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

Abstract

. Significance: Monte Carlo radiation transfer (MCRT) is the gold standard for modeling light transport in turbid media. Typical MCRT models use voxels or meshes to approximate experimental geometry. A voxel-based geometry does not allow for the precise modeling of smooth curved surfaces, such as may be found in biological systems or food and drink packaging. Mesh-based geometry allows arbitrary complex shapes with smooth curved surfaces to be modeled. However, mesh-based models also suffer from issues such as the computational cost of generating meshes and inaccuracies in how meshes handle reflections and refractions. Aim: We present our algorithm, which we term signedMCRT (sMCRT), a geometry-based method that uses signed distance functions (SDF) to represent the geometry of the model. SDFs are capable of modeling smooth curved surfaces precisely while also modeling complex geometries. Approach: We show that using SDFs to represent the problem’s geometry is more precise than voxel and mesh-based methods. Results: sMCRT is validated against theoretical expressions, and voxel and mesh-based MCRT codes. We show that sMCRT can precisely model arbitrary complex geometries such as microvascular vessel network using SDFs. In comparison with the current state-of-the-art in MCRT methods specifically for curved surfaces, sMCRT is more precise for cases where the geometry can be defined using combinations of shapes. Conclusions: We believe that SDF-based MCRT models are a complementary method to voxel and mesh models in terms of being able to model complex geometries and accurately treat curved surfaces, with a focus on precise simulation of reflections and refractions. sMCRT is publicly available at https://github.com/lewisfish/signedMCRT .

scatterBrains: an open database of human head models and companion optode locations for realistic Monte Carlo photon simulations

“…In the past several decades, Monte Carlo (MC) light simulations have emerged as the gold standard technique for simulating photon transport through tissue. 1 , 2 Advances in these algorithms have allowed for modeling increasingly complex transport geometries or tissue types 3 – 9 while drastically reducing the runtime through parallel or cloud computing architectures. 10 – 14 Such developments have spawned new studies that use MC simulations to, among many other efforts, investigate potential tissue areas to image, 15 – 18 determine the promise of new imaging modalities, 19 – 22 optimize hardware in existing modalities, 23 – 28 improve recovery of desired biomarkers, 29 , 30 and further elucidate the physical principles behind light-tissue interaction.…”

Special Section Guest Editorial: Introduction to the Special Section Celebrating 30 years of Open Source Monte Carlo Codes in Biomedical Optics

“…A novel shape representation using a signed distance function is explored by McMillan, Bruce, and Dholakia. 15 Similarly, the variability of optical properties remains a challenge to the field and the work by Kao and Sung, 16 employing CW spectroscopy and anatomically correct MC models to quantify personalized properties values, presents an interesting approach with direct translation for photothermal and photodynamic therapies.…”