A novel algorithm of the digital nervous tissue phantom creation based on 3D Voronoi diagram application

Abstract

The essential part of mathematical modelling of nutrients convectional reaction-diffusion is creation of a digital phantom of considered biological object. This process becomes an especial problem which needs to be solved before numerical calculations of the concentration gradients will be done. There are two principal ways to get the solution in this case. The first approach is the reconstruction of a digital phantom on the base of the experimental data directly. The second one is the creation of a virtual object according to the experimental evidence and the known principals de novo. The main advantage of the created phantom is a high adaptability to modelling demands and a physical problem formulation. In the present study a new algorithm of a digital phantom creation has been established. The principles of the claimed procedures are demonstrated by the example of a nervous tissue. Initially, one needs to create N 3D objects according to Voronoi diagrams. Each object has 144 edges and 69 boundaries on average. Having chosen M rear objects, a long 3D structure mimicking neurons axons is created according to a loft procedure from the start boundaries to the end ones. Then, the set of Boolean operations has been applied to form continuous smooth objects. The remain (N-(M+s)) objects are combined into several whole bodies using the loft procedures between the closet neighbours. The final structure has a good conformity with a nervous tissue architecture. Furthermore, the obtained phantom is correct to the mesh application and further numerical calculations.