Meshless Monte Carlo radiation transfer method for curved geometries using signed distance functions

Area of Science:

• Optics and photonics
• Computational modeling
• Biomedical engineering

Background:

• Monte Carlo radiation transfer (MCRT) is crucial for light transport simulation in turbid media.
• Current MCRT methods using voxels or meshes struggle with precise modeling of smooth, curved surfaces.
• Voxel-based methods lack precision for curved surfaces, while mesh-based methods face computational costs and inaccuracies in handling reflections/refractions.

Purpose of the Study:

• To introduce signedMCRT (sMCRT), a novel geometry-based MCRT algorithm utilizing signed distance functions (SDFs).
• To demonstrate the capability of SDFs in accurately representing complex geometries, including smooth curved surfaces.
• To compare the precision and performance of sMCRT against traditional voxel and mesh-based MCRT methods.

Main Methods:

• Developed the signedMCRT (sMCRT) algorithm employing signed distance functions (SDFs) for geometric representation.
• Validated sMCRT against theoretical calculations and existing voxel and mesh-based MCRT codes.
• Applied sMCRT to model complex geometries, such as microvascular networks.

Main Results:

• sMCRT using SDFs provides more precise geometric representation compared to voxel and mesh-based methods.
• The algorithm accurately models arbitrary complex geometries, including intricate microvascular structures.
• sMCRT demonstrates superior precision for curved surfaces, especially when geometries are defined by combined shapes, outperforming current state-of-the-art methods.

Conclusions:

• SDF-based MCRT, as implemented in sMCRT, offers a complementary approach to existing methods for complex geometry modeling.
• sMCRT excels in accurately simulating reflections and refractions on curved surfaces.
• The sMCRT algorithm is publicly available, promoting further research and application in light transport modeling.