||Applied Mathematics, Biology
|| Genomic Data-Guided Mathematical Modeling of Cancer
Cancer arises when genetic and epigenetic mutations result in a selective advantage for a particular cell. Due to their genetic disparities, the human immune system can recognize cancerous cells as a threat to the body, and attempt to kill these foreign cells . This creates a battle between the cancer cells trying to grow and the immune system working to rid the body of them. In order to study the effect of this competitive growth environment on the progression of the cancer, we will create a mathematical model of the tumor microenvironement, deriving the model equations from the Lotka-Volterra predator-prey system. The model parameters will be estimated using cell count data from pancreatic adenocarcinomas through optimization in MATLAB. Although in most cases, the immune system is not strong enough on its own to completely reduce a tumor, immunotherapy, a treatment which involves enhancement of the body's own cells, has proven effective in treating some cancers. Thus, we we will use MATLAB simulations of model to study the effectiveness of a variety of treatment strategies, including chemotherapy, immunotherapy, and combinations of the two. -->
- Week 1: May 26th-31st
- This week began with orientation on Tuesday, at which all of the participants, program directors, and mentors introduced themselves. I met with my mentor, Dr. Subhajyoti De, later in the day to hear about my project. I spent Wednesday and Thursday reading some really interesting papers which my mentor sent to me, which made me really excited to begin my project. I also decided to obtain a notebook to keep track of everything I was learning and write down all of my questions. On Friday morning, I attended the weekly meeting of my new group. Later in the day, I met with my mentor to discuss a more specific focus, and ask all of my questions. With a better idea of my project in mind, I spent Saturday and Sunday working on my presentation for Tuesday.
- Week 2: June 1st-7th
- After listening to some really interesting presentations on Monday, I decided it was time to update this website with my project description and log for week 1. I then created a list of tasks to get done for the week and practiced my presentation. My presentation on Tuesday went pretty well, and it was interesting to her about everyone else's work. I spent the rest of the week learning about how the immune system responds to cancer and looking at models of the immune response to get an idea about what I would like to include in my own model. On Friday, I was able to connect with another member from the De Laboratory, Bassel Ghaddar, to get data about the levels of certain cells in tumors of various stages. This data should be quite useful in creation of my model, and will guide what I choose to include.
- Week 3: June 8th-14th
- On Monday and Tuesday, I learned a lot more about the specific types of immune cells tracked in Bassel's data, and wrote my model equations. On Wednesday, I met with my mentor and Bassel to simplify my model, and collect some additional data. Thursday and Friday were spent writing an optimization program in MATLAB which would fit the parameters of my model to the experimental data.
- Week 4: June 15th-21st
- Most of this week was spent using my optimization program to attempt to gather parameters so that my model would be consistent with the experimentally obtained cell counts from pancreatic cancer tumors. This proved to be quite difficult due to the complexity of my model so I attempted the same task with various simplifications of my model.
- Week 5:June 22nd-28th
- After considering the difficulties which I was having with parameter optimization, I realized I had been using the data incorrectly. I began this week by learning about how gene expression data is normalized and using this technique to ensure I was properly using my data. This led me to discover a simplification of my model was needed, so I made this adjustment and continued my fitting attempts.
- Week 6:June 29th-July 5th
- I met with my mentor at the beginning of the week, hoping I could present a model which I could begin studying. However, this meeting led me to realize that unfortunately, the optimization portion of my project was not yet done. I did a lot of research about pancreatic cancer specifically to get basic ideas for what the parameters should look like (mostly in terms of order of magnitude estimates). I used this research to make a few more tweaks to my model which resulted in interesting model behavior, albeit not exactly what I was looking for. However, with a bit more work, I think I have something which I can study.
- Week 7:July 6th-12th
- Having begun the week by finalizing the mathematical model and parameters, I spent most of the week using the model to study cancer treatment. I incorporated immunotherapy and chemotherapy and varied duration and strength of treatment to determine how use of treatments can be optimized. I was very glad to finally be done with the model fitting stage, and be able to move on to the fun part, exploring its behavior.
- Week 8: July 13th-19th
- This week I wrapped up my final research, trying out various treatment combinations with my model. I then began thinking about my paper and presentation. I spent a few days putting together my presentation, and then presented it on Thursday in my lab group meeting. The presentation went well, and I got a lot of good notes. However, it was a little bit too long so I had to work on being more concise in my presentation. Having completed this, I began to outline my paper. I chose a template for Latex, and reorganized the sections as needed for my work. I then wrote my abstract, which took me far longer than I thought it would, but gave me clear direction in writing my paper. I decided to finish up my presentation over the weekend so I could focus on my paper next week.
- Week 9:July 20th-24th
- This was the final week of the program so I spent most of it writing my paper and practicing my presentation. I wrote the introduction on Monday and did another practice run-through of my presentation, which was exactly 10 minutes this time. On Tuesday, I started gathering my sources, and wrote about my model and methods. On Wednesday, I recreated my figures for my presentation and paper to ensure they were clear and easy to read, and practiced my presentation a few more times. On Thursday I woke up early so that I could finish my paper before another round of presentations. It took longer than expected, but I finally got it done, got my mentor's approval, and met with my mentor a final time. My presentation went pretty well, despite a few technological issue at the start. On Friday, it was nice to watch the presentations having mine done with. I submitted all of my final documents to close out the program.
My Mentor: Dr. Subhajyoti De
Laboratory Website: SjD Laboratory
I would like to thank Bassel Ghaddar for data and valuable discussions, Dr. Subhajyoti De for his mentorship and guidance throughout the project, the NSF for funding the work under grant CCF-1852215, and the DIMACS REU program.
Andren-Sandberg A. (2011). Pancreatic cancer: chemotherapy and radiotherapy. North American journal of medical sciences, 3(1), 1-12.
Li, X., & Xu, J. (2016). A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.Journal of Theoretical Biology, 406, 42-51.
Peng, Junya, Sun, Bao-Fa, Chen, Chuan-Yuan, Zhou, Jia-Yi, Chen, Yu-Sheng, Chen, Hao, . . . Wu, Wenming. (2019). Single-cell RNA-seq highlights intra-tumoral heterogeneity and malignant progression in pancreatic ductal adenocarcinoma. Cell Research, 29(9), 725-738.
Qomlaqi, M., Bahrami, F., Ajami, M., & Hajati, J. (2017). An extended mathematical model of tumor growth and its interaction with the immune system, to be used for developing an optimized immunotherapy treatment protocol. Mathematical Biosciences, 292, 1-9.