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Equations against cancer: Using math to predict a tumor's path

Hassan Fathallah-Shaykh, M.D., Ph.D., believes that math can transform medicine, and he has the numbers to prove it. In the clinic, this UAB neurologist specializes in treating brain tumors. In his lab at the Comprehensive Cancer Center, Fathallah-Shaykh, who is also a professor of mathematics at UAB, wields equations as well as petri dishes. His mathematical models of cancer behavior are offering new insights on tumor growth. Eventually, they could be used to personalize treatment based on the unique characteristics of each patient’s cancer cells and anatomy.

Fathallah-Shaykh is one of a growing number of researchers worldwide exploring the field of mathematical biology, which “uses mathematical tools to generate models of biological problems,” he said. Building mathematical models based on the current understanding of a disease, for example, allows researchers to “test whether the assumptions are accurate,” Fathallah-Shaykh said.

Hassan Fathallah-ShaykhHassan Fathallah-ShaykhModels can also be used “to test a treatment strategy, understand why it fails or works, and optimize therapy,” he added. The results of these tests can also generate new insights and hypotheses that can be investigated in the laboratory. “None of these goals can be achieved by traditional methods,” Fathallah-Shaykh said.

Model Behavior

Working with colleagues at the University of Bordeaux, and UAB graduate student Elizabeth Scribner, Fathallah-Shaykh has created an elegant model of the aggressive brain cancer glioblastoma multiforme (GBM). It produces simulations on the scale of clinical MRI scans, so that its predictions can be tested directly against patient data. In a paper published on Dec. 15 in PLOS ONE, the researchers demonstrated that their model can reproduce the typical GBM growth patterns seen on patient scans. They also revealed its value as a research tool.

The model predicted a previously unknown pattern of tumor growth in patients with recurrent GBM treated with the anti-angiogenesis drug bevacizumab. This growth, powered by a cycle of proliferation and brain invasion, is characterized by an expanding area of invasive cells and dead cells known as necrosis, the researchers say. A subsequent search of 70 patient MRI scans by the researchers turned up the same pattern in 11 cases.

That pattern explains the disappointing results of recent Phase III clinical trials of anti-angiogenesis therapies against GBM, the researchers say. Anti-angiogenesis drugs attempt to kill tumors by preventing them from growing new blood vessels. But the model demonstrated how GBM cells can flee from the oxygen-depleted treatment area — and quickly begin expanding again as soon as therapy stops or the tumor becomes resistant to the drugs. (For more on the model and these findings, see “SimTumor.”)

“We hope to tailor radiation therapy, chemotherapy and other treatments based on a personalized model of a patient’s tumor.”

“We’ve shown that we can predict new insights on cancer behavior,” Fathallah-Shaykh said. The results have already spurred Fathallah-Shaykh to pursue new therapies in his lab to limit tumor mobility. Ultimately, the researchers hope to use their model to personalize therapy to the unique characteristics of a patient’s tumor. They could do that by analyzing the existing growth pattern of a tumor and building that into the model’s parameters. Then they could simulate its future behavior on a virtual MRI slice that reproduces the unique anatomy of the patient’s brain. “We hope to tailor radiation therapy, chemotherapy and other treatments based on a personalized model of a patient’s tumor,” said Fathallah-Shaykh.

From Flies to Colon Cancer

Since he joined the UAB faculty in 2008, Fathallah-Shaykh has been developing ever more advanced models to predict the behavior of biological networks. He began by building a model of the molecular clock in a fruit fly’s brain. Despite the fly’s tiny size, it’s a challenging puzzle. The clock is a tangled web of positive and negative feedback loops, with five different genes producing proteins that inhibit and activate one another (as well as themselves, in some cases) in a regular cycle.

First, Fathallah-Shaykh and his collaborators “showed we can replicate everything the clock is known to do,” he said. Then they proved it was a useful research tool, answering a perplexing question about the fruit-fly gene Clockwork Orange that had stumped biologists for years.

The researchers next adapted their model to track the developing neural networks in fruit-fly embryos. To do this, they utilized the Kalman filter, a mathematical technique to analyze and predict changes that helps track planes in flight. Now, “we’re using the model to study molecular networks in colon cancer,” Fathallah-Shaykh said.

Coping with an Information Explosion

Fathallah-Shaykh has always been fascinated with math. “It’s like a symphony; it’s beautiful,” he said. “But it’s also very applicable.” He cemented the connection between medicine and math as a neurologist at Rush University Medical Center in Chicago when he enrolled in a doctoral program in mathematics at the nearby University of Illinois–Chicago. “I would go to class in between patients,” he said.

Math is essential to making progress against the toughest questions in medicine, Fathallah-Shaykh contends. To illustrate the problems that researchers face, he points to a chart of all the known molecular pathways involved in Alzheimer’s disease. It’s a mass of interlocking loops and tangles that fills an entire page. Researchers specialize in tiny sections of this wiring diagram, but understanding how it all works together is another problem entirely. Even worse, these networks are intertwined in such a way that multiple paths can lead to the same destination. That may help explain why treatments that work beautifully in isolated cell lines in a lab so often fail when they encounter the complex networks of the body.

There’s another wrinkle. “Cells migrate, they communicate, they interact with one another over time,” said Fathallah-Shaykh. The waves of mutations, which are a hallmark of cancer, make the problem particularly complex, he noted. “Whole pathways are deleted and new connections start turning up.” It’s a perfect example of a nonlinear dynamic system, like the weather or the stock market, in which slight changes in one parameter can lead to wildly diverging outcomes.

The good news, said Fathallah-Shaykh, is that “mathematics has very rich tools” to model just these types of systems, as he has demonstrated with his cancer simulations. But this work has another exciting element for Fathallah-Shaykh as a mathematician: It opens new horizons in math theory. “Equations have already been developed from biological problems,” he said, “and there is very strong evidence that they will produce spectacular advances in mathematics.”


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SimTumor

At the heart of Hassan Fathallah-Shaykh’s new mathematical model of glioblastoma multiforme (GBM) are 10 partial differential equations. Here’s how it works — and what it has revealed about GBM behavior.

Formula 10

Equations track each of four different cell types, with unique rules of behavior.

Proliferative GBM cells (P), which make up the bulk of the tumor, divide but don’t move.

proliferative cells

Invasive GBM cells (I), found on the fringes of the tumor, move but don’t divide.

invasive cells

Healthy brain cells (B) neither divide nor move, although they are displaced by the growing tumor.

brain cells

Cells in the center of the tumor, cut off from nourishing blood vessels, are starved of oxygen (hypoxia) and die, becoming necrotic cells (N).

necrotic cells

The remaining six equations track angiogenesis (new blood vessel formation), oxygen levels, and rates of necrosis and cell division.

Built for Speed

Fathallah-Shaykh’s first GBM model, published in August 2014 in the Bulletin of Mathematical Biology, consisted of many more equations. It required a supercomputer, and several days, to run. The model published in PLOS One can run in 50 seconds on a typical desktop computer.

And They’re Off!

The simulation begins with a tiny clump of tumor cells surrounded by healthy brain. As the program continues over several virtual weeks, this mass expands in the characteristic manner seen on patient MRIs, with a dark region of necrotic cells in the center, surrounded by a large group of proliferative cells and an outer rim of invasive cells.

Grow or Go

The model’s main assumption is that proliferative cells can turn into invasive cells in hypoxic conditions. This is in keeping with the “grow or go” hypothesis of GBM behavior, which says that low oxygen levels spur GBM cells to flee the dying core of the tumor. When these new invasive cells reach healthy, oxygenated areas of brain, they switch back into proliferative mode and start growing again.

How GBM Escapes Anti-Angiogenesis Therapy

As tumors grow, cells at the core lose contact with nourishing blood vessels and die.

To get around this problem, tumors release VEGF (vascular endothelial growth factor), which induces the body to create new blood vessels (a process known as angiogenesis). In fact, the well-known Folkman Hypothesis states that tumors must be able to induce blood vessel growth in order to keep growing.

Clinicians had high hopes that anti-angiogenesis medications such as bevacizumab (Avastin), could keep tumor growth in check. But two high-profile Phase III clinical trials, which released results in early 2014, found that bevacizumab therapy did not prolong overall survival in patients with recurrent GBM, although it did extend progression-free survival and patient quality of life.

Fathallah-Shaykh’s model, programmed to simulate the effects of anti-angiogenesis therapy, reveals an explanation for this “unusual clinical finding.” When bevacizumab therapy causes oxygen levels to drop, proliferative cells turn into invasive cells and flee the scene. When they reach an area with sufficient oxygen, they convert back into proliferative cells and begin a new cycle of growth. This sets up the tumor for rapid “rebound” growth as soon as it becomes resistant to bevacizumab or therapy is discontinued. That explains why patients treated with bevacizumab in the recent trials didn’t experience any increase in overall survival rates over those who were not treated.

Toward New Treatment Approaches

The model underlines the importance of better understanding the molecular mechanisms of brain cell invasion, particularly the active transport of invasive cells toward healthy brain regions, says Fathallah-Shaykh.

There are currently no available biomarkers to identify the quantity of invasive cells in a patient’s tumor. But finding such a biomarker, and drugs that can target these cells to prevent tumor migration, is a current research focus in Fathallah-Shaykh’s lab. “If we’re going to kill these tumors,” he said, “we have to target the cells that are invading.”






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Advancing Mathematical Biology Research

Hassan Fathallah-Shaykh is a perfect ambassador for the highly interdisciplinary field of mathematical biology. In addition to his faculty positions in the departments of Neurology, Mathematics and Cell, Developmental and Integrative Biology, he holds an appointment in the School of Engineering. That breadth of expertise has enabled him to establish collaborations with researchers at UAB and at several international universities, and he is working to interest more colleagues in mathematical biology.

This spring, Fathallah-Shaykh helped organize a symposium on the topic as part of the College of Arts and Sciences’ Interdisciplinary Innovation Forum series. The meeting attracted some of the mathematical biology’s most famous names. Meanwhile, he is helping to attract new talent to the discipline by teaching undergraduate and graduate courses on Mathematical Biology in the math department.

“It is quite clear that the next great advances in medicine cannot happen without math,” Fathallah-Shaykh said. “These are exciting times.”


By: Matt Windsor


New clinic at UAB measures risk of Dementia

Alzheimer's is the sixth leading cause of death in the United States. One in three seniors dies with Alzheimer's. Five million Americans are living with the disease right now.

While family history does play a role, there are some controllable health factors that can reduce the chance of having Alzheimer's. As we age, each of us needs to be aware of our weight, cholesterol and blood pressure. These are factors that can contribute to dementia, but if controlled can help reduce the risk.


The goal of a new Dementia Risk-Assessment Clinic At UAB is to help a patient focus on those reversible risk factors.


For Jon Kling, a daily exercise routine means more than maintaining his weight.


"My mother had three sisters and all of them had dementia or Alzheimer's,” Kling told ABC 33/40.

Kling is doing everything in his power not to follow in their footsteps.

"Being proactive is important instead of reactive,” said Kling. “So if there's things I can do today, lose weight, exercise, nutrition, lower my blood pressure, any of those types of risk factors that I can change, that I can modify, then I thought that would be very important."


That's why he took the exam at UAB's new Alzheimer's Risk-Assessment Clinic.


Dr. David Geldmacher says he can assess the risk of dementia for the next twenty years for patients 45 to 65 years old.


"Research over the last five years has really pointed out to why things like exercise and blood pressure are important dementia risk,” Geldmacher said. “We're now able to focus on very detailed research oriented checks to see what we can do to lower someone's risk."


In addition to aging and family history, Geldmacher says exercise, blood pressure, cholesterol and alcohol intake can all influence one's risk.


Part of the exam is a MRI scan of the brain. It also includes a memory exam and medical exam.


“Overall, we're looking at a profile of many things, that although each doctor might check those, putting them together into a dementia risk is something that's newly available and that's what makes our clinic a little different here,” said Geldmacher.


For patients older than 65, like Kling, the exam measures risk for six years.

Kling's risk is two percent.

"It's very comforting and peace of mind that you at least know where you stand and you have that base line,” said Kling.


Most insurance plans do not cover the exam. At UAB, it costs $1,000.

Story compliments of ABC3340 - Lauren Walsh

Brain inflammation a hallmark of autism, according to large-scale analysis

While many different combinations of genetic traits can cause autism, brains affected by autism share a pattern of ramped-up immune responses, an analysis of data from autopsied human brains reveals. The study, a collaborative effort between Johns Hopkins and the University of Alabama at Birmingham, included data from 72 autism and control brains. It was published online in the journal Nature Communications.“There are many different ways of getting autism, but we found that they all have the same downstream effect,” said Dan Arking, Ph.D., an associate professor in the McKusick-Nathans Institute for Genetic Medicine at the Johns Hopkins University School of Medicine. “What we don’t know is whether this immune response is making things better in the short term and worse in the long term.”

The causes of autism, also known as autistic spectrum disorder, remain largely unknown and are a frequent research topic for geneticists and neuroscientists. But Arking noticed that studies of whether and how much genes were being used — known as gene expression — involved too little data to draw many useful conclusions about autism. Unlike a genetic test, which can be done using nearly any cells in the body, gene-expression testing has to be performed on the specific tissue of interest — in this case, brains that could be obtained only through autopsies.

To combat this problem, Arking and his colleagues analyzed gene expression in samples from two different tissue banks, comparing gene expression in people with autism to that in controls without the condition. All told, they analyzed data from 104 brain samples from 72 individuals — the largest data set so far for a study of gene expression in autism.

Previous studies identified autism-associated abnormalities in cells that support neurons in the brain and spinal cord. In this study the research team was able to narrow in on a specific type of support cell known as a microglial cell, which polices the brain for pathogens and other threats. In the autism brains, the microglia appeared to be perpetually activated — and the genes for inflammation responses turned on.

“This type of inflammation is not understood well, but it highlights the lack of current understanding about how innate immunity controls neural circuits,” said Andrew West, Ph.D., an associate professor in the UAB Department of Neurology and co-author of the study.

“Given the known genetic contributors to autism, inflammation is unlikely to be its root cause,” Arking said. “Rather, this is a downstream consequence of upstream gene mutation.”

The next step, he says, would be to find out whether treating the inflammation could ameliorate symptoms of autism.

Other authors on the study are Simone Gupta, Shannon E. Ellis, Foram N. Ashar, Anna Moes, Joel S. Bader and Jianan Zhan, all of The Johns Hopkins University.

The study was funded by the Simons Foundation and the National Institute of Mental Health.

By Bob Shepard
UAB Media Relations

Worried about dementia? New UAB clinic offers personalized risk assessment

Neurologist David Geldmacher, M.D., who leads the University of Alabama at BirminghamDivision of Memory Disorders, sees many older patients with memory loss, dementia or Alzheimer’s disease. He also sees their caregivers, who often are spouses or adult children.

“I recognized the need for a dementia risk-assessment clinic because a lot of my time in the care of people with memory loss is spent advising people without memory loss how to protect themselves,” Geldmacher said.

Building on international studies that examined risk factors for dementia, Geldmacher created the UAB Alzheimer’s Risk Assessment and Intervention Clinic, the first such clinical service in the nation. Patients receive a detailed, personalized risk assessment, which includes family history, a detailed memory history for the patient, cognitive testing and a baseline MRI scan. That information is incorporated into existing risk-predictor models, which have been validated by research studies that followed thousands of patients for as many as 20 years to produce an accurate risk assessment.

“It’s about an hour-and-a-half process of collecting a detailed risk-factor history, and we focus on the reversible risk factors,” Geldmacher said. “So many people facing dementia focus on the irreversible risk factors, such as ‘I’m getting older’ or ‘my dad or mom had dementia.’ We can’t change those things, but we can change things like levels of physical activity and cholesterol counts and blood-pressure numbers.”

Geldmacher says the studies have shown that reducing one or more risk factors can have a significant effect on reducing one’s overall chances of developing Alzheimer’s disease.

“For most people, Alzheimer’s disease is an illness you live with, not an illness from which you die,” Geldmacher said. “With a better understanding of individual risk, there are steps that people can take to minimize the risk for serious memory loss. One of the common themes for both short-term and long-term risk is cardiovascular health, which is something that is more or less under our control through lifestyle changes or medications.”

He presents a hypothetical patient — a woman in her 50s with a family history of dementia who is mildly obese and has cardiovascular issues.

“If she reverses one of three things — loses weight, brings her cholesterol under control or brings her blood pressure into the normal range — she can cut her risk in half,” Geldmacher said. “And if she manages all three of those reversible risk factors and brings them all into the desirable range, she can cut her dementia risk in half again.”

Jon Kling is a nonhypothetical patient. His mother had dementia, as did all four of her sisters. The 72-year-old, semiretired financial planner is reasonably healthy, but worries about his risk of dementia. He was one of the first patients to see Geldmacher at the new clinic.

“I really wanted to be able to establish a baseline of where I am today,” Kling said. “I didn’t feel like I was at particular risk right now, but down the road I didn’t know. I just wanted to see where I stood.”

Kling got good news: His dementia risk is relatively low. Geldmacher’s assessment included recommendations on how to keep that risk low, including increased physical activity and proper diet. Kling was already practicing some of those recommendations.

“The physical activity of walking and working with light weights — those were things I’ve been doing for years,” Kling said. “The assessment was really a reinforcement that I was doing the right things and that I need to continue to do so.” 

Geldmacher says the research models offer a long-term risk assessment of 20 years for people in their late 40s and 50s and a six-year assessment for older patients. Kling believes the assessment also helps with awareness and education.

“If I asked you what your ideal weight was, you could probably tell me exactly what that weight should be,” he said. “If I asked you to name three or four risk factors for dementia or Alzheimer’s, could you do it? Most people really don’t know, and this will provide a great deal of needed awareness.”

For Geldmacher, preventing or slowing the progression of dementia is key.

“At this point in 2014 and for the foreseeable future, we don’t have any medications that meaningfully attack the processes in the brain that lead to Alzheimer’s disease,” he said. “We still don’t understand the cause of Alzheimer’s disease, so prevention by medication is a distant goal for us. It’s something we work on every day in our research labs and our clinical testing, but it’s not something that will emerge tomorrow or next week.”

For Kling, having the assessment and a baseline of where he stands today is comforting.

“There’s peace of mind with knowing my risk,” he said. “And knowing that we have this type of help in our own backyard right here in Birmingham, Alabama, is fantastic. It’s great to have the type of professional risk assessment that Dr. Geldmacher and his program provide. I think it’s invaluable.”

Patients will have two clinical visits with Geldmacher and his staff. The first will be to compile histories and conduct testing. The second will be to review the personalized treatment plan, including how to access resources to help achieve lifestyle changes, and where to find supportive and educational materials. The clinic will also suggest coping strategies that can be employed to ease the burden of dementia on the individual and his or her family. The two-visit assessment is fee-for-service and will cost about $1,000, which includes the MRI scan.

Geldmacher anticipates that the risk-assessment clinic will ultimately serve as a gateway to research projects aimed at finding medications or other treatments designed to lower risk of memory disorders.

Call 205-975-7575 for more information or to make an appointment for a personalized dementia risk assessment.

By Bob Shepard
UAB Media Relations