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CAMM Projects

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Mathematical Modeling of Colon Cancer Development


​Team members: Bruce Boman, Brooks Emerick and Gilberto Schleiniger

The goal of this project is to better understand what causes disruption of normal tissue homeostasis in the colonic epithelium leading to neoplastic tissue changes and loss of function, and ultimately colon cancer. Models being considered are spatial-temporal description of cell population dynamics within normal human colonic crypts (small invaginations in the epithelium). Our models are designed to discover mechanisms that give rise to alterations in tissue dynamics that occur during colon cancer development. This research will also provide a mathematical definition for stem cells and provide an explanation for how stem cell overpopulation occurs in colon cancer and drives tumor growth. The biochemical signals received by the colonic crypt cells are also modeled in order to understand possible disruptions of normal cell behavior and its consequent effect on cell dynamics in the crypt. Understanding cancer in mathematical terms will provide new insights into how to design new more effective, potentially even curative, treatment for patients with advanced cancers.  The project involves an integration of biology, mathematics and cancer medicine.  ​

Modeling of Cancellous Bone and Osteoporosis

Team members: Y. Ou

This research project is directed towards developing mathematical and computational methods arising from quantitative ultrasound techniques (QUT) for detecting osteoporosis, a major public health threat affecting more than 44 million Americans. Understanding the bio-mechanical advance of the disease and developing quantitative mathematical techniques for its monitoring is the first step towards efficient treatment and prevention. Diagnostics based on QUT is relatively inexpensive and, unlike X-ray densitometry, it does not ionize the tissue. The strength of cancellous bone plays an essential role in the diagnosis of osteoporosis. The proposed work aims at developing mathematical tools for determining various parameters that describe the strength of porous-elastic materials, by probing the materials with mechanical waves such as ultrasound. The educational component emphasizes the interdisciplinary nature of the proposed research in several STEM fields. Through joint work with the PI's collaborators in mechanical and biomedical engineering, facilitated by the Center for Biomedical Engineering Research at the University of Delaware, a new interdisciplinary educational initiative linking biomedical engineering and mathematics for undergraduate and graduate student training is planned. The results from this project will be of interest to researchers who conduct laboratory experiments to study the relation between bone strength and bone micro-architecture and will open an avenue for more accurate and reliable ultrasound devices for measuring properties of porous-elastic materials.

Modeling of vulnerable plaques in heart disease

Team members: P.-W. Fok

Cardiovascular disease (CVD) is a widespread and expensive medical condition in Western developed nations. Atherosclerotic plaque, which is a manifestation of CVD, is a fatty deposit that lines the interior of large arteries. The growth and subsequent rupture of so-called "vulnerable" plaques account for the majority of myocardial infarctions. The prevention and treatment of atherosclerosis, and heart disease in general, is an outstanding problem in medicine today.

Dr Fok's research aims to understand the biological mechanisms behind atherosclerotic plaque growth through mathematical models. Specifically, he is interested in how vessels remodel as they become more diseased, how their dimensions change and how these dimensions are affected by growth factors and vasodilating agents. The main tools he employs are computation, partial differential equations and elasticity theory​. More information can be found at Prof. Fok's research page.

Modeling of connections between associated diseases

Team members: S. Cioaba, W.A. Weintraub (Christiana Care)

More information can be found at Prof. Cioaba's research page.​

Real-time modeling of hypoplastic left heart syndrome

Team members: T.A. Driscoll, G. Schleiniger, Lei Chen, M.A. McCulloch (Nemours Cardiac Center)

Hypoplastic left heart syndrome is a cardiac birth defect with a 20% mortality rate in the first year of life. Understanding the physiology of a patient in real time in the hospital is difficult. We are using mathematical models of the heart and circulatory system and selecting the parameters of the model based on continuously collected bedside vital signs. Our goal is to provide clinicians with patient-specific warnings and diagnostics.

Mathematical modeling of the tear film dynamics

Team members: R.J. Braun, T.A. Driscoll, M. Stapf, Lan Zhong, A. Janett, P.E. King-Smith (OSU), C.G. Begley (IU), K.L. Maki (RIT), Longfei Li (RPI), W. Henshaw (RPI)

The group develops mathematical models for tear film dynamics in close collaboration with optometrists' experiments to better understand various aspects of the tear film. Every time you blink, your upper lid paints on a thin multilayered fluid film that protects the ocular surface and helps you to see clearly. When the tear film doesn't have enough water, evaporates too quickly, or has other issues, the normal function may be compromised and lead to conditions such as "dry eye" that affect millions of people. Our models help ocular scientists understand the tear film in both health and disease. For a more detailed overview of the projects, please see the project site. 

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  • Department of Mathematical Sciences
  • University of Delaware
  • 501 Ewing Hall
  • Newark, DE 19716, USA
  • Phone: 302-831-2653