Modeling

Abstract & Introduction

Mycelium is an ideal candidate for the construction of building materials on Mars due in most part to its replicability; a builder will end up with more material than he brought with him. However, while concrete and rebar are not easily transported, they are conveniently measured in volume and in weight, and a builder can precisely simulate the things that he can build given his material constraints. The model developed for our project attempts to confer this ease of measurability onto mycelium in order to better understand its utility as a building material—given a starting amount of mycelium, how much can a builder grow given his time constraints? Alternately, if a builder brings fillable molds and a starter colony of mycelium—how long will it take for his fungus to fill the mold? I constructed a Python model to answer these questions, and to simulate the fractal and competitive growth pattern of mycelial hyphae, in the hopes that it will be used to inform others’ efforts in growing mycelium in the future.

Materials and Methods

To begin, I got growth data—a few weeks’ worth—from the growth team responsible for actually growing mycelium in the lab. I put this data into a spreadsheet and ran various regression analyses on it. I found that an exponential model fit the data with high fidelity, with an R2 value of 0.93. I devised an exponential growth model in Python and ran several simulations. However, I found that the data for the quantity of mycelium grown was dubious as growth periods grew longer, giving enormous values that did not reflect the data gathered in the lab. I began researching models online, and eventually found a tumor growth model, called the “Eden Model” (after the person who initially developed it; the link to the literature I referenced is given in the “Discussion” section of this page). I was interested in tweaking the Eden model for mycelial growth, because the way that tumors grow is remarkably similar to mycelial proliferation: both incorporate substrate adjacent to their borders into their bodies, initially growing incredibly quickly but becoming “crowded out” by their own bodily projections as they grow ever larger. I had to code a model into Python from the ground up. The first successful model that I devised was for unconstrained, 2-dimensional growth of mycelium. While this was an exciting development, I doubted this model’s utility for our purposes, because in our lab we’d been growing mycelium within molds (which are both constrained and 3-dimensional). So—could I tweak the 2-D model to more accurately reflect the lab’s objectives? Luckily, the “3-tiered” growth pattern that I’d incorporated into my 2-D model provided the solution. The 3 tiers of the model were “grown”—sites that have grown mycelium—; “growthsites”—sites that will grow mycelium—; and “target”—sites that might grow mycelium. On each day of growth, each “grown” site has the opportunity to stake its claim on a “growthsite”/”target”. It becomes increasingly less likely that a new target site will be found by a grown site as the grown site finds itself more crowded by other grown sites (this accounts for the competition between hyphae in mycelial growth). We’d found in the lab that 3-D growth generally does not occur in a mold until the mycelium has filled the base of the mold. Therefore, I inserted a provision that “target” sites could be neither “growthsites” nor “grown” sites until the area encompassed by the “grown” sites was equivalent to the base area of the mold. Only then could the mycelium grow upward. How could upward growth be modeled? Once the base of the mold had been filled, the model would change the parameters of the “target” sites: “target” sites could only be “grown” sites. This ensured that the mycelium could only grow on top of itself, and only upward. The competition provision—that a “grown” site could not secure a “target” site if that site had already been claimed as a “growthsite” by another “grown” site—was still intact during this new, upward period of growth. This was the most involved period of coding, and involved five separate attempts before a suitable sixth model was developed.