Persistent homology-based optical properties of microscopic turbid media for realistic light propagation analysis

Abstract

The optical properties of microscopic turbid media are critical for understanding light-tissue interactions with applications in biomedical imaging and diagnostics. However, traditional scattering coefficient-based methods are limited in their ability to capture topological heterogeneities within tissue structures, which play a crucial role in describing the relationship between microscopic tissue characteristics and their corresponding light propagation behaviors. In this study, we propose using persistent homology-based persistent images (PIs) as a descriptor and optical property of microscopic tissues. As a proof of concept, we analyzed particle-distributed turbid media with uniform and clustered particle distributions by persistent homology analysis, demonstrating that PIs can capture topological characteristics that are not discernible using traditional scattering coefficient-based methods. Light propagation simulations using the beam propagation method (BPM) demonstrated that PIs correlate with optical behaviors, such as beam centroid displacement and distortion, providing a foundation for linking microscopic topological heterogeneities to light propagation behaviors. Our results validate PIs as a meaningful and predictive optical property, bridging microscopic turbid media topology with their light propagation behaviors. This work establishes PIs as a potential optical property of microscopic tissue, capturing its topological characteristics and offering predictive insights into light propagation behaviors.

Fig. 1.

Persistent homology analysis of uniform and clustered microscopic turbid media with varying particle sizes and spatial organization.

Fig. 2.

Heterogeneous scattering media examples with varying scatterer concentrations (50k, 200k, 300k, 400k [1/mm³]) and their corresponding PIs and simulated light distributions at the focal plane.

Fig. 3.

(a) MSE convergence of PI across various simulation samples with referential PI at 1,000 simulation samples. (b) Standard deviation of beam centroid displacement. (c) Standard deviation of beam distortion. Standard deviations of beam characteristics were investigated for 5 simulation trials across 1,000 simulation samples.

Fig. 4.

Beam centroid displacement (a) and beam distortion (b) as functions of particle densities.

Fig. 5.

Turbid media with (a) uniform and (b) clustered particle distributions, along with their corresponding persistent images (c,d) respectively. (e) Beam centroid displacement and (f) beam distortion characteristics. The dashed green line in the boxplots represents the mean value of the beam characteristics.

Fig. 6.

Beam centroid displacement and distortion for uniform and cluster models (500 samples) across different simulation trials (n=1,2,3), demonstrating that similar PI groups yield consistent beam characteristics.

Fig. 7.

Scattering coefficient calculated from BPM system of turbid media with particle size condition 3 μm, 4 μm, 6 μm in comparison with Mie theoretical values of each condition. The shaded region represents 95 percent confident interval (CI).