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Mathematical modeling of drug release and the advantages of lipid matrix formers
Mathematical modeling of mass transport in controlled drug delivery systems can be highly beneficial: On the one hand side, the underlying drug release mechanisms can be elucidated, on the other hand side, time-consuming and cost-intensive series of trial-and-error experiments can be replaced by rapid in-silico simulations (Siepmann, 2006-2012a-2013a ; Peppas, 2013). Compared to other scientific domains, such computer-assisted device design is yet rarely applied in pharmaceutics.
A mechanistically realistic mathematical theory should always be based on a thorough physico-chemical characterization of the dosage form before and after exposure to the release medium. Based on this knowledge, appropriate model assumptions should be defined. Ideally, only the dominant mass transport phenomena should be included, whereas processes which have only a minor impact, should be neglected in order to keep the model straightforward and simple to use. Examples for mass transport phenomena, which might play a role in oral controlled drug delivery systems include water penetration into the system (Hariharan, 1993), drug particle dissolution (Siepmann, 2013b), drug diffusion through water-filled channels and/or polymeric networks (Siepmann, 2012 ; Grassi, 1999-2003 ; Frenning, 2011 ; Yin, 2011), polymer swelling, degradation and/or dissolution (Brazel, 2000 ; Borgquist, 2006 ; Sackett, 2011 ; Kaunisto, 2011), time-and position-dependent changes in the mobility of water and drug within the dosage form (Mallapragada, 1997), and system disintegration. In certain cases, only one of these phenomena might be dominant and the mathematical description of the delivery system might be straightforward (Siepmann, 2010). However, in other cases a multitude of processes might be decisive at the same time and an accurate mathematical treatment is complex (Siepmann, 2012b). Due to the large variety of controlled release dosage forms it can also not be expected that one single model could be valid for all types of systems. Instead, on a case-by-case basis, the validity of a model must be evaluated for each type of systems.
Some reports are available on lipid controlled drug delivery systems (Zaky, 2010 ; Siepmann, 2011), in which a drug is embedded within a lipid matrix former. In particular for lipid implants different mathematical theories have been described so far (Siepmann, 2011 ; Guse, 2006). However, these models: (i) were either developed for relatively complex systems, in which for instance protein precipitation due to the presence of co-dissolved polyethylene glycol is of importance (Herrmann, 2007a ; Herrmann, 2007b ; Siepmann, 2008), or (ii) take only one single mass transport phenomenon into account, e.g. diffusion (Kreye, 2011a-2011b-2011c-2011d ; Gueres, 2012). Yet, there is a lack of appropriate, mechanistically realistic mathematical theories quantifying mass transport in lipid tablets and allowing for the prediction of the impact of key formulation and processing parameters, such as the initial drug loading, tablet height and tablet radius as well as the manufacturing procedure of the systems on the resulting drug release kinetics.
Lipids have recently been proposed as alternative material for the preparation of controlled drug delivery systems (Kreye et al., 2008, 2011a, 2011b; Maschke et al., 2004; Vogelhuber et al., 2003). The development of new drug delivery systems with these later can be explain by a broad spectrum of excipient type due to differences in fatty acid chain length, esterification or as lipid blends. They offer several advantages: being physiological substances, lipids show good biocompatibility, and they might be less expensive than polymeric materials. Being water-insoluble and non-swellable, lipid materials have major applications in sustained-release systems, especially for systems containing high loadings of freely water-soluble drugs. Drug release is also dependant of the diffusion coefficient and due to the degradation of the matrix induces by the lipases or an erosion of the device.
Application of terahertz pulsed imaging for film coating
Multiparticulate dosage forms are desirable drug delivery systems owing to a number of advantages over single unit dosage forms, such as better control of the gastric transit time and associated drug absorption, and a lower susceptibility to dose dumping (Bechgaard and Nielsen, 1978). Frequently, the particles are coated to modify drug release kinetics. Thus, the product performance directly correlates with critical film coating quality attributes, including the coating thickness and uniformity (Haddish-Berhane et al., 2006).Routinely, indirect monitoring methods such as the product weight-gain and the amount of coating polymer applied are used to infer the pellet film coating thickness (and thus the coating quality) (Ringqvist et al., 2003). For complex systems, e.g. drug-layered sugar starter cores coated with a sustained-release coating, the non-specific character of the weight-gain measurements as well as the fact that coating thickness uniformity can be related to the drug layer surface morphology, render weight-gain as a sole indication of the coating quality insufficient (Ho et al., 2008; Ho et al., 2010).
First point with multiple-unit system is the elucidation of properties of each subunit separately. An idea of release characteristic can be applied by the studies of variation in kinetics between subunits. Thus, a number of studies using mechanical analysis, e.g. in vitro drug release testing, have been used to obtain more insight into pellet coating structures and their effects on drug release (Siepmann et al., 2007; Siepmann et al., 2008; Muschert et al., 2009). Those mechanistic methods provide deeper understanding of the drug release mechanism from the coated dosage form. But there is still a lack of detailed information on critical film coating quality attributes such as coating thickness, uniformity and morphology. Information on the coating thickness, uniformity and morphology may be obtained with other analytical techniques including scanning electron microscopy (SEM)(Heinicke and Schwartz, 2007), fluorescence microscopy (Andersson et al., 2000), atomic force microscopy (AFM)(Ringqvist et al., 2003), optical coherence tomography (OCT)(Zhong et al., 2011), confocal Raman microimaging (Ringqvist et al., 2003), energy dispersive X-ray imaging (EDX)(Ensslin et al., 2008), nuclear magnetic resonance spectroscopy (NMR)(Ensslin et al., 2008), electron paramagnetic resonance spectroscopy (EPR)(Ensslin et al., 2009) anconfocal laser scanning microscopy (CLSM)(Depypere et al., 2009).Cahyadi et al. in 2010 make an interesting comparison between some non-destructive techniques used to characterise the coating thickness. Direct observation in Direct Optical Microscopy seems the best technique, with SEM observations, to be the model references to validate others analytical techniques. However, both need time and money consuming, and destruction of the sample. Second technique which allows rapid and on-line characterisation is using the micrometer to measure the difference between the thickness coated and non coated pellets (Römer et al., 2008), but it’s again time-consuming technique. Based on these observations Cahyadi and al., supposed Raman spectroscopy seems to be the best method for characterisation. Problems with this technique is the interpretation of signals which needs some calculations. In-line NIR (Near Infra Red) can be used to detect quantitative film coating too (Andersson et al.,2000 ; Lee et al., 2011 ; Moes et al., 2008). Cogdill et al., in 2007 compare NIR with Terahertz technology and bienque this last shows a problem of sensitivity, Terahertz technology seems to be the directe technique to characterise coating thickness. Indeed, like Raman spectroscopy, lots of noise are read in the diffractograms for NIR interpretation and a bad estimation of the results are observed. Recently, Möltgen combined NIR with science based calibration to determine noise in the diffractograms and by calculation with this value, coating thickness can be approximate on-line (Möltgen et al., 2013).
Model fittings to experimental results
The curves in figures. 12 and 13 show the fittings of the above described mathematical model to the experimentally determined niacin release kinetics from the different types of lipid tablets. It must be pointed out that the term “fitting” means that at least one model parameter was adjusted to minimize the resulting differences between theory and experiment. In the present study, only 1 parameter was initially unknown and adjusted by model fitting: the apparent diffusion coefficient of the vitamin in the lipid matrix. As is can be seen, good agreement between theory and experiment was obtained in all cases, irrespective of the initial niacin loading and type of preparation method (curves and symbols in figures. 12 and 13). This can serve as an indication for the fact that the hypothesized model assumptions might indeed be valid. However, caution must be paid: The observed good agreement is not a real proof for the validity of the model, since these are model fittings.
Based on these calculations, the apparent diffusion coefficient of niacin in the glyceryl dibehenate matrices could be determined. The black bars in figure 14 show the values obtained with tablets prepared by direct compression, the white bars the respective values for tablets prepared via hot-melt extrusion/grinding/compression. Two tendencies are clearly visible: (i) With increasing initial vitamin content, the apparent niacin mobility within matrices significantly increases, irrespective of the type of preparation technique. (ii) Niacin mobility in tablets prepared by direct compression is much higher than in tablets of identical composition, but prepared via hot-melt extrusion/grinding/compression. These tendencies are consistent with the vitamin release kinetics illustrated in figures. 12 and 13. The substantial increase in vitamin mobility with increasing initial niacin loading can be attributed to the fact that the lipid matrices become more and more porous upon vitamin exhaust with increasing initial vitamin content: As discussed above, the outer dimensions of the lipid tablets remained unaltered during niacin release. Thus, positions initially occupied by vitamin particles become occupied by water once niacin is released. The higher the initialvitamin content, the higher the resulting porosity. Consequently, the vitamin mobility in the lipid matrices increases with increasing initial niacin loading. Note that the D values are time-and position-averaged parameters. Importantly, the following quantitative empirical relationships could be established between the apparent niacin diffusivity in the lipid tablets and the initial vitamin content.
Table of contents :
Table of content
1. Introduction (English)
1.1. General
1.2. Purposes of this work
1.3. Mathematical modeling of drug release and the advantages of lipid matrix formers
1.4. Application of terahertz pulsed imaging for film coating characterization (from Haaser et al., 2013)
1.5. Ethanol-resistant polymeric film coatings
2.Introduction (Français)
2.1 Généralité
2.2. Objectifs de la thèse
2.3. Modèle mathématique de libération de principe actif et avantages des matrices lipidiques
2.4. Imagerie terahertz pulsee pour la caracterisation de film d’enrobage
2.5. Ethanol-resistant polymeric film coatings
3. References
4. In-silico simulation of niacin release from lipid tablets:
Theoretical predictions and independent experiments
4.1. Materials and methods
4.1.1. Materials
4.1.2. Tablet preparation
4.1.3. Tablet characterization
4.1.4. Equilibrium solubility measurements
4.2. Results and discussion
4.2.1. Model development
4.2.2. Model fittings to experimental results
4.2 3. Deeper insight into vitamin release mechanisms
4.2.4. Model predictions and independent experiments
4.3. Conclusion
5. Investigation of the viscosity grade of guar gum in polymer blends to overcome ethanol sensitivity of ethylcellulose-based coated pellets.
5.1. Materials and Methods
5.1.1. Materials
5.1.2. Preparation and characterization of thin polymeric films
5.1.3. Pellet coating
5.1.4. Drug release measurements
5.1.5. SEM studies
5.2. Results and discussion
5.2.1. Ethylcellulose/guar gum ratio
5.2.2. Guar gum concentration in the total dispersion
5.2.3. Coating level
5.2.4. Storage stability
5.2.5. Guar gum viscosity
5.3. Conclusion
6. Elucidation of the underlying drug release mechanism of ethanol resistant coated pellets
6.1. Materials and methods
6.1.1. Materials
6.1.2. Preparation and characterization of thin polymeric films
6.1.3. Pellet coating
6.1.4. Drug release measurements
6.1.5. SEM studies
6.1.6 Diffusion cell studies
6.1.7. Determination of the drug solubility and of the partition coefficient of the drug
6.2. Results and discussion
6.2.1. Drug release from single pellets
6.2.2. Impact of the osmolality of the release medium
6.2.3. Morphology and mechanical properties of the film coatings
6.2.4. Drug mobility within the film coatings
6.2.5. Mathematical modeling of drug release
6.2.6. Intermediate ethanol concentrations
6. 4. Conclusion
7. Effects of film coating thickness on in-vitro drug release about sustained-release coated pellets: Using terahertz pulsed imaging
7.1. Materials and Methods
7.1 1. Materials
7.1 2. Preparation of the Pellets
7.1.3. Terahertz Pulsed Imaging (TPI)
7.1.4. Dissolution Testing
7.1.5. Scanning Electron Microscopy (SEM)
7.2. Results and discussion
7.3. Conclusion
8. Summary
