Mathematical and Pharmacokinetic Approaches for the Design of New 3D Printing Inks Using Ricobendazole.

PURPOSE: 3D printing (3DP) makes it possible to obtain systems that are not achievable with current conventional methods, one of them, sustained release floating systems. Floating systems using ricobendazole (RBZ) as a model drug and a combination of polymers were designed and obtained by melt solidification printing technique (MESO-PP). METHODS: Four different MESO-PP inks were formulated based on combinations of the polymers Gelucire 43/01 and Gelucire 50/13 in different ratios. For each of the formulated inks, physicochemical characterization was performed by thermal analysis (thermogravimetric analysis [TGA] and differential scanning calorimetry [DSC]), fourier transform infrared spectrophotometer (FTIR) and X-ray diffraction (XRD). Pharmaceutical characterization was performed by in vitro assays to determine pharmaceutically relevant parameters. These parameters were calculated by applying mathematical models developed to evaluate in vitro drug release profiles. On the other hand, a physiologically based pharmacokinetic (PBPK) model was developed to predict the in vivo performance of RBZ loaded in the different inks by determining the Cmax, and the AUC0-∞. RESULTS: By increasing the proportion of Gelucire 50/13 co-surfactant in the mixtures (the proportion in Ink 1 was 33%, while the proportion in Ink 4 was 80%), the dissolution capacity of RBZ increases substantially, decreasing flotation times. CONCLUSION: MESO-PP produced ink 1 (50% Gelucire 43/01, 25% Gelucire 50/13 and 25% RBZ), which has a zero-order release (RR = 0.180%/min) and the longest flotation time (545 ± 23 min), and in turn would produce a significant increase in oral absorption of the drug, with an AUC0-∞ 2.16-fold higher than that obtained in animals treated with RBZ loaded in conventional tablets.

Dissolution profiles of fenbendazole from binary solid dispersions: a mathematical approach.

Aim: Understanding a drug dissolution process from solid dispersions (SD) to develop formulations with predictable in vivo performance. Materials & methods: Dissolution data of fenbendazole released from the SDs and the control physical mixtures were analyzed using the Lumped mathematical model to estimate the parameters of pharmaceutical relevance. Results: The fit data obtained by Lumped model showed that all SDs have a unique dissolution profile with an error of ±4.1% and an initial release rate 500-times higher than the pure drug, without incidence of drug/polymer ratio or polymer type. Conclusion: The Lumped model helped to understand that the main factor influencing the fenbendazole release was the type formulation (SD or physical mixture), regardless of the type or amount of polymer used.

Dual Release Model to Evaluate Dissolution Profiles from Swellable Drug Polyelectrolyte Matrices.

BACKGROUND: Mathematical modeling in modified drug release is an important tool that allows predicting the release rate of drugs in their surrounding environment and elucidates the transport mechanisms involved in the process. OBJECTIVE: The aim of this work was to develop a mathematical model that allows evaluating the release profile of drugs from polymeric carriers in which the swelling phenomenon is present. METHODS: Swellable matrices based on ionic complexes of alginic acid or carboxymethylcellulose with ciprofloxacin were prepared and the effect of adding the polymer sodium salt on the swelling process and the drug release was evaluated. Experimental data from the ciprofloxacin release profiles were mathematically adjusted, considering the mechanisms involved in each stage of the release process. RESULTS: A proposed model, named "Dual Release" model, was able to properly fit the experimental data of matrices presenting the swelling phenomenon, characterized by an inflection point in their release profile. This entails applying the extended model of Korsmeyer-Peppas to estimate the percentage of drug released from the first experimental point up to the inflection point and then a model called Lumped until the final time, allowing to adequately represent the complete range of the drug release profile. Different parameters of pharmaceutical relevance were calculated using the proposed model to compare the profiles of the studied matrices. CONCLUSION: The "Dual Release" model proposed in this article can be used to predict the behavior of complex systems in which different mechanisms are involved in the release process.

Films based on the biopolymer poly(3-hydroxybutyrate) as platforms for the controlled release of dexamethasone.

Controlled drug delivery aims to achieve an effective drug concentration in the action site for a desired period of time, while minimizing side effects. In this contribution, biodegradable poly(3-hydroxybutyrate) films were evaluated as a reservoir platform for dexamethasone controlled release. These systems were morphological and physicochemically characterized. In vitro release assays were performed for five different percentages of drug in the films and data were fitted by a mathematical model developed and validated by our research group. When the profiles were normalized, a single curve properly fitted all the experimental data. Using this unique curve, the dissolution efficiency (DE), the time to release a given amount of drug (tX% ), and the mean dissolution time were calculated. Furthermore, the dissolution rate, the initial dissolution rate (a%) and the intrinsic dissolution rate were determined. The a% mean value was 1.968 × 10-2% released/min, t80% was about 14 days, and the DE was 59.6% at 14 days and 66.5% at 20 days. After 2 days, when approximately 40% of the drug was released, the dissolution rate decreased about 60% respect to the initial value. The poly(3-hydroxybutyrate) platforms behaved as an appropriate system to release and control the dexamethasone delivery, suggesting that they could be an alternative to improve drug therapy.

Development and in vitro evaluation of solid dispersions as strategy to improve albendazole biopharmaceutical behavior.

AIM: Solid dispersions using Poloxamer 407 as carrier were developed to improve albendazole (ABZ) solubility and dissolution profiles. METHODS: ABZ/poloxamer solid dispersions were prepared, and dissolution profiles were mathematically modeled and compared with physical mixtures, pharmaceutical ABZ and a commercial formulation. RESULTS: Poloxamer 407 increased exponentially ABZ solubility, in about 400% when 95% w/w of polymer compared with its absence. Solid dispersions initial dissolution rate was three to 20-fold higher than physical mixtures, the drug and the commercial formulation. All the solid dispersions required less than 2.2 min to reach an 80% of ABZ dissolution, while the commercial formulation needed around 40 min. CONCLUSION: Solid dispersions improved ABZ solubility and dissolution rate, which could result in a faster absorption and an increased bioavailability.

Net growth rate of continuum heterogeneous biofilms with inhibition kinetics.

Biofilm systems can be modeled using a variety of analytical and numerical approaches, usually by making simplifying assumptions regarding biofilm heterogeneity and activity as well as effective diffusivity. Inhibition kinetics, albeit common in experimental systems, are rarely considered and analytical approaches are either lacking or consider effective diffusivity of the substrate and the biofilm density to remain constant. To address this obvious knowledge gap an analytical procedure to estimate the effectiveness factor (dimensionless substrate mass flux at the biofilm-fluid interface) was developed for a continuum heterogeneous biofilm with multiple limiting-substrate Monod kinetics to different types of inhibition kinetics. The simple perturbation technique, previously validated to quantify biofilm activity, was applied to systems where either the substrate or the inhibitor is the limiting component, and cases where the inhibitor is a reaction product or the substrate also acts as the inhibitor. Explicit analytical equations are presented for the effectiveness factor estimation and, therefore, the calculation of biomass growth rate or limiting substrate/inhibitor consumption rate, for a given biofilm thickness. The robustness of the new biofilm model was tested using kinetic parameters experimentally determined for the growth of Pseudomonas putida CCRC 14365 on phenol. Several additional cases have been analyzed, including examples where the effectiveness factor can reach values greater than unity, characteristic of systems with inhibition kinetics. Criteria to establish when the effectiveness factor can reach values greater than unity in each of the cases studied are also presented.

Validation of kinetic modeling of progesterone release from polymeric membranes.

Mathematical modeling in drug release systems is fundamental in development and optimization of these systems, since it allows to predict drug release rates and to elucidate the physical transport mechanisms involved. In this paper we validate a novel mathematical model that describes progesterone (Prg) controlled release from poly-3-hydroxybutyric acid (PHB) membranes. A statistical analysis was conducted to compare the fitting of our model with six different models and the Akaike information criterion (AIC) was used to find the equation with best-fit. A simple relation between mass and drug released rate was found, which allows predicting the effect of Prg loads on the release behavior. Our proposed model was the one with minimum AIC value, and therefore it was the one that statistically fitted better the experimental data obtained for all the Prg loads tested. Furthermore, the initial release rate was calculated and therefore, the interface mass transfer coefficient estimated and the equilibrium distribution constant of Prg between the PHB and the release medium was also determined. The results lead us to conclude that our proposed model is the one which best fits the experimental data and can be successfully used to describe Prg drug release in PHB membranes.

The continuum heterogeneous biofilm model with multiple limiting substrate Monod kinetics.

We describe a novel procedure to estimate the net growth rate of biofilms on multiple substrates. The approach is based on diffusion-reaction mass balances for chemical species in a continuum biofilm model with reaction kinetics corresponding to a Double-Monod expression. This analytical model considers a heterogeneous biofilm with variable distributions of biofilm density, activity, and effective diffusivity as a function of depth. We present the procedure to estimate the effectiveness factor analytically and compare the outcome with values obtained by the application of a rigorous numerical computational method using several theoretical examples and a test case. A comparison of the profiles of the effectiveness factor as a function of the Thiele modulus, φ, revealed that the activity of a homogeneous biofilm could be as much as 42% higher than that of a heterogeneous biofilm, under the given conditions. The maximum relative error between numerical and estimated effectiveness factor was 2.03% at φ near 0.7 (corresponding to a normalized Thiele modulus φ* = 1). For φ < 0.3 or φ > 1.4, the relative error was less than 0.5%. A biofilm containing aerobic ammonium oxidizers was chosen as a test case to illustrate the model's capability. We assumed a continuum heterogeneous biofilm model where the effective diffusivities of oxygen and ammonium change with biofilm position. Calculations were performed for two scenarios; Case I had low dissolved oxygen (DO) concentrations and Case II had high DO concentrations, with a concentration at the biofilm-fluid interface of 10 g O2 /m(3) . For Case II, ammonium was the limiting substrate for a biofilm surface concentration, CNs , ≤13.84 g of N/m(3) . At these concentrations ammonium was limiting inside the biofilm, and oxygen was fully penetrating. Conversely, for CNs > 13.84 g of N/m(3) , oxygen became the limiting substrate inside the biofilm and ammonium was fully penetrating. Finally, a generalized procedure to estimate the effectiveness factor for a system with multiple (n > 2) limiting substrates is given.

Towards a rational strategy for monitoring of microbiological quality of ambient waters.

Water is one of the main sources of human exposure to microbiological hazards. Although legislation establishes regulatory standards in terms of fecal indicator bacteria to assess the microbiological quality of water, these do not necessarily predict the presence of pathogens such as parasites and viruses. Better surveillance and management strategies are needed to assess the risk of pathogens' waterborne transmission. We established a baseline dataset to characterize river water quality, identify changes over time, and design a rational monitoring strategy. Data from a year-long monthly monitoring campaign of the polluted Arenales River (Argentina), were analyzed to statistically correlate physicochemical and microbiological variables, the seasonal and longitudinal variations of the water quality and determine the similarity between study sites. The measured variables (sixteen) reflected the deterioration in the river quality through the city. Different viruses and parasites found did not correlate with the concentration of total and thermotolerant coliforms. There was significant seasonal variation for temperature, turbidity, conductivity, dissolved oxygen, enterococci, and norovirus. Strong correlations between some variables were found; we selected eight variables (dissolved oxygen, conductivity, turbidity, total and thermotolerant coliforms, Enterococcus, and adenovirus and Microsporidium as viral and parasitological indicators, respectively) for future monitoring. There was similarity between the monitoring locations, which were grouped into four clusters validated by cophenetic correlation and supported by discriminant analysis. This allowed us to reduce the number of sites, from eleven down to five. Sixty seven percent of the total variance and the correlation structure between variables were explained using five principal components. All these analyses led to a new long-term systematic monitoring scheme. A rational monitoring strategy based on the selection of the most suitable monitoring points and of the most significant variables to measure, will result in optimal use of the limited resources available to adequately protect the public and environmental health.

Continuum heterogeneous biofilm model--a simple and accurate method for effectiveness factor determination.

We present a novel analytical approach to describe biofilm processes considering continuum variation of both biofilm density and substrate effective diffusivity. A simple perturbation and matching technique was used to quantify biofilm activity using the steady-state diffusion-reaction equation with continuum variable substrate effective diffusivity and biofilm density, along the coordinate normal to the biofilm surface. The procedure allows prediction of an effectiveness factor, η, defined as the ratio between the observed rate of substrate utilization (reaction rate with diffusion resistance) and the rate of substrate utilization without diffusion limitation. Main assumptions are that (i) the biofilm is a continuum, (ii) substrate is transferred by diffusion only and is consumed only by microorganisms at a rate according to Monod kinetics, (iii) biofilm density and substrate effective diffusivity change in the x direction, (iv) the substrate concentration above the biofilm surface is known, and (v) the substratum is impermeable. With this approach one can evaluate, in a fast and efficient way, the effect of different parameters that characterize a heterogeneous biofilm and the kinetics of the rate of substrate consumption on the behavior of the biological system. Based on a comparison of η profiles the activity of a homogeneous biofilm could be as much as 47.8% higher than that of a heterogeneous biofilm, under the given conditions. A comparison of η values estimated for first order kinetics and η values obtained by numerical techniques showed a maximum deviation of 1.75% in a narrow range of modified Thiele modulus values. When external mass transfer resistance, is also considered, a global effectiveness factor, η(0) , can be calculated. The main advantage of the approach lies in the analytical expression for the calculation of the intrinsic effectiveness factor η and its implementation in a computer program. For the test cases studied convergence was achieved quickly after four or five iterations. Therefore, the simulation and scale-up of heterogeneous biofilm reactors can be easily carried out.