Field cancerization

Primary tumors in epithelial tissues often emerge within genetically altered fields of premalignant cells that appear histologically normal, but have a high chance of progression towards malignancy. This phenomenon is known as the cancer field effect. In collaboration with surgeons at Duke Medicine we develop stochastic spatial models to quantify the field cancerization dynamics and optimize surgical resection margins.

Tumor heterogeneity

Most cancer types exhibit both inter- and intra-tumor heterogeneity. The presence of heterogeneity obscures our understanding of the natural history, and renders systematic treatment approaches difficult. In collaboration with researchers from Duke Medicine we develop tissue-level and population-level models to understand the dynamics and consequences of tumor heterogeneity.

HPV infection dynamics

Most human papillomavirus (HPV) infections are asymptomatic and get cleared rapidly. However, if an infection persists for several years, it can cause cancer. To understand the complex interplay between the stochastic dynamics of resident epithelial cells, the immune system and the virus itself, we develop stochastic models at the tissue-level and combine them with population-level data.

Optimal HPV vaccination strategies

Vaccination against the human papillomavirus (HPV) is an effective public health strategy to reduce the incidence of anogenital and oropharyngeal cancers. In the USA, HPV vaccine uptake has stagnated at relatively low levels among females, and remains very small among males. We develop mathematical models to understand how variable costs of vaccine distribution and gender-specific asymmetries in the natural history of the infection dictate the optimal vaccination strategies.

Pattern formation in synthetically engineered bacterial cultures

Most proposed biological pattern formation mechanisms rely on spatial morphogen gradients. In collaboration with biomedical engineers at Duke we combine experiments with synthetically engineered bacteria and mathematical models to explore novel pattern formation mechanisms that are based on temporal rather than spatial cues.

Bone (re)modeling

Bone remodeling is the vital physiological process responsible for renewal of old or damaged bone tissue. Imbalances in this process are the root cause for conditions such as osteoporosis and osteoarthritis. In addition, cancer cells that have metastasized to the bone are capable of hijacking the remodeling dynamics, usually with lethal consequences. We have previously developed a system of nonlinear partial differential equations (PDE) to describe the spatial evolution of the bone cell populations as well as the most relevant regulatory pathways. Currently, we are developing spatial stochastic models in the spirit of evolutionary game theory to understand the complex dynamics between bone, resident bone cells and metastasizing cancer cells.