Math 495 Project Page

Spring 2019

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A major component of this course will involve a project. Information on the project can be found on this page.

Description

The project will be involve reading and understanding one (or more) published research papers in the field of mathematical oncology. The project should focus on a specific biological problem studied (at least partially) from a mathematical perspective. That is, the paper should not be entirely experimental, but should have quantitative aspects. Topics can be chosen as you'd like, but should both (1) relate to cancer, and (2) be distinct from work directly covered in class. To make (2) more clear: you may investigate a topic discussed (such as optimal therapy, quiescence, data fitting, competition, etc.), but you should not work entirely from a paper explicitly discussed. You will be expected to submit a typed report, as well as give a short presentation on May 4th (the day of the scheduled Final Exam). You must work in groups of about three fellow students, and all work will be submitted (and graded) as one. More explicit information on the individual components can be found below.

Topics

Topics can be selected as you like, but hopefully will reflect the interest of everyone in the group. The work does need to be based in mathematics, so that there is a substantive quantitative component. Note that you will be expected to reproduce major results from the work, so I suggest carefully considering the feasibility of this before making final selections. I will ask for prior approval on the topic and the primary paper (see Tentative Schedule below), so as to assess the level of difficulty, and to confirm there are aspects which I think are reasonably reproducible. For an idea of possible topics, see below. If your group would like further assistance in choosing a topic/paper, feel free to contact me.

Possible Topics

• Spatially structured tumor growth models (partial differential equations)
• Competition between stable and unstable clonal variants
• Chromosomal instability in cancer
• Models of angiogenesis and treatment
• Specific examples of optimal control problems (chemotherapy, drug resistance, etc.)
• Physiologically structured population models (such as the effect of cell-cycle dynamics)
• Prostate cancer (prediction using PSA measurements, and/or androgen deprivation therapy)
• Ecology of cancer: effects of microenvironment on evolution
• Cancer evolution through stochastic tunneling
• Resistance to chemotherapy as a random event (for example in CML)
• Luria-Delbruck fluctuation analysis of resistance evolution (or Goldie-Coldman)
• Models of immune system and cancer dynamics
• Ecological principles to understand treatment/development (really game theory, see work by Basanta)

Components

Expository Report

You and your group will be expected to read, understand, and reproduce certain aspects of your chosen paper(s). To submit to me, you should include a basic summary of the work and the results. This should include an introduction discussing the biological problem, methods used (mathematical and experimental), and conclusions. You should also include a critique of the work, e.g. does it answer the question?, what assumptions are made and are they reasonable?, what could be improved upon?, etc. Essentially, I am asking you to rewrite the paper as you understand it, with a critique and possibly even future directions. Note that this should not be a verbatim reproduction, but rather a summary of your understanding in your own words. You should include mathematical calculations/derivations; specifically elaborating on details which may omitted (this is common in papers). You will also be expected to reproduce some figures via numerical calculations, and the entire document should be typed (I suggest LaTeX, but you may use anything you'd like). By mid-April, I will ask for progress reports, including figures and calculations which you will reproduce (see Tentative Schedule below); some results you may copy/paste directly (for example, any experimental data), as I don't expect you to rewrite the paper entirely. The final report will be due on May 4th (the day of the scheduled Final Exam). There is no explicit requirement on length, but I do expect the main aspects of the original paper to be included.

Presentation

During the scheduled Final Exam period (May 4th), your group will be asked to give a short presentation to the rest of the class. It should be around twenty minutes in length, and will most likely be given with slides (although you can give a "chalk talk" if you'd like, it may be hard with certain figures). Each member of the group should participate, and your goal will be summarize the work and your results/conclusions, as well as to motivate the problem biologically. You should be prepared to answer any questions I or others in the class may have.

Tentative Schedule

1. Friday, March 1^rd: Groups due via email. Please send me an email with the name of your group members by 5 pm. If you would like me to assign you a group, please request via email by this date, and include topics of interest to you, so as to help better assign like-minded groups. In this case, please list a few possible topics that you would be interested in studying.
2. Friday, March 15^th: Topics and paper for each group. Please send an email with the biological topic and the paper (attached as a pdf) you intend to use as your primary source for the project. I will approve or disapprove (with reasons and suggestions) of the choice promptly.
3. Friday, April 19^th: Progress report. I would like to send me (by 5 pm) a PDF document summarizing your understanding and plans for the project. It should not be a verbatim copy of the Abstract or of the advice I sent your group; this will count as part of your grade, and I will know if it is directly copied from me or the source). It doesn't need to be long, but should include the four sections discussed below. The main function of this is to ensure that the groups are not falling behind, since the project is worth a large portion of the grade. As a progress report, I won't expect everything to be completed, but at this point you should have some results, and an idea of what the Expository Report will look like. Indeed, this report can be thought of as a first draft.
   • Summary of paper: a few paragraphs outlining your topic (in your own words). This should be at a high level, and (hopefully) motivated by the biological problem of interest. What are the author's main findings, and what significance do they provide? Again, make sure that this is not taken directly from the source itself.
   • Mathematical techniques: describe the quantitative framework utilized to study the biological problem. Why did they choose that specific model? How are they incorporating the relevant assumptions quantitatively? What kind of analysis is done? Be as precise as possible, and include equations directly.
   • Completed results: include any aspects of the paper that you have already reproduced and/or expanded upon. A major aspect of the project is to reproduce both analytic and numerical results appearing in the paper, and not copying their figures and analysis. Include any derivations that you have expanded, and any of the fiugres you have reproduced. Feel free to include as much detail as you'd like, and even portions of analysis/code are encouraged. Hopefully you will have something in this section by the due date.
   • Results in progress: results that you have not reproduced, but plan to in the final report. I want to explicitly know what you intend to reproduce. As in the Completed results section, this should have both mathematical analysis and numerical portions. Looking at this, I can then give advice and make further suggestions.
4. Friday, May 10^th: Expository Report and Presentations due. Final versions of the Expository Report will be collected. Presentations will also be given by each group. Our allotted time is 12-3 pm, in the normal classroom (ARC-110, Busch campus).