Mathematically Modelling The Dissolution Of Solid Dispersions

summary:A solid dispersion is a dosage form in which an active ingredient (a drug) is mixed with at least one inert solid component. The purpose of the inert component is usually to improve the bioavailability of the drug. In particular, the inert component is frequently chosen to improve the dissolution rate of a drug that is poorly soluble in water. The construction of reliable mathematical models that accurately describe the dissolution of solid dispersions would clearly assist with their rational design. However, the development of such models is challenging since a dissolving solid dispersion constitutes a non-ideal mixture, and the selection of appropriate forms for the activity coefficients that describe the interaction between the drug, the inert matrix, and the dissolution medium is delicate. In this paper, we present some preliminary ideas for modelling the dissolution of solid dispersions

Modelling phase separation in amorphous solid dispersions

Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available. In this paper, we address some of these deficiencies by (i) constructing a general multicomponent diffusion model for a dissolving solid dispersion; (ii) specializing the model to a binary drug/polymer system in storage; (iii) deriving an effective concentration dependent drug diffusion coefficient for the binary system, thereby obtaining a theoretical prediction for the timescale over which phase separation occurs; and (iv) presenting a detailed numerical investigation of the HPMCAS/Felodipine system assuming a Flory-Huggins activity coefficient. The numerical simulations exhibit numerous interesting phenomena, such as the formation of polymer droplets and strings, Ostwald ripening/coarsening, phase inversion, and droplet-to-string transitions

Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusivity is many orders of magnitude smaller. The classical Neumann similarity solution holds while the front is passing through the first layer, but this breaks down in the second layer. Asymptotic methods are used to understand what is happening in the second layer. Although this necessitates numerical computation, one interesting outcome is that only one calculation is required, no matter what the diffusivity is for the second laye

Prelithification and synlithification tectonic foliation development in a clastic sedimentary sequence

The current view regarding the timing of regionally developed penetrative tectonic fabrics in sedimentary rocks is that their development postdates lithification of those rocks. In this case, fabric development is achieved by a number of deformation mechanisms, including grain rigid body rotation, crystal-plastic deformation, and pressure solution. The latter is believed to be the primary mechanism responsible for the domainal structure of cleavage in low-grade metamorphic rocks. In this study we combine field observations with strain studies to characterize considerable (>50%) Acadian crustal shortening in a Devonian clastic sedimentary sequence from southwest Ireland. Despite these high levels of shortening there is a marked absence of the domainal cleavage structure and intraclast deformation that are expected with this level of deformation. Fabrics in these rocks are predominantly a product of rigid body rotation and repacking of extraformational clasts during deformation of a clastic sedimentary sequence before lithification was complete

Prelithification and synlithification tectonic foliation development in a clastic sedimentary sequence

The current view regarding the timing of regionally developed penetrative tectonic fabrics in sedimentary rocks is that their development postdates lithification of those rocks. In this case, fabric development is achieved by a number of deformation mechanisms, including grain rigid body rotation, crystal-plastic deformation, and pressure solution. The latter is believed to be the primary mechanism responsible for the domainal structure of cleavage in low-grade metamorphic rocks. In this study we combine field observations with strain studies to characterize considerable (>50%) Acadian crustal shortening in a Devonian clastic sedimentary sequence from southwest Ireland. Despite these high levels of shortening there is a marked absence of the domainal cleavage structure and intraclast deformation that are expected with this level of deformation. Fabrics in these rocks are predominantly a product of rigid body rotation and repacking of extraformational clasts during deformation of a clastic sedimentary sequence before lithification was complete

Testing assumptions for endophenotype studies in ADHD: Reliability and validity of tasks in a general population sample

BACKGROUND: Advances in both genetic and cognitive-experimental studies on attention deficit hyperactivity disorder (ADHD) have opened new opportunities for cognitive endophenotype research. In such genetic designs the focus is on individual differences in characteristics, associated with ADHD, that can be measured reliably over time. Genetic studies that take a 'quantitative trait loci' approach hypothesise that multiple susceptibility genes contribute to a continuous dimension of ADHD symptoms. As an important initial step, we aimed to investigate the underlying assumptions that (1) key cognitive-experimental tasks indicate adequate test-retest reliability and (2) ADHD symptom scores in a general population sample are associated with performance on these tasks. METHODS: Forty-nine children were assessed on a go/no-go task and a reaction time task (the 'fast task') that included manipulations with event rate and incentives. The children were assessed twice, with a test-retest interval of two weeks. RESULTS: The majority of the task variables demonstrated moderate-to-good test-retest reliability. The correlations between teacher ratings of ADHD symptoms and key task variables were .4–.6: ADHD symptoms were associated with poor performance (especially high reaction time variability) in a slow baseline condition, whereas there was low or no association in conditions with a faster event rate or incentives. In contrast, no clear pattern of findings emerged based on parent ratings of ADHD symptoms. CONCLUSION: The data support the usefulness of the go/no-go and fast tasks for genetic studies, which require reliable and valid indices of individual differences. The overall pattern of associations between teacher ratings of ADHD symptoms and task variables is consistent with effects of event rate and incentives on performance, as predicted by the model of activation and arousal regulation. The lack of a clear pattern of findings with parent ratings of ADHD symptoms warrants further study

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found

The Three Models of Emotional Intelligence and Performance in a Hot and Cool go/no-go Task in Undergraduate Students

Emotional intelligence (EI), or the ability to perceive, use, understand and regulate emotions, appears to be helpful in the performance of “hot” (i.e., emotionally laden) cognitive tasks when using performance-based ability models, but not when using self-report EI models. The aim of this study is to analyze the relationship between EI (as measured through a performance-based ability test, a self-report mixed test and a self-report ability test) and cognitive control ability during the performance of hot and “cool” (i.e., non-emotionally laden) “go/no-go” tasks. An experimental design was used for this study in which 187 undergraduate students (25% men) with a mean age of 21.93 years (standard deviation [SD] = 3.8) completed the three EI tests of interest (Mayer-Salovey-Caruso Emotional Intelligence Test [MSCEIT], Trait Meta-Mood Scale [TMMS] and Emotional Quotient Inventory–Short Form [EQi:S]) as well as go/no-go tasks using faces and geometric figures as stimuli. The results provide evidence for negative associations between the “managing” branch of EI measured through the performance-based ability test of EI and the cognitive control index of the hot go/no-go task, although similar evidence was not found when using the cool task. Further, the present study failed to observe consistent results when using the self-report EI instruments. These findings are discussed in terms of both the validity and implications of the various EI models.This research was supported in part by the projects Innovation and Development Agency of Andalusia, Spain (SEJ-07325), and the Spanish Ministry of Economy (PSI2012-37490)