Instructor: Prof. Kathleen Wilkie
Email: kpwilkie@torontomu.ca

Course Dates: January 15th - April 15th, 2024
Mid-Semester Break: February 19th-23rd, 2024
Lecture Times: Mondays & Thursdays | 10:00 AM - 11:30 AM (ET)
Office Hours: by appointment

Registration Fee: PSU Students - Free | Other Students - CAD$500

Capacity Limit: 30 students

Format: Online synchronous

Course Description

Please view the course outline HERE.

This first course in mathematical oncology will focus on ordinary differential equation based models for cancer and its treatment. It will introduce standard models for tumour growth and various anti-cancer therapies. The course will then transition to techniques required when using ODE models in mathematical oncology and other modelling applications. Topics may include: model parameterization and curve fitting, local and global model sensitivity analysis, structural and practical model identifiability, virtual clinical trials, and parameter landscape analysis (pca and clustering).

The class is in preparation to the Fall 2024 Thematic Program on Mathematical Oncology at the Fields Institute.

Prerequisites: A course in ODE theory, dynamical systems, and stability analysis is required. Familiarity with programming and cancer biology are assets.

Evaluation: 

• 20% In Class Presentations and Discussions
• 40% Assignments - scaffolded pieces of the final project distributed throughout the term
• 10% Presentation of Final Project
• 30% Written Final Project Report

Numerical Simulation:
Assessments will involve the use of numeric computation software such as MATLAB / Julia / Maple / python etc. I will provide sample programming scripts for Julia (a freely available software https://julialang.org). You are required to have access to a computer with your software of choice and to provide your own technical support.

Course Expectations and Learning Outcomes:
Students will gain an introduction to mathematical oncology modelling and methods using ordinary differential equations. They will gain hands-on experience implementing the methods and techniques to parameterize, simulate, and analyze the mathematical models. They will learn standard mathematical models for oncology applications and develop proficiency in a programming language (Julia). Auditing is permitted but to gain the full hands-on experience, completion of assignments and the final project is recommended. Assignments will focus on implementation of the studied techniques to an application that will be collected and presented as a final project at the end of the course.

Suggested Reading:
Selected topics will be taken from textbooks or research papers as appropriate, such as:

• Introduction to Mathematical Oncology by Yang Kuang, John D. Nagy, and Steffen E. Eikenberry. https://doi.org/10.1201/9781315365404.
• Dela A, Shtylla B, de Pillis L. Multi-method global sensitivity analysis of mathematical models. J Theor Biol 546:111159, 2022. https://doi.org/10.1016/j.jtbi.2022.111159
• Porthiyas J, Nussey D, Beauchemin CAA, Warren DC, Quirouette C, Wilkie KP. A closer look at parameter identifiability, model selection and handling of censored data with Bayesian Inference in mathematical models of tumour growth. arXiv: 2309.13319, 2023. https://arxiv.org/abs/2309.13319
• Eisenberg MC, Jain HV. A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study. J Theor Biol 431, 2017. https://doi.org/10.1016/j.jtbi.2017.07.018
• Craig M, Gevertz JL, Kareva I, Wilkie KP. A practical guide for the generation of model-based virtual clinical trials. Front Syst Biol 3, 2023. https://doi.org/10.3389/fsysb.2023.1174647