Boundary discretization in the numerical simulation of light propagation in skin tissue: problem and strategy

Vascular damage mechanism and parameter optimization under alexandrite laser irradiation: a theoretical study

The 755-nm Alexandrite Laser has a good clinical effect in treating resistant port wine stain, without causing thermal damage of normal tissue and side effects such as purpura. However, little is known about the mechanism of vascular damage induced by 755-nm laser irradiation, which restricts the optimization of laser parameters. In this work, the thermal damage model and the pressure damage model were used to study the damage mechanism of 755-nm laser irradiation on vessels, and the incident energy density and pulse width required for vascular damage were determined according to the damage mode. Under the irradiation of 755-nm laser, the vascular injury pattern was the co-occurrence of vessel rupture and vessel constriction, and the energy density required for the treatment of vessels with a diameter of 200 μm to reach the damage threshold was the lowest.

Strategy of boundary discretization in numerical simulation of laser propagation in skin tissue with vascular lesions

Understanding light propagation in skin tissues with complex blood vessels can help improve clinical efficacy in the laser treatment of cutaneous vascular lesions. The voxel-based Monte Carlo (VMC) algorithm with simple blood vessel geometry is commonly used in studying the law of light propagation in tissues. However, unavoidable errors are expected in VMC because of the zigzag polygonal interface. A tetrahedron-based Monte Carlo with extended boundary condition (TMCE) solver is developed to discretize complex tissue boundaries accurately. Tetrahedra are generated along the interface, resulting in a polyhedron approximation to match the real interface. A comparison between TMCE and VMC shows neglected differences in the overall distribution of energy deposition of different models, but poor adaptability of the curved tissue interface in VMC leads to a higher energy deposition error than TMCE in a mostly deposited region in blood vessels. Replacing the real blood vessel with a cylinder-shaped vessel shows an error lower than that caused by VMC. Statistical significance analysis of energy deposition by TMCE shows that mean curvature has stronger relationship with energy deposition than the Gaussian curvature, which indicates the importance of this geometric parameter in predicting photon behavior in vascular lesions.

Modeling voxel-based Monte Carlo light transport with curved and oblique boundary surfaces

SIGNIFICANCE

Monte Carlo (MC) light transport simulations are most often performed in regularly spaced three-dimensional voxels, a type of data representation that naturally struggles to represent boundary surfaces with curvature and oblique angles. Not accounting properly for such boundaries with an index of refractivity, mismatches can lead to important inaccuracies, not only in the calculated angles of reflection and transmission but also in the amount of light that transmits through or reflects from these mismatched boundary surfaces.

AIM

A new MC light transport algorithm is introduced to deal with curvature and oblique angles of incidence when simulated photons encounter mismatched boundary surfaces.

APPROACH

The core of the proposed algorithm applies the efficient preprocessing step of calculating a gradient map of the mismatched boundaries, a smoothing step on this calculated 3D vector field to remove surface roughness due to discretization and an interpolation scheme to improve the handling of curvature.

RESULTS

Through simulations of light hitting the side of a sphere and going through a lens, the agreement of this approach with analytical solutions is shown to be strong.

CONCLUSIONS

The MC method introduced here has the advantage of requiring only slight implementation changes from the current state-of-the-art to accurately simulate mismatched boundaries and readily exploit the acceleration of general-purpose graphics processing units. A code implementation, mcxyzn, is made available and maintained at https://omlc.org/software/mc/mcxyzn/.

Theoretical Study on Pressure Damage Based on Clinical Purpura during the Laser Irradiation of Port Wine Stains with Real Complex Vessels

Port wine stains (PWSs) are congenital dermal vascular lesions composed of a hyperdilated vasculature. Purpura represented by local hemorrhage from water vaporization in blood during laser therapy of PWS is typically considered a clinical feedback, but with a low cure rate. In this study, light propagation and heat deposition in skin and PWSs is simulated by a tetrahedron-based Monte Carlo method fitted to curved bio-tissues. A curvature-corrected pressure damage model was established to accurately evaluate the relationship between purpura-bleeding area (rate) and laser therapy strategy for real complex vessels. Results showed that the standard deviation of Gaussian curvature of the vessel wall has negative relation with the fluence threshold of vessel rupture, but has positive relation with the effective laser fluence of vessel damage. This finding indicated the probable reason for the poor treatment of PWS, that is, considering purpura formation as a treatment end point (TEP) only leads to partial removal of vascular lesions. Instead, appropriate purpura area ratio with marked effects or rehabilitation should be adopted as TEP. The quantitative correlation between the fluence of a pulsed dye laser and the characteristics of vascular lesions can provide personalized and precise guidance for clinical treatments.

Advances in Monte Carlo Simulation for Light Propagation in Tissue

Monte Carlo (MC) simulation for light propagation in tissue is the gold standard for studying the light propagation in biological tissue and has been used for years. Interaction of photons with a medium is simulated based on its optical properties. New simulation geometries, tissue-light interaction methods, and recording techniques recently have been designed. Applications, such as whole mouse body simulations for fluorescence imaging, eye modeling for blood vessel imaging, skin modeling for terahertz imaging, and human head modeling for sinus imaging, have emerged. Here, we review the technical advances and recent applications of MC simulation.

Propagation of polarized light in the biological tissue: a numerical study by polarized geometric Monte Carlo method

To investigate the influence of polarization on the polarized light propagation in biological tissue, a polarized geometric Monte Carlo method is developed. The Stokes-Mueller formalism is expounded to describe the shifting of light polarization during propagation events, including scattering and interface interaction. The scattering amplitudes and optical parameters of different tissue structures are obtained using Mie theory. Through simulations of polarized light (pulsed dye laser at wavelength of 585 nm) propagation in an infinite slab tissue model and a discrete vessel tissue model, energy depositions in tissue structures are calculated and compared with those obtained through general geometric Monte Carlo simulation under the same parameters but without consideration of polarization effect. It is found that the absorption depth of the polarized light is about one half of that determined by conventional simulations. In the discrete vessel model, low penetrability manifests in three aspects: diffuse reflection became the main contributor to the energy escape, the proportion of epidermal energy deposition increased significantly, and energy deposition in the blood became weaker and more uneven. This may indicate that the actual thermal damage of epidermis during the real-world treatment is higher and the deep buried blood vessels are insufficiently damaged by consideration of polarization effect, compared with the conventional prediction.

Selection of voxel size and photon number in voxel-based Monte Carlo method: criteria and applications

The voxel-based Monte Carlo method (VMC) is now a gold standard in the simulation of light propagation in turbid media. For complex tissue structures, however, the computational cost will be higher when small voxels are used to improve smoothness of tissue interface and a large number of photons are used to obtain accurate results. To reduce computational cost, criteria were proposed to determine the voxel size and photon number in 3-dimensional VMC simulations with acceptable accuracy and computation time. The selection of the voxel size can be expressed as a function of tissue geometry and optical properties. The photon number should be at least 5 times the total voxel number. These criteria are further applied in developing a photon ray splitting scheme of local grid refinement technique to reduce computational cost of a nonuniform tissue structure with significantly varying optical properties. In the proposed technique, a nonuniform refined grid system is used, where fine grids are used for the tissue with high absorption and complex geometry, and coarse grids are used for the other part. In this technique, the total photon number is selected based on the voxel size of the coarse grid. Furthermore, the photon-splitting scheme is developed to satisfy the statistical accuracy requirement for the dense grid area. Result shows that local grid refinement technique photon ray splitting scheme can accelerate the computation by 7.6 times (reduce time consumption from 17.5 to 2.3 h) in the simulation of laser light energy deposition in skin tissue that contains port wine stain lesions.