# A contemporary systematic review on deterministic numerical simulations of light propagation in head tissues

## TL;DR

This paper reviews deterministic simulations of light propagation in head tissues as a potential alternative to Monte Carlo methods for biomedical applications.

## Contribution

The study provides a systematic review of recent deterministic numerical simulations for light propagation in head tissues.

## Key findings

- Most studies used 3D simulations with FEM to solve the Diffusion Equation for improved imaging techniques.
- Deterministic simulations are shown to be efficient and relatively accurate alternatives to Monte Carlo methods.
- Challenges include tissue optical property variations and oversimplified geometric models.

## Abstract

Understanding how light interacts with the head’s tissues is relevant for several biomedical applications. Since in vivo studies involve ethical considerations, numerical simulations have become a recognised alternative method for studying light propagation in biological tissue. Although Monte Carlo methods are the gold standard for these studies, deterministic simulations are becoming more common due to their lower computational cost. Thus, this document reviews articles published after 2010, containing deterministic numerical simulations of light propagation (visible to infrared wavelengths) in human head tissues, to define how these methods are implemented and whether they are a viable alternative to the stochastic Monte Carlo algorithms. Most of the selected articles included a 3D simulation, using Finite Element Methods (FEM) to solve the Diffusion Equation (DE), with Robin boundary conditions, and considering the tissues as horizontal rectangular layers, to improve imaging techniques’ algorithms. Regarding target areas, there is an almost identical number of records studying the brain as a whole or dividing it into grey and white matter, while more studies consider the scalp and skull as individual layers instead of grouping them. The cerebrospinal fluid (CSF) was included in more than half of the studies, confirming that it is possible to simulate this tissue using the DE, if the optical parameters are adequate. Some of the challenges identified in the reported simulations are the variations in the optical properties of tissues (reduced scattering and absorption coefficients) and oversimplifications of the geometric models, which raise the question of whether using subject-specific data could improve the outcomes of light-based diagnosis and therapies. Although Monte Carlo methods are still the most commonly used for the simulation of optical properties, all the reviewed works reached comprehensive results, with most of them showing that deterministic numerical simulations can be an efficient and relatively accurate alternative to the time-consuming Monte Carlo methods.

The online version contains supplementary material available at 10.1007/s12551-025-01403-w.