Implicit Monte Carlo method: an innovation for light modeling in complex tissue structures
We proposed a new, innovative implicit meshed-based Monte Carlo (iMMC) algorithm based upon the conventional meshed based Monte Carlo (MMC) light transport algorithm . By taking advantage of the intrinsic topology of the tetrahedral mesh-node, edge and face, iMMC is able to largely reduce the mesh density. The idea behind of the algorithm is to use:
1. edge for vessel network
2. node for porous medium
3. face for thin biological membrane.
To simulate the light propagation in these biological tissue, the conventional MMC requires a high-density mesh (Fig. a), which is memory- and time-consuming. However, by relying on the intrinsic edge of the tetrahedron, the mesh density can be reduced by hundreds fold (Fig. b). In the meantime, the speed can be improved by 20%. More speed improvement is expected for the vessel network with higher complexity.
In our preliminary results, the conventional MMC and iMMC methods show perfect match (Fig. c). Our next step will be generating mesh for realistic vessel network and then applying iMMC on the mesh. Fig. d and Fig. e show the groundtruth and the vessel edges used for iMMC respectively.
 Fang, Qianqian. "Mesh-based Monte Carlo method using fast ray-tracing in Plücker coordinates." Biomedical optics express1.1 (2010): 165-175.