1 10 2 https://urss.warwick.ac.uk/files/original/b368159dd4637fa30d56e2dd80835dc9.pdf 66157d34d8be467e71d082cfe55f1747 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Science, Engineering and Medicine Presentation Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Impact of Environmental and Metabolic Pressures in Circadian Rhythms of Mammalian Osteosarcoma Cells Subject The topic of the resource Warwick Medical School Creator An entity primarily responsible for making the resource Rithvik Shadhanamoorthy Date A point or period of time associated with an event in the lifecycle of the resource 2023 Chronotherapy Circadian rhythms Like Sciences Rithvik Shadhanamoorthy https://urss.warwick.ac.uk/files/original/489977e99db0bedc6abbecda8c479779.pdf 4f41d64dd43ae80773557c7e4d18cbd5 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Mathematics Academic Paper An academic paper Abstract The abstract of the paper It is hypothesised that both cancer cell growth and chemotherapy drug tolerance can be dependent on the circadian rhythm, causing differences in treatment efficiency at different times of the day. Chronotherapy aims to exploit this dependency to provide an optimal treatment plan for patients. This plan seeks to maximise the elimination of cancer cells while minimising drug toxicity resulting from chemotherapy. This paper aims to extend previous works and provide analyses of optimal solutions for various cancer treatment models, including scenarios in which growth is partially coupled with the circadian rhythm, cases where drugs target growth, and models that account for delayed drug effects. Using Pontryagin’s Minimum Principle (PMP), we found the switching function of each model that decides the optimal time period to apply or stop the drugs. In the first two models, we noted the aperiodic switching between full and no drugs in optimal solutions and explored the nature of the switching zones. While the optimal solution for the last case is complex, it is proven to be bang-bang and can be reduced to a simpler growth model using the Pseudo-Steady State Hypothesis (PSSH) for sufficiently fast drug absorption speeds. Furthermore, we presented the backward integration method to analyse the nature of optimal solutions. The exploration of optimal solutions provides a better understanding of optimal treatment plans for chronotherapy models and offers insights into potential future analyses of more complex and clinically applicable models. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Optimal Solutions of Chronotherapy Models Subject The topic of the resource Mathematics Creator An entity primarily responsible for making the resource Xingyu (Steve) Wu Date A point or period of time associated with an event in the lifecycle of the resource 2023 Chronotherapy Mathematics Non-autonomous Dynamical Systems Optimal Control Xingyu (Steve) Wu