Optimising Multidrug Pharmacological Protocols

Evolutionary dynamics, optimal control, and machine learning

Tumours and other evolving cell populations are rarely homogeneous. They are often composed of multiple clones with different proliferative capacities, drug sensitivities, and evolutionary trajectories. Treatment therefore acts not only as a mechanism of cell killing, but also as a selective pressure capable of reshaping the population itself.

In this project, I study the evolutionary dynamics of multiclonal cell populations under pharmacological treatment, with the goal of designing treatment schedules that exploit rather than ignore this evolutionary structure. Mathematical models are used to describe competition between clones, treatment-induced selection, the emergence of resistant populations, and possible trade-offs between sensitivity to different drugs.

I develop both analytical and numerical optimal-control approaches to investigate multidrug therapies. Rather than considering drug dose and scheduling as fixed inputs, treatment becomes a dynamic control variable that can be optimised according to different objectives, such as minimising tumour burden, delaying resistance, reducing cumulative toxicity, or maintaining long-term population control.

Alongside mechanistic optimisation, I use machine-learning approaches to analyse the large space of possible treatment protocols. Clustering methods, including K-means-type approaches, can be used to identify families of treatments associated with similar dynamical outcomes, while decision trees provide interpretable rules linking tumour characteristics and treatment choices to therapeutic success or failure. This combination of optimal control and data-driven analysis provides both theoretically optimal strategies and more interpretable treatment principles.

The broader aim is to understand when adaptive, sequential, or combination therapies can outperform standard treatment schedules and which characteristics of an evolving tumour should guide therapeutic decisions.

This work is carried out in collaboration with researchers at Ankara University and the Institute for Applied Mathematics and Information Technologies “Enrico Magenes” (IMATI-CNR), Genoa Unit.

Main themes: evolutionary dynamics · multiclonal populations · drug resistance · multidrug therapies · optimal control · numerical optimisation · machine learning · clustering · decision trees · adaptive therapy