I am a PhD student at the Mathematics of Real World Systems Center of Doctoral Training. My research area lies in the domains of optimal control theory with applications in cancer biology. Chemotherapies can be viewed as protocols that dictate the timing of drug administration and the quantity of the drugs administered. My research focuses on the development of optimal control strategies and on designing therapy objective functions, which aim to improve the efficacy of cancer chemotherapies and advance efficient therapeutic strategies that can be used by practitioners. My supervisor is Professor Nigel Burroughs and my co-supervisor is Dr Annabelle Ballesta.

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Research projects:

Futures outcome optimization payoff

We are working on the development of a novel payoff formulation that evaluates the efficacy of treatments in terms of the expected lifetime of a patient and the possible cancer futures/outcomes.

We investigate methods to determine the possible future outcomes and their probability to occur. Statistical data of primary causes of death could be used to estimate the expected lifetime of a patient, for each future outcome.

The advantage of such a payoff functional is that its parameters have a direct physical interpretation and hence could be potentially used in the development of personalised treatments.

We have considered simple cancer cell population models and two possible futures/outcomes, i.e. tumor elimination and patient mortality due to the drug. In order for this formulation to be applied in a real world setting (namely in the case of Acute Myeloid Leukemia (AML)) we are gradually adding complexity on the optimisation framework.

Aperiodic optimal chronotherapy in single compartment tumour growth models with drug tolerability constraints

( MSc Individual Research Project and PhD work )

Chronotherapies are cancer therapies that utilise the fact that cancer cells often have a disrupted circadian clock and therefore their cell cycle has weaker coupling to the bodies' 24 hour cycle.

In this work we examined optimal chronotherapy strategies for tumours that are completely decoupled from the circadian clock.

The cost functional that was employed is comprised of a terminal cost that calibrates the size of the tumour at the end of the treatment and a periodically driven running cost, that expresses drug tolerability constraints.

The cost was minimised, subject to single compartment tumour growth models; optimal solutions revealed complex dynamics, that were studied in detail. For both cytotoxic drugs and drugs that target cell division, we showed that optimal drug administration schedules are aperiodic with the duration of the daily drug administration increasing, as the treatment progresses. Singular solutions can exist in the case where the models per capita tumour growth rate is convex. We compared optimised periodic chronotherapy drug regiments to aperiodic optimal solutions and showed that both drug regiments cause similar tumour reduction, the latter relating to lower levels of drug toxicity than the former.

Adaptive management during an ongoing pandemic

(MSc Research Study Group Project)

Adaptive management is an iterative decision making process that can improve the efficacy of a policy by accounting on future uncertainty.

We applied adaptive management techniques in the framework of a COVID-19 outbreak. The objective was to determine efficient lockdown policies with the aim on minimizing the maximum number of concurrent infections while keeping the lockdown period low.

Applications of Hamiltonian Dynamical Systems in Classical Mechanics and Fluid Dynamics

(Undergraduate dissertation)

In this work we studied several example cases of Hamiltonian dynamical systems in the domains of classical and fluid dynamics.