Mathematical model for drug molecules encapsulated in lipid nanotube

Mathematical Modelling of Acetaminophen Release in HPC/PAAm Hydrogel: Synthesis and Application

International Journal of Polymer Science ◽

10.1155/2019/9306459 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

Abigail M. Díaz-Guerrero ◽

Claudia A. Castillo-Miranda ◽

Carlos F. Castro-Guerrero ◽

Hernán Peraza-Vázquez ◽

Ana B. Morales-Cepeda ◽

...

Keyword(s):

Mathematical Model ◽

Mathematical Modelling ◽

Phosphate Buffer Solution ◽

Absolute Error ◽

Programming Algorithm ◽

Test Results ◽

Buffer Solution ◽

Drug Molecules ◽

Hydrogel Synthesis ◽

The Mathematical Model

Hydrogels are commonly used as Drug Delivery Systems (DDS) as patches due to its ability to store drug molecules within their structures. The release can be activated under certain stimuli, such as temperature and pH. In this paper, the mathematical modelling of acetaminophen release in hydroxypropyl cellulose with polyacrylamide (HPC/PAAm) is reported. The HPC/PAAm gel was synthesized in proportions of 25/75 wt% and was characterized by FTIR, DSC, optical microscopy, SEM, and TGA, with and without acetaminophen. The release tests were performed for hypothermic, normal, and febrile human body conditions, at 35, 37, and 39°C, respectively, on two release media: water and phosphate buffer solution. In order to describe the release of acetaminophen in HPC/PAAm gel, a genetic programming algorithm was used to accomplish Multigene Symbolic Regression (MSR). Characterization results showed that the drug was crystallized on the surface of the HPC/PAAm gel. Release test results showed that several simultaneous processes occurred in the acetaminophen diffusion phenomenon. A unique mathematical model was obtained by MSR. This model was able to describe the release of acetaminophen in HPC/PAAm gel with high values of R2 and adjusted R2 and to simulate the drug release at times beyond the end of the experiment. High values of R2 and low values of Coefficient of Variation (CV), Root-Mean-Square Error (RMSE), and Mean Absolute Error (MAE) were obtained from the comparison between the simulated and the experimental data. This allows to conclude that the mathematical model is reliable to represent and simulate the acetaminophen release in HPC/PAAm gel at 35, 37, and 39°C.

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A Mathematical Model for Prediction of Drug Molecule Diffusion Across the Blood-Brain Barrier

Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques ◽

10.1017/s0317167100003759 ◽

2004 ◽

Vol 31 (4) ◽

pp. 520-527 ◽

Cited By ~ 7

Author(s):

Jonathan Burns ◽

Donald F. Weaver ◽

Jonathan Burns ◽

Donald F. Weaver

Keyword(s):

Mathematical Model ◽

Blood Brain Barrier ◽

Brain Barrier ◽

Topological Descriptors ◽

Final Model ◽

Drug Molecules ◽

Blood Brain ◽

Brain Uptake Index ◽

The Brain ◽

Potential Therapeutics

Background:Predicting the ability of drugs to enter the brain is a longstanding problem in neuropharmacology. The first step in creating a much-needed computational algorithm for predicting whether a drug will enter brain is to devise a rigorous mathematical model.Methods:Employing two experimental measures of blood-brain barrier (BBB) penetrability (brain/plasma ratio and the brain-uptake index) and 14 theoretically derived biophysical predictors, a mathematical model was developed to quantitatively correlate molecular structure with ability to traverse the BBB.Results:This mathematical model employs Stein's hydrogen bonding number and Randic's topological descriptors to correlate structure with ability to cross the BBB. The final model accurately predicts the ability of test molecules to cross the BBB.Conclusion:A mathematical method to predict blood-brain barrier penetrability of drug molecules has been successfully devised. As a result of bioinformatics, chemoinformatics and other informatics-based technologies, the number of small molecules being developed as potential therapeutics is increasing exponentially. A biophysically rigorous method to predict BBB penetrability will be a much-needed tool for the evaluation of these molecules.

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