Mathematical Modeling and Estimation of Physicochemical Properties of Non-Steroidal Anti-Inflammatory Drugs Via an Innovative Approach of Biquadratic Regression Analysis

Abstract

Background: In mathematical chemistry (particularly in chemical graph theory), reverse degree-based topological indices provide good correlations with respect to both mathematical and chemical perspectives for the prediction of biological activities of diverse nature with a variety of relationships between physical, chemical, and thermodynamic parameters. Objective: The main aim of this study is to provide the reverse degree-based graph polynomial, along with its corresponding topological indices. The objective of this methodology is to estimate the physical and chemical properties of specific molecular parameters through an innovative approach, biquadratic regression analysis. Methods: Reverse degree-based graph polynomials are utilized to compute various reverse degree-based topological indices. The outcomes of this study are utilized to perform an innovative approach, biquadratic regression analysis, to estimate the various physicochemical properties of NSAID drugs. This approach provides the best approximations for the said properties. Results: The main focus of the research is the connection between changes in topological indices and physical characteristics. Based on these findings, this article may aid chemists and pharmaceutical industry professionals in the development of novel pharmaceuticals. A similar relationship can be found between topological indices and the physical characteristics of newly discovered medications for treating specific diseases to assess the physical characteristics of those medications. This study provides a QSPR experiment using biquadratic regression models to yield greater estimates for the properties of the NSAIDs. Conclusion: Through the utilization of Biquadratic regression models, we have discovered that the indices that we have presented have a close relationship with both the chemical and physical parameters. © 2025 Bentham Science Publishers.