Numerical Simulation of Light Beam Propagation in Heterogeneous Biological Tissues using a Finite Element-Based Fractal Propagation Method

Biological tissues are composed of multiple layers with distinct optical parameters, such as the brain and skin. In biomedical optical microscopy, simulation methods for light propagation in biological tissues struggle to strike a balance between computational accuracy and time. To simulate light propagation within multilayered biological tissues featuring irregular boundary shapes, we proposed a finite element-based fractal propagation method for solving the scalar Helmholtz equation. The weak form of the scalar Helmholtz equation is derived and integrated with a fractal model of refractive index turbulence. The solving domain is partitioned using an unstructured triangular mesh, enabling adaptation to curved boundaries. We prepared phantoms with both regular and irregular shapes, as well as with a layered heterogeneous refractive index. We validated our simulation method by conducting beam steering experiments with the polymethacrylamide hydrogel phantoms. And the results also demonstrated, compared with previous researches, our method performs better in complex tissue phantoms, which may be used in the simulation of various patterned beams in real biological microscopy.