Weibull Equation Research Articles

Quality variation analysis and rehydration kinetics modeling of yuba subjecting to three different drying process

This study investigated the effects of hot air drying (HAD), microwave vacuum drying (MVD), and vacuum frying drying (VFD) on the quality of yuba and utilized mathematical models (Peleg model, Weibull equation, first-order kinetic model, and exponential association model) to explore the rehydration kinetics of yuba. The results indicated that, compared to HAD, MVD significantly increased yuba's L* value and sensory score, while VFD notably reduced the cooking loss rate and enhanced moisture retention. Significant changes were observed in the texture of yuba before and after cooking, with distinct differences noted under microscopic observation, and a pronounced change in protein secondary structure. The Peleg model can effectively fit the rehydration processes of HAD and VFD yuba, while the first-order kinetic model can effectively fit the rehydration processes of MVD yuba. This study provides a valuable reference for yuba's drying method and rehydration Kinetics model.

Effect of initial temperature damage on the static and fatigue performance of all-lightweight shale ceramsite concrete

The effects of initial temperature damage on the static and compressive fatigue properties of LC30 all-lightweight shale ceramsite concrete (ALWSCC) were studied. The curing conditions ranged from -5 °C to -30 °C without antifreeze, with an elevated temperature range of 100 °C to 400 °C applied after 28 days of standard curing. We tested the static strength, elastic modulus, and stressstrain curves of ALWSCC, as well as its uniaxial compression fatigue life and ƐN curves under different stress levels. The credibility of data from only three test samples per condition was statistically analyzed, and we explored how temperature, aggregate properties, and concrete pore structure affect performance. The results indicate that the impact of temperature on the static and fatigue performance of ALWSCC can be described by a unified damage model. The Hillerborg characteristic length effectively captures the brittleness induced by temperature changes. Using the two-parameter Weibull equation and various fatigue equations that account for failure probability and temperature, the fatigue life predictions were accurate. Although low and high temperatures affect ALWSCC differently, temperature effects combined with static and fatigue loads further accelerate its deterioration.

The release behavior and in vitro osteogenesis of quercetin-loaded bioactive glass/hyaluronic acid/sodium alginate nanocomposite paste

Injectable pastes based on bioactive compounds and natural polymers are of interest in non-invasive bone surgeries. Several quantities of quercetin (100, 150, and 200 μM) were added to a sol-gel derived mesoporous bioactive glass. Injectable pastes based on quercetin-loaded bioactive glass, sodium alginate, and hyaluronic acid were prepared. Aggregated nanoparticles of bioactive glass and quercetin-loaded bioactive glass with mesoporous morphologies were confirmed by TEM and BET techniques. The quercetin release study was assessed in phosphate-buffered solution medium over 200 h and the obtained data were fitted by different eqs. A sustained release of quercetin was found, in which a better regression coefficient was achieved using Weibull equation. Human-derived mesenchymal stem cells were utilized to determine alkaline phosphatase activity and bone-related protein expression by western blotting and real-time PCR evaluations. Quercetin-loaded pastes increased the levels of alkaline phosphatase activity and the expression of Collagen-1, Osteopontin, Osteocalcin, and Runx2 proteins in a concentration-dependent manner. Due to the mesoporous architecture and high specific surface area of bioactive glass, the paste made of these particles and sodium alginate/hyaluronic acid macromolecules is appropriate matrix for quercetin release, resulting in promoted osteogenesis. The further in vivo studies can support the osteogenesis capacity of the quercetin-loaded paste.

New mathematical model from dynamic dissolution rate tests

In vitro dissolution experiments are becoming increasingly complex attempting to replicate in vivo behavior. The objective of these new methods is to explore the behavior of low-solubility drugs. This is more relevant for drugs classified in subclasses 2a, 2b and 2c of the BCS, considering their pH-dependent solubility and dissolution characteristics.A novel mathematical approach using a modified double Weibull equation is proposed to model the dissolution and precipitation kinetics observed in two-stage and transfer dissolution experiments (dumping test). This approach demonstrates a high level of accuracy in fitting experimental data for two drugs BCS class 2a and two BCS class 2b, providing valuable insights into their dissolution behavior under different conditions.The results highlight the versatility of the proposed model in capturing complex dissolution phenomena, including rapid dissolution, precipitation, and redissolution. The ease of implementation in Excel, using the Solver tool, makes it a practical and accessible tool for pharmaceutical researchers.Overall, the study contributes to the development of more effective in vitro dissolution testing methods, facilitating the formulation and optimization of pharmaceutical products and potentially aiding in the establishment of in vitro-in vivo correlations (IVIVC).

Self Nanoelmusifying Drug Delivery System of Rosuvastatin: Bioavailability Evaluation and In vitro - In vivo Correlation.

Rosuvastatin, most commonly used in the form of calcium salt, belongs to the statin groups of synthetic antihyperlipidemic agents. Rosuvastatin possesses high permeability, however, its aqueous solubility is poor, causing a slow dissolution rate in water. Consequently, this dissolution rate has a decisive role in the release and absorption of rosuvastatin in the gastrointestinal tube. The aims of this study were to evaluate the absorption of the drug from the self-nano emulsifying drug delivery system of rosuvastatin (Ros SNEDDS) compared to rosuvastatin substance and to develop a level-A in vitro-in vivo correlation (IVIVC) for Ros SNEDDS. An in-house developed LC-MS/MS method was used to determine the concentrations of rosuvastatin in dog plasma. Six beagle dogs received an intravenous dose, Ros SNEDDS, rosuvastatin substance. In vitro dissolution of the Ros SNEDDS was carried out with different conditions. Correlation models were developed from the dissolution and absorption results of Ros SNEDDS. The results showed a 1.7-fold enhanced oral bioavailability and 2.1-time increase of rosuvastatin Cmax in Ros SNEDDS form, compared to the rosuvastatin substance. A 900 ml dissolution medium of pH of 6.6 has demonstrated its suitability, the in vitro dissolution model was studied and supported by the Weibull equation with a weighting factor of 1/y2 as it presented the lowest values of AIC. Ros SNEDDS demonstrated higher bioavailability of rosuvastatin in comparison to rosuvastatin substance and established a level A IVIVC used in future bioequivalence trials.

Carvacrol and thymol effect in vapor phase on Escherichia coli and Salmonella serovar Typhimurium growth inoculated in a fresh salad

This study aimed to evaluate the antimicrobial effect of thymol and carvacrol in inhibiting Escherichia coli and Salmonella serovar Typhimurium inoculated on a fresh green salad through the vapor phase. A film-forming solution was prepared by dissolving starch, sorbitol, and variying concentrations of carvacrol, thymol, and a mixture of both. The film-forming solution containing the respective antimicrobial agent was then added lid, which was sealed rigidly and hermetically to achieve different concentrations (105 mg/L of air of carvacrol, 105 mg/L of air of thymol, and a mixture of 52 mg/L of air of carvacrol and 52 mg/L of air of thymol). Each active package contained fresh green salad inoculated with E. coli or Salmonella serovar Typhimurium. The active packages were then sealed and refrigerated at a temperature of 6 °C for 48 h. Growth/inhibition curves were modelled using the Weibull equation, and consumer acceptance was evaluated. Carvacrol can reduce up to 0.5 log-cycles, while thymol can reach almost 1 log cycle. Blending the components with half the concentration has a synergistic effect, inhibiting up to 2.5 log cycles. Consumer ratings revealed no significant differences between the packages. However, the average score was 5.4 on a 9-point hedonic scale, evaluators' comments did not indicate dislike or a strong taste characteristic of thymol and carvacrol.

Temporal Dynamics and Dispersal Patterns of the Primary Inoculum of Coniella diplodiella, the Causal Agent of Grape White Rot.

Grape white rot can cause considerable yield losses in viticulture areas worldwide and is principally caused by Coniella diplodiella. The fungus overwinters in berry mummies on the soil surface or on the trellis and produces pycnidia and conidia that serve as primary inoculum. However, little is known about the temporal dynamics and dispersal pattern of C. diplodiella conidia. In this study, we investigated the production and dispersal of C. diplodiella conidia from a primary inoculum source, namely, affected mummified berries that overwintered in two vineyards in northern Italy in 2021 and 2022. Conidia of C. diplodiella were repeatedly produced in berry mummies from the budburst of vines to harvesting, with approximately 50 and 75% of the total conidia in a season being produced before fruit set and véraison, respectively. The production dynamics of C. diplodiella conidia over time were described by a Weibull equation in which the thermal time is the independent variable, with a concordance correlation coefficient of ≥0.964. A rainfall cutoff of ≥0.2 mm provided an overall accuracy of ≥0.86 in predicting conidial dispersal through rain splashes from berry mummies on the soil surface, with the number of dispersed conidia increasing with the amount of rainfall. The dispersal of conidia from mummies on the trellis by washing with rain required at least 6.1 mm of rain. The proposed mathematical equations and rain cutoffs can be used to predict periods with a high dispersal risk of C. diplodiella.

Modeling the Monthly Distribution of MODIS Active Fire Detections from a Satellite-Derived Fuel Dryness Index by Vegetation Type and Ecoregion in Mexico

The knowledge of the effects of fuel dryness on fire occurrence is critical for sound forest fire management planning, particularly in a changing climate. This study aimed to analyze the monthly distributions of MODIS active fire (AF) detections and their relationships with a fuel dryness index (FDI) based on satellite-derived weather and vegetation greenness. Monthly AF distributions showed unimodal distributions against FDI, which were described using generalized Weibull equations, fitting a total of 19 vegetation types and ecoregions analyzed in Mexico. Monthly peaks of fire activity occurred at lower FDI values (wetter fuels) in more hygrophytic ecosystems and ecoregions, such as wet tropical forests, compared to higher fire activity in higher FDI values (drier fuels) for the more arid ecosystems, such as desert shrublands. In addition, the range of fuel dryness at which most monthly fire activity occurred was wider for wetter vegetation types and regions compared to a narrower range of fuel dryness for higher monthly fire occurrence in the more arid vegetation types and ecoregions. The results from the current study contribute towards improving our understanding of the relationships between fuel dryness and fire occurrence in a variety of vegetation types and regions in Mexico.

Modeling the combined resistance to microwave treatments and salt conditions of Escherichia coli and Staphylococcus aureus.

In the present study, the efficiency of the combined effect of microwave irradiation treatments together with salt concentration was assessed against Escherichia coli and Staphylococcus aureus. Microbial survival has been modeled through a one-step Weibull equation considering the non-isothermal profiles during the heating treatments. Three sodium chloride concentrations 0.5%, 3.5%, and 8.5% (w/v) treated under three microwave power levels (450, 600, and 800 W) were studied. Predictive models were validated using the determination coefficient (R2), root mean squared error and the acceptable prediction zone with external data obtained from ultra high temperature milk. The results obtained suggested that increasing microwave power levels and decreasing salt concentrations led to a higher microbial inactivation, being the δ values (time for achieving a first decimal reduction) for E coli of 19.57 s at 800 W and 0.5% NaCl. In contrast, experimental data of S aureus showed a higher variability since it presented more resistance to the microwave treatments. The results obtained and generated models can be used as decision-making tools to set specific guidelines on microwave treatments for assuring food safety.

Structure, rheology and gastrointestinal release kinetics of new-type curcumin-based nanofibers nanohydrogel assisted prepared with subcritical water at different treatment times

This study aimed to design a new-type curcumin (Cur)-based network nanohydrogel (H), which was composed of whey protein isolate nanofibers (WPINs) and pectin (P). Among them, WPINs were prepared with subcritical water at different treatment times (90 min: WPINs-90, 120 min: WPINs-120, and 180 min: WPINs-180). The structural characteristics, rheology and gastrointestinal release kinetics of Cur-based nanohydrogel were investigated. The results showed that WPINs-120-P-H showed the most favorable particle size (659.00 ± 3.90 nm), potential (−30.00 ± 2.00 mV), peak temperature (110.57 °C) and heating stability. The rheological results revealed that each group of nanohydrogels formed strong elastic gels. In addition, WPINs-120-P-H exhibited the highest encapsulation efficiency (98.42 ± 5.00%) of Cur with the strongest network structure. Moreover, the release curved line of Cur showed an initial release of 19.23% in the stomach, and afterwards, a continuous release trend in the small intestine, reaching a final release amount of 84.80%. Interestingly, the release kinetics of Cur was in line with the Weibull equation model, evidencing a continuous and dynamic release process. This study provided a novel way to prepare the WPINs-P nanohydrogel as delivery for Cur, which demonstrated great potential application prospects in the functional food industry.

Development and characterization of crosslinked k-carrageenan/sericin blend with covalent agents or thermal crosslink for indomethacin extended release

Modified release of multiparticulate pharmaceutical forms is a key therapeutic strategy to reduce side effects and toxicity caused by high and repeated doses of immediate-release oral drugs. This research focused on the encapsulation of indomethacin (IND) in the crosslinked k-Car/Ser polymeric matrix by covalent and thermal methods to evaluate drug delivery modulation and properties of the crosslinked blend. Therefore, the entrapment efficiency (EE %), drug loading (DL %) and physicochemical properties of the particles were investigated. The particles presented a spherical shape and a rough surface with a mean diameter of 1.38–2.15 mm (CCA) and 1.56–1.86 mm (thermal crosslink). FTIR investigation indicated the presence of IDM in the particles and X-ray pattern showed the maintenance of crystallinity of IDM. The in vitro release in acidic medium (pH 1.2) and phosphate buffer saline solution (pH 6.8) was 1.23–6.81 % and 81–100 %, respectively. Considering the results, the formulations remained stable after 6 months. The Weibull equation was adequately fitted for all formulations and a diffusion mechanism, swelling and relaxation of chain were observed. IDM-loaded k-carrageenan/sericin/CMC increases cell viability (> 75 % for neutral red and > 81 % for MTT). Finally, all formulations present gastro-resistance, pH response and altered release and have the potential to be used as drug delivery careers.

Controlled release of a non-steroidal anti-inflammatory drug from a photocurable polymeric calcium phosphate cement

In this research, a photocurable composite based on tetracalcuim phosphate ceramic and, hydroxyethyl methacrylate-modified poly(acrylic-maleic acid) was developed and studied as a potential drug delivery system for bone defects. Different concentrations (5, 10 and 20 wt. %) of a non-steroidal anti-inflammatory drug, Indomethacin, were loaded on to the composite and its release behavior was investigated in phosphate buffered solution during 504 h. The obtained release data were fitted by both power law (Peppas) and Weibull equations. The composites were also characterized after different soaking periods using X-ray diffractometry (XRD), scanning electron microscopy (SEM) and Fourier transforming infrared spectroscopy. The results of XRD and SEM analyses revealed the formation of nanosized needle/flake-like apatite crystals on the composites surfaces; however, better apatite formation was observed for the composites loaded with higher amounts of Indomethacin. The morphological observations and quantitative estimations revealed that the loaded composites were gradually degraded in the phosphate-buffered saline. Moreover, a controlled release of Indomethacin was found from the composites in which a higher drug concentration led to a more drug level as well as sustained release profile. In drug release modeling, better regression coefficient was obtained from the Weibull equation, compared to the power law, meaning that the Weibull equation suggests a better description of the indomethacin release from the composites during the whole period of the test. In conclusion, the photocurable composite with apatite formation ability can be successfully used for the controlled release of indomethacin as an anti-inflammatory drug in bone defects.

Influence of binder concentration in zeolitic ZSM-5/bentonite 3D-printed monoliths manufactured through robocasting for catalytic applications

In this work, a 3D printing method, robocasting was utilized to manufacture zeolite ZSM-5-based woodpile monolith catalysts of approximately 10-mm diameter, using bentonite clay as binding matrix. The effect of three different binder concentrations, in the 40–60 wt.% range, on the rheological, physicochemical, and mechanical properties was examined. The rheometer measurements showed that the printing pastes have identical shear thinning behavior and demonstrate sufficient storage modulus, irrespective of the binder concentration. The printed monoliths had high BET surface areas and porosity. The results showed that the ZSM-5 crystals retained their porous structure, textural characteristics, and crystalline structure during the additive manufacturing process. Pyridine FTIR measurements demonstrated reduced total acidity and number of Brønsted acid sites in the final specimens due to the dilution with the bentonite powder. However, the acidity reduction was roughly proportional to the binder concentration, signifying that the ZSM-5 crystallites also retain their acidity during the robocasting printing. Finally, the mechanical reliability of the thermally treated monoliths was determined by calculating the Weibull modulus values through linear regression of the Weibull equation. The increase in the binder concentration increased the compression strength by a factor of 4.5 and achieved superior mechanical reliability.Graphical abstract

Investigation of the Effect of pH on the Adsorption-Desorption of Doxycycline in Feed for Small Ruminants.

Orally administered tetracycline antibiotics interact with feed, which may impact their bioavailability and efficacy. Therefore, the pH-dependent adsorption of doxycycline and its interaction with feed for ruminants was studied in vitro. Adsorption experiments on animal feed (135 and 270 mg) with initial doxycycline concentrations of 35, 75, and 150 µg/mL were performed. Desorption experiments were conducted by agitation of a predetermined mass of doxycycline-loaded animal feed in PBS, at pH = 3.0, 6.0, and 7.4, to simulate changes in the gastrointestinal tract. Antibiotic concentrations were determined by LC-MS/MS analysis. The adsorption/desorption of doxycycline was described by mathematical models. Chemisorption with strong intermolecular interactions between the active functional groups of doxycycline and the organic biomass was found. The experimental release curve comprised three sections: initial prolonged 27-30% release (pH = 6.0), followed by moderate 56-59% release (pH = 3.0), and final 63-74% release (pH = 7.4). The sigmoidal model showed a considerable role of diffusion with an initial prevalence of desorption and a decreased desorption rate thereafter. The Weibull equation revealed an initial release stage followed by a lag time section and sustained release. The study of doxycycline adsorption by the animal feed proved a maximum 80% encapsulation efficiency and revealed initial diffusion followed by chemisorption. The highest release efficiency of 74% suggests high bioavailability of doxycycline after oral administration in ruminants.

Experimental determination of bimodal strength distribution of S-glass fibers

Tensile strength distribution of S-Glass fibers at small gage lengths on the order of the ineffective length is required for both analytical and numerical models of composite unidirectional tensile strength. Historically unimodal Weibull strength distributions measured at large gage lengths are extrapolated to smaller length scales (5–200 μm). The accuracy of this approach is assessed by using 2 different experiments – the filament tensile test (gage lengths > 4 mm) and a continuously-monitored Single Fiber Fragmentation Test (SFFT, gage length = 544 μm). Extrapolation of the unimodal Weibull distribution to the 544 μm gage length leads to significant overprediction of fiber strengths (by ∼60%). The Weibull distribution obtained from SFFT also shows a significantly higher Weibull Modulus (12.9) as opposed to the tension dataset (4.5). This indicates that a different population of defects dominate at the shorter gage lengths. A bimodal Weibull equation has been fit to the combined data to account for the 2 different defect populations to provide accurate strength predictions over fiber lengths from ∼500 μm to 30 mm. An independent validation experiment was performed at 2 mm gage length to validate the Bimodal Equation.

Developing and Comparing Individual Tree Growth Models of Major Coniferous Species in South Korea Based on Stem Analysis Data

Tree growth in Korean red pine (Pinus densiflora, hereafter Pd), Korean white pine (Pinus koraiensis, hereafter Pk), and Japanese larch (Larix kaempferi, hereafter Lk) was modeled using Logistic, Korf, Gompertz, Chapman-Richards, and Weibull equations and stem analysis data from sample trees: 38 trees for Pd, 46 trees for Pk, and 45 trees for Lk. The models were fitted to the total increment of tree size variables, diameter at breast height (DBH), height, basal area, and stem volume, as a function of age. After selecting the best-fit growth function, the current annual increment (CAI) and mean annual increment (MAI) were compared for each variable by species. The optimal growth functions were Chapman-Richards for DBH and stem volume, Korf for height, and Gompertz for basal area. The parameter estimates in the final models were all significant (p < 0.01) with best-fit statistics and unbiased residual plots. When plotted with observed values, the growth patterns of each variable were represented properly. The predicted growth curves over age were concave with respect to the Y-axis in DBH and height but lightly convex in basal area, and explicitly convex in stem volume, whereas an asymptote of sigmoid curve in stem volume was not apparent until 100 years. Age with the maximum MAI among variables was arranged similarly to CAI; the age with maximum MAI was earliest for DBH and latest for volume. The maximum growth was achieved earliest in Lk, followed by Pk and Pd. The developed models were able to predict tree size variables and serve as a reference to understand growth characteristics by species.

A Solution to the Validity Problem of Qualitative Instrument Reliability through the Mathematical Derivation of the Weibull Equation

A Solution to the Validity Problem of Qualitative Instrument Reliability through the Mathematical Derivation of the Weibull Equation

An In Vitro Dissolution Determination of Multi-Index Components in Tibetan Medicine Rhodiola Granules.

The composition of the Tibetan medicine Rhodiola granules (RG) is complex, and the overall quality of RG is difficult to determine. Therefore, establishing a method to determine the multi-component in vitro dissolution of RG is of great significance for quality control. This study uses the second paddle method of the fourth general rule 0931 from the Chinese Pharmacopoeia (2020 edition), compliant with apparatus 2 of the United States Pharmacopeia (USP). The dissolution apparatus was set to a rotation speed of 100 rpm with ultrapure water as the dissolution medium. A sample volume of 1 mL was collected at each timepoint. Furthermore, the cumulative dissolution of gallic acid, salidroside, and ethyl gallic acid in RG at different time points was determined by high-performance liquid chromatography (HPLC). Finally, the dissolution curves were drawn, and the curves were fitted to the GompertzMod, the Gompertz, the Logistic, and the Weibull equations. The results showed that the cumulative dissolution of gallic acid in RG was over 80% at 1 min, the cumulative dissolution of salidroside and ethyl gallic acid was over 65% at 5 min, and the cumulative dissolution of each index component decreased after 30 min. The curve fitting demonstrated that the GompertzMod equation was the best-fitting model for each index component of RG. In conclusion, the dissolution test method described in this protocol is simple, accurate, and reliable. It can characterize the dissolution behavior of the index components in RG in vitro, which provides a methodological reference for quality control of RG and quality evaluation of other ethnic compounds.

Strengthening Process by Electron Beam to Carbon Fiber for Impact Strength Enhancement of Interlayered Thermoplastic-Polypropylene Carbon Fiber Composite.

Strong adhesion between recyclable thermoplastic (TP) polymer and carbon fiber (CF) has always been highly sought after. Therefore, for an interlayered CF reinforced TP polypropylene (CFRTPP) composite composed of 3 sized CF plies, alternating between 4 PP sheets, designated [PP]4[CF]3, a process of activating CF plies directly on both sides with homogeneous low energy electron beam irradiation (EBI) under N2 gas, prior to lamination assembly and hot press of 4.0 MPa at 493 K for 3 min was carried out. Experimental results showed EBI dose of 43.2, 129, or 216 kGy significantly raised Charpy impact values, auc at all fracture probabilities, Pf. The 129 kGy dose appeared to be at or near optimum increasing auc 103%, 83%, and 65% at low-, median-, and high-Pf = 0.07, 0.50, and 0.93; while raising statistically lowest impact value, as at Pf = 0 calculated by 3-dimensional Weibull equation about 110%, indicating increased safety and reliability. It is assumed dangling bonds generated by the EBI rapidly form covalent bonds CF:C:O:C:PP and CF:C:C:PP at the interface, along with cross-linking in the PP near the CF. This is by charge transfer from CF to PP.

Design and production of 3D printed oral capsular devices for the modified release of urea in ruminants

The use of 3D printing for the production of systems intended for oral delivery of diet supplements in the veterinary pharmacy constitutes an attractive technology that has remained unexplored. In this sense, this work studies the design and 3D printing of capsular devices that allow the modified release of urea, which is frequently used as a source of non-protein nitrogen in ruminants, but highly toxic if fast ingested. The devices were printed with combinations of polylactic acid (PLA, water-insoluble) and polyvinyl alcohol (PVA, water-soluble) in order to modulate the urea release through the different parts. The optimization of the designs as well as printing parameters such as extrusion temperature, printing speed, retraction distance and nozzle speed resulted critical to obtain successful capsular devices. In addition, the dissolution studies confirmed that the developed designs showed a controlled release of urea, especially the ones that presented internal partitions. Finally, Logistic and Weibull equations were the kinetic models that best fitted the experimental data corresponding to functions that describe S-shaped dissolution profiles. Overall, this work constitutes a proof of concept and provides the first steps in the development of 3D printed simple devices for the controlled release of supplements and drugs in veterinary pharmacy.