Cardiac simulations typically involve volumes containing millions to billions of cells. To make computations feasible, most existing work relied on homogenization. However, homogenized models cannot accurately capture microscale phenomena, such as arrhythmia formation in myopathic or aging tissue. We aim to develop cell-resolved simulations to support the investigation of such phenomena. This requires the generation of large 3D synthetic tissue meshes.
Our meshes rely on a network of cell centers and their connections. This network must satisfy a set of constraints in order to reproduce realistic tissue properties, including cell density and connectivity. Therefore we investigated how the number of links per center depends on three parameters: maximum angle between links, minimum separation between links that do not share a center, and maximum link length. Our aim was to find a parameter set that would achieve an average of 10 connections per cell. We also tested the effect of different methods to place the centers.
We found that the connectivity did not depend on the method to generate the center distribution, but that Poisson disk sampling was much faster than the others. As expected, the connectivity increased with increasing maximum angle, decreasing minimum separation, and maximum length. The minimum separation had the strongest influence. The maximum connectivity achieved with plausible parameter values was 8 links per center. We generated networks with 9 links per center but this led to unrealistically long cells.
These results provide useful guidance for further optimization of our methods. We conclude that the myocardium cannot be modeled with a network of centers and straight links using only one center per cell; it is probably necessary to use two or three centers per cell. This conclusion aligns with confocal microscopy data which show that many, but not all links point towards the cell center.