Hydroxyethylcellulose (HEC) is a biodegradable, biocompatible polymer which is responsive to the temperature and pH values that can be reached by the human body. Polyacrylamide (PAAm) is a biocompatible and absorbent material which is highly used as a Drug Delivery System (DDS) due to its swelling capacity. In this work, a composite of HEC and PAAm was synthesized at a ratio of 25/75 wt% in order to evaluate its use as a transdermal DDS for acetaminophen. Drug release tests were performed in a phosphate buffer solution (PBS) at 35, 37, and 39 °C. The Korsmeyer-Peppas model was presented as a mathematical optimization problem and solved by Differential Evolution (DE) algorithm. Additionally, drug release data was modelled by Multigene Symbolic Regression (MSR) based on Genetic Programming (GP) algorithm. A drug release mathematical model was generated by MSR. The model is capable to reliably describe the kinetics of acetaminophen release from HEC/PAAm and to predict the concentrations of drug that is released in times beyond the experiment runtime.

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.