Weibull Equation Research Articles

Monte Carlo simulations for the study of drug release from cylindrical matrix systems with an inert nucleus

In this work, drug release from matrices with an inert nucleus using Monte Carlo simulation was studied. Drug-excipient systems were simulated, where the drug is a soluble material while the excipient is a non-soluble material. In the center of these devices, an inert nucleus was placed. The release of the drug was unidirectional and the results were fitted to the square root of time law (Higuchi law), the power law and the Weibull equation. The percolation threshold of the drug was found to be near 0.35 close to the expected value for the cubic lattice, the difference is due to the finite and rather small size of the systems in study as well as to the fact that the lattice in use is not exactly cubic. Near the percolation threshold, the parameters of the different release models presented a drastic change; this was due to a phase transition of the system. On the other hand, it was found that the size of the matrix system modifies the transport properties of the release platform. In general, the release kinetics was adequately described by the Weibull equation.

Kinetics of Disappearance and Discoloration of L-Ascorbic Acid 2-Glucoside Powders with Different Water Contents

The disappearance and discoloration of L- ascorbic acid 2- glucoside powders with water contents of 2 to 12% (w/w) during storage at a temperature from 70 to 90℃ were investigated. The disappearance of L-ascorbic acid 2-glucoside with the higher water content proceeded faster at the higher temperature. The disappearance process was expressed by the Weibull equation. The change in the L-ascorbic acid was analyzed by assuming that both the hydrolysis and decomposition of L-ascorbic acid were expressed by first-order kinetics. A kinetic comparison of the overall disappearance by the hydrolysis indicated that the hydrolysis was not the sole route for the disappearance. The discoloration kinetics was also analyzed on the basis of the modified Weibull equation. It was shown that the enthalpy-entropy compensation held for all the processes involved in the overall disappearance of L-ascorbic acid 2-glucoside, its hydrolysis, the decomposition of L-ascorbic acid and the discoloration of L-ascorbic acid 2-glucoside. It was also demonstrated that the discoloration was suppressed by the glucosylation of L-ascorbic acid, but that L-ascorbic acid 2-glucoside was more easily discolored than L-ascorbyl 6-palmitate.

Drying and Rehydration of Calcium Alginate Gels

In this paper, we study the rehydration properties of air-dried calcium alginate gel beads. Rehydration is shown to depend on alginate source (i.e. mannuronic to guluronic acid ratio) and the salt concentration in the rehydration medium. Rehydration curves are described adequately by the empirical Weibull equation. Wide-angle X-ray diffraction measurements are performed to obtain information on the microstructure of dried alginate gels. The X-ray diffraction patterns provide evidence for formation of ordered domains in which alginate polymers are laterally associated. Formation of ordered structures during drying is found to have a large impact on rehydration properties. Lateral association of alginate chains is reduced (and rehydration improved) by removing excess calcium ions from the gel beads in a washing step prior to air drying. In addition, rehydration properties of mixed alginate–carboxymethyl cellulose (CMC) gel beads are investigated. The presence of CMC in the gel matrix is found to reduce lateral association of alginate chains during drying and to improve rehydration properties.

WCS120 protein family and frost tolerance during cold acclimation, deacclimation and reacclimation of winter wheat

We studied how long-term cold acclimation of winter wheat (variety Mironovskaya 808), interrupted by deacclimation and then followed by reacclimation, affected the levels of cold-induced WCS120 proteins, dry-weight content, and frost tolerance in leaves. Two experiments were performed: (1) plants undergoing long-term cold acclimation (up to 112days) were quickly deacclimated (for 5days), and then reacclimated again to cold; (2) plants vernalized for varying periods of time in an early stage of their development were, after a longer deacclimation of about 14days, exposed for the same time period to cold. Five members of the WCS120 protein family were detected and quantified by image analysis in protein gel blots (in the first experiment); as well as in two-dimensional electrophoresis gels (in the second experiment). In both experiments, partially vernalized plants, after reacclimation, re-established their frost tolerance to levels similar to plants having had the same duration of cold treatment, but without deacclimation. On the other hand, these partially and fully vernalized plants reaccumulated WCS120 proteins to lower levels than plants that were not deacclimated. Further, using a mathematical model (the peak four-parameter Weibull equation), the same type of response curve was observed during plant cold treatment not only for the level of frost tolerance, but also for dry-weight content and accumulation of WCS120 proteins, with the maximum values reached at about the same time as vernalization saturation.

Modeling Size‐number Distributions of Seeds for Use in Soil Bank Studies

Knowledge of soil seed banks is essential to understand the dynamics of plant populations and communities and would greatly benefit from the integration of existing knowledge on ecological correlations of seed size and shape. The present study aims to establish a feasible and meaningful method to describe size-number distributions of seeds in multi-species situations. For that purpose, size-number distributions of seeds with known length, width and thickness were determined by sequential sieving. The most appropriate combination of sieves and seeds dimensions was established, and the adequacy of the power function and the Weibull model to describe size-number distributions of spherical, non-spherical, and all seeds was investigated. We found that the geometric mean of seed length, width and thickness was the most adequate size estimator, providing shape-independent measures of seeds volume directly related to sieves mesh side, and that both the power function and the Weibull model provide high quality descriptions of size-number distributions of spherical, non-spherical, and all seeds. We also found that, in spite of its slightly lower accuracy, the power function is, at this stage, a more trustworthy model to characterize size-number distributions of seeds in soil banks because in some Weibull equations the estimates of the scale parameter were not acceptable.

Investigation of the release behavior of cupric ion for three types of Cu-IUDs and indomethacin for medicated Cu-IUD in simulated uterine fluid

Background A number of copper-bearing intrauterine devices (Cu-IUDs) are now commercially available in China. The release behavior of cupric ion from Cu-IUDs is essential to the success of contraception, and the release behavior of indomethacin from medicated Cu-IUD is related to its therapeutic effect. Study Design In this study, analytical methods were established to investigate the release behavior of cupric ion of three existing types of Cu-IUDs and indomethacin of one medicated Cu-IUD (Yuangong 365 Cu-IUD). Cu-IUDs were incubated in simulated uterine fluid (SUF). The concentrations of cupric ion and indomethacin were analyzed by flame atomic absorption spectrometer (FAAS) for 250 days and UV 752 spectrophotometer for 300 days, respectively. Results The release behavior of cupric ion for three types of Cu-IUDs was biphasic, which consisted of the initial burst release and then slow and constant release. The release of cupric ion from the medicated Cu-IUD Yuangong 365 showed a zero-order process. In vitro release experiment confirmed a sustained release of indomethacin from Yuangong 365 and the release was in accordance with the Weibull equation. Conclusion The cupric ion release appears to be more constant in the medicated Cu-IUD than in the others. In view of the feature of indomethacin release from medicated Cu-IUD, it is conjectured that the design of this device could be useful to avoid the adverse effects caused by all Cu-IUDs.

Enzymatic synthesis of conjugated linoleoyl ascorbate in acetone

Conjugated linoleoyl ascorbates were synthesized through the condensation of cis-9, trans-11-conjugated linoleic acid ( c9, t11CLA) or trans-10, cis-12-conjugated linoleic acid ( t10, c12CLA) with l-ascorbic acid (AsA) using immobilized lipase in a water-soluble organic solvent at 50 °C. The conversion was higher at higher polarity of the solvent and a higher ratio of CLA to AsA. The conversion for the synthesis of t10, c12CLA-AsA was higher than those for c9, t11CLA-AsA and linoleoyl ascorbate (LA-AsA), when Chirazyme ® L-2 C2 from Candida antarctica type B, which has been commonly used for enzymatic reaction in organic solvent, was used as a catalyst. The unmodified CLA isomers were almost completely oxidized within 4 h at 65 °C and 75% relative humidity, whereas all the CLA-AsAs were significantly resistant to oxidation. The oxidation kinetics was empirically expressed by the Weibull equation, and the rate constant, k, was estimated. The k values for CLA-AsAs and LA-AsA were about 1/30 and 1/60, respectively, of that for the corresponding unmodified CLA isomers. The enzymatic modification of CLA with AsA was an effective technique for improvement in the oxidative stability of CLA.

Decomposition Kinetics of 6-O-Monoacyl Ascorbate in Air

6-O-Monoacyl ascorbates were synthesized by the condensation of L-ascorbic acid with caprylic, capric, lauric, myristic or palmitic acid using immobilized lipase in acetone. The decomposition processes of the acyl ascorbates in air were measured, and the decomposition kinetics were analyzed based on the Weibull equation. The rate constant, k, increased with increasing relative humidity and temperature for all acyl ascorbates; k also depended on acyl chain length, as the decomposition rates of ascorbates increased as acyl chains decreased. The enthalpy-entropy compensation held during the decomposition, suggesting that the decomposition of all acyl ascorbates proceeded by essentially the same mechanism. Furthermore, it was suggested that the oxidative degradation of the ascorbyl moiety of acyl ascorbate primarily proceeded during the decomposition, and was followed by the hydrolysis of the ester bond between the acyl and ascorbyl moieties.

Preparation and evaluation of stealth Tashinone IIA-loaded solid lipid nanoparticles: Influence of Poloxamer 188 coating on phagocytic uptake

Stealth Tashinone IIA-loaded solid lipid nanoparticles (TA-SSLN) have been prepared by a nanoprecipitation/solvent diffusion method. Poloxamer 188 was used as a stealth agent. Nanoparticles were characterized by transmission electron microscopy (TEM) and dynamic light scattering (DLS). The profile of Tashinone IIA release from TA-SSLN was studied. Phagocytosis was evaluated by incubating TA-SSLN and non-stealth Tashinone IIA-loaded solid lipid nanoparticles (TA-NSLN) with murine macrophages. Human serum was added to evaluate opsonization of serum proteins. Rhodamine B was incorporated into nanoparticles as a fluorescent marker to observe and compare the phagocytic uptake of two kinds of nanopreticles. The results showed that TA-SSLN had an average diameter of (92.4 ± 5.2) nm, zeta potential of (−20.4 ± 1.3) mV, drug loading of (4.6 ± 0.2)% and entrapment efficiency of (93.3 ± 2.1)%. In vitro release experiment confirmed a sustained release of TA-SSLN and showed that the release of Tashinone IIA from TA-SSLN was in accordance with the Weibull equation. Phagocytosis studies showed significant differences between TA-SSLN and TA-NSLN and demonstrated that the Poloxamer 188 coating could decrease the macrophages uptake.

Polyelectrolyte–Drug Complexes of Lambda Carrageenan and Basic Drugs: Relevance of Particle Size and Moisture Content on Compaction and Drug Release Behavior

The interaction between polyelectrolytes (PE) and oppositely charged drugs (D) results in complexes (PE–D) that can be exploited in controlled release drug delivery systems. The aim of this work is to better understand the relevance of some preparative parameters such as moisture content and particle size on the performance of two PE–D complexes to be used in oral controlled release tablets. PE–D complexes containing diltiazem HCL (DTZ) or metoprolol tartrate (MTP) and lambda carrageenan were obtained at two particle size levels (<45 μm and 75–105 μm), maintained at different values of relative humidity (RH) (11, 52, 75, and 93%), and compressed. The tablets were characterized for porosity, hardness, moisture content, and contact angle. Drug release profiles were fitted to the Weibull equation, and a factorial design was used to understand the relevance of particle size and RH% on release rate as a function of medium pH. The results indicated that the hydrophobic character of the complex between PE and D depended on the drug and in the present case was more pronounced for DTZ than for MTP. This in turn affected the possible release mechanism and therefore the importance of particle size and RH%.

Decomposition and discoloration kinetics of L-ascorbic acid powders in superheated steam

The decomposition and discoloration of powdery L-ascorbic acid in superheated steam were observed in the temperature range of 140–180 °C. For comparison, the decomposition and discoloration were also measured in the temperature range in hot air and at 180 °C in nitrogen. L-Ascorbic acid decomposed faster in superheated steam than in hot air. Discoloration was also more remarkable for the L-ascorbic acid treated in the superheated steam. The Weibull equation was applicable to the decomposition in both superheated steam and hot air. The early stage of discoloration was assumed to be expressed by zeroth-order kinetics. In the latter stage, fading occurred and the process was expressed by first-order kinetics which was modified to level off at a certain value.

Rapid method to study the sedimentation of a pigment suspension prepared for coating fluids

Film coating fluids commonly contain a pigment suspension. The sedimentation of insoluble particles in the coating suspension is one of the main problems during the formulation of the coating fluid. The aims of this work were to investigate the suitability of an energy-dispersive X-ray fluorescence analyser for rapid measurement of the sedimentation of titanium dioxide in aqueous suspensions. The suspensions were produced with a high-speed Ultra-Turrax. The process factors evaluated were the stirring rate, time and volume, and the process of sedimentation of the pigment. The enrichment of the pigment at the bottom of the sample holder was followed by means of the very rapid method of energy-dispersive X-ray fluorescence analysis. It can be concluded that the sedimentation of the particles is described by the Weibull equation. With an appropriate combination of the factors, a threefold increase in the sedimentation time was achieved. The mathematically based information (sedimentation time, kinetics of sedimentation, etc.) is essential for an exact evaluation of the preparation of the coating fluid. The understanding of the process through use of this test method leads to the ability to identify the critical control points of film coating.

Decomposition and discoloration of L-ascorbic acid freeze-dried with saccharides

Abstract L -Ascorbic acid (vitamin C) was freeze-dried along with the following six types of wall materials: soluble soybean polysaccharide (SSPS), gum arabic (GA), maltodextrin (MD), α-cyclodextrin (α-CD), trehalose (Tre) and lactose (Lac). α-CD, Tre and Lac were used in mixtures with MD (weight ratio of 1:1). The decomposition kinetics of L -ascorbic acid in these powders stored at 80 °C and relative humidities of 11, 51 and 79% were expressed by the Weibull equation. The discoloration of the powders was also monitored by measuring the absorbance at 500 nm for solutions which were obtained by dissolving the systems in water. The L -ascorbic acid powders prepared with GA and SSPS were significantly discolored and the processes could be expressed by a modified Weibull equation. The discoloration of the L -ascorbic acid powders prepared with other saccharides was very slow. The discoloration rate constants were significantly greater at temperatures higher than the glass transition temperatures of the saccharides under the stated storage conditions, while the decomposition rate constant was only slightly affected by the system glass transition temperature. Industrial relevance Decomposition and discoloration are examples of food deterioration. Food usually represents a multi-component system in which components interact with each other. Both their state and interaction would affect the deterioration. L -Ascorbic acid is one of the food components which are subject to decomposition and discoloration during storage. The decomposition and discoloration of L -ascorbic acid powders freeze-dried with saccharides were measured under various conditions and kinetically analyzed to understand an aspect of food deterioration.

Discoloration Kinetics of L-Ascorbyl 6-Palmitate Powders with Various Water Contents

The discoloration of L-ascorbyl 6-palmitate, with water contents ranging from 2 to 10% (w/w) during storage at temperatures of 60 to 90°C, was investigated by monitoring the absorbance at 500nm of its solutions dissolved in methanol. The discoloration process of the substrate was expressed by the modified Weibull equation under all conditions, and the kinetic parameters were evaluated. The activation energy and frequency factor were estimated based on the Arrhenius equation for the substrates of various water contents, and the enthalpy-entropy compensation held for the discoloration process. Comparison of the discoloration kinetic parameters for L-ascorbyl 6-palmitate with those for L-ascorbic acid revealed that the discoloration of L-ascorbyl 6-palmitate was weaker than that of L-ascorbic acid.

A Parenteral Econazole Formulation Using a Novel Micelle-to-Liposome Transfer Method: In Vitro Characterization and Tumor Growth Delay in a Breast Cancer Xenograft Model

The aim of the study is to develop modified, branched versions of the Noyes-Whitney and the Weibull equations, including explicitly the solubility/dose parameter, for the analysis of dissolution data, which reach the plateau either at infinite or finite time. The modified Weibull function is applied to the analysis of experimental and literature dissolution data. To demonstrate the usefulness of the mathematical models, two model drugs are used: one highly soluble, metoprolol, and one relatively insoluble, ibuprofen. The models were fitted successfully to the data performing better compared with their classic versions. The advantages of the use of the models presented are several. They fit better to a large range of datasets, especially for fast dissolution curves that reach complete dissolution at a finite time. Also, the modified Weibull presented can be derived from differential equations, and it has a physical meaning as opposed to the purely empirical character of the original Weibull equation. The exponent of the Weibull equation can be attributed to the heterogeneity of the process and can be explained by fractal kinetics concepts. Also, the solubility/dose ratio is present explicitly as a parameter and allows to obtain estimates of the solubility even when the dissolution data do not reach the solubility level. The use of the developed branched equations gives better fittings and specific physical meaning to the dissolution parameters. Also, the findings underline the fact that even in the simplest, first-order case, the speed of the dissolution process depends on the dose, a fact of great importance in biopharmaceutic classification for regulatory purposes.

Predicting dynamic failure of dense granules from static compression tests

This paper shows how static failure loads can be used to predict impact failure of granules. A theoretical model is presented that gives the maximum force experienced during impact and equates this to experimentally measured static failure load to define a critical impact velocity for impact failure. A granule will fail if the predicted theoretical maximum force during impact due to the impact velocity is greater than the real force required to produce failure in that particular granule. The random nature of granules produces a spread of velocities at which granules of a given size will fail; this spread is the failure distribution. In this paper it is shown that the failure distribution of a series of impact experiments can be represented by a 2-parameter Weibull equation. The important c-parameter is related to the impact angle and the critical normal impact velocity that is found from static compression tests. Thus the number of granules failing by impact at each velocity can be found by performing static failure tests.

Suppressive effect of alkyl ferulate on the oxidation of microencapsulated linoleic acid

AbstractThe oxidation processes of linoleic acid mixed with ferulic acid or the 1‐pentyl, 1‐hexyl and 1‐heptyl ferulates, encapsulated with gum arabic or maltodextrin, were studied. The alkyl ferulates had a higher antioxidative effect than ferulic acid, but there was no significant difference among the three alkyl ferulates. Suppression of the oxidation by 1‐hexyl ferulate or ferulic acid was more effective at the higher molar ratios of the additive to linoleic acid. The processes were analyzed using the Weibull equation to evaluate the rate constant, k, and the shape constant, n. Although the k values for linoleic acid encapsulated with gum arabic were lower than that with maltodextrin, the suppressive effect of the alkyl ferulates was more remarkable for linoleic acid encapsulated with maltodextrin than with gum arabic because of the non‐antioxidative ability of maltodextrin. Because the partition coefficient of the alkyl ferulates was much greater than that of ferulic acid, most of the alkyl ferulates would be located in the linoleic acid phase of the microcapsules and effectively suppress the oxidation of linoleic acid.

A model-dependent approach to correlate accelerated with real-time release from biodegradable microspheres

The purpose of this study was to determine the feasibility of applying accelerated in vitro release testing to correlate or predict long-term in vitro release of leuprolide poly(lactide-co-glycolide) microspheres. Peptide release was studied using a dialysis technique at 37 degrees C and at elevated temperatures (50 degrees C-60 degrees C) in 0.1M phosphate buffered saline (PBS) pH 7.4 and 0.1M acetate buffer pH 4.0. The data were analyzed using a modification of the Weibull equation. Peptide release was temperature dependent and complete within 30 days at 37 degrees C and 3 to 5 days at the elevated temperatures. In vitro release profiles at the elevated temperatures correlated well with release at 37 degrees C. The shapes of the release profiles at all temperatures were similar. Using the modified Weibull equation, an increase in temperature was characterized by an increase in the model parameter, alpha, a scaling factor for the apparent rate constant. Complete release at 37 degrees C was shortened from approximately 30 days to 5 days at 50 degrees C, 3.5 days at 55 degrees C, 2.25 days at 60 degrees C in PBS pH 7.4, and 3 days at 50 degrees C in acetate buffer pH 4.0. Values for the model parameter beta indicated that the shape of the release profiles at 55 degrees C in PBS pH 7.4 (2.740) and 50 degrees C in 0.1M acetate buffer pH 4.0 (2.711) were similar to that at 37 degrees C (2.677). The E(a) for hydration and erosion were determined to be 42.3 and 19.4 kcal/mol, respectively. Polymer degradation was also temperature dependent and had an E(a) of 31.6 kcal/mol. Short-term in vitro release studies offer the possibility of correlation with long-term release, thereby reducing the time and expense associated with long-term studies. Accelerated release methodology could be useful in the prediction of long-term release from extended release microsphere dosage forms and may serve as a quality control tool for the release of clinical or commercial batches.

Ascorbic Acid Thermal Degradation during Hot Air Drying of Camu-Camu (Myrciaria dubia [H.B.K.] McVaugh) Slices at Different Air Temperatures

Air drying of camu-camu slices was performed in order to estimate the effect of air temperature on the kinetics of ascorbic acid thermal degradation. Moisture variation during the air drying process was monitored gravimetrically by weighing the trays at predetermined time intervals. The experimental points were adjusted by Fick's diffusion model and by the Page empirical model. The effective diffusion coefficient (Deff) ranged from 8.48 × 10−10 to 1.34 × 10−9 m2/s.The ascorbic acid content was evaluated in samples taken during the drying process using Iodine titration, and the results modeled by the Weibull equation. Concerning ascorbic acid retention the best drying condition required air at 50°C. The ascorbic acid retention was 78%, when the moisture content of the product reached 10% (wet basis).

Carbon and biomass partitioning in balsam fir (Abies balsamea)

Balsam fir (Abies balsamea (L.) Mill) was extensively sampled to investigate the effects of forest management practices, site location, within-crown position, tree component (i.e., stem, foliage, branches and roots), and tree social classes on biomass and carbon (C) partitioning at the individual tree level and across ecological regions. The sites were located in three ecologically distinct forest regions of west-central New Brunswick, Canada. There were no significant differences in %C content of trees across ecological regions or across tree social classes. However, at the individual tree level, significant differences were evident in biomass and C allocation between different parts of the tree, between treatment types (i.e., unmanaged and pre-commercially thinned stands) and between within-crown positions, indicating the need for separate estimates of biomass and C content of tree components to obtain more precise estimates of quantities at the stand level. Calculating stand C content based on constant allocation values, as is commonly done, produced errors of up to 15% compared with the values calculated in this study. Three allometric equations of biomass and C that account for partitioning among different parts of the tree were developed and compared: (1) a third-order polynomial, (2) a modified inverse polynomial and (3) a modified Weibull equation. Diameter at breast height (DBH) was used as the only explanatory variable to describe fresh biomass, dry biomass and C content. All regressions derived showed a high correlation with DBH, with most r2 values > 0.95. A comparison of the equation results showed that the modified Weibull equation gave consistent results with the best overall fit and was the simplest of the three equations investigated. The regressions can be used to estimate forest biomass and tree C content at the stand level, given specific information on DBH.