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

Lewis McMillan, Graham D. Bruce, Kishan Dholakia

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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

Original languageEnglish
Article number083003
JournalJournal of Biomedical Optics
Issue number8
Publication statusPublished - 2022 Aug 1

Bibliographical note

Funding Information:
The work was supported by funding from the UK Engineering and Physical Sciences Research Council (EP/R004854/1) and the European Union H2020 projects “Dynamic” (EC-GA 863203) and “Proscope” (871212). KD acknowledges support of the Australian Research Council through a Laureate Fellowship.

Publisher Copyright:
© The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Biomaterials
  • Biomedical Engineering


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