Doing A Number On Disease

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By Mike Pettapiece

Migraine with aura (classic migraine) : Treat it with Math – lecture title at the Centre for Mathematical Medicine, Fields Institute, Toronto.

When neurosurgeon Sheila Singh focuses on the hierarchy of cancer stem cells in brain tumours, she often turns for help not to medical professionals but to mathematicians.

She’s not particularly math savvy-and they’re somewhat alien to biological mysteries-but this unusual marriage of math and medicine is right on the cutting edge of fighting cancer and other deadly diseases.

“Biologists are not very statistically sound in terms of how we like to analyze large piles of data,” says Dr. Singh, a pediatric neurosurgeon and cancer stem cell investigator at McMaster University, in Hamilton.

“We are prone to looking at a long list of differentially expressed genes, and we will notice our favourite gene, and choose to focus our study on that gene . . .”

As technology allows researchers to literally see the face of disease – the oncogenes, coronaviruses, Streptococcus bacteria – investigators must sift through a mass of quantitative details.

Interactions at molecular and gene levels are awesomely complex.

Increasingly, medical professionals are turning to applied mathematicians to make sense of this storm of data. Math helps to bring order and insight to the various parameters. Deciding, for example, on the best types and sequencing of cancer treatments – such as surgery, radiotherapy and chemotherapy – can be troublesome and time-consuming. A math model that simulates protocols can lend guidance to regimen options.

Biomathematicians can network-model the invasive spread of swine flu. They can build a virtual model of a tumour. And they can paint math pictures of non-linear chemical waves in the brain of a migraine sufferer.

“This is sort of an exciting new direction,” says Siv Sivaloganathan, director of the Centre for Mathematical Medicine, at the Fields Institute, University of Toronto. “Our feeling has always been that if mathematicians don’t get into this area now, we will be missing out on the chance for significant advances.”

Simulations not only impose rational discipline, they can also bring fiscal control to healthcare costs.

“I definitely think so,” says Sivaloganathan. “If you can imagine a clinical trial, for example, on surgical-chemotherapy sequencing, that’s a huge trial. The cost runs into the millions of dollars.”

Modelling a tumour or the spread of a disease on high-speed computer frames is far less costly.

It was in the 20th Century that the pairing of physics and mathematics created a giant. Many believe the same potential exists for math and medicine in this century.
It’s a young bond, formed only 30 years or so ago. Sivaloganathan says a former Oxford professor, Dr. James Murray, who founded the centre for mathematical biology at the University of Oxford in 1983, was a math-medicine pioneer. The Centre for Mathematical Medicine (CMM), at Fields, is only five years old. The centre began life as the mathematical medicine group at the University of Waterloo, where Sivaloganathan is a professor of applied mathematics.

Centres such as the CMM are often a temple of many disciplines. They’re a home to applied math specialists, biologists, immunologists, epidemiologists, disease researchers, even software developers.

These experts study areas as diverse as modelling and patterning tumour dynamics, bacterial chemotaxis, infectious disease outbreak and progression, and gene delivery.

Like diseases, the institutes have no borders. CMM, for example, has links with Vanderbilt University, Oxford, Moffitt Cancer Center (in Florida), and others.

The Center for the Development of a Virtual Tumor, based at Massachusetts General Hospital, has members from around the world.

Working together, biomathematicians and integrative biologists can build predictors as to the invasion patterns of a contagious illness. They can project how rapidly it may evolve and at what times vaccinations – where they are available – are most optimally used. They can study cancer initiation, angiogenesis and metastasis.

Dr. Singh, a pioneer in investigating brain tumour-initiating cells, has worked with biomathematicians Sivaloganathan and Mohammad Kohandel about two years. They are trying to better define “the cellular hierarchy of cancer stem cells in brain tumours, and [predict] the manner in which these cells generate proportionally the heterogeneous tumour,” she says.

Their research involves “new ways of performing microarray analysis” of the thousands of genes and proteins expressed in brain cancer stem cells “in comparison with normal neural stem cells.”

While Dr. Singh might use a laser or ultrasonic aspiration as basic tools, a biomathematician’s tools might be statistical analysis, stochastic (random-variable) spatial systems, high-speed computer modelling, or differential equations.

It’s all about collecting information. Any study of disease yields data, such as weekly reported cases or infection rates within a specific sub-population. Medical mathematicians can turn these numbers into data-driven models and simulations. Modelers can program in singular concepts, such as human behaviour patterns or disease spread trends.

With differential equation models, health professionals and policy makers have a basis on which to implement control measures, such as how vigorously to effect community health edicts, what to tell people about the importance of hand-washing, when to quarantine the infected or urge vaccinations, or the elimination of non-essential travel.

“Mathematical models allow us to simulate the spread of diseases through different settings and to evaluate possible intervention strategies,” integrative biologist Lauren Ancel Meyers, of the University of Texas at Austin, said in an email exchange. “This can give policy makers the tools and confidence to make effective decisions.”

Dr. Meyers worked intimately with University of British Columbia researchers as they battled the deadly SARS epidemic in 2003.

In Vancouver, SARS investigators input a mass of data to puzzle out the spread of the disease and to gauge its likely impact over time. They used demographic and census data to build a model of the patterns of interaction within the city.

By looking at household sizes, the number of houses, schools and hospitals, and other data, they were able to build a contact network. In effect, that model was a mirror for how people interacted.

Knowing that allows one to project where and how rapidly a disease may spread.

Analysis of SARS infection rates and the course that it took allowed investigators to say the SARS coronavirus – related to 44 deaths in Canada during the 2002-2003 outbreak – was transmissible enough to cause a large epidemic, if unchecked.

But the analysis also enabled them to say that SARS was not so contagious as to run rampant, as long as basic public health steps were taken.

Of course, conclusions are only as good as the raw data. Under-diagnoses or misdiagnosed cases will bias projections on the invasiveness of an epidemic.

Biomathematicians have been out-front in studying the recent outbreak of novel influenza A (H1N1 flu, the so-called swine flu). They were able to predict transmission patterns from patient to patient as they interpreted epidemiological data. Researchers could see that H1N1, although a fatal disease, was unlikely to rage into a pandemic across North America.

At the University of Rochester Medical Center in New York state, researchers actually built a computer simulation of major portions of the body’s immune reactions to influenza type A. By modeling immune responses, such as the actions of killer T-cells or antibody-producing B-cells, they created a virtual battleground based on response scenarios.

The Rochester war model made use of earlier models that captured, in mathematical equations, millions of simulated interactions between virtual immune cells and viruses. Dr. Singh’s work with the Waterloo/Fields Institute colleagues has buttressed her earlier research on glioblastomas. The team has been able to validate the principle that (biomarker) CD133+ cells from tumours can generate the heterogeneity behind the brain tumour through asymmetric divisions.

“Now, we are working toward looking at a new method of gene expression analysis that is both mathematically sound and biologically informed,” she said.

Mike Pettapiece writes and edits the newsletter for the Golden Horseshoe Biosciences Network, based at McMaster University in Hamilton. He can be reached at: mikepettapiece@cogeco.ca