle and produced regular and spherical beads. Further formulations were prepared by adding laponite to GG solution before beads formation. In this case, the beads were formed using the GG solution 1.5% w/w with laponite 1% w/w and with the lower concentration 0.3% w/w of CaCl

_{2}, which was chosen by considering that the clay is able to act as cross-linker itself, thus contributing to the polymeric network formation.

_{2}, concentration), most likely because the clay, acting as filler, increases the particle surface compactness.

_{b}is extremely low and comparable for all formulations. Specifically, ρ

_{b}= 0.109 ± 0.02 g/cm

^{3}for GG/Ca 0.3% and ρ

_{b}= 0.0926 ± 0.02 g/cm

^{3}for GG/LAPO/Ca 0.3%.

#### 4.3. Swelling Experiments

_{eq}(after 24 h).

_{eq}as already observed in [17] dealing with beads made of pH sensitive laponite/alginate/CaCl

_{2}hybrid hydrogel. In agreement with experimental findings reported in [17], the effect of clay is not only to decrease the equilibrium swelling degree but also to reduce the solvent diffusion coefficient D

_{s}

^{sg}in both media, as reported in Table 2. In agreement with swelling degrees at equilibrium, Table 2 also shows that D

_{s}

^{sg}is larger for SIF than for SGF for particles with and without clay. The values of D

_{s}

^{sg}reported in Table 2 for different beads and different media are obtained from the best-fit of experimental data for the time evolution of the swelling degree S(t) with the swelling model developed in Section 3.1.

- (1)
- the parameter β has been set to the value β = 2 in order to account for the large porosity/small density of beads;
- (2)
- the solvent volume fraction (SGF or SIF) at equilibrium φ
_{eq}is directly estimated from the equilibrium swelling degree S_{eq}as$${\phi}_{eq}=\frac{{x}_{eq}/{\rho}_{s}}{\left(1-{x}_{eq}\right)/{\rho}_{b}+{x}_{eq}/{\rho}_{s}},\text{}{x}_{eq}=1-1/\left(1+{S}_{eq}\right),$$_{eq}is the solvent weight fraction at equilibrium and ρ_{b}is the dry particle density; - (3)
- φ
_{G}has been set to φ_{G}= 0.1φ_{eq}, given the ease of beads re-hydration after freeze-drying.

_{eq}/d

_{0})

^{2}where d

_{eq}and d

_{0}are the equilibrium and initial particle diameter, respectively.

#### 4.4. Entrapment Efficiency

#### 4.5. Release Data Analysis

#### 4.5.1. Theophylline Release

_{res}(t

_{w}

^{i}), from now on referred to as differential release curve, and of the integral release curve M

_{t}/M

_{∞}.

_{s}

^{sg}and β, reported in Section 4.3, were estimated from independent swelling measurements. The only best-fit parameter entering the drug release model is the theophylline diffusivity in the swollen gel D

_{d}

^{sg}, whose values are reported in Table 4 for both media.

_{d}

^{sg}, the model best-fit must be performed on differential experimental data of C

_{res}(t

_{w}

^{i}), instead of on the integral release curve M

_{t}/M

_{∞}, C

_{res}(t

_{w}

^{i}) data being more sensitive to D

_{d}

^{sg}both in the initial phase of rapid concentration rise and in the subsequent phase where the effect of withdrawals become significant and not negligible.

_{res}of the reservoir is explicitly taken into account in model formulation, as well as the withdrawals, as can be observed from the sawtooth behavior of the differential release model curve. In fact, smaller values of V

_{res}, which do not guarantee the perfect sink condition, are to be preferred as they ensure better mixing and greater uniformity of drug concentration in the reservoir. Imperfect mixing is difficult to model and leads to a withdrawal drug concentration that may depend on the withdrawal point. On the contrary, the non-negligible drug concentration in the perfectly mixed reservoir (C

_{res}> 0, no sink condition) can be easily modeled by means of a macroscopic balance equation (see Equation (13)). The only requirement is that V

_{res}must be greater than a minimum value that guarantees that the maximum value attained by C

_{res}(t) during the release experiment is significantly lower than drug solubility in the release medium. This condition is always fulfilled in our release experiments for both drugs and for all V

_{res}analyzed.

_{TPH}≈ 8.2 × 10

^{−10}m

^{2}/s, while it reduces to a quarter of D

_{TPH}in the bead swollen in SIF. This can be explained in terms of the screening effect of the COO

^{–}groups of GG by the ions in SGF solution, thus reducing the possible interaction between theophylline and the charged polymer. A similar phenomenon has been observed by Coviello et al. (1999) [37] for theophylline in sclerox, a polycarboxylated derivative of scleroglucan.

_{d}

^{sg}reported in Table 4. In the presence of clay, theophylline diffusivity reduces by an order of magnitude with respect to D

_{TPH}in both media, but it is significantly smaller in SGF than in SIF. In this case, diffusivity values are in agreement with swelling data, S

_{eq}being significantly larger in SIF than in SGF for GG beads including laponite (see Table 2). Therefore, the screening effect of the COO

^{–}groups of GG by the ions in SGF solution, although still present, is balanced and overcome by the reduced mesh size of the network, this last observation being supported by swelling data in Figure 7 and Table 2.

_{2}hybrid hydrogel. These authors observed that the presence of laponite induced a significant slowing down of the release kinetic of hydrophilic drugs especially in acid medium.

_{d}

^{sg}previously estimated and reported in Table 4.

#### 4.5.2. Vitamin B12 Release

_{d}

^{sg}in SGF and SIF are reported in Table 5.

_{B12}≈ 2.1 × 10

^{−10}m

^{2}/s reported in [38] for vitamin B12 in scleroglucan/borax hydrogel swollen in distilled water (pH 5.4).

_{t}/M

_{∞}≈ t

^{n}with an exponent n = 1.2 much bigger than ½.

_{d}

^{sg}and transfer rate constant k

_{bg}

^{sg}in SIF and SGF are reported in Table 5.

_{bg}

^{sg}for vitamin B12 in SGF is one order of magnitude smaller than that in SIF. The diffusivity D

_{d}

^{sg}is smaller in SGF than in SIF.

^{2}(introduced in Section 3.3), we observe that Φ

^{2}for vitamin B12 in GG/LAPO/Ca 0.3% attains the following values: Φ

^{2}≈ 80 in SIF and Φ

^{2}≈ 9 in SGF. Therefore, Φ

^{2}in SGF is one order of magnitude smaller than Φ

^{2}in SIF. This quantitatively explains why drug-polymer/clay complex interaction leads to a strong non-Fickian behavior in SGF, characterized by a slower release at short time scale because the diffusion time-scale is comparable to the transfer time scale, while a Fickian behavior is observed for vitamin B12 in SIF because diffusion is definitely the rate controlling step.

_{d}

^{sg}for vitamin B12 are actually much lower in the beads with laponite in both media, and this, together with drug interaction with the polymer/clay complex, reflects in the gastrointestinal release curve shown in Figure 13 together with the corresponding vitamin B12 release curve from beads without laponite. The continuous blue curve represents the two-phase model prediction, from Equations (13)–(16), of the gastrointestinal release without any adjustable parameters.

## 5. Conclusions

_{2}0.3% w/w. Gellan gum beads including laponite have shown a smoother and regular surface and a larger diameter, namely d

_{0}≈ 2.8 mm and d

_{0}≈ 2.1 mm before and after freeze-drying, respectively. The ability to swell in different media mimicking biological fluids, namely SGF and SIF, was investigated. The bead swelling degree at equilibrium was lower in SGF than in SIF and further reduced in the presence of laponite.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic representation of moving fronts and solvent concentration profiles in a swelling process of a dry spherical bead. The two cases of a non-porous and a highly porous particle (blue dotted line) are shown.

**Figure 2.**Rescaled solvent volume fraction φ(r,t)/φ

_{eq}, vs. dimensionless radius r/R

_{0}for increasing times during the swelling process. Dashed line indicates the value of φ

_{G}/φ

_{eq}, Black boxes highlight the thickness of the diffuse glassy-rubbery interface. (

**A**) β = 2, porous particle; (

**B**) β = 8, non-porous particle.

**Figure 3.**Normalized drug concentration (c

_{d}−C

_{res})/(c

_{d}

^{0}−C

_{res}) vs. dimensionless radius r/R

_{0}for increasing times as obtained by adopting β = 2 ((

**A**), highly porous particle) and β = 8 ((

**B**), non-porous particle) for particle swelling and drug transport. Black boxes highlight the thickness of the diffuse glassy-rubbery interface.

**Figure 4.**(

**A**) Flow curves of gellan gum (GG) at different concentrations 1%, 1.5% and 2% w/w; (

**B**) corresponding mechanical spectra.

**Figure 5.**(

**A**) Flow curves of GG solution with and without laponite and (

**B**) mechanical spectra of the same solutions. Arrow indicates the inversion point G’’ ≈ G’ at a frequency of about 1 Hz for the mechanical spectra of the GG solution including laponite.

**Figure 6.**(

**A**) Pictures of beads of GG/LAPO/Ca 0.3%; pictures of beads at the optical microscope; (

**B**) GG/Ca 0.3%; (

**C**) GG/Ca 0.6%; (

**D**) GG/LAPO/Ca 0.3%.

**Figure 7.**Comparison between the swelling model predictions (continuous lines) and experimental data (points) for the temporal evolution of the swelling degree S(t) for two different bead formulations (GG/Ca 0.3% and GG/LAPO/Ca 0.3%) and two different swelling media (SGF and SIF). The best fit values for the solvent diffusion coefficient in the swollen gel D

_{s}

^{sg}are reported in Table 2.

**Figure 8.**Comparison between the swelling model predictions (continuous lines) and experimental data (points) for the temporal evolution of the particle diameter for two different bead formulations (GG/Ca 0.3% and GG/LAPO/Ca 0.3%) and two different swelling media (SGF and SIF).

**Figure 9.**Differential (

**A**) and integral release curves (

**B**) for theophylline (TPH) from beads GG/Ca 0.3% w/w without laponite in SGF and SIF. Continuous lines represent model predictions Equations (11)–(13). Estimated values of the TPH effective diffusivity D

_{d}

^{sg}are reported in Table 4.

**Figure 10.**Differential (

**A**) and integral release curves (

**B**) for theophylline (TPH) from beads GG/LAPO/Ca 0.3% with laponite in SGF and SIF. Continuous lines represent model predictions from Equations (11)–(13). Estimated values of the TPH diffusivity D

_{d}

^{sg}are reported in Table 4.

**Figure 11.**Gastrointestinal differential (

**A**,

**C**) and integral release curves (

**B**,

**D**) for theophylline (TPH) from beads GG/Ca 0.3% without laponite (

**A**,

**B**) and GG/LAPO/Ca 0.3% with laponite (

**C**,

**D**), p < 0.001. Continuous lines represent model predictions from Equations (11)–(13) with TPH diffusivity D

_{d}

^{sg}reported in Table 4.

**Figure 12.**Differential (

**A**) and integral release curves (

**B**) for vitamin B12 from beads GG/Ca 0.3% without laponite in SGF and SIF. Continuous lines represent model predictions from Equations (11)–(13). Estimated values of the B12 diffusivity D

_{d}

^{sg}are reported in Table 5.

**Figure 13.**Gastrointestinal integral release curve for vitamin B12 from beads GG/Ca 0.3% with and without laponite (p < 0.001). Continuous lines represent model predictions for the Fickian release model from Equations (11)–(13) and for the two-phase release model from Equations (13)–(16) with model parameters reported in Table 5.

**Figure 14.**Integral release curve for vitamin B12 from beads GG/LAPO/Ca 0.3% with laponite in SGF and SIF. Dotted curves highlight the Fickian and non-Fickian behaviors in SIF and in SGF, respectively. Continuous lines represent model predictions from Equations (13)–(16).

Beads Formulation | Beads Diameter (mm ± SD) | Freeze-Dried Beads Diameter (mm ± SD) |
---|---|---|

GG/Ca 0.3% | 2.41 ± 0.06 | 1.63 ± 0.03 |

GG/Ca 0.6% | 2.44 ± 0.07 | 1.56 ± 0.09 |

GG/LAPO/Ca 0.3% | 2.79 ± 0.11 | 2.06 ± 0.08 |

**Table 2.**Swelling degree at equilibrium S

_{eq}(measured after 24 h) and effective solvent diffusion coefficient D

_{s}

^{sg}of different bead formulations in Simulated Gastric Fluid (SGF; HCl 0.1 M) and Simulated Intestinal Fluid (SIF; phosphate buffer 0.044 M, pH 7.4).

Beads Formulation | S_{eq} in SGF | S_{eq} in SIF | D_{s}^{sg} in SGF [m^{2}/s] | D_{s}^{sg} in SIF [m^{2}/s] |
---|---|---|---|---|

GG/Ca 0.3% | 9.08 ± 0.3 | 45.80 ± 0.9 | (8.8 ± 0.3) × 10^{−10} | (1.5 ± 0.1) × 10^{−9} |

GG/Ca 0.6% | 8.97 ± 0.2 | 25.44 ± 0.6 | - | - |

GG/LAPO/Ca 0.3% | 9.14 ± 0.3 | 20.60 ± 0.3 | (6.5 ± 0.3) × 10^{−10} | (1.1 ± 0.1) × 10^{−9} |

Beads | Drug Molecule | Entrapment Efficiency (%) |
---|---|---|

GG/Ca 0.3% | Vitamin B12 | 53.62 |

GG/LAPO/Ca 0.3% | Vitamin B12 | 61.26 |

GG/Ca 0.3% | Theophylline | 20.26 |

GG/LAPO/Ca 0.3% | Theophylline | 36.49 |

**Table 4.**Theophylline diffusivity in the swollen gel D

_{d}

^{sg}for two different bead formulations (with and without laponite) and two different media SGF and SIF.

Beads | D_{d}^{sg} in SGF [m^{2}/s] | D_{d}^{sg} in SIF [m^{2}/s] |
---|---|---|

GG/Ca 0.3% | (4.26 ± 0.15) × 10^{−10} | (2.62 ± 0.2) × 10^{−10} |

GG/LAPO/Ca 0.3% | (2.73 ± 0.3) × 10^{−11} | (1.43 ± 0.1) × 10^{−10} |

**Table 5.**Vitamin B12 diffusivity in the swollen gel D

_{d}

^{sg}and transfer rate coefficient k

_{bg}

^{sg}for two different bead formulations (with and without laponite) and two different media SGF and SIF.

Beads | D_{d}^{sg} in SGF [m^{2}/s] | D_{d}^{sg} in SIF [m^{2}/s] | k_{bg}^{sg} in SGF [1/s] | k_{bg}^{sg} in SIF [1/s] |
---|---|---|---|---|

GG/Ca 0.3% | (1.53 ± 0.15) × 10^{−10} | (1.85 ± 0.15) × 10^{−10} | - | - |

GG/LAPO/Ca 0.3% | (2.87 ± 0.1) × 10^{−11} | (5.33 ± 0.1) × 10^{−11} | 2.35 × 10^{−4} | 4.12 × 10^{−3} |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Adrover, A.; Paolicelli, P.; Petralito, S.; Di Muzio, L.; Trilli, J.; Cesa, S.; Tho, I.; Casadei, M.A.
Gellan Gum/Laponite Beads for the Modified Release of Drugs: Experimental and Modeling Study of Gastrointestinal Release. *Pharmaceutics* **2019**, *11*, 187.
https://doi.org/10.3390/pharmaceutics11040187

**AMA Style**

Adrover A, Paolicelli P, Petralito S, Di Muzio L, Trilli J, Cesa S, Tho I, Casadei MA.
Gellan Gum/Laponite Beads for the Modified Release of Drugs: Experimental and Modeling Study of Gastrointestinal Release. *Pharmaceutics*. 2019; 11(4):187.
https://doi.org/10.3390/pharmaceutics11040187

**Chicago/Turabian Style**

Adrover, Alessandra, Patrizia Paolicelli, Stefania Petralito, Laura Di Muzio, Jordan Trilli, Stefania Cesa, Ingunn Tho, and Maria Antonietta Casadei.
2019. "Gellan Gum/Laponite Beads for the Modified Release of Drugs: Experimental and Modeling Study of Gastrointestinal Release" *Pharmaceutics* 11, no. 4: 187.
https://doi.org/10.3390/pharmaceutics11040187