Research Highlights
Carey’s Equality and Fundamental Theorem on Stationary Population Models
Arni S.R. Srinivasa Rao, Georgia Regents University, Augusta and James R. Carey, University of California, Davis, who met for the first time during an MBI workshop in June 2013, jointly formulated and proved a result dubbed by many "the fundamental theorem" of stationary population models. The event that inspired this collaboration was a three-day symposium held at MBI to honor the birth centenary of a renowned mathematical demographer Nathan Keyfitz.
John Snow's Cholera Outbreaks Revisited: From Blackboard to Bench
Cholera is a disease with a long history, with John Snow's investigations of the Broad Street pump and London cholera outbreaks during the 1800s as a celebrated example of research on the disease. Despite this long history, cholera outbreaks remain a serious public health concern today. For example, the cholera outbreak beginning in Haiti in October 2010 had caused nearly 700,000 cases as of November 2013. In addition to its public health relevance, several features of cholera make the disease of mathematical interest as well.
Chaos in the Brain's Networks
At first thought, it doesn't seem like a good thing that we may have ended up with chaotic brains -- that is, neural networks which produce highly sensitive dependence on their initial states. Indeed, chaotic dynamics produce variability that threatens to interfere with the signals that neural networks encode and process.
A Personalized Model of Prostate Cancer Progression Under Hormonal Therapy
The prostate is a vital component of the male reproductive anatomy, which produces an alkaline fluid that is one of the key constituents of semen. Additionally, prostatic epithelial cells also produce prostate specific-antigen (PSA), that aids in sperm motility. Unfortunately, the prostate is also one of the most common sites of cancer incidence, with prostate cancer being the second most common type of cancer affecting men in the United States. In 2010 alone, more than 200,000 cases were diagnosed, resulting in 32,000 deaths.
Modeling the Prevention and Reversal of Type 2 Diabetes
A highlight of the August 2013 Workshop for Young Researchers in Mathematical Biology held at MBI was a presentation by Dr. Arthur Sherman of the National Institutes of Health, describing work with NIH post-doctoral fellow, Joon Ha, on modeling the disease process in type 2 diabetes (T2D). Diabetes is an unfortunate byproduct of the phenomenal success of the human race in providing inexpensive and abundant food on a mass scale.
Stochastic Models of Disease Spread
At a yearlong program at MBI, mathematicians, engineers, and bioscientists discussed new ways of analyzing the effects of random events on the long term behavior of large biological systems. A particular topic of interest was the development of stochastic methods in the study of infectious diseases.
Fighting TB Might be a Matter of 'Flipping a Switch' in Immune Response
In the lung, alternatively activated macrophages (AAM) form the first line of defense against microbial infection. Due to the noninflammatory nature of AAM, the lung can be considered as an immunosuppressive organ for respiratory pathogens. However, as infection progresses in the lung, another population of macrophages, known as classically activated macrophages (CAM) enters. CAM are far more effective than AAM in clearing the microbial load, producing pro-inflammatory cytokines and anti-microbial defense mechanisms necessary to mount an adequate immune response.
Therapeutic Use of Oxygen for Chronic Wounds
Chronic wounds, like venous leg and diabetic foot ulcers are wounds that do not heal in a timely fashion, generally two-to-four weeks. Chronic wounds can cause pain and discomfort and also limit mobility. They are often a consequence of a more serious health problem, such as diabetes, heart disease, or blood circulation disorders. Left untreated, chronic wounds can lead to problems like infection, amputation, or even death.
The LifeLine: Vascular Access Dysfunction in Chronic Hemodialysis Patients
Healthy kidneys filter wastes from blood and keep body chemicals in balance. When the kidneys fail to perform their functions to full capacity, one cannot live long without some form of renal replacement therapy. One available treatment is hemodialysis, in which the patients’ blood is pumped into an artificial kidney where metabolic waste products diffuse out of the blood, and the cleansed blood is then returned back to the body. Most people have 3 dialysis sessions every week, each session for about 3 to 4 hours.
Uncovering Genes Associated with the Process of Aging
The cerebellum is essential for the control of balance, posture, and motor coordination. During normal aging, the cerebellum can become progressively dysfunctional, which may be attributed to alterations of specific molecular components. Progressive dysfunction of the cerebellum can lead to life-threatening accidents.
Reverse Engineering Gene Regulatory Networks
Gene regulatory networks (GRNs) are pathways of genes whose induced proteins regulate the expression of other genes and their products. They orchestrate biochemical processes that specify spatial and temporal patterns or govern the formation of tissues and organs. GRNs reveal the causality of these processes through activation or repression of targets by regulatory proteins.
Modeling the Dynamic Range of a Neuronal Network for Breathing
For humans and other mammals, breathing is essential to life. The breathing rhythm relies on an area of the brain stem known as the pre Bötzinger complex, a network of neurons exhibiting rhythmic bursts of activity that initiate inspiration. The frequency of the rhythm varies in response to such challenges as exercise, sleep, or changes in altitude.
Spatial Models for Rabies and Other Epidemic Diseases
A human bitten by an animal with rabies will almost certainly die within days unless immediately treated with a multistage vaccine regimen initially developed by Louis Pasteur in 1885. To combat the spread of rabies today, which nationwide affects over 40,000 people annually and countless wild and domestic animals, the United States spends over $300 million each year on its prevention and control. One important ecological feature that makes this disease difficult to contain is that animals with rabies tend to increase their ranges substantially after they become infected, and thus are more likely to come into contact with and bite other uninfected (or susceptible) animals.
Representation of Oders in the Honeybee Brain
A honeybee may forage on 1,000s of flowers for nectar and pollen in its lifetime. Scent is one of the primary means that it uses for identifying rewarding flowers. How honeybees and other animals learn to associate complex and variable scents with important events is still not well understood. Honeybees are an excellent model system for studying olfaction because their physiology and behavior has been the subject of much research in the past 100 years.
Modeling Olfaction
The process of smelling, called olfaction, requires reliable communication of information about chemical identity and concentration of odors from the environment to the brain. Many animals use olfaction to find food, locate mates, avoid danger and navigate their surroundings. The chemical reactions and neural processes required of olfaction involve several temporal and spatial scales which makes a detailed understanding of its functional basis quite challenging.