MIT Research News' Journal

Fast, noninvasive technique for probing cells may reveal disease

The stiffness or elasticity of a cell can reveal much about whether the cell is healthy or diseased. Cancer cells, for instance, are known to be softer than normal, while asthma-affected cells can be rather stiff.

Determining the mechanical properties of cells may thus help doctors diagnose and track the progression of certain diseases. Current methods for doing this involve directly probing cells with expensive instruments, such as atomic force microscopes and optical tweezers, which make direct, invasive contact with the cells.

Now MIT engineers have devised a way to assess a cell’s mechanical properties simply by observation. The researchers use standard confocal microscopy to zero in on the constant, jiggling motions of a cell’s particles — telltale movements that can be used to decipher a cell’s stiffness. Unlike optical tweezers, the team’s technique is noninvasive, running little risk of altering or damaging a cell while probing its contents.

“There are several diseases, like certain types of cancer and asthma, where stiffness of the cell is known to be linked to the phenotype of the disease,” says Ming Guo, the Brit and Alex d'Arbeloff Career Development Assistant Professor in MIT’s Department of Mechanical Engineering. “This technique really opens a door so that a medical doctor or biologist, if they would like to know the material property of cell in a very quick, noninvasive way, can now do it.”

Guo and graduate student Satish Kumar Gupta have published their results in the Journal of the Mechanics and Physics of Solids.

Stirring spoons

In his 1905 PhD thesis, Albert Einstein derived a formula, known as the Stokes-Einstein equation, that makes it possible to calculate a material’s mechanical properties by observing and measuring the movement of particles in that material. There’s just one catch: The material must be “in equilibrium,” meaning that any particle motions must be due to the effect of the material’s temperature rather than any external forces acting on the particles.

“You can think of equilibrium as being a hot cup of coffee,” Guo says. “The coffee’s temperature alone can drive sugar to disperse. Now if you stir the coffee with a spoon, the sugar dissolves faster, but the system is not driven solely by temperature any more and is no longer in equilibrium. You’re changing the environment, putting energy in and making the reaction happen faster.”

Within a cell, organelles such as mitochondria and lysosomes are constantly jiggling in response to the cell’s temperature. However, Guo says, there are also “many minispoons” stirring up the surrounding cytoplasm, in the form of proteins and molecules that, every so often, actively push vibrating organelles around like billiard balls.

The constant blur of activity in a cell has made it difficult for scientists to discern, simply by looking, which motions are due to temperature and which are due to more active, “spoon-like” processes. This limitation, Guo says, has “basically shut the door on using Einstein’s equation and pure observation to measure a cell’s mechanical properties.”

Frame by frame

Guo and Gupta surmised that there might be a way to tease out temperature-driven motions in a cell by looking at the cell within a very narrow timeframe. They realized that particles energized solely by temperature exhibit a constant jiggling motion. No matter when you look at a temperature-driven particle, it’s bound to be moving.

In contrast, active processes that can knock a particle around a cell’s cytoplasm do so only occasionally. Seeing such active movements, they hypothesized, would require looking at a cell over a longer timeframe.

To test their hypothesis, the researchers carried out experiments on human melanoma cells, a line of cancer cells they chose for their ability to grow easily and quickly. They injected small polymer particles into each cell, then tracked their motions under a standard confocal fluorescent microscope. They also varied the cells’ stiffness by introducing salt into the cell solution — a process that draws water out of cells, making them more compressed and stiff.

The researchers recorded videos of the cells at different frame rates and observed how the particles’ motions changed with cell stiffness. When they watched the cells at frequencies higher than 10 frames per second, they mostly observed particles jiggling in place; these vibrations appeared to be caused by temperature alone. Only at slower frame rates did they spot more active, random movements, with particles shooting across wider distances within the cytoplasm.

For each video, they tracked the path of a particle and applied an algorithm they had developed to calculate the particle’s average travel distance. They then plugged this motion value into a generalized format of the Stokes-Einstein equation.

Guo and Gupta compared their calculations of stiffness with actual measurements they made using optical tweezers. Their calculations matched up with measurements only when they used the motion of particles captured at frequencies of 10 frames per second and higher. Guo says this suggests that particle motions occurring at high frequencies are indeed temperature-driven.

The team’s results suggest that if researchers observe cells at fast enough frame rates, they can isolate particle motions that are purely driven by temperature, and determine their average displacement — a value that can be directly plugged into Einstein’s equation to calculate a cell’s stiffness.

“Now if people want to measure the mechanical properties of cells, they can just watch them,” Guo says.

The team is now working with doctors at Massachusetts General Hospital, who hope to use the new, noninvasive technique to study cells involved in cancer, asthma, and other conditions in which cell properties change as a disease progresses.

“People have an idea that structure changes, but doctors want to use this method to demonstrate whether there is a change, and whether we can use this to diagnose these conditions,” Guo says.

This research was funded, in part, by MIT’s Department of Mechanical Engineering.

Designing the microstructure of printed objects

Today’s 3-D printers have a resolution of 600 dots per inch, which means that they could pack a billion tiny cubes of different materials into a volume that measures just 1.67 cubic inches.

Such precise control of printed objects’ microstructure gives designers commensurate control of the objects’ physical properties — such as their density or strength, or the way they deform when subjected to stresses. But evaluating the physical effects of every possible combination of even just two materials, for an object consisting of tens of billions of cubes, would be prohibitively time consuming.

So researchers at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) have developed a new design system that catalogues the physical properties of a huge number of tiny cube clusters. These clusters can then serve as building blocks for larger printable objects. The system thus takes advantage of physical measurements at the microscopic scale, while enabling computationally efficient evaluation of macroscopic designs.

“Conventionally, people design 3-D prints manually,” says Bo Zhu, a postdoc at CSAIL and first author on the paper. “But when you want to have some higher-level goal — for example, you want to design a chair with maximum stiffness or design some functional soft [robotic] gripper — then intuition or experience is maybe not enough. Topology optimization, which is the focus of our paper, incorporates the physics and simulation in the design loop. The problem for current topology optimization is that there is a gap between the hardware capabilities and the software. Our algorithm fills that gap.”

Zhu and his MIT colleagues presented their work this week at Siggraph, the premier graphics conference. Joining Zhu on the paper are Wojciech Matusik, an associate professor of electrical engineering and computer science; Mélina Skouras, a postdoc in Matusik’s group; and Desai Chen, a graduate student in electrical engineering and computer science.

Points in space

The MIT researchers begin by defining a space of physical properties, in which any given microstructure will assume a particular location. For instance, there are three standard measures of a material’s stiffness: One describes its deformation in the direction of an applied force, or how far it can be compressed or stretched; one describes its deformation in directions perpendicular to an applied force, or how much its sides bulge when it’s squeezed or contract when it’s stretched; and the third measures its response to shear, or a force that causes different layers of the material to shift relative to each other.

Those three measures define a three-dimensional space, and any particular combination of them defines a point in that space.

Researchers used their algorithm to design soft grippers with microstructures that can grasp objects by moving their tips when external forces are applied to their extremities. (The Computational Fabrication Group at MIT)

In the jargon of 3-D printing, the microscopic cubes from which an object is assembled are called voxels, for volumetric pixels; they’re the three-dimensional analogue of pixels in a digital image. The building blocks from which Zhu and his colleagues assemble larger printable objects are clusters of voxels.

In their experiments, the researchers considered clusters of three different sizes — 16, 32, and 64 voxels to a face. For a given set of printable materials, they randomly generate clusters that combine those materials in different ways: a square of material A at the cluster’s center, a border of vacant voxels around that square, material B at the corners, or the like. The clusters must be printable, however; it wouldn’t be possible to print a cluster that, say, included a cube of vacant voxels with a smaller cube of material floating at its center.

For each new cluster, the researchers evaluate its physical properties using physics simulations, which assign it a particular point in the space of properties.

Gradually, the researchers’ algorithm explores the entire space of properties, through both random generation of new clusters and the principled modification of clusters whose properties are known. The end result is a cloud of points that defines the space of printable clusters.

The soft mechanisms for flapping wings are embedded in the material by topology optimization. The wings of the ray are specified to flap up and down when vertices on its spine contract and expand. (The Computational Fabrication Group at MIT)

Establishing boundaries

The next step is to calculate a function called the level set, which describes the shape of the point cloud. This enables the researchers’ system to mathematically determine whether a cluster with a particular combination of properties is printable or not.

The final step is the optimization of the object to be printed, using software custom-developed by the researchers. That process will result in specifications of material properties for tens or even hundreds of thousands of printable clusters. The researchers’ database of evaluated clusters may not contain exact matches for any of those specifications, but it will contain clusters that are extremely good approximations.

“The design and discovery of structures to produce materials and objects with exactly specified functional properties is central for a large number of applications where mechanical properties are important, such as in the automotive or aerospace industries,” says Bernd Bickel, an assistant professor of computer science at the Institute of Science and Technology Austria and head of the institute’s Computer Graphics and Digital Fabrication group. “Due to the complexity of these structures, which, in the case of 3-D printing, can consist of more than a trillion material droplets, exploring them manually is absolutely intractable.”

“The solution presented by Bo and colleagues addresses this problem in a very clever way, by reformulating it,” he says. “Instead of working directly on the scale of individual droplets, they first precompute the behavior of small structures and put it in a database. Leveraging this knowledge, they can perform the actual optimization on a coarser level, allowing them to very efficiently generate high-resolution printable structures with more than a trillion elements, even with just a regular computer. This opens up exciting new avenues for designing and optimizing structures at a resolution that was out of reach so far.”

The MIT researchers’ work was supported by the U.S. Defense Advanced Research Projects Agency’s SIMPLEX program.