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Explore a mathematical modeling framework for understanding drug-induced resistance in cancer treatment through this 49-minute conference talk by Eduardo Sontag from Northeastern University. Delve into how resistance to chemotherapy can arise not only through random genetic mutations but also through drug-induced mechanisms, including genetic changes and epigenetic alterations that cause phenotype switching in cancer cells. Examine a comprehensive mathematical model that incorporates both spontaneous and drug-induced resistance, demonstrating how a drug's ability to induce resistance can lead to qualitatively different treatment responses even with identical dosing schedules. Learn about structural identifiability theorems that enable determination of resistance induction rates for specific treatment protocols, and discover optimal control problem solutions characterized through bang-bang and path-constrained arcs using the Pontryagin Maximum Principle and differential Lie algebraic techniques. Analyze how the model successfully fits time-resolved in-vitro experimental data to reveal relative proportions of sensitive and resistant cell subpopulations and their dynamics as functions of drug dose. Understand how these mathematical insights, combined with optimal control techniques, can inform the design of improved dosing strategies that minimize total cell volume and reduce resistance evolution risk, representing collaborative research with multiple institutions focused on advancing personalized cancer therapy approaches.
