Keiser University - Institutional RepositoryComparative Rational Pharmacokinetic Modeling for Therapeutic Window Adjustment: A Computational–Analytical Framework Integrating College Algebra, Applied Calculus, and Model Selection TheoryKamilaBorgeauthorRamónSalgadoauthorJoséZelayaauthorThis research introduces a valuable educational framework that bridges mathematical theory and applied pharmacokinetics by utilizing an analytically tractable rational model to teach model selection and parameter estimation. The study’s primary strength lies in its pedagogical design: by deriving exact closed-form expressions for peak time and peak concentration, it provides an intuitive, deterministic link between parameter shifts and physiological realities, such as renal impairment. Supported by rigorous statistical diagnostics (AIC, BIC, Levenberg–Marquardt optimization) and a clever Padé-like connection to the classic Bateman function, the authors successfully establish a transparent, FAIR-compliant learning environment. Although the framework currently relies on synthetic datasets rather than noisy, real-world clinical trials, it stands out as an exceptionally well-conceived tool for fostering quantitative literacy and model-based reasoning in STEM and pharmacology education. --------------------- Esta investigación presenta un valioso marco educativo que conecta la teoría matemática con la farmacocinética aplicada, utilizando un modelo racional analíticamente manejable para enseñar la selección de modelos y la estimación de parámetros. La principal fortaleza del estudio reside en su diseño pedagógico: al derivar expresiones exactas en forma cerrada para el tiempo pico y la concentración pico, proporciona un vínculo intuitivo y determinista entre los cambios de parámetros y las realidades fisiológicas, como la insuficiencia renal. Respaldado por rigurosos diagnósticos estadísticos (AIC, BIC, optimización de Levenberg-Marquardt) y una ingeniosa conexión tipo Padé con la función clásica de Bateman, los autores logran establecer un entorno de aprendizaje transparente y conforme a los principios FAIR. Si bien el marco actualmente se basa en conjuntos de datos sintéticos en lugar de ensayos clínicos reales con ruido, se destaca como una herramienta excepcionalmente bien concebida para fomentar la alfabetización cuantitativa y el razonamiento basado en modelos en la educación en ciencia, tecnología, ingeniería y matemáticas (STEM) y farmacología.Mathematics [QA]Mathematical physics. Applied mathematics. General works [QA401]Pharmacokinetics / Applied clinical pharmacokinetics [RM301.5]Keiser University Latin American Campus, San Marcos, NicaraguaMonograph

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