2018 Undergraduate Summer Training Program: Modeling and Computation in Biomedical Sciences (USTP-MCBS)
Organizer: Wenrui Hao
2018 USTP-MCBS welcomes carefully selected undergraduate students from Penn State for a rich mathematical modeling research experience in June. A three-week training class in computational modeling and basic numerical methods for modeling will be taught from 6/11-6/29. The class will be taught in the morning and the computational lab will be followed each afternoon. The students are expected to practice and do assignments during the lab. After the three-week class, students will have an opportunity to do a group research project and present their results.
Goal
To train undergraduates at Penn State with a high-quality and enriching mathematical modeling research experience in the interface of mathematics and medical sciences. Students work in a collaborative research team closely with their classmates under supervision of Dr. Wenrui HaoApplication
A brief CV and the transcript are required, and one paragraph of description of why you would like to participate in this program and what you want to get from this program is also expected. The application can be emailed to wxh64@psu.edu by April 15, 2018. Up to 10 students are selected from applicants to participate in the program.Each participant may receive $800 stipend through this program.
Classroom
Morning class will take place at McAllister BLDG 216 from 10 am to 11 am. Afternoon Lab will take place at Willard BLDG 069 from 1 pm to 2:30 pm.Tentative Calendar
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
|
| Week 1 (06/11-06/15) | Basic math modeling |
Numerical ODE (Hong) |
Numerical PDE (Hong) |
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| Week 2 (06/18-06/22) | Numerical methods for bifurcations | Competition models (Li) |
Growth models (Li) |
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| Week 3 (06/25-06/29) | Optimization techniques (Zhao) | Fluid dynamics (Zhang) | Cardiovasuclar modeling (Zhang) |
Program summary report
During three-week training for enhancing the mathematical modeling research experience, we learned about Numerical ODE, Numerical PDE, and Optimization. Under supervision of Professor Hao, we worked in our own projects with our teammates. Finally, we did the final presentation for our own projects.Project title: |
Cardiovascular modeling |
Alzheimer's disease |
Finite element method |
Precision medicine |
Method |
We did the exploratory data analysis for Framingham Heart Study data. Then, we used fluid structure interaction to analyze surrounding fluid blood flow. In the future, we will put the patients' data in the convection diffusion equation, and change the parameter of that PDE equation to do more analysis about vascular disease. | In Alzheimer's disease project. We used the Matlab and FreeSuefer to read patients' MRI data, and then got the 3-D brain model. We also used FreeSurfer to emphasis the lesions' location in patients' brains and tried to calculate the concentration of amyloid and tau protein. Then, we put the numerical data which is converted from the raw imagine data in our ODE model. Using the ODE model, we can predict the development of Alzheimer's disease by analyzing the change of amyloid concentration, tau protein concentration, damaged neurons, and Cognition Impairment. | We used the finite element method to study the Poisson equation and tested the numerical convergence. | We studied a database from American Heart Association, then we performed basic statistical analysis (mean and variance) using Python and wrote Python scripts to visualize the data. In future, we plan to use PDE Navier stokes to analyze fluid blood flow. We will set up fluid structure interaction models to predict and study heart diseases and use the database to verify and improve our models. |
Mentor |
Zhao, Li |
Hao, Luo |
Hong |
Hao, Li |
Group members |
Wu, Felemban, Cho |
Lu, Zhu, Suhendra |
Lee, Chen |
Ge |
Pictures:
Visiting Fluid dynamics laboratory
Celebrating for the final presentation
Final presentation