Welcome to FOCUS In Sound, the podcast series from the FOCUS newsletter published by the Burroughs Wellcome Fund. I’m your host, science writer Ernie Hood.
My guest on this edition of FOCUS In Sound is Dr. Laura Miller, Assistant Professor of Mathematics at the University of North Carolina at Chapel Hill. She is the principal investigator in the Mathematical Physiology Group at UNC.
In 2006, Laura received the Career Award at the Scientific Interface from the Burroughs Wellcome Fund. That award calls for Candidates to draw from their training in a scientific field other than biology to propose innovative approaches to answer important questions in the biological sciences. Now if there was ever a recipient who personifies that concept, it’s Laura Miller. She works in a very specialized scientific niche called mathematical biology, combining approaches from mathematics, biology, and fluid dynamics to reveal some remarkable insights about the natural world.
Laura, welcome to FOCUS In Sound…
Thank you very much.
To get us started, let’s give our listeners a bit of an orientation about the field of mathematical biology itself. What exactly is it?
Mathematical biology is basically taking tools from mathematics and applying them to biology, similar to how people have been doing that in physics and engineering, and some of the earlier areas, or initial areas of mathematical biology included modeling diseases and how diseases spread through a population, as well as population growth. So many people are familiar with exponential population growth models to predict the population of the world in a hundred years, and this is one component of mathematical biology. Beyond that, people have used mathematics to understand neurobiology, fluid dynamics, biomechanics, cellular processes, and just about all areas of biology.
I see…Now, by adding in the element of fluid dynamics, you’ve really carved out a unique area of research…tell us how that enters into this picture…
The body is made up mostly of water, and that’s true of most organisms. And so understanding fluid dynamics is important to understanding how the blood flows in our bodies, how air enters our lungs, and for other animals, how they swim and fly through the air and water.
How did you become interested in this particular area and choose to pursue it?
Back when I was in high school, I wasn’t sure if I wanted to do mechanical engineering, or biology, or mathematics, and I cycled through all of them. For a while, I wanted to do aerodynamics, and then I was a bio major in undergrad, and eventually became a mathematics Ph.D. student, and found a way to slowly combine all three areas of interest.
So how did you combine those three fields in your Ph.D. work?
My Ph.D. was based on the aerodynamics of insect flight, in the smallest flying insects. And what I did in order to study this, since the smallest insects are only half a millimeter in length, they’re very difficult to study, even with video cameras. They flap their wings at 2-300 hertz, and the depth of field for filming them is very small. Now recently I have been able, with some of my collaborators, to film them. But back when I was a Ph.D. student the technology really wasn’t available. So the idea was that you could use mathematical analysis to study things that were experimentally difficult, and insect flight aerodynamics was one of these. And the question I wanted to understand is that as insects got smaller and smaller and smaller, how does flight aerodynamics change? And you can use mathematics to come up with an equation that describes the motion of the air around the wings, which you can’t solve with pen and paper; you have to use computers. And that was the basis of my thesis, combining biology of flight with aerodynamics with the mathematical models.
So that was really a model of where your work was going to go subsequently…
Exactly. So since then, I have studied problems in jellyfish swimming and heart development, using the same approach—taking the equations of fluid motion and using them to understand how the blood flows in the embryonic heart, which again is a problem that is difficult to pursue experimentally. Obviously, in human embryos it’s virtually impossible. In jellyfish swimming, the useful thing that you can do is to design jellyfish that you wouldn’t find in nature, to see how that messes things up. So what are the essential things that jellyfish are doing? And that’s a question you can probe by changing the jellyfish in some way and seeing if it still works. And unless you were going to get into the strange genetic engineering, it’s much easier just to make a mathematical jellyfish.
You have a virtual jellyfish, then…
Neat! Laura, fluid dynamics is largely an unknown, almost completely ignored field within biology…why do you think that is? Because your work has certainly shown that it’s a vital element of biological systems…
Interestingly, although it isn’t a focus of what you would find in an undergraduate education, let’s say, people have been doing these experiments for hundreds of years. Da Vinci made a model of the aortic valve, and looked at flow through it and the vortices that formed in the valve. And Harvey was another pioneer in terms of physiology. In current biology, there has been a strong emphasis on the Human Genome Project and biochemistry, and biologists typically get trained with a very strong chemistry background, which really doesn’t leave much time to also learn mechanics. And as a result of the education process, you don’t have a whole lot of people in biology exploring problems in mechanics, but that’s starting to change, particularly as engineers in mechanical engineering have become more and more interesting in biomimetics, which is basically using biology to help engineering design. So there are a number of engineering departments across the country that are starting to look at cardiovascular flows, as well as animal locomotion, swimming and flying, and they’re collaborating with biologists. And there has always been a small school of biologists that have been looking at fluid dynamics, and one of the strongest groups came out of Duke University back in the 70s—a local group that’s been studying these things for a long time.
I see. So the trend, perhaps, towards cross-disciplinary work in the field in general is moving in this direction; that mechanical engineers and fluid dynamics people are starting to become more involved in the biological sciences…
Definitely. And you can go to the meetings of the American Physical Society and find very large sessions of people from physics, engineering, and mathematics starting to look at biology problems. You can also go to biology meetings and see engineers, mathematicians, and physicists starting to attend those meetings. And a lot of groups that are working together and writing grants together and publishing together from disciplines that used to very rarely talk to each other.
Laura, I know that you are investigating three main scientific problems, and you’ve touched on each one of them briefly, but could you tell us a little bit about each one of the problems you’re looking at?
Sure. So the insect flight problem…below a wingspan of about, let’s say, half a millimeter or so, you don’t find insects that fly by flapping their wings. And it’s a big question in the field why that’s true. So what is limiting miniaturization in biology? And as you begin to study these insects, you find that as they miniaturize over evolutionary time, the flight aerodynamics change. So viscous or sticky forces become more and more significant, and you can think of the insect as really rolling its wings back and forth in corn syrup. So it’s very different than the flight of airplanes. And it becomes difficult to produce lift, and as the insect flaps their wings they actually start producing more drag than lift, so flight becomes increasingly inefficient. And around the smallest insect that you’ll find, when you do the simulations of the insect flight, what you’ll see is that right around this point the drag forces relative to lift start really increasing quite a bit. And so if the insect were to fly anywhere, most of the energy would be lost to drag.
So what about the other two problems you’re looking at?
They’re both related to this one.
So I’ll talk about jellyfish swimming. Similar to insect flight, there’s a size limit for swimming, either fish swimming or jet propulsion, and it’s probably roughly around one millimeter too. So any animal that uses flapping fins or jetting hatch from the egg at some particular size, and then they grow from there. So it’s another question of, why do you not see fish or octopus or squid that are smaller than this size? And so what our simulations are showing is again that viscosity becomes increasingly important, and something happens around this lower limit where, let’s say you’re looking at a jetting jellyfish. So the jellyfish could contract its bell, and move forward. And then when the bell expands or re-bells, it gets pulled back to exactly where it started. So we make these virtual jellyfish, and they try to swim. They squeeze the bell, they move forward, expand and move back. So they just don’t get anywhere.
So at that level of viscosity, it’s kind of like running in place…
Exactly. And there was an interesting historical incident in Boston, where there was a huge molasses spill, and so people and horses and animals experienced this as they tried to swim or escape from the molasses, they couldn’t do it, and the more that they struggled, the deeper into the molasses they got. You can really think of trying to swim at these scales as being like, similar to trying to swim in molasses.
I see. That’s fascinating. And that was back around the turn of the century…
That’s right. So the same trade-off between viscosity and inertia is important for pumping, too. And when the human embryonic heart first forms, it’s about the width of a thin hair, and it’s a tube, it’s not a four-chambered, four-valve pump. And it grows to be about the size of your fist, and the chambers and valves form during the growth. Viscosity dominates when it first forms, and in the adult heart it’s inertia that dominates. And the heart has to grow through these sizes and change its morphology as it grows as well. During the same scale where we see the transition to jetting and flapping and swimming, we also see a transition to valve and chambered hearts. And as the heart grows, it goes from this tube that uses this sort of valveless pumping mechanism into the chambered heart. And the fluid dynamics change quite drastically during this stage, and the flow really isn’t well-understood at all.
It’s important because the cells that line the inside of the heart are sensing the fluid and responding to it. So the forces the blood is putting on the walls of the heart are a signal that help the valves form and the chambers form, and as the flow is changing as the heart grows and changes in shape, the forces are changing too. The details of this process really aren’t understood, but the idea is that if we know what the flow should look like, then we could use some diagnostic tools to figure out when the flow is not correct, and use that to diagnose congenital heart disease. And perhaps we could also use the fact that the growing heart responds to the flow in order to use something like microfluidic surgery to re-shape the heart and the valves if they aren’t forming correctly. So that’s a long-term goal, and at this stage we’re just trying to figure out what the flow should be doing at all.
I see. And that’s really true of all three areas you’ve described, that the mechanistic means of dealing with that flow change at the different sizes.
And these scales of flow are not well understood because they’re hard to deal with mathematically, and also experimentally. So if you look at the field of aerodynamics, in terms of planes and helicopters, very large scale, you can take the equations of fluid motion and drop out some of the terms, the ones that deal with viscosity. And that makes the math much easier. And at the smaller scale, if you look at the flow that’s happening inside one cell, for instance, you can neglect inertia and just look at viscosity, and the math becomes much simpler. But in between you really can’t make these simplications, and you have to do large-scale simulations on a computer to figure out what’s going on.
And it’s that mid-range that you mainly are exploring, right?
Tell us about some of the methods you’re using, because you have to come at some of those questions from a variety of angles to get some answers, right?
We try to combine numerical simulations with experiments that use physical models. One thing you can do in order to make an easy model to deal with tiny insect flight is that you can build a robotic insect that say has a wingspan of a foot, and then put that insect in mineral oil or corn syrup, and then the balance of inertial to viscous forces is preserved. So it’s very hard to work with an insect that’s only half a millimeter in size, but then if you have a robot that’s a foot in length, than that’s much easier.
So you’re just scaling up, basically, to make it easier to work with.
Yes. And then we can use the results from those experiments to validate our numerical simulations to make sure that we’re getting the right answers and that our model is correct. And then we do have to do some work with the actual insects in order to figure out how the wings are flapping, what the frequency is, how they’re changing angle of attack. And we use the same three-pronged approach for the embryonic heart problem and the jellyfish problem, although at this stage we don’t have a robotic jellyfish, but maybe down the road we will.
Well, we’ll have to come back and see that! Laura, what are some of the potential practical applications of the insect flight work?
One thing the engineers are trying to do is to design micro air vehicles, for surveillance work. That could either be for the military or in outer space. And if you want to have a small-sized flyer, you can’t design it like an airplane. So what engineers have tried to do is to design these micro air vehicles to flap like insects. But until recently very little was understood about how insects with flapping wings actually generated lift. And a lot of advances have been made from teams of biologists working with engineers, mathematicians, and physicists. And the problem is fairly well understood for larger insects, but the question is, if you keep miniaturizing these insects, what’s going to happen? And you can look to biology for an answer to that. So it seems likely that at some size, probably around a millimeter in length, that a robotic insect just wouldn’t generate enough lift to fly. So that’s going to be your limit on how small you can make such a micro air vehicle. But now if you start talking about going to other planets, viscosity and density of the atmosphere is different. So on Mars, for instance, you might be limited now at, let’s say, a wingspan of half an inch instead of half a millimeter. And if you go to Europa or somewhere like that, it could be even different. So rather than spending a lot of time designing a micro air vehicle, sending it to another planet and figuring out that it’s just impossible to make such an insect fly, looking at the scaling arguments for what sort of mechanisms of flight work at what scale is going to be important.
Now the same thing is true if you have swimmers. So if you have a nanoparticle that you want to put some sort of self-propulsion mechanism into, then you have to know what’s going to work at that scale, too.
Which is certainly something that’s being actively looked at in bio-nanomedicine.
Definitely. And one thing that you would probably want to do is to try to design it like a bacteria, since it’s going to be about the same size. And maybe you would put a flagella onto this nanoparticle. A flagella is basically like a corkscrew that spins. If you try to put flapping fins on the nanoparticle, because of the same argument before where if you had the fin flap forward, the nanoparticle would move forward, and then flap back, it would move back to where it started, and it just wouldn’t get anywhere. But what becomes even more interesting for these biomedical applications is if you start changing the fluid from blood or water into something that has more complicated properties, like mucus in your stomach or in your lungs, the rules for all of this change. So you can potentially have something that’s propelled by a flagellum, that can swim in water. Say you drink a nanoparticle with a flagellum, and then that nanoparticle needs to get through a lining of mucus. Is it going to work? And it might not. So figuring out both how scaling and then these complex properties of fluids and mucuses change the rules for what methods of locomotion works when, is another area that we’ve started looking into.
That sends you right back to the computer to re-model, right?
Laura, we’ve actually picked up and moved from your office upstairs here at Phillips Hall on the UNC campus and moved a few floors down to the basement, where you guys have set up some salt water tanks for your sea animal experiments and observations. Tell us more about what you’re up to with these tanks, and I understand it’s also been a pretty challenging process getting these things set up…
One of our main goals is to do some experiments on an upside-down jellyfish. So we want to measure the flow velocities around the bell as the bell contracts and expands. And the first tank that we got, we mostly wanted to see what it would be like to keep a salt water tank. And in this tank we were actually able to set up an ecosystem. So as we fed the arrow crab, for instance, which you can see right now, and the brittle star, and food that’s left behind gets picked up by these two animals, which are scavengers. And there are a number of filter feeders, sponge and some sea squirts, that are growing as well. And this tank we have absolutely no problems with. But the jellyfish tank, because the jellyfish are so sensitive, we can’t keep other animals, or rocks, in with them. They’re basically made of jelly, and any corners or hard surfaces can tear the bell.
Now another challenge with raising them is that they have zooxanthellae, which is symbiotic algae that live inside of them, and the condition for keeping them healthy is the same as keeping algae healthy. So we have a very bright metal halide lamp that is designed to provide light into the depths of the tank, and then we feed them brine shrimp. But they don’t capture all of the brine shrimp, and the brine shrimp decay, and the algae that’s already in the tank start growing exponentially because of the light and the debris. And then we have repeated algae blooms, and we have to change out the salt water pretty regularly. So what we’re doing now is to try to re-design the tank, add a protein skimmer, more filters, and set up the tank so that we can control the algae blooms a little bit better. One thing that we’re going to be doing, because if you have the filters in the tank close to the jellyfish the jellyfish can get sucked up into the filter and destroyed, so we’re basically going to divide the tank into two sections with the soft mesh, and have filters and heaters and coolers on one side, and then the jellyfish on the other.
So this is where you really put the biology into mathematical biology.
Exactly. And it’s good for the students too, just to see how difficult it is to do work in biology. Most of the mathematics students take theoretical classes; they really don’t do much lab work. And any lab work they do is in an introductory class where the experiments work, and there is a recipe that you follow, and everything is made to work out nicely. But with real experiments, things don’t work like that. So for instance, we plan to do some filming and then there is an algae bloom and we can’t even see the jellyfish. Or we did something wrong, and the one jelly we had went up the filter. Something terrible like that. So the students are really learning that even just keeping animals is quite difficult, and then working with them requires quite a bit of patience, and is not at all easy.
On another level, you have to constantly check your mathematics to what’s going on in reality. So you can make simplifications that make your life easy, but then if the results don’t match the biology, then you have to add the messy details, which no one really likes doing until they start working with the animals, I think, and then understand that you gain a deeper appreciation by combining the math with the biology work.
And I’m sure at that level they’re able to see the actual real world implications of the numbers…
They’re also able to see that there are a lot of things that we just don’t know about biology. Biology isn’t like mathematics, where you can write down a proof, and you know that you’re right. You can think you’re right and actually end up being wrong because of the complexity, and just how much isn’t known about the natural world. And the students really get a sense of that when they work down in the lab.
Thanks for showing us the tanks, Laura…
So what types of experiments are you able to conduct by having the animals on hand?
One thing that we’re doing is using PIV, which is Particle Image Velocimetry, to measure the flow velocities around the jellyfish as they pulse. And what that means is that we shine a laser sheet through the aquarium, over the jellyfish, and that illuminates particles in the fluid. This could be some food debris, or dirt, or stuff that we actually put in to do this. And then we take two snapshots, and you can see the particles move a little bit between the two snapshots. And from that what you can do is figure out how much the fluid is moving in one small region of the flow, just by looking at how far those particles moved during some length of time, and then velocities, just change in distance over change in time. What you can get from that is a picture of the jet that comes out of the jellyfish bell as it pulses, and how the fluid is brought into the bell during contractions. And then what you can do from there is compare it to the simulations of the virtual jellyfish that we’re doing, and make sure that our simulations are right. Now this isn’t so easy, because you can’t put all of the complexity of the jellyfish into a simulation. The jellyfish have oral arms and tentacles, and they aren’t completely symmetric, and as mathematicians we initially just like to make them a symmetrical dome without any arms or anything. And does this matter? And in some cases it does, so we have to slowly add more and more of the details into the mathematical model to get things right.
This is really valuable for the students, because I think that we all have a tendency, after we have worked hard on a project, to believe that it’s right, and to hope that it’s right, because if it’s not we have more work to do. When the jellyfish is right there in the lab, and you can compare the result, then you have to compare your theoretical model to reality, and you have to face the fact that sometimes you have a whole lot more work to do.
Right. But that sounds like a lot of fun, in its way…
Oh, definitely. We’ve definitely had more visitors come down to the lab, and asking questions about the type of things that we’re doing, and the students get more involved. I think they make more time for research, too, because they enjoy working with the jellyfish so much.
Where is your research headed at this point, Laura? Will you continue along the lines you’ve been exploring up to this point, or are you contemplating new directions?
A large part of what I’m doing will be along the same lines. One thing that I would like to do is to expand to more areas of biology also related to mechanics. For instance, we’ve been focused on looking at fluid dynamics, and wings flapping and fins flapping and so forth, or chambers contracting, but how are these things moving and contracting? You have to look at the muscle structure, and also the neurobiology. With the jellyfish in particular, what I’d like to do is to start modeling the actual muscular structure of the jellyfish bells, and how that muscle is activated, and put that into our mathematical models and numerical simulations. So we can see, how is the organism actually generating this bell motion that’s moving the fluid for eating and propulsion. And how does muscular structure and muscle orientation change as a function of size? And as the fluid dynamics change, how does the muscular structure have to change to adapt as well? One major focus, then, is to expand even more into the solid mechanics in addition to the fluid mechanics.
It sounds like you have plenty more work to do…
A lifetime, I think.
Terrific…Laura, it’s been just fascinating to have the opportunity to learn about your work and your field…thanks so much for joining us today on FOCUS In Sound…
Thanks very much for having me.
We hope you’ve enjoyed this edition of the FOCUS In Sound podcast. Until next time, this is Ernie Hood. Thanks for listening!
Image credit: Dan Sears, UNC News Services