Mechanistic modelling of drug release from multi-layer capsules

Kaoui, Badr; Lauricella, Marco; Pontrelli, Giuseppe

doi:10.1016/j.compbiomed.2017.12.010

Cited by 47 publications

(63 citation statements)

References 26 publications

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“…(32)-(35) can be solved symbolically in a computer algebra system such as Maple [20], which leads to the following functions: which describe how MAT varies with position x within the first and second layers, respectively. Both M 1 (x) and M 2 (x) are monotonically increasing on (x 0 , x 1 ) and (x 1 , x 2 ), which makes intuitive sense, as one would expect MAT to be greater the further away from the left end point (x = x 0 ) where the disturbance is introduced into the system via the boundary condition (17). As previously mentioned, for the external boundary conditions (17)- (18), the maximum value of MAT across both layers occurs at the right end point (x = x m ).…”

Section: Resultsmentioning

confidence: 98%

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Characteristic time scales for diffusion processes through layers and across interfaces

Carr

2018

Phys. Rev. E

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This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

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Section: Resultsmentioning

confidence: 98%

“…In groundwater flow models, R i is the storage coefficient and D i is the hydraulic conductivity in layer i. At the interfaces between adjacent layers, we study the following types of internal boundary conditions which are commonly applied at the interfaces [6,15,17,19]:…”

Section: Characteristic Timescales For Multilayer Diffusionmentioning

confidence: 99%

Characteristic time scales for diffusion processes through layers and across interfaces

Carr

2018

Phys. Rev. E

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“…The formula (4.4) requires knowledge of γ 0 and β 0 , which are related to the dominant eigenvalue and eigenfunction pair of the underlying Sturm-Liouville problem [8]. Alternatively, γ 0 and β 0 can be calculated by using appropriate temporal moments of the concentration as we now describe.…”

Section: Estimating the Release Time Using High Order Momentsmentioning

confidence: 99%

“…Analysis and solution of mechanistic models taking into account the multi-layer structure of the microcapsule has been recently addressed by Kaoui et al [8] and Carr and Pontrelli [9]. However, even in situations where the transport phenomena are well represented mathematically, the need exists to develop analytical tools or simple indicators to extract meaning from the model and the data.…”

Section: Introductionmentioning

confidence: 99%

Drug delivery from microcapsules: How can we estimate the release time?

Carr

Pontrelli

2019

Mathematical Biosciences

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Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches that provide useful indicators of the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration versus time curve at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides simple algebraic expressions involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) to characterize the release time while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally-cheap and useful measure to compare a priori the release time of different composite microcapsule configurations.

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“…One application of this type of materials is in the encapsulation of biologically active molecules and drugs for tissue engineering, 25 that is, in patches. [34][35][36][37] According to the release mechanism of the drug, there are different release percentages and time to reach equilibrium; these parameters must be related to the required dose for each type of drug. [34][35][36][37] According to the release mechanism of the drug, there are different release percentages and time to reach equilibrium; these parameters must be related to the required dose for each type of drug.…”

Section: Introductionmentioning

confidence: 99%

Study of the release kinetics of (−) epicatechin: Effect of its location within the fiber or sphere

López-Peña

Castillo‐Ortega

Plascencia-Martínez

et al. 2018

J of Applied Polymer Sci

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The (−) epicatechin (Epi) is a flavonoid with antioxidant and regenerative properties for cardiac tissue. In this work, a study of release assays and their corresponding adjustments to models was performed to determine the mechanism of (−) Epi release in the cellulose acetate (CA)-polyvinylpyrrolidone (PVP) system. The morphology of the material was considered, fibers, or spheres, as well as the possible chemical interactions between Epi, PVP, and CA. It was observed that in the systems in which the PVP is present, a high release is observed in comparison with those that only contained CA and (−) Epi, which showed very low release. This difference can be explained considering the possible hydrogen bond interaction between CA and (−) Epi, as well as the insolubility of the CA, in the release medium. The factors that have an important effect on the release of (−) Epi in the different systems are: the morphology, a faster release in morphologies with greater surface area, and the chemical interactions that can be formed among the (−) Epi and the components of the matrix. Another factor is the solubility of the components in the release medium, which allows the diffusion and drag phenomena to be observed simultaneously.

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Mechanistic modelling of drug release from multi-layer capsules

Cited by 47 publications

References 26 publications

Characteristic time scales for diffusion processes through layers and across interfaces

Characteristic time scales for diffusion processes through layers and across interfaces

Drug delivery from microcapsules: How can we estimate the release time?

Study of the release kinetics of (−) epicatechin: Effect of its location within the fiber or sphere

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