3D printing is a relatively new invention that could prove to be the next printing press when it comes to the sheer possibilities of what it could produce. This fact is especially true for the fields of medical science and tissue engineering, where it will soon be feasible to print artificial organs or skin to provide to the sick and injured.
One such possible new product are lattice-frames on which to grow artificial skin for burn and trauma victims. To illustrate possible uses, imagine that a hospital could grow shaped lattices out of a biodegradable material, seed it with self-replicating cells and leave it in storage until the cells self-multiply until ‘filling’ the frame. Once complete, the artificial skin could be immediately applied to a patient similarly to a cast or bandage.
My research project’s primary aim was to simulate such a scenario on a basic square-frame lattice, by solving the equation that governs the cell behaviour under these circumstances: the generalised Porous-Fisher equation. The crux of my work revolved around solving this equation, as it possesses no closed-form solution, meaning that numerical approximation methods had to be used in order to generate results.
Because approximations had to be used to find solutions, there were no ways to properly verify whether the results are actually correct. To address this problem, I investigated simpler equations that were similar to Porous-Fisher which did possess analytical solutions. After confirming the accuracy of the approximations compared to these analytical solutions, I had enough evidence to support the accuracy of the solver and confidently perform Porous-Fisher simulations over a two-dimensional domain.
In a future research project, I aim to expand the scope of my simulator/solver in order to investigate more complicated lattices, as well as record these results for further analysis alongside other researchers currently working in this field.
Queensland University of Technology