Creating quasi two-dimensional, curved molds with 3D-printing technology

Diego Miramontes Delgado

2016

In this thesis, the modeling software Rhinoceros was used to create planar and non-planar media in which to study reaction-diffusion systems and especially the Belousov-Zhabotinsky reaction. Geometrical conditions such as surface curvature and topology determine the stability or dynamical conditions that are not possible in planar systems. The first mold created contains a hollow region of depth 0.4 mm with two complementary curved surfaces described by the equation z(x, y) = |A sin(bx) sin(by)| surrounded by a planar region which allows wave fronts to propagate.

Another important aspect in the study of nonlinear waves is the study of how obstacles affect the propagation of waves. In cardiac tissue, nonexcitable tissue acts as an obstacle to electrical waves in the heart, which can cause vortex shedding and result in abnormal heart activity and in many cases death. Planar molds were created to test the influence in the propagation of planar wave fronts of four different obstacle shapes (square, rhombuses, circular and elliptical), orientations and sizes. The previously theoretically studied influence of square obstacles is complemented by the creation of analogue curved obstacles of the same dimensions as their square pairs.

Cortical spreading depression has been shown to trigger migraine auras. A fMRI of the visual cortex provided by Dr. Hadjikhani from Harvard Medical School was exported into Rhinoceros and converted into a mesh. This mesh was subsequently converted into a mold with a hollow region of depth 0.4 mm that traces the surface of the visual cortex. This mold will allow for the first time to study spreading depression on a geometry that is extremely similar to that of the visual cortex.