What a Mouthful! Modeling Geographic Tongue as a Reaction Diffusion System

May 4, 2020   /  

Student: Margaret McGuire
Major: Mathematics
Advisors: Dr. R. Drew Pasteur, Dr. Robert Kelvey

CoRE Award for Critical Digital Engagement
1st Place (tie)

Margaret McGuireGeographic tongue is a condition of unknown cause characterized by chronic lesions on the surface of the tongue. The condition’s appearance of wave fronts suggests the condition can be modeled as a reaction-diffusion system. Here we construct a model of geographic tongue using reaction-diffusion equations and Objective-C to suggest that the underlying cause of geographic tongue may be a reaction-diffusion system. We demonstrate and explain the model’s behavior on a sinusoidal surface and on a hemisphere to illustrate its qualitative similarities to laboratory experiments. We show our final model of reaction diffusion waves propagating on the tongue and compare it to patients who have geographic tongue. We then identify next steps in modeling and future projects that would extend our work.

*This presentation is only available to College of Wooster students, faculty, and staff.

View on Microsoft Stream

Margaret will be online to field comments on May 8:
10am-noon EDT (Asia: late evening, PST 6am-8am, Africa/Europe: late afternoon)

44 thoughts on “What a Mouthful! Modeling Geographic Tongue as a Reaction Diffusion System”

  1. Hi Margaret 🙂 If you are able to simulate the tongue and these lesions very well, what implications does that have on a future treatment/cure/anything else about the condition?

    1. Hi Dr. Morrison,
      Once we know it is a reaction diffusion system, we can begin to ask the questions, “what are the likely chemicals and/or cell lines that might be reacting and then diffusing across the tongue?” We know the filliform papilla are stationary and act as excitable media, so we might then look at the histology and examine them for mobile cells, for example, perhaps it is a hyperactive cell line invading the tissue that is part of the immune system.

  2. Hi Margaret,
    I liked your presentation and your method of presenting the material! As a chem major, I’m really interested in the BZ reaction. Could you tell me a little bit about how they were able to simplify the ten chemical equations down to the eventual two that you used? Did they have to make any assumption when developing this model?
    Congratulations on being done!

    1. Yes indeed, a good 15 pages thereabouts of the IS was purely slogging through exactly how you can make those simplifications, and there’s lots of assumptions. So there are 3 processes taking place in the BZ reaction, call them A, B and C. At high Br-, A is the dominant process, then when it depletes the Br-, B becomes dominant, then B produces Ce(IV) which then begins C, which replaces the Br- and A starts up again. Process C is mostly understood but the exact mechanism remains fuzzy, so it’s simplified to one non-elementary reaction where “f” is the stoichiometric coefficient on the Br- produced, which is variable depending on what is actually going on in process C because depending on the current conditions in solution it will produce more or less Br- (it’s kind of wild, I think there’s more than one possible mechanism of process C and not all of them are fully understood.). Then for each process you throw out the equations that proceed virtually instantaneously relative to the others, then you assume your proton [H+] concentration in solution is so high that the concentration is constant despite [H+] being consumed in small amounts so that you can absorb the value of [H+] into your rate constants for the remaining equations. Then you’ve cut the number of rate laws down a bit, and you can then combine rate laws to track the change of the chemical species of interest over time. An example of what one of these formulas would look like is:

      dY/dT = 1/2 * f * k_(o5) B*Z – k_(o1) A * Y – k_(O2) X* Y

      Where A, B, X, Y, and Z are all theoretical chemical species involved in the reaction after you’ve made the above simplifications. This is one of the three equations you get from the 5 rate laws of the Oregonator model. Later, you non-dimensionalize the equations and make one more assumption about the relationships between the rate constants that allows you to drop one more equation and you’re at the Tyson Fife. It gets pretty hairy at the end with the algebra and the theory, but you can find the full derivation on pages 13-26 of the IS here if you so desire, it’s fun stuff: https://www.overleaf.com/read/zxhthrcfwgzp (view only Overleaf file)

      1. Thanks for taking the time to write out a reply that answers my question. It makes a lot of sense and I can empathize with the pain of trying to wade through rate laws (although it is nothing compared to your’s)! I’ll definitely check it out in your IS! Also, I’m not envious that you all have to write your IS in Latex.
        -John

        1. Haha, trust me, once you get used to LaTeX, you can’t go back! You should send me your IS too sometime.

  3. Congratulations Margaret! What (if any) are the negatives of not using the 10 equation model versus the 2 (Tyson-Fife) equations that you selected? You stated it was simpler to code 2 versus 10 (or 5), but wondering if there was any loss of benefit using the more simplified model? I really appreciate that you were using a curved, non-linear tongue model to extrapolate your diffusion reaction — seems much more logical to me. Best wishes!

    1. This is a super fascinating area. Of course, you are definitively losing something when you simplify the picture so much. Of particular interest to me was that in the Oregonator model, the spiral patterns produced from the simulation will actually migrate their center over time (as occurs in real life for these systems), as opposed to remaining stationary as in the Tyson Fife. So I can tell you at least one of the emergent features of the system is lost in simplification. Ideally in the future we can move up one level of complexity to use the Oregonator in future modeling (in fact, we did implement this as a proof of concept that it can be done, we simply did not continue with it past that point due to limited time and the added computation it requires). I currently do not know of any researchers that have ever used a complete model that makes no simplifications, probably owing to the complexity of it.

  4. Margaret, it is always cool to see students connect mathematics to their other academic interests. It wasn’t clear that this was going to be easy with dentistry, but you have done a very nice job of this both in your junior (M225) and senior projects!

  5. Congratulations, Margaret! My daughter has GT and I noticed the pattern changes over time. It doesn’t seem to affect her taste buds other than being super sensitive with spicy food. Is it genetic? Can normal tongues grow into GT? What factors may have affected the pattern changes? Any treatment? Thank you and best of luck with your future endeavors!

    1. These are exactly the types of questions that motivated the IS. As of now, there is no definitive treatment for GT and very little evidence to suggest a genetic link or apparent cause of the condition. While it seems to be possible to develop GT over time, it is usually noted in childhood and persists throughout life, suggesting those who “developed” it may have just been unaware of it or had a mild version in childhood. While there are a number of people arguing that it has an auto-immune basis because it is frequently found in people with psoriasis (and sometimes even gets called psoriasis of the tongue!) this connection is not definitive because many studies has shown that you can have GT and not have any other apparent medical problems. I think because it is largely benign it has been understudied and there is lots of conflicting evidence for how propagation is affected by environmental factors like foods or medications, for instance, so these questions remain unanswered to a satisfactory degree.

      1. After your email went out looking for volunteers, I talked to Dr. Manz. My daughter would be happy to help with the GT research if you’re in Wooster. I was first made aware of her GT from her Chinese pediatrician (after we moved to China from Indonesia). She was 5 years old then. I had always thought that she got her tongue burnt due hot meals (lack of tolerance of hot meals). I didn’t think much about it nor checked on her until the email came and she’s 16! With God’s blessings, she always has good health and rarely gets sick. Good luck with your future research and career. Again, you did a great job!

  6. Congratulations on your IS, it is a huge accomplishment. Your project caught my eye b/c I have geographic tongue and don’t know of many others who do. I always thought it was due to a vitamin deficiency (my mom told me that). While methods and math are WAY above my understanding your project sounds really interesting and I hope you find lots of avenues to extend your work.

    1. Hi Cassandra! Vitamin deficiency may be a contributing factor, but as of now it is not reported as a definitive cause. It does tie into the possibility that GT is related to immune deficiency or over-reactivity, as vitamins can impact/modulate the immune system.

  7. Great job Margaret! Your I.S. is super interesting. Do you plan on continuing this research? If you are, how do you plan on incorporating it into dental school?

    1. Hi Emily! I’m not sure in what capacity I will be able to continue this project. I definitely want to put together a paper to publish about it, but it may be that when I get to dental school I’ll find a new research team with a totally different project that I’ll want to be part of. I really miss doing statistical analyses in R, so I might find a team of people who want me to help them with that if possible.

  8. Great framing of your question and process throughout your presentation. It’s wonderful that you’ve initiated and pursued this cross-disciplinary study that integrates your interests in mathematics and dentistry. The curvature element of your model is a logical and helpful extension of the (limited) literature on this topic as well. Congratulations!

    1. Hi Katie! Thank you! I was also extremely pleased by what a great opportunity this was to employ cross-disciplinary techniques and topics. The truth is, I’m just as excited about biology, chemistry and dentistry as I am about math, so this was a perfect project to bring those interests together. Never a dull moment!

  9. Excellent work, Margaret! It was a pleasure to get to know you these past few years. I have a few questions:

    -Why did you choose the boundary conditions you chose? What is the “boundary” of the actual tongue, as it applies to GT?
    -Have you considered how you might model the shape of the tongue more accurately?
    -Did the book I lent you end up being at all useful in what you ended up doing? And, did you end up using the stuff we decoded from that other textbook?

    I also had a question about the 10 equations versus 2, but others have asked about that and you’ve given quite thorough answers.

    1. 1) The boundary conditions allow the wavefront to propagate off the “edge” of the tongue and effectively annihilate, which is in theory what would happen on the tongue once the wave met a tissue on the tongue that was not predominantly filiform or, is filiform that are not susceptible (perhaps something has to make them permeable/susceptible, i.e. they have to be primed by something else happening in the tissue? We don’t know yet). So in standard GT the boundary is where the filliform tissue gives way to the lining of the bottom of the tongue or possibly where the foliate papilla begin (these are on the edge of the tongue) or they stop as you move farther back in the tongue where the papilla types changes, but it is hard to say exactly where it stops in some images. The problem is further complicated by the fact that some people get GT-like lesions on the bottom of their tongue or even the roof of their mouth where the tissue type is some other type of squamous cell and entirely unlike the filiform (for example, see https://ars.els-cdn.com/content/image/3-s2.0-B9780323552257000166-f016-044-9780323552257.jpg ).

      2) One really cool thing we managed to do early on (though we later altered the code and didn’t save a functioning copy, oops!) is make a simulation of a sinusoidal surface whose amplitude varied with time and propagated a wave on that. If we could implement something like that for the tongue, then we could account for the tongue’s movement and thus variation in curvature over time. I suspect, however, that though the tongue moves around a lot, its usual resting state is the same, so the temporary manipulations through speech or eating may have less of an effect on a long term process such as GT than we might initially think. But having the functionality in the program would be ideal!

      3) I’m blanking right now on exactly what it was that you and I were working through that one day (feels like so long ago to me, not sure why), but I do remember we were struggling through something… I think that book helped me with brushing up on some MVC stuff I was forgetting in the moment though!

      1. I don’t remember exactly what it was either. It was something with an operator, where there was an annoying distinction between two things that were basically actually the same thing.

        I know that one thing that is sometimes done with numerical PDE on complicated surfaces is triangulation. In this case, this could mean taking an actual tongue, triangulating it, and then numerically solving the PDE system on the resulting triangulation.

        1. Yes! Perhaps we were trying to distinguish the difference between the first fundamental form and ds^2, the line element. I think I present them in separate sections but then later say they’re effectively the same for our purposes.

          It would definitely be interesting to be able to 3D scan a tongue and extract a mesh from that. I presume that would take us down a Finite Element Method road, or at least require some more advanced software. I’m not very familiar with triangulation, and how much different it is than breaking the mesh up into squares like we did.

  10. You spoke a lot about propagation…With “geographic tongue” is the pattern of lesions static or dynamic? (i.e. does the pattern on the tongue change over time)

    1. It may depend on the patient, but for the most part the white front that you see on patients with GT does move over the surface of the tongue over time. So for example, you might have a point of excitation, and then outward from that point a front will propagate out in all directions, though often faster in some regions than others, causing an oblong shape. Then eventually that front will hit a point that it dies away, and a new one might start up at the same origin point, or a different point. The lesion is extremely dynamic, which is one of the most fascinating aspects of it; it has captured the attention of doctors and scientists throughout history as evidenced by the woodcut prints from the late 1800s that track GT’s progression in two patients, which I included in my IS.

  11. Congratulations Margaret! We enjoyed watching your video! Super cool that you were able to connect math to dentistry so smoothly (with curvature 😉 ! Good luck at dental school, please stay in touch, and Carys wishes you many more opportunities to wear your pink wig 🙂

    1. So good to hear from you both! And yes, the pink wig lives on alongside a teal 1980s jumpsuit- they will probably find their way to some performances at the many fun venues of Chapel Hill in the future… Very excited as we both step into the next phases of life!

  12. Margaret. Congratulations on some many wonderful successes during your time at Wooster. We will miss you! Great video, by the way. Best wishes, and keep finding ways to do math!

  13. Congrats on the award, Margaret! It’s super cool that you got to combine your interests in this project!

    1. Thank you Maya! I was super stoked about how interdisciplinary this project turned out to be. And congrats to you as well!

  14. Hi Margaret. I am so proud of you and all that you have accomplished at Wooster. It has been so wonderful to work with you and to see you enthusiasm and your hard work pay off in such a beautifully executed project. What a fabulous job! All the best as you go to NC. Keep in touch!

    1. Hi Dr. Pierce! Thanks so much, and thanks for letting me talk your ear off whenever I wandered into your office. I missed you during senior year!

  15. Margaret, this is a really cool and interdisciplinary project. I think only someone like you, who understands knows about chem, bio, and math could have done it. Great job! Missing you 🙂

    1. Literally all the same to you, Pedro. You were colliding worlds in your project too! And I miss you too but we will find ways to stay connected!

  16. Thanks for sharing this important project, and in such an engaging and accessible way! And congratulations on winning the Critical Digital Engagement prize!!

    1. Thank you! I’m glad you found it engaging and accessible, that’s something I strive to achieve when I make videos like these!

  17. Dear Margaret,

    Congratulations on your IS! This is a really interesting project, and it is great to see the way that building in curvature of the surface provides such an improvement in the ability of the numerical model to approximate what is seen in this condition! You are very good at explaining complex things in a way that is compelling to a non-expert. I felt like I learned a lot in just five minutes. I hope that you enjoyed doing this project, and I think you are right that it should be published somewhere.
    All my best to you for all of your future endeavors. We will miss you! Best, Pres. Bolton

    1. President Bolton, I am so glad that you found the video compelling. I think it’s really important to be a good communicator in science and math research and I am pleased to hear you felt that this video accomplished some of that goal!

  18. Margaret, I was so impressed with your project! What a brilliant integration of one’s clinical and mathematical interests. It sounded from your answer to a previous question as though you anticipate possibly not being able to publish this work because you will – of course – need to synchronize with your new colleagues’ research priorities. So would it make any sense to publish it strictly as a methodological piece without any further data (‘here’s how to do it, here’s an initial bit of data to demonstrate, here are all the tricky bits we know of… now good luck to you refining it’)? Or even as a preprint? Might others be inspired to pick up the initial model and methodology and push it down the court? It’s not my area, so this thinking could be all wet. Thank you again for the inspiration.

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