Abstract
This study combines advanced pharmacokinetic modelling techniques and machine learning-based approaches
to optimise drug dosage and enhance therapeutic outcomes in clinical practice. The first component uses
fractional-order differential equations to model pharmacokinetic processes, offering a novel alternative to conventional
ordinary differential equations. Fractional-order models capture the complex dynamics of drug absorption,
distribution, metabolism, and excretion (ADME) more accurately, particularly for drugs with non-linear kinetics
or prolonged distribution phases. Two numerical methods, the Grunwald–Letnikov and L1 approximations,
were validated for their ability to solve fractional models, demonstrating robust performance without analytic
solutions. These methods were applied to two-compartment models for intravenous and oral drug administration
routes, with sensitivity analyses revealing the significant role of fractional parameters in representing memory
effects in drug kinetics. Clinical validation further supported the hypothesis that fractional models can better
describe pharmacokinetics than their traditional counterparts.
The second component of this research introduces a data-driven machine-learning framework for the individualised
prediction of pharmacokinetic parameters. Using neural networks to address the inverse parameter
estimation problem, the method integrates patient-specific data, such as medical history and physiological
variables, to refine model parameters. These parameters are subsequently used in forward modelling to predict
drug concentration-time profiles under various dosing regimens. The framework combines the flexibility of
machine learning with the rigour of differential equation-based pharmacokinetics, achieving high accuracy in
parameter estimation and close alignment between predicted and observed drug concentration profiles. Across
multiple dose levels, the approach consistently demonstrated minimal error and a strong correlation between
observed and predicted values.
By integrating fractional modelling and machine learning, this study presents a hybrid methodology that
bridges theoretical advancements in pharmacokinetics with practical, patient-centred applications. This dual
approach improves the precision of drug dosage regimens and lays the groundwork for personalised medicine,
enabling clinicians to optimise therapeutic strategies based on individual patient profiles.