Dr. Emily Evans, Department of Mathematics
Scientific Merit of Project
Understanding cell-cell and cell-extracellular interactions is important because these inter- actions play a role in wound healing, developmental processes, and pathological conditions such as cancer. The work done for this project is in some sense joint work with biologists, in the sense that biologists perform experiments, which give direction to the mathematical model. The results obtained from the mathematical model then inspire the biologists to run different experiments validating the mathematical conjectures and the process begins anew. In particular, the work done studying the interactions of biological tissue with engineered tissues will help biologists develop improved biologically engineered materials that could potentially replace failing tissues in humans. Understanding the role of curvature and tension on cell motion is important to help govern the in need a better understanding of cell-cell and cell-extracellular interactions.
Accomplishments as result of the project
The funds for this project were used to provide a mentored research experience for nine undergraduates. Dr. Evans maintains two active research programs, one in mathematical biology and one in network theory. The funds for this project were used to support students in both areas. All of the students who have participated in research for at lest 6 months have given talks in CPMS venues. In addition, when appropriate students present at national conferences. Of the mentored undergraduate students who have graduated, all 5 of them are currently attending graduate school (2 at BYU and 3 elsewhere).
- Accomplishments directly related to the stated goals of the project:
- An important aspect for modeling cell morion in collagen was discovered. This discovery has led to two talks and will result in at least one paper.
- Stochastic fractal surfaces were developed for modeling the interaction of biological tissues with engineered materials. In addition animation code was written so that researchers can interact better with biological models.
- Unfortunately we were unsuccessful at replicating biological results of curvature and tension on cell motion. This is still an area of active research.
Students mentored by Emily Evans during the duration of the grant
- Emma Dallon (undergraduate), January 2014 – August 2016
– Modeling Movement of a Cell on a Single Fiber
– Spoke at 2014 CPMS Student Research Conference
– Spoke at 2015 CPMS Student Research Conference
– Spoke at 2016 CPMS Student Research Conference
– Current Master’s student in BYU biochemistry department
- Marissa Graham (undergraduate and graduate), February 2015 – Current
– Multigrid Methods for Isogeometric Analysis.
– Spoke at 2016 CPMS Student Research Conference
– Spoke at 2017 CPMS Student Research Conference
– Current Master’s student in BYU Mathematics Department
- Amelia Henriksen, April 2015 – June 2016
– Improved Modeling for Prosthetic Implants.
– Spoke at 2016 CPMS Student Research Conference
– Current Ph.D. student at the University of Texas Austin – Institute for Computational Engineering and Sciences
- Nathaniel Merrill (undergraduate), April 2015 – August 2016
– A Model of Collagen Contraction and The Drazin Inverse for Effective Resistance.
– Spoke at 2016 CPMS Student Research Conference
– Effective Resistance via the Drazin Inverse E. J. Evans, J. Humpherys, N.J. Merrill – In preparation
– Current Ph.D. student at Rutgers Center for Computational and Integrative Biology
- Allyson Tom (undergraduate), October 2016-July 2017
– Link Prediction on Directed Networks
– Spoke at 2016 CPMS Student Research Conference
– Spoke as Spring Western Regional MAA conference
– Current MS student at University of Washington
- Juan Rodriquez (undergraduate), May 2016-present
– Centrality Measures for Large Networks
– Spoke at 2016 CPMS Student Research Conference
- Maria Fabiano (undergraduate) May 2017-August 2017,
– Improved Modeling for Prosthetic Implants.
- Jason Kinghorn (undergraduate) October 2017-present
– Graph similarity metrics.
- Benjamin Burt (undergraduate) October 2017-present
– Graph similarity metrics.
Expenditures
The funds allocated for this project were primarily spent paying the salaries of the under- graduate researchers. A small amount of money (Less than 500 dollars) was spent on books and conference fees for the students.