David Basanta was on his way to getting a Ph.D. in mechanical engineering when he discovered he’d rather write algorithms that model the role that evolution plays in cancer’s spread than study evolution’s effect on materials, his original goal.

Cancer is not only a terrible disease, but it is one with an added challenge, Basanta says. “The tumors often evolve resistance to any treatments we throw at them; so it felt like a natural fit for my interests.” It’s also a field, he says, that is “crying out for mathematical modeling.”

David Basanta,  H. Lee Moffitt Cancer Center and Research InstituteDavid Basanta, H. Lee Moffitt Cancer Center and Research Institute To investigate biological systems with a mechanical engineering approach, Basanta and others are creating computerized mathematical models that have the potential to explain the mechanics of cancer: what sparks it, how and why it spreads, and the mechanisms that feed it.

Tumors evolve and grow due to evolutionary factors. Indeed, the evolutionary dynamics of tumors can be modeled to help explain their progression, says Basanta, now a mathematical oncologist at the H. Lee Moffitt Cancer Center and Research Institute in Tampa, Fla.

Basanta and his colleagues are working on computer models that help explain the evolutionary dynamics of bone cancer.

In the same way that engineering simulations depict and analyze how physical forces affect a manufactured part, biological models can provide insight into the factors that aid bone cancers’ growth. Those same simulations may help identify mechanisms that might halt its progression.

Viewing cells and molecules as “engineered systems” that can be investigated in the way same that engineers analyze man-made machines can help uncover unifying principles between these systems, says Philip LeDuc, professor of mechanical engineering at Carnegie Mellon University. And although tumors communicate with their surroundings in a multitude of ways, mechanical signals are now recognized as one of the major ways they interact.

Philip R. LeDuc, Carnegie Mellon UniversityPhilip R. LeDuc, Carnegie Mellon University LeDuc heads the Center for the Mechanics and Engineering of Cellular Systems. The Center brings together more than 20 professors from engineering, biology, chemistry, physics and computer science to use mechanical engineering techniques at the cellular system level to help solve biological riddles, including cancer.

Advanced Machinery

In short, mechanical signals can influence cell migration, growth, and differentiation. Understanding the input and output of mechanical signals that occur both inside living cells and between cells and the environment can improve cancer treatment and perhaps even prevent the disease. Therefore, by manipulating mechanical interactions in integrated biological systems at the molecular, cellular, and multi-cellular scales, cancer might be treated or even prevented, he says.

“As a mechanical engineer, I think about how biological systems work in the same way that I think about how engineered systems work,” LeDuc says. He has written that much of his life has been spent taking apart complex systems to understand how they function. As a youth he took apart lawn mowers and cars. Today, his interests extend to the human cell’s “tremendously more advanced machinery.”

“Yet I am particularly fascinated by nature’s machines, and I look to the intersection of biology and mechanical engineering as a source of discovery. I wonder: Do engineered, man-made systems have anything in common with the biological systems of nature?” he says.

Recognizing the need for engineers and physical scientists to apply their methods to cancer research, in 2009 the National Cancer Institute (NCI) funded 12 physical science-oncology centers that carry out cancer research from an interdisciplinary viewpoint.

Around the same time, the NCI started the Physical Sciences in Oncology Initiative, which brings together cancer biologists and oncologists with specialists in physics, mathematics, chemistry and engineering to work together on cancer research.

Environmental Interactions

It wasn’t until the late 1990s that scientists determined that the way cancer cells interact with their environment can be critical to understanding cancer itself. At around the same time they also began to understand that each patient’s tumor environment differs. As a result, even if two patients have the same kind of cancer, individual factors can affect the way the cancer grows and spreads.

It also became clear that cancer cells display mechanical properties that could be studied; those properties may, in fact hold a key to how those cells spread and move to different parts of the body.

The thinking was that if cancer cells were to remain stable, they wouldn’t spread--or “metastasize” as the process is known in the cancer world--to healthy tissue. Curbing or stopping cell spread is a key to fighting the cancer, Basanta says.

That means scientists need to understand the way cells behave, including their mechanical properties. And mechanical engineers, with their particular skill set, posses the means to study those properties.

3-D Insights

With that insight, it became clear that computational models could aid cancer research—that scientists could model the way cells interact with their environment, says Brian Fallica formerly a research assistant in the Laboratory for Molecular and Cellular Dynamics at Boston University, now a consultant at The Amundsen Group, a health company.

Brian Fallica, The Amundsen GroupBrian Fallica, The Amundsen GroupBefore the realizations of the late 1990s into the ways cancer cells communicate with their surroundings, scientists studied cancer cell migration by looking at them under a microscope. When seen in two dimensions the cells displayed no mechanical properties to study, Fallica says. In a 3-D environment, however, those mechanical properties become clear.

At the Boston University lab, Fallica worked under Muhammad Zaman to model the physical and mechanical properties of cancer cells in an effort to determine if those properties could explain their growth and movement. But researchers need tools to model biological problems. And that is where Paul Macklin, assistant professor at the Center of Applied Molecular Medicine at the University of Southern California, comes in.

Paul Macklin, University of Southern CaliforniaPaul Macklin, University of Southern California His lab developed two-open source 3-D simulation packages: BioFVM, which simulates diffusion of dozens of substrates in 3-D tissues, and PhysiCell, which simulates multicellular systems of in 3-D tissues.

Many biological problems require solving for secretion, diffusion, uptake, and decay of multiple substrates in three dimensions, Macklin says. Although many codes have been written to tackle this problem--particularly outside of biology--they’re often lacking in one or more of those areas.

“A lot of cancer cells vary their behavior in things like signaling factors,” he says. “The availability of things like oxygen and glucose, which are diffused through the environment and taken up by cells can influence whether a cell will move or die.”

Scientists and engineers know that oxygen and glucose are carried in the bloodstream and enter individual cells by passing through the cell membrane via diffusion. Oxygen enters the cells through simple diffusion. Meanwhile, glucose, amino acids and other large insoluble compounds enter through facilitated diffusion.

“So we knew we needed to solve for diffusion, but most biological codes have been doing this in the roll-your-own fashion,” Macklin says. By that, he means they “use one partial differential equation for oxygen, another for glucose, and solve one at a time for each signaling factor.”

As a result, if a researcher wants to solve for 10 factors at a time, the work has multiplied by a factor of 10. “In 3-D that gets complicated and darned expensive,” he says.

BioFVM allows users to solve for 10 or more signaling factors at a time, in 3D, and on desktop computers. Rather than using individual partial differential equations to solve for each factor, the BioFVM solves for a collection of factors at the same time. It uses an approach called operator splitting; breaking a complicated partial differential equation into a series of simpler partial and ordinary differential equations that can be solved for one at a time.

Mathematical cancer models let researchers identify and test novel treatments in ways and at speeds that weren’t previously possible.Mathematical cancer models let researchers identify and test novel treatments in ways and at speeds that weren’t previously possible. “This allowed us to write a very fast diffusion-decay solver, a bulk supply-uptake solver and a cell-based secretion-uptake solver,” Macklin says.

The Power of Mathematical Models

Mathematical models can test hypothesis at a much faster rate, for longer periods of time, and in a more humane way than can mouse models, Basanta says. And they allow researchers to test promising results with experiments.

Differences between experimental information and model-returned information can also be resolved to better understand how metastasis works and, perhaps, fine-tune models, he says.

Collaborators, including Leah Cook and Conor Lynch, both members of the Lynch Lab at the H. Lee Moffitt Cancer Center, spend substantial amounts of time relaying their findings to Basanta’s team, he says. “Many months of frequent conversations and hackathons were required before we established the foundations of this mathematical model,” he says. What’s more, understanding metastasis requires the researchers to “embrace the complexity” of a process involving several cell types, molecules, and scales. “So getting to the point where both the modelers and the experimentalists were comfortable took some time,” he says.

The time investment was worth it, he says, as the researchers were able to identify key aspects of the biology that the model should be able to capture and that the experimentalist should be able to check and validate. The models are used to discover how tumor cells and healthy cells interact within an environment and what factors lead tumor cells toward metastasis.

Like all work toward curing cancer, the work continues. But LeDuc and others believe that a cure may well begin with understanding cell mechanisms. Mathematical cancer models won’t do away with the need for experiments or for clinical tests and trials. Rather, they let researchers identify and test novel treatments in ways and at speeds that weren’t previously possible.