Mathematical models for estimating effective diffusion parameters of spherical drug delivery devices

Mathematical modeling of drug delivery is of increasing academic and industrial importance in manyaspects. In this paper, we propose an optimization approach for the estimation of the parameters characterizing the diffusion process of a drug from a spherical porous polymer device to an external finite volume. The approach is based on a nonlinear least-squares method and a novel mathematical model which takes into consideration both boundary layer effect and initial burst phenomenon. Ananalytical solution to the model is derived and a formula for the ratio of the mass released in a given time interval and the total mass released in infinite time is also obtained. The approach has been tested using experimental data of the diffusion of prednisolone 21-hemisuccinate sodium saltfrom spherical devices made of porous poly(2-hydroxyethyl methacrylate) hydrogels. The effectiveness and accuracy of the method are well demonstrated by the numerical results. The model was used to determine the diffusion parameters including the effective diffusion coefficient of the drug from a series of devices that vary in both the porous structure and the drug loading levels. The computed diffusion parameters are discussed in relation to the physical properties of the devices

Single-Valued Neutrosophic DEMATEL for Segregating Types of Criteria: A Case of Subcontractors’ Selection

The decision-making trial and evaluation laboratory (DEMATEL) has been used to solve numerous multicriteria decision-making (MCDM) problems, where real numbers are utilised in defining linguistic variables. Although the DEMATEL has shown its success in solving many decision-making problems, researchers have not fully understood how the DEMATEL works on non-real-number linguistic variables. Recent discovery of single-valued neutrosophic sets (SVNSs) can offer a new method to solve decision-making problems, where three memberships of SVNSs are used to define experts’ linguistic judgment. This paper aims to propose a novel MCDM method, where SVNSs and the DEMATEL are fully utilised. Different from the DEMATEL, which directly utilises real numbers, this proposed method introduces SVNSs to better deal with truth, indeterminacy, and falsity in solving MCDM problem. As an application of the proposed method, subcontractors’ selection problem is investigated using the proposed method, where four types of criteria are developed. A group of experts were invited to provide opinions and linguistic judgment regarding the degree of influence between criteria of subcontractors’ selection. The linguistic evaluations defined in SVNSs were computed using the eight-step procedures of the proposed method. Based on the degree of influence, the computational results successfully segregated all ten criteria into four types, in which two to three criteria are grouped in each type. The results also suggest that “Experience” and “Quality” are the most influential criteria in subcontractors’ selection. The segregation based on degree of influence would be greatly significant for the practical implementation of the subcontractors’ selection

Mathematical Model for Estimating Parameters of Swelling Drug Delivery Devices in a Two-Phase Release

Various swelling drug delivery devices are promising materials for control drug delivery because of their ability to swell and release entrapped therapeutics, in response to physiological stimuli. Previously, many mathematical models have been developed to predict the mechanism of drug release from a swelling device. However, some of these models do not consider the changes in diffusion behaviour as the device swells. Therefore, we used a two-phase approach to simplify the mathematical model considering the effect of swelling on the diffusion coefficient. We began by defining a moving boundary problem to consider the swelling process. Landau transformation was used for mitigating the moving boundary problem. The transformed problem was analytically solved using the separation of variables method. Further, the analytical solution was extended to include the drug release in two phases where each phase has distinct diffusion coefficient and continuity condition was applied. The newly developed model was validated by the experimental data of bacterial cellulose hydrogels using the LSQCURVEFIT function in MATLAB. The numerical test showed that the new model exhibited notable improvement in curve fitting, and it was observed that the initial effective diffusion coefficient of the swelling device was lower than the later effective diffusion coefficient

Analytical Solution for Controlled Drug Release with Time-Dependent Diffusion Parameter

Drugs seem to diffuse in different manners in a delivery device due to the increment of the device pore size during swelling. However, the diffusion parameter, D, is often assumed constant. In this work, a new developed controlled drug release model with a time-dependent diffusion parameter is compared to one- and two-phase models. The new model was obtained as an improvement of the previous constant and piece-wise constants models. The models are developed by solving an advection–diffusion equation using the Landau transformation method and the separation of variables method. To test these models, we fit experimental data by the developed models using the least squares fitting technique. The curve-fitting result shows that the least squares error of the two-phase and the time-dependent models are 10 times smaller than the single-phase model. The CPU time for the time-dependent model is the lowest, showing that a time-dependent model is the best option among all three tested models considering both factors of the determined least squares error and the time consumption

Fifteen years of research on oral-facial-digital syndromes: from 1 to 16 causal genes

Oral-facial-digital syndromes (OFDS) gather rare genetic disorders characterised by facial, oral and digital abnormalities associated with a wide range of additional features (polycystic kidney disease, cerebral malformations and several others) to delineate a growing list of OFDS subtypes. The most frequent, OFD type I, is caused by a heterozygous mutation in the OFD1 gene encoding a centrosomal protein. The wide clinical heterogeneity of OFDS suggests the involvement of other ciliary genes. For 15 years, we have aimed to identify the molecular bases of OFDS. This effort has been greatly helped by the recent development of whole-exome sequencing (WES). Here, we present all our published and unpublished results for WES in 24 cases with OFDS. We identified causal variants in five new genes (C2CD3, TMEM107, INTU, KIAA0753 and IFT57) and related the clinical spectrum of four genes in other ciliopathies (C5orf42, TMEM138, TMEM231 and WDPCP) to OFDS. Mutations were also detected in two genes previously implicated in OFDS. Functional studies revealed the involvement of centriole elongation, transition zone and intraflagellar transport defects in OFDS, thus characterising three ciliary protein modules: the complex KIAA0753-FOPNL-OFD1, a regulator of centriole elongation; the Meckel-Gruber syndrome module, a major component of the transition zone; and the CPLANE complex necessary for IFT-A assembly. OFDS now appear to be a distinct subgroup of ciliopathies with wide heterogeneity, which makes the initial classification obsolete. A clinical classification restricted to the three frequent/well-delineated subtypes could be proposed, and for patients who do not fit one of these three main subtypes, a further classification could be based on the genotype

Atomic force microscopy (AFM) and field emission scanning electron microscopy (FESEM) images of CA-PEI micelles.

<p>(a) AFM of CA-PEI micelles; (b) AFM of siRNA-loaded CA-PEI micelles; (c) FESEM of BSA-loaded CA-PEI micelles; (d) FESEM of siRNA-loaded CA-PEI micelles. All these images were of micelles with a CA-PEI molar ratio of 1∶3.</p

Fertilizer Subsidy and Agricultural Productivity: Empirical Evidence from Nepal

<p>(a) SDS-PAGE and (b) circular dichroism analyses of BSA released from different molar ratio CA-PEI micelles (1∶1, 1∶3, and 3∶1).</p

Schematic representation of the synthesis of cholic acid-polyethylenimine (CA-PEI) copolymer via carbodiimide-mediated coupling.

<p>Schematic representation of the synthesis of cholic acid-polyethylenimine (CA-PEI) copolymer via carbodiimide-mediated coupling.</p

Zeta potentials and LE (%) of CA-PEI micelles.

<p>*^{, **, ∞, *∞, α, *α} p< 0.05 for the comparison between group means.</p

Curves fitted using the cylindrical diffusion model for cumulative <i>in vitro</i> release profiles of (a) BSA and (b) siRNA at pH 5 and pH 7.4.

<p>Curves fitted using the cylindrical diffusion model for cumulative <i>in vitro</i> release profiles of (a) BSA and (b) siRNA at pH 5 and pH 7.4.</p