NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.

Synthesis of visible-light-activated yellow amorphous TiO2 photocatalyst

Visible-light-activated yellow amorphous TiO₂ (yam- TiO ₂) was synthesised by a simple and organic-free precipitation method. TiN, an alternative precursor for TiO₂ preparation, was dissolved in hydrogen peroxide under acidic condition (pH∼1) adjusted by nitric acid. The yellow precipitate was obtained after adjusting pH of the resultant red brown solution to 2 with NH₄OH. The BET surface area of this sample was 261 m²/g. The visible light photoactivity was evaluated on the basis of the photobleaching of methylene blue (MB) in an aqueous solution by using a 250 W metal halide bulb equipped with UV cutoff filter (λ>420 nm) under aerobic conditions. Yam- TiO₂ exhibits an interesting property of being both surface adsorbent and photoactive under visible light. It was assigned to the η²-peroxide, an active intermediate form of the addition of H₂O₂ into crystallined TiO₂ photocatalyst. It can be concluded that an active intermediate form of titanium peroxo species in photocatalytic process can be synthesised and used as a visible-light-driven photocatalyst

Thermodynamically stable amorphous drug dispersions in amorphous hydrophilic polymers engineered by hot melt extrusion.

In this study thermodynamically stable dispersions of amorphous quinine, a model BCS class 2 therapeutic agent, within an amorphous polymeric platform (HPC), termed a solid-in-solid dispersion, were produced using hot melt extrusion. Characterisation of the pre-extrudates and extrudates was performed using hyper-differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD) and Raman spectroscopy. Water uptake by the raw materials was determined using dynamic vapour sorption (DVS) analysis. Furthermore, the presence or absence of crystalline drug following storage at 25 °C/60% relative humidity and 40 °C/75% relative humidity in a sealed glass jar, and at 40 °C/75% relative humidity in an open glass jar for 3 months was determined using PXRD. Amorphous quinine was generated in situ during extrusion from both quinine base (5%, 10%, 20% w/w drug loading) and from quinine hydrochloride (5%, 10% w/w drug loading) and remained thermodynamically stable as a solid-in-solid dispersion within the HPC extrudates. When processed with HPC, quinine hydrochloride (20% w/w) was converted to amorphous quinine hydrochloride. Whilst stable for up to 3 months when stored under sealed conditions, this amorphous form was unstable, resulting in recrystallisation of the hydrochloride salt following storage for 1 month at 40 °C/75% relative humidity in an open glass jar. The behaviour of the amorphous quinine hydrochloride (20% w/w) HPC extrudate was related, at least in part, to the lower stability and the hygroscopic properties of this amorphous form.

An Investigation into the Role of Polymeric Carriers on Crystal Growth within Amorphous Solid Dispersion Systems

Using phase diagrams derived from Flory–Huggins theory, we defined the thermodynamic state of amorphous felodipine within three different polymeric carriers. Variation in the solubility and miscibility of felodipine within different polymeric materials (using F–H theory) has been identified and used to select the most suitable polymeric carriers for the production of amorphous drug–polymer solid dispersions. With this information, amorphous felodipine solid dispersions were manufactured using three different polymeric materials (HPMCAS-HF, Soluplus, and PVPK15) at predefined drug loadings, and the crystal growth rates of felodipine from these solid dispersions were investigated. Crystallization of amorphous felodipine was studied using Raman spectral imaging and polarized light microscopy. Using this data, we examined the correlation among several characteristics of solid dispersions to the crystal growth rate of felodipine. An exponential relationship was found to exist between drug loading and crystal growth rate. Moreover, crystal growth within all selected amorphous drug–polymer solid dispersion systems were viscosity dependent (η–ξ). The exponent, ξ, was estimated to be 1.36 at a temperature of 80 °C. Values of ξ exceeding 1 may indicate strong viscosity dependent crystal growth in the amorphous drug–polymer solid dispersion systems. We argue that the elevated exponent value (ξ > 1) is a result of drug–polymer mixing which leads to a less fragile amorphous drug–polymer solid dispersion system. All systems investigated displayed an upper critical solution temperature, and the solid–liquid boundary was always higher than the spinodal decomposition curve. Furthermore, for PVP–FD amorphous dispersions at drug loadings exceeding 0.6 volume ratio, the mechanism of phase separation within the metastable zone was found to be driven by nucleation and growth rather than liquid–liquid separation.

Novel Supercritical Carbon Dioxide Impregnation Technique for the Production of Amorphous Solid Drug Dispersions: A Comparison to Hot Melt Extrusion

The formulation of BCS Class II drugs as amorphous solid dispersions has been shown to provide advantages with respect to improving the aqueous solubility of these compounds. While hot melt extrusion (HME) and spray drying (SD) are among the most common methods for the production of amorphous solid dispersions (ASDs), the high temperatures often required for HME can restrict the processing of thermally labile drugs, while the use of toxic organic solvents during SD can impact on end-product toxicity. In this study, we investigated the potential of supercritical fluid impregnation (SFI) using carbon dioxide as an alternative process for ASD production of a model poorly water-soluble drug, indomethacin (INM). In doing so, we produced ASDs without the use of organic solvents and at temperatures considerably lower than those required for HME. Previous studies have concentrated on the characterization of ASDs produced using HME or SFI but have not considered both processes together. Dispersions were manufactured using two different polymers, Soluplus and polyvinylpyrrolidone K15 using both SFI and HME and characterized for drug morphology, homogeneity, presence of drug-polymer interactions, glass transition temperature, amorphous stability of the drug within the formulation, and nonsink drug release to measure the ability of each formulation to create a supersaturated drug solution. Fully amorphous dispersions were successfully produced at 50% w/w drug loading using HME and 30% w/w drug loading using SFI. For both polymers, formulations containing 50% w/w INM, manufactured via SFI, contained the drug in the γ-crystalline form. Interestingly, there were lower levels of crystallinity in PVP dispersions relative to SOL. FTIR was used to probe for the presence of drug-polymer interactions within both polymer systems. For PVP systems, the nature of these interactions depended upon processing method; however, for Soluplus formulations this was not the case. The area under the dissolution curve (AUC) was used as a measure of the time during which a supersaturated concentration could be maintained, and for all systems, SFI formulations performed better than similar HME formulations.

Solubility parameter based screening methods for early stage formulation development of itraconazole amorphous solid dispersions

Objectives: This article uses conventional and newly extended solubility parameter (δ) methods to identify polymeric materials capable of forming amorphous dispersions with itraconazole (itz). Methods: Combinations of itz and Soluplus, Eudragit E PO (EPO), Kollidon 17PF (17PF) or Kollidon VA64 (VA64) were prepared as amorphous solid dispersions using quench cooling and hot melt extrusion. Storage stability was evaluated under a range of conditions using differential scanning calorimetry and powder X-ray diffraction. Key findings: The rank order of itz miscibility with polymers using both conventional and novel δ-based approaches was 17PF > VA64 > Soluplus > EPO, and the application of the Flory–Huggins lattice model to itz–excipient binary systems corroborated the findings. The solid-state characterisation analyses of the formulations manufactured by melt extrusion correlated well with pre-formulation screening. Long-term storage studies showed that the physical stability of 17PF/vitamin E TPGS–itz was poor compared with Soluplus and VA64 formulations, and for EPO/itz systems variation in stability may be observed depending on the preparation method. Conclusion: Results have demonstrated that although δ-based screening may be useful in predicting the initial state of amorphous solid dispersions, assessment of the physical behaviour of the formulations at relevant temperatures may be more appropriate for the successful development of commercially acceptable amorphous drug products.

Optimising drug solubilisation in amorphous polymer dispersions: rational selection of hot-melt extrusion processing parameters

The aim of this article was to construct a T–ϕ phase diagram for a model drug (FD) and amorphous polymer (Eudragit® EPO) and to use this information to understand the impact of how temperature–composition coordinates influenced the final properties of the extrudate. Defining process boundaries and understanding drug solubility in polymeric carriers is of utmost importance and will help in the successful manufacture of new delivery platforms for BCS class II drugs. Physically mixed felodipine (FD)–Eudragit® EPO (EPO) binary mixtures with pre-determined weight fractions were analysed using DSC to measure the endset of melting and glass transition temperature. Extrudates of 10 wt% FD–EPO were processed using temperatures (110°C, 126°C, 140°C and 150°C) selected from the temperature–composition (T–ϕ) phase diagrams and processing screw speed of 20, 100 and 200rpm. Extrudates were characterised using powder X-ray diffraction (PXRD), optical, polarised light and Raman microscopy. To ensure formation of a binary amorphous drug dispersion (ADD) at a specific composition, HME processing temperatures should at least be equal to, or exceed, the corresponding temperature value on the liquid–solid curve in a F–H T–ϕ phase diagram. If extruded between the spinodal and liquid–solid curve, the lack of thermodynamic forces to attain complete drug amorphisation may be compensated for through the use of an increased screw speed. Constructing F–H T–ϕ phase diagrams are valuable not only in the understanding drug–polymer miscibility behaviour but also in rationalising the selection of important processing parameters for HME to ensure miscibility of drug and polymer.

Using Flory-Huggins phase diagrams as a pre-formulation tool for the production of amorphous solid dispersions; a comparison between hot-melt extrusion and spray drying

Objectives: Amorphous drug forms provide a useful method of enhancing the dissolution performance of poorly water-soluble drugs; however, they are inherently unstable. In this article, we have used Flory–Huggins theory to predict drug solubility and miscibility in polymer candidates, and used this information to compare spray drying and melt extrusion as processes to manufacture solid dispersions.
Method:  Solid dispersions were characterised using a combination of thermal (thermogravimetric analysis and differential scanning calorimetry) and spectroscopic (Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction methods. 
Key Findings: Spray drying permitted generation of amorphous solid dispersions to be produced across a wider drug concentration than melt extrusion. Melt extrusion provided sufficient energy for more intimate mixing to be achieved between drug and polymer, which may improve physical stability. It was also confirmed that stronger drug–polymer interactions might be generated through melt extrusion. Remixing and dissolution of recrystallised felodipine into the polymeric matrices did occur during the modulated differential scanning calorimetry analysis, but the complementary information provided from FTIR confirms that all freshly prepared spray-dried samples were amorphous with the existence of amorphous drug domains within high drug-loaded samples. 
Conclusion: Using temperature–composition phase diagrams to probe the relevance of temperature and drug composition in specific polymer candidates facilitates polymer screening for the purpose of formulating solid dispersions.

A Correlation between the Dynamic Viscosity and Crystallisation of Felodipine from its Amorphous Polymer Solid Dispersion

Purpose Previously, it has been reported that molecular mobility determines the rate of molecular approach to crystal surfaces, while entropy relates to the probability of that approaching molecule having the desirable configuration for further growth of the existing crystal; and the free energy dictates the probability of that molecule not returning to the liquid phase1. If we plot the crystal growth rate and viscosity of a supercooled liquid in a log-log format, the relationship between the two is linear, indicating the influence viscosity has upon crystal growth rate. However, such approximation has been derived from pure drug compounds and it is apparent that further understanding of crystallization from drug-polymer solid dispersion is required in order to stabilise drugs embedded within amorphous polymeric solid dispersions. Methods Mixtures of felodipine and polymer (HPMCAS-HF, PVPK15 and Soluplus®) at specified compositions were prepared using a Restch MM200 ball mill. To examine crystal growth within amorphous solid dispersions, samples were prepared by melting 5-10 mg of ball milled mixture at 150°C for 3-5 minutes on a glass slip pre-cleaned with methanol and acetone. All prepared samples were confirmed to be crystal free by visual observation using a polarised light microscope (Olympus BX50). Prepared samples were stored at 0% RH (P2O5), inside desiccators, maintained in ovens at 80°C. For the dynamic viscosity measurement, approximately 100-200mg ball milled mixture was heated on the base plate of a rotational rheometer at 150°C for 5 minutes and the top plate was lowered to a defined gap to form a good contact with the material. The sandwiched amorphous material was heated to 80°C and the viscosity was measured. Results The equation was used to probe the correlation of viscosity to crystal growth rate. In comparison to the value of xi in log-log equation reported from pure drug compound, a value of 1.63 was obtained for FD-polymer solid dispersions irrespective of the polymer involved. &#8733 Conclusion The high xi value suggests stronger viscosity dependence may exist for amorphous FD once incorporated with amorphous polymer.

Drug Polymer Thermodynamic Phase Diagrams in the Selection of Optimal API-Polymer Compositions for Amorphous Solid Dispersions

Purpose The aim of this work was to examine, for amorphous solid dispersions, how the thermal analysis method selected impacts on the construction of thermodynamic phase diagrams, and to assess the predictive value of such phase diagrams in the selection of optimal, physically stable API-polymer compositions. Methods Thermodynamic phase diagrams for two API/polymer systems (naproxen/HPMC AS LF and naproxen/Kollidon 17 PF) were constructed from data collected using two different thermal analysis methods. The “dynamic” method involved heating the physical mixture at a rate of 1 &[deg]C/minute. In the "static" approach, samples were held at a temperature above the polymer Tg for prolonged periods, prior to scanning at 10 &[deg]C/minute. Subsequent to construction of phase diagrams, solid dispersions consisting of API-polymer compositions representative of different zones in the phase diagrams were spray dried and characterised using DSC, pXRD, TGA, FTIR, DVS and SEM. The stability of these systems was investigated under the following conditions: 25 &[deg]C, desiccated; 25 &[deg]C, 60 % RH; 40 &[deg]C, desiccated; 40 &[deg]C, 60 % RH. Results Endset depression occurred with increasing polymer volume fraction (Figure 1a). In conjunction with this data, Flory-Huggins and Gordon-Taylor theory were applied to construct thermodynamic phase diagrams (Figure 1b). The Flory-Huggins interaction parameter (&[chi]) for naproxen and HPMC AS LF was + 0.80 and + 0.72, for the dynamic and static methods respectively. For naproxen and Kollidon 17 PF, the dynamic data resulted in an interaction parameter of - 1.1 and the isothermal data produced a value of - 2.2. For both systems, the API appeared to be less soluble in the polymer when the dynamic approach was used. Stability studies of spray dried solid dispersions could be used as a means of validating the thermodynamic phase diagrams. Conclusion The thermal analysis method used to collate data has a deterministic effect on the phase diagram produced. This effect should be considered when constructing thermodynamic phase diagrams, as they can be a useful tool in predicting the stability of amorphous solid dispersions.