Modelling Doxorubicin effect in various cancer therapies by means of fractional calculus

Understanding and capturing the complex kinetics of drugs and their effects in the body plays a key role in optimal and patient-safe medical treatment. Classical models for drug uptake and diffusion are limited in characterizing anomalous diffusion, memory effects and power-law clearance rates. Unlike classical modelling techniques, fractional models can represent all these and reveal unseen dynamics which have the potential to be life-threatening to the patient receiving care. This paper presents a study case of Doxorubicin drug modelling, used for cancer therapy. We present several types of titration methods and their clearance dynamics using classical and fractional models. Our results suggest that continuous titration, or equidistant bolus administration leads to drug accumulation in the body, inducing many life-threatening side-effects in the patient. By applying power-law titration rates, or equivalently, logarithmic time-spaced boluses, unbounded drug accumulation is avoided.