Significant Reduction in Bowel Cancer Cases

Rates of new cases of bowel cancer have decreased 20% in the last ten years. The associated mortality rate has also decreased by 30%. These decreases are due to improvements made in preventive screening. Colonoscopies have now been modified to remove identified precancerous stages before they can develop into cancer. The large reduction in associated percentages is due to improved technologies, as was confirmed in a study done by Monika Ferlitsch, from the Department of Medicine II at MedUni Vienna and Vienna General Hospital.

A Quality Assurance Project was implemented in 2007 that focused on the quality of colonoscopies during a 7 year period. During that time 159,246 colonoscopies were analysed to better understand how these procedures could be improved. In the observed period there was an increase in the number of early signs of colon cancer seen in patients and a decrease in the rate of advancement in the procedure itself. Ferlitsch states,

“The results confirm that there has been a clear improvement in the quality of screening examinations. We discover changes earlier and more frequently, thus preventing tumours from developing or metastasising”

Currently Monika Ferlitsch and her colleges are involved in other Quality Assurance projects that will further investigate the quality of the clinical procedures used to remove colorectal polyps and endoscopic mucosal resection. Improving these procedures may also affect the rate of colon cancer,

“If polyps are removed during screening colonoscopy in compliance with the Guidelines, there is a much greater probability that they will be removed completely. This means that the polyp cannot grow again and so cannot develop into bowel cancer.”

Read the original research article here!

Researcher Profile: Dr. Mary Claire King

Dr. Mary Claire King has made significant contributions in the field of genetics over the past couple decades. She is responsible for discovering that humans and chimpanzees are 99% similar, DNA wise. She has also discovered various genes responsible for hereditary ovarian and breast cancer. Currently, Dr. King has a lab at the University of Washington and is continuing her research in the field of human genetics.

Dr. King was inspired by word problems growing up, in particular those focuses around baseball. As a child, King watched baseball with her father who would make up math problems involving pitching statistics, batting averages, and fielding percentages of the White Sox and Cubs. Her love of puzzles lead her to complete an undergrad in mathematics at Carleton College. She originally began a Ph.D. in statistics at UC Berkeley, only to realize she wanted something more applied and less theoretical. Dr. King found her true passion after taking a genetics class taught by Dr. Curt Stein. She relates her love of genetics to that of story problems stating,

“This is nothing but story problems. One story problem after another…this is terrific!”

Without any background in lab work or research, Dr. King found the transition to genetics very difficult and at times thought about leaving school. Dr. Allan Wilson, her advisor, convinced her to stay and worked with her to find a project with an emphasis on analysis, and not lab work. The pair later went on to publish an infamous paper on molecular evolution that suggested that the genetic similarities between humans and chimps was due to regulatory mutations.

After completing her postdoctoral work at UCSF, Dr King went on to join the faculty at UC Berkeley. There she focused her sights on a new issue: why does breast cancer appear to run in families? With grants received from the National Cancer Institute she went out in search of genes responsible for breast cancer. She built a mathematical model that provided statistical evidence for a gene that increases the risk of breast cancer. In 1990, she located the gene in question and named it BRCA1.

Dr. King’s discovery changed the field of oncology and cancer research. Now scientists have identified mutations which significantly increase the risk of ovarian or breast cancer. She is now focusing on how to remove the genes identified and how to provide genetic testing to all women by the time they are 35.

Read the original article here!

Book Review: The Joy of Game Theory

How can the ability to recognize a situation help you optimize your outcome? Is it possible to change lose-lose situations to those of mutual benefits? Game theory may be the answer to all your questions. In his book, The Joy of Game Theory, mathematician and economist Presh Talwalkar explores the idea that a knowledge of game theory may allow you to change the outcome of a situation to one that maximizes your benefits.

Although suggested by the name itself, game theory is not a field confined to board games. It has practical application in many fields, such as ecology and political science. The term game, in this sense, is defined as a situation in which there are player with distinct strategies and a clear result or payoff for each individual strategy. Game theory can then be described as simply, the study of logical and ration decision making.

Game theory began in the field of economics as a way to describe duopolies, or a market with two firms, and how they should set their prices to maximize profits. Many classic game theory examples are merely thought experiments in which the situations do not occur, but are only thought of theoretically. Abstractly, within the respective field, game theory provides excellent insight into how to make rational decisions. In the real world, however, players within a game do not act “rationally”. Due to this everyday examples of game theory are very rare and often offer no insight into the benefits of the field itself.

Talwalkar provides numerous examples of situations encountered every day that can be explained or “solved” with game theory. With each example he removes the intimidating façade that surrounds game theory and begins to show the common practicality of knowing and understanding the subject. With first person narration and a casual tone, the individual examples are weaved together into a comprehensive argument on the importance of knowing terms such as Nash equilibrium and best response. Diagrams are provided to help visualize certain examples, such as Hotelling’s Game, a classic application to game theory in the field of economics.

 

 

Book Spotlight: The Joy of Game Theory

I have recently finished reading The Joy of Game Theory: An Introduction to Strategic Thinking by Presh Talwalkar. This book is a great introduction to game theory for those who are interested but are unsure of where to start. The author introduces basic and simple game theory concepts through the use of real-world examples and diagrams. Presh Talwalkar studied Mathematics and Economics at Stanford University and has published multiple books on math and logic puzzles. He is also the author of Mind Your Decisions, a blog with original videos that center around math. Game theory, in the simplest terms, is the study of logical decision making. It has practical applications in the fields of economics, political science, psychology, logic, biology, and computer science. It is most frequently associated with Economics due to 1994 Nobel Memorial Prize in Economic Sciences winner, John Nash. The book introduces classic game theory games and famous economics applications in an extremely detailed way, without getting overly complicated and wordy. Other examples Talwalkar introduces are very creative and are very far from convention, in a good way. There is a mild amount of math, but not so much that an inexperienced reader would be confused or lost; it is merely there for those interested in it. This book does an excellent job of taking seemingly complicated terms, like pure strategy Nash equilibrium, and describing them in a way that makes sense to even the most inexperienced of readers. As a student in an Undergraduate game theory class I found this book simple and precise, but not too simple that I found myself becoming bored. The examples provided keep even experienced game theorists interested and attentive.

Purchase your copy here!

Surface Sugars and Immune Responses to Cancer Cells

Scientists have always wondered why the immune system doesn’t attack cancer cells like they would a virus. Cancer cells seemingly have the ability to disguise themselves as healthy. This process was largely unknown until fairly recently; cancer cells may be using sialic acid to allow themselves to pass immune cell inspection. Sialic acid is a class of sugars found on the surface of a cell. Sugars play a huge role in healthy cell identification done by the immune system. When a cell has sialic acid it informs the immune cells that it is healthy and to simply move on. Other diseases, such as gonorrhea or streptococcal infections, have adopted a similar camouflage defense to hide from the immune system.

While numerous papers have been published on this topic, it is still in its beginning stages due to the immense complexity of sugar molecules. Unlike proteins, sugars have no distinct pattern as their structures are determined by enzymatic reactions. The hope is to create a new class of cancer treatments that would manipulate the surface sugars of cancer cells, allowing them to be susceptible to immune system attacks. There are currently immune therapies for cancers such as melanoma, kidney cancer, and non-small cell lung cancer, interactions that help in suppressing the immune system.

Carolyn Bertozzi, a chemist at Stanford University, has recently reinvented Herceptin, a popular cancer drug. Herceptin is an antibody that is useful in detecting HER2, a protein, on the surface of breast cancer cells. When the protein is identified Herceptin attaches to it, marking it for an immune attack. Bertozzi uses this antibody as a carrier for salidase, an enzyme that removes sialic acid. This idea and process was recently published in Proceedings of the National Academy of Sciences and was successful in lab experiments. It will have to undergo refinement before it can be introduced to clinical experiments. This is because HER2, while mainly found in excess on breast cancer cells, is also found in small amounts on healthy cells.

Read the original article here!

Interview with Researcher James Greene

I recently met with Dr. James Greene to discuss his research and his views on the future of the field of mathematical oncology. Dr. Greene’s previously published papers focus on cell heterogeneity and drug resistance. The physical part of the research is not conducted by Greene himself, but rather by colleagues at the Laboratory of Cell Biology at the National Cancer Institute in Bethesda, Maryland. One paper in particular is entitled, “Modeling intrinsic heterogeneity and growth of cancer cells” and it describes two mathematical models produced to describe the growth of cancer cells as a transition between two cell states. These models were designed to predict the variations in growth as a function of heterogeneity, or cell variation. The models being presented are the work of Dr. Greene and his colleagues. They work strictly deal with the data aspect of the research done in Bethesda. Greene describes modeling as

“Trying to tell a story while at the same time, producing something that is a useful statement.”

Often times the model produced is not “complete” in a sense, it is instead a building block for other researchers. In some cases, the model presented may answer questions, no one has thought to ask. Dr. Greene states that that there is no one way to build a model and that every model evolves of its own accord. He begins modeling cancer growth by first looking at things as simple as possible, with the least amount of assumptions. He then attempts to model basic biological mechanisms using differential equations, a branch of mathematics consisting of systems of equations that are functions of their own derivatives, or rate of change in the variable. The end goal of a model depends on the data and type of research. Often times the objective is to be able to predict future tumor growth or predict the future effect of treatment on tumor size. Other times, the goal is to just simply understand the mechanisms at work.

Mathematical oncology is relatively new field that is just beginning to be recognized for its achievements in the field of oncology itself. While Dr. Greene claims mathematicians still have a lot to learn from biologists and oncologists alike, the addition of more mathematical thinking has greatly benefited the research being done and the outlook on the future. With mathematical models researchers are now able to predict (within reason) the effect of genetic mutation, treatment options, and time on the size of a tumor. They can then simulate certain viable biological situations using these models, saving the time and money necessary to perform them in a lab. Mathematicians also bring a new way of thinking about treatment to the standard clinical way that has been used for decades. Previously, treatments were aggressive, subjecting patients to the highest dosage possible for the longest amount of time the patient can handle. Now, researchers are beginning to look into the idea of optimization. This will allow treatment to be tailored to the needs of the patient which includes optimizing the time before a tumor reaches a certain size, possibly adding months or years of survival. The majority of the time treatments fail is because the cancer cells become resistant to multiple medicines, and there are no other options. Resistant cells cannot be controlled, unlike the cancer cells we can control called sensitive cells. In the case where all the sensitive cells are killed and resistant cells are the only thing left, many oncologists are unsure of the treatment plan. As Dr. Greene states,

“The problem isn’t killing cells. We know how to kill cells, almost too well actually. The issue is of growing rates of resistant cells.”

While this question is still largely unanswered, Dr. Greene’s research is well on its way to finding a solution to this problem.

Modeling Oncolytic Viruses

Researchers at the Ottawa Hospital Research Institute have published a paper outlining the importance of advanced mathematical modeling in the fight against cancer. With math modeling, scientists can predict how genetic modifications and different treatment methods can assist oncolytic viruses in their quest to kill cancer cells.

Oncolytic viruses are a specific type of virus that targets cancer cells. Because cancer is so diverse and intricate, these viruses do not work well in every case. Genetic modification have become a focus in cancer research, in an attempt to have oncolytic viruses work in all cases of cancer. This is because, unlike other treatment options, oncolytic viruses only harm cancer cells and do not effect healthy cells.

The modeling is used by author Dr. Bell and co-author Dr. Mads Kaern to devise plans of action for making virus infections lethal to cancer cells. As Dr. Kaern states,

 “By using these mathematical models to predict how viral modifications would actually impact cancer cells and normal cells, we are able to accelerate the pace of research […]It allows us to quickly identify the most promising approaches to be tested in the lab, something that is usually done through expensive and time-consuming trial and error.”

Together they have derived a model that describes the infection cycle, a process in which a virus is replicated, spread, and activated. They then used key physiological distinctions between cancer cells and healthy cells to identify which genome modifications would efficiently kill cancer cells. The model simulations were extraordinarily accurate. Identified aspects of the viruses were modified, and they efficiently destroyed all cancer present in a mouse.

The research is funded by the Canadian Cancer Society and is just the beginning of research of this nature. The focus has now shifted to multiple types of cancer, instead of the specific one Dr. Bell and Dr. Kaern worked on. Mathematical modeling, along with this research, has proved beneficial in assisting the way scientists understand the relationship between cancer cells and viruses.

Read the original article here!

Researcher Profile: James C. Greene

As I mentioned previously, I am currently taking a math class at Rutgers titled “Math of Cancer”. This class is the first of its kind to be offered here through the math department and is part of the course “Topics in Mathematics” which is available only in the spring semester. This class is what sparked my interest in mathematical oncology in the first place. So far we have only begun to delve into the modeling aspect of this field, but I’ve definitely learned a lot and realized that bio math is something that I’m actually really interested in.

My professor for this class is, as I mentioned before, James Greene who is currently a postdoctoral fellow in the Department of Mathematics here at Rutgers University. He attended Pennsylvania State University, where he received his undergraduate degrees in Mathematics and Physics. He then attended University of Maryland, College Park for his PhD in Math. He is an applied mathematician, meaning that he focuses mainly on applying mathematical methods to science, engineering, computer science, etc. Professor Greene focuses mainly on understanding resistance in cancer cells, as well as, finding optimal treatments. His work centers on Differential Equations, Agent-Based Modeling, Numerical Analysis, and Probability Theory.

 

His CV can be found here

 

His published works include:

Mathematical Modeling Reveals that Changes to Local Cell Density Dynamically Modulate Baseline Variations in Cell Growth and Drug Response

Modeling Intrinsic Heterogeneity and Growth of Cancer

Simplifying the Complexity of Resistance Heterogeneity in Metastatic Cancer

The Impact of Cell Density and Mutations in a Model of Multidrug Resistance in Solid Tumors

The Role of Cell Density and Intratumoral Heterogeneity in Multidrug Resistance

Unrelated But Still Important-Primes Aren’t Random!

On an (somewhat) unrelated note, prime have recently been deemed non-random by two mathematicians Robert J Lemke Oliver and Kannan Soundararajan.

I normally would be posting about something related to oncology but this was so mind blowing, that I had to write about it. Mind blowing seems a tad dramatic but think about how many centuries we assumed something that turned out to be dead wrong.

Number theorists have always assumed that the nature of primes was purely ‘random’, in the sense that predicting when the next prime will occur is almost incalculable. While they do appear to act as a list of random numbers, they have one underlying rule: the number of primes surrounding any number is inversely proportional to the number of digits the number has itself. This is known as the prime number theorem. We also know that there are an infinite number of primes, and that because of this no equation can yield all possible primes. In a paper written by Lemke Oliver and Soundararajan, they introduce a new pattern found within the infinite set of primes, and possible evidence proving a famous conjecture.

Prime numbers are defined as natural numbers with factors of one and itself. With certain factors being the only required rule for this sequence, predicting the next prime is almost impossible, this appearance of randomness means that in an infinite sequence of primes, a prime ending in the same digit as another prime would occur 25% of the time. This due to the fact that, after 5, primes end in one of four numbers: 1, 3, 7, and 9. This idea was explored in 1936 by mathematician Harald Cramer, who created a model for generating random prime numbers. At each whole number a special coin is flipped to decide whether or not that number is to be included in your list of primes. The coin is weighted with the density of primes near the number itself. Cramer’s coin tossing model accurately predicted many features of primes, including how many would be expected in between any two consecutive primes. While this model has great predictive power, it was very simplistic. Mathematicians have since then improved this model and find that primes ending in 1, 5, 7, and 9 occur with equal frequency, giving us the probability of ¼ or 25%.

 

This probability, however, was not seen in the actual sequence of primes. For the first few billion primes, numbers with the same ending digit occurred next to each other less than 25% of the time. This trend persists even as the sample size increase, although it does gradually decrease.

 

The proof of this discovered arrangement comes with a disclaimer. The tool used to prove and present the existence of this pattern is a widely known conjecture, which means it only appears to be true because it has yet to be disproven. This conjecture, in particular, is known as the Hardy-Litlewood k-tuple conjecture.

This adds yet another level of drama, in that this may be a way to prove a decades long conjecture! So basically these two mathematicians are flipping the math world upside down…and it’s awesome.

For more on this pattern of primes, check out these articles:

• “Mathematicians find a peculiar pattern in primes” ScienceNews
• “Maths experts stunned as they crack a pattern for prime numbers” Independent
• “Mathematicians Discover Prime Conspiracy” Quanta Magazine

 

 

Mathematical Models Used to Understand Drug Resistance in Cancer Cells

When using medication to treat anything, there is a possibility of resistance. This is certainly the case for cancer treatments. Cancer cells use a process known as bet-hedging to resist medication and create a population of resistant cells. In an article published by ScienceDaily, researchers at the Moffitt Cancer Center are using mathematical models to explain how bet-hedging can lead to treatment resistance.

As clichéd as it sounds, math truly is in everything, although it is mainly thought of as a single “boring” entity. As a math major, I had always thought that I wasn’t able to do research the same way other STEM majors were. Articles like these helped me realize that mathematicians often join forces with other scientists and are able to combine fields of expertise to conduct research. As the article states,

“Mathematical modeling allows scientists to study complex biological systems and processes that could not feasibly be studied with common laboratory and clinical experimental approaches”

Mathematical oncology is an up and coming field that is greatly influencing the field of oncology and treatment methods in general. One of the reasons I decided to major in math, besides loving the subject itself, was because a degree in mathematics is extremely flexible. Although I am not a medical professional (very far from it) I may be able to one day contribute to a ground breaking finding on cancer. The implications of this study alone on treatment resistant cancer cells is shocking, especially when you realize math played such a major role.

I am currently taking a math class here at Rutgers on mathematically oncology and my professor, James Greene, has been published multiple times for his contributions to research in drug resistance. He also has an undergraduate degree in mathematics and is a “self-taught” microbiologist.

In conclusion, math is cool and it could save your life.