This article discusses various research works by engineering teams working on computer models that help explain the evolutionary dynamics of bone cancer. In order to investigate biological systems with a mechanical engineering approach, medical research teams are creating computerized mathematical models that have the potential to explain the mechanics of cancer. Researchers have found that mechanical signals can influence cancer cell migration, growth, and differentiation. Engineering models, such as the one simulating cancer immunotherapy, not only are visually striking, but also can help researchers better understand how cells respond to potential treatments. Researchers at the Center of Applied Molecular Medicine at the University of Southern California have developed two open source 3D simulation packages: BioFVM, which simulates diffusion of dozens of substrates in 3D tissues, and PhysiCell, which simulates multicellular systems in 3-D tissues. According to experts, differences between experimental information and model-returned information can also be resolved to better understand how metastasis works and, perhaps, fine-tune models.


David Basanta was on his way to getting a doctorate 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 one with an added challenge,” Basanta said. “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 that is crying out for mathematical modeling.”

Tumors evolve and grow, he said, due to evolutionary factors.

Indeed, the evolutionary dynamics of tumors can be modeled to help explain their progression, said 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.

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.

In the same way that engineering simulations depict and analyze how physical forces affect a part, biological models can provide insight into the factors that aid 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, said Philip LeDuc, a 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, he said.

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.

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, he said.

By manipulating mechanical interactions in integrated biological systems at the molecular, cellular, and multi-cellular scales, LeDuc said, biomedical engineers may be able to treat cancer—or even prevent it.

Mechanical Properties

“As a mechanical engineer,” LeDuc said, “I think about how biological systems work in the same way that I think about how engineered systems work.”

LeDuc has written that he has spent much of his life taking apart complex systems to gain an understanding of how they function. His interest began early on when as a youth he took apart lawn mowers and cars. Today, his interest encompasses the 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,” he said. “I wonder: Do engineered, man-made systems have anything in common with the biological systems of nature?”



Recognizing the need for engineers and physical scientists to apply their methods to cancer research, in 2009 the National Cancer Institute 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.

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 remained stable, they wouldn’t spread, or “metastasize,” to healthy tissue. Curbing or stopping cell spread is a key to fighting the cancer, Basanta said.

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

With that understanding, it became clear that computational models could aid cancer research—that scientists could model the way cells interact with their environment, said 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.

Before 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 said. In a 3-D environment, however, those mechanical properties become clear, he added.


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. 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 in 3-D tissues.

Many biological problems require solving for secretion, diffusion, uptake, and decay of multiple substrates in three dimensions, Macklin said. While 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 said. “The availability of things like oxygen and glucose, which are diffused through 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, while 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 said. 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 said.

BioFVM allows users to solve for 10 or more signaling factors at a time, in three dimensions, 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 a time.

“This allowed us to write a very fast diffusion-decay solver, a bulk supply-uptake solver, and a cell-based secretion-uptake solver,” Macklin said.

Emerging Tools

Mathematical models can also test a hypothesis at a much faster rate, for longer periods of time, and in a more humane way than can mouse models, Basanta said. 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 said.

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.

“Many months of frequent conversations and hackathons were required before we established the foundations of this mathematical model,” Basanta said. “Understanding metastasis requires us 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.”

The time investment was well worth it, he said, 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 research toward curing cancer, the work continues. But a cure begins with understanding cell mechanisms, LeDuc said.

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 previous possible, he said.

Although models like the ones Basanta, LeDuc, and others are at work on just emerging as a tool for cancer drug discovery, they’ve already demonstrated their potential to simulate the cancer environment and how environmental and drug factors affect that environment and, thus, the cancer itself.

Though cross-disciplinary physical and biological science partnerships, and engineering-based models for cancer research at still new, the National Cancer Institute expects them to pick up speed in future years and, hopefully, lead to important breakthroughs in cancer treatments.