School of Mathematics & Statistics

Radiotherapy Treatment Planning: A Mathematician Perspective (Power) and A New Active-Strain Formulation for Left Ventricular Dynamics (Donaldson)

Jenny Power and Sarah Donaldson

Thursday 12th March 14:00-15:00
Maths 311B

Abstract

Abstract Power: Radiotherapy is among the most common methods for treating cancer. Treatment planning is a crucial
step of the treatment process. Clinicians carefully create treatment plans to ensure the radiation is
directed at the tumour and not at the healthy tissue, which if damaged could result in further health
complications. Mathematically, this problem can be formulated as a PDE-constrained optimisation
problem, where the goal is to find the optimal radiation source to irradiate the tumour, while minimising
radiation damage to surrounding organs. This talk will focus on the mathematical formulation of the
treatment planning problem, with a specific emphasis on brachytherapy, a type of radiation treatment
where radioactive seeds are surgically implanted directly onto the tumour

Abstract Donaldson: Mathematical models of the heart provide unique insights into cardiac function and have the potential to realise precision cardiology. Nevertheless, it remains challenging to model the mechanical properties of the myocardium because passive and active responses are essential components of cardiac models. Among existing approaches are active-stress and active-strain formulations. In this talk, a new active-strain model is introduced, incorporating an asymmetric activation waveform and a limiting function on effective fibre stretch to ensure the maximum fibre stress lies within physiological ranges. A comprehensive comparison between the two approaches is performed. The proposed active-strain model reproduces realistic left ventricular pump function in close agreement to the active-stress model, including pressure-volume loops, fibre stress/stretch, wall thickening and torsion. It also captures key functional relationships, including the end-diastolic pressure-volume relation and end-systolic pressure-volume relation. Although differences exist in local stress and strain patterns, global behaviours of simulated LV dynamics are similar compared to the active-stress model, suggesting that this simplified active-strain model is feasible for patient-specific cardiac modelling.

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