Now that I’ve finally got my computer set up and am working, perhaps I should talk a little about why I’m in Beijing?
EAPSI: Investigation of the wrinkling and buckling behavior of layered soft materials, with applications in the developing brain.
During the third trimester of gestation, the human brain evolves from having a mostly smooth surface to the characteristic ’wrinkled’ appearance of the adult brain. How does this happen, and why does it sometimes go wrong? The mechanics community has been interested in these questions for decades, attempting to model the brain as a thin, stiff, growing layer (gray matter) attached to a thicker, softer layer (white matter). Recent mechanical tests, however, have revealed that gray matter is actually slightly less stiff than the underlying white matter, challenging many prior models and assumptions. Through collaboration with Dr. Feng Xi-Qiao of Tsinghua University in Beijing, China, an expert in the wrinkling and buckling of soft films, this project will explore the behavior of thin growing layers on substrates of a similar stiffness. This research will lead to a greater understanding of brain development in light of these recent findings.
For a stiff growing layer on a soft substrate, the formation of sinusoidal waves is expected, while the growth of a soft layer on a stiffer substrate will lead to creases with pinched valleys. The transition between waves and creases happens gradually in the region of interest for brain tissue. Using both analytical and numerical approaches, this research will explore the behavior of soft layered materials with stiffness ratios close to unity. Numerical simulations will be performed in the finite element software Abaqus, using the built-in linear perturbation analysis as well as user-defined material models that simulate volumetric growth.
This was written for lay people (especially the first paragraph) so I’m assuming this is all crystal clear to you, right?
If not . . . Okay, so I’m a mechanical engineer, and I study the brain. Yeah, it’s weird. My field, more specifically, is solid mechanics, which is the study of how solids respond to forces (as opposed to fluid mechanics, which is the study of how fluids react to forces). Even more specifically, I do computational (as opposed to experimental) solid mechanics, which means I make mathematical or computer models of objects in order to predict how they will respond to forces. Even more specifically, I do computational biomechanics, so the objects I study are biological systems. And, for one level of specificity beyond that, the group I work in at Stanford focuses on biological systems that grow (add mass) or remodel (change their physical properties).
During my undergraduate degree in mechanical engineering, I spent four years studying the behavior of engineering materials, like steel and concrete. These are super important, as we build houses and bridges out of them and stuff. They’re also fairly simple (well, at least in hindsight). Under normal conditions, their behavior is well-known and reliable.
Picture an ordinary steel pipe. If you compress it (squeeze it from both ends), it will get shorter, exhibiting a linear elastic response. “Linear” means that if you doubled the load on it (squeezed twice as hard), it would deform twice as much (shorten by twice as much). “Elastic” means that if you unloaded it (stopped squeezing), it would return to its original length immediately. Not that you would probably notice – under normal loading conditions steel exhibits small strain deformation, meaning that its length would change so little that we can assume its new length is approximately the same as its original length. It is also “homogeneous”, meaning that if you cut it into shorter pipes, each of them would behave identically because the material is the same everywhere. And finally, it is “isotropic”, meaning that if you cut square out of this steel, you could compress it from side to side or from top to bottom, and it would behave the same.
But, I study the brain. Many biological materials, including the brain, differ from engineering materials in a few major ways. They are generally not linear, elastic, small-strain, homogeneous, or isotropic. Instead, they are usually “nonlinear”, meaning that as you compress or stretch them, it may get easier or harder to do so. They may be “viscoelastic”, which means their response depends on how fast you compress or stretch them (like Silly Putty), or “plastic”, which means they don’t return to their original shape when unloaded (think of a paper clip). Or both! They can exhibit large strains. Squeeze some of the skin on your arm together – if you can reduce the distance between your fingers by half, that’s 50% strain, waaay larger than the 0.02% strain range that engineering materials operate in. They’re usually “inhomogenous” – your bones, for instance, have different densities throughout, in order to bear the weight of your body most efficiently. And they’re often “anisotropic” – muscles are a great example of a fibrous tissue, with muscle fibers running along their length because the direction in which they contract. Finally, biological materials can grow, or add mass. Steel doesn’t do this – if you have some quantity of steel now, you’ll have the same quantity of steel a year from now.
All of this stuff makes biological materials more difficult (and more interesting?) than engineering materials. Just like engineering materials, however, biological materials respond to their mechanical environment – the forces they experience acting upon them. I’m studying the development of the brain, trying to understand what influence mechanical forces have on the development of the wrinkled shape of our brain.
A lot of things in computational mechanics start very simply. Very much like the joke, “assume a spherical cow”, all of my work this summer will likely be on rectangular brains. This allows us to focus on what we think are the essential characteristics of the brain, at least from a mechanics point of view – there are two materials (a thin layer of gray matter laying on a thicker layer of white matter) and they are connected to each other as they grow.
Over the last ~30 years of people studying the brain, we thought the thin gray matter layer was stiffer than the white matter. These equations are fairly easy to solve (on rectangular brains, at least!), especially when the gray matter is a lot stiffer. When the top layer grows or is compressed (mechanically, the two loadings are the same), the results look something like this, with regular sinusoidal waves.
But last year, some colleages of mine tested animal brains – literally, got them from a slaughterhouse and poked them with a very sensitive machine to see how stiff they were. They found two things: First of all, brain is less soft than Jello! More importantly (although probably less likely to be shared as a fun anecdote at your next dinner party), the white and gray matter are pretty much equally stiff; if anything, the white matter is stiffer.
(My dad asked me why it’s so hard to measure the stiffness of the brain – “Come on, it’s 2015!” he said. Things like steel or aluminum or even wood are easy to test because you can cut perfect shapes, and you can grab on and pull them easily. It’s much harder to cut a nice cube or bar out of a slowly disintegrating fresh brain, and harder still to stretch or squish it in some measurable, repeatable way.)
Given this, there are a lot of past assumptions that need to be reevaluated. For layered materials with an “inverse” stiffness ratio (where the substrate is stiffer than the thin layer), you see patterns more like this, with creases developing under loading:
These two behaviors transition into each other gradually, looking something like this in between:
The brain lies somewhere around here. My project this summer is to increase our understanding of the behavior of layered materials with inverse stiffness ratios (the 2nd and 3rd pictures), which I would then apply to my research on brain folding.
Bo Li, one of the professors I’m working with, found a paper that’s similar to what we’re hoping to do – they investigated both wrinkles (the first picture) and creases (the second picture) but in a single material, whereas we are looking at two layers of different materials. I spent the day working through the first part of the paper, making sure I understand what they did and looking for the parts that we will have to change for our purposes. It was nice to have a very concrete task and get a glimpse of an outcome similar to what we’re hoping for.
It kind of rained today, which was nice for two reasons. First of all, the sky had a legitimate reason for being gray, and actually had some cloud-like texture to it instead of its usual appearance, which has all the variety of a concrete wall. Secondly, rain usually brings cleaner air. (Which, I can’t help thinking, means that the rain is washing the pollution out of the sky. It’s a wonder the raindrops don’t burn my skin!) Look at what happened after Friday night’s storm:
Too bad we weren’t outside from 10pm to 1am, when the air was so nice! I’m hopeful that today’s improvement will last a bit longer . . .
This evening, I tried to Skype with my Dad but the hotel internet is terrible in the evenings. It’s kind of absurd to me that I have Skyped with my parents from all over the world, including a “small” Chinese city five years ago, but here in the capital of China in 2015 it’s just too much.
Today I learned:
My N100 mask keeps out scents significantly better than my N95 mask. I bike by a large, open garbage dump on my way to work, and the smell makes me almost throw up every single time I pass it. I’ve been trying to hold my breath, but I can’t hold it for long enough. The N100 mask worked well enough that I think I’ll start wearing it, even though it’s too big for my face.