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

Hao Jia; Bin Chen; Dong Li; Yuzhen Jin; Hao Jia; Bin Chen; Dong Li; Yuzhen Jin

doi:10.3934/mbe.2021125

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2455-2472. doi: 10.3934/mbe.2021125

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

1.
State-Province Joint Engineering Lab of Fluid Transmission System Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China
2.
State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China

Received: 10 November 2020 Accepted: 03 March 2021 Published: 12 March 2021

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.
- port wine stains,
- medical optics,
- Monte Carlo method,
- tetrahedron mesh,
- skin tissues
Citation: Hao Jia, Bin Chen, Dong Li, Yuzhen Jin. Strategy of boundary discretization in numerical simulation of laser propagation in skin tissue with vascular lesions[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2455-2472. doi: 10.3934/mbe.2021125

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Abstract

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.

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