Research

I am one of Professor Jasmine Foo's students. My research area is math biology. In particular, I use stochastic processes to model cancer. I am especially interested in modeling drug resistance and circulating tumor DNA (ctDNA). 

Circulating tumor DNA (ctDNA)

When tumor cells die, they release fragments of their DNA into the bloodstream. Novel sequencing techniques makes it possible to detect and analyze these fragments from plasma samples. This process is known as liquid biopsy and is much less invasive and costly than traditional solid biopsy of tumors. The relative ease of collecting liquid biopsy makes it possible to collect samples much more frequently, which may allow physicians to assess and adjust treatment plans much more effectively. 

Mathematically, the rise of ctDNA sampling has created a myriad of rich new problems to explore. Only cells that have died create ctDNA, so liquid biopsy can only produce an incomplete picture of a particular tumor. I am excited to explore what can and cannot be inferred about tumor progression and composition from ctDNA data. 

Malignant peripheral nerve sheath tumors (MPNST)

In an interdisciplinary collaboration with members of the Largaespada Lab from the Division of Pediatric Hematology and Oncology at the University of Minnesota, I am studying drug resistance in Malignant peripheral nerve sheath tumors (MPNST). 

Our goal is to use stochastic branching process models to help optimize the pathway from treatments in vitro to treatments in vivo. It is much faster and more cost effective to test drug combinations and dosing schedules in vitro. However, in vitro experiments cannot fully account for physiological factors in vivo such as drug metabolism and as a result observations in vitro often do not carry over in vivo. My hope is that incorporating in vitro results and pharmacokinetic data into a birth death process whose net growth rate is a function of plasma drug concentrations will better forecast results in vivo. 

A proposal for this project by Dr. Kyle Williams and I has been awarded a Trainee Brainstorm Pilot Grant by the UMN Brain Tumor Program and a Junior Investigator Pilot Grant by the UMN Cancer Bioengineering initiative. 

Gene amplification

I am also interested in examining how different mechanisms of tumors acquiring drug resistance affects their composition and development. For example, in non-small cell lung cancer (NSCLC), resistance to EFGR-inhibitors can arise as a result of either point mutation or gene amplification. In a recent paper [1], I examine tumor recurrence time in these two scenarios. Tumor recurrence is the time at which an initially shrinking drug sensitive tumor acquires drug resistance and grows to reach its original size again. 

Evolutionary processes

Evolutionary processes are characterized by distinct lineages that experience mutation, speciation, and extinction and can be connected by examining heritable traits. Both cancer tumors and infectious diseases can be modeled as evolutionary processes. Cancer tumors consist of many heterogeneous subpopulations that mutate, divide, and reproduce. Transmission trees where nodes represent carriers of the disease and speciation events represent transmission can also be examined in this way. 

Publications and Preprints