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5MONTE CARLO SIMULATION OF LIGHT DISTRIBUTION IN MULTILAYER BIOLOGICAL
TISSUE
IZABELLA SEREBRYAKOVA12. YURIY SURKOV12, ARSENII FASHCHEVSKII1, YANWEN XU4,5,
QING XIA4,5. DONGYU LI5,6. DAN ZHU4 5, ELINA GENINA1,7, VALERY TUCHIN1,7,8
1Educational Laboratory of Atomic Physics, Quantum Electronics and Spectroscopy, Saratov State University, Russia 2Laboratory of Biomedical Photoacoustics, Saratov State University, Russia 3Scientific medical center of Saratov State University, Russia 4China Britton Chance Center for Biomedical Photonics - MoE Key Laboratory for Biomedical Photonics, Huazhong
University of Science and Technology, China 5Wuhan National Laboratory for Optoelectronics - Advanced Biomedical Imaging Facility, Huazhong University of
Science and Technology, China 6School of Optical Electronic Information - Advanced Biomedical Imaging Facility, Huazhong University of Science and
Technology, China 7Tomsk State University, Russia 8Institute of Precision Mechanics and Control, FRC "Saratov Scientific Centre of the RAS, " Russia
ABSTRACT
The Monte-Carlo (MC) method has become a main tool for simulating light transport in multilayer biotissues, aiding significantly in medical diagnostics and therapeutic procedures. This study explores the application of the MC method for simulating photon paths in multilayer biotissues. The method involves generating random photon paths and calculating the probability of photon absorption at each tissue layer. The study focuses on the development and implementation of a computer program to simulate photon paths in biotissues and investigate their absorption characteristics. The results demonstrate the effectiveness of the MC method in accurately predicting photon paths and absorption in multilayer biotissues.
KEYWORDS: Monte Carlo method, photon paths, biotissues, absorption, radiation therapy.
INTRODUCTION
The accurate simulation of photon transport in biological tissues is imperative for the development of non-invasive diagnostic techniques and therapeutic procedures. Compared to other analytical and numerical methods, the MC method stands out due to its flexibility and accuracy in modeling complex tissue structures [1].
Understanding how photons propagate within and escape from a tissue is necessary for proper interpretation of optical diagnostic measurements. The field of biomedical optics and biophotonics is currently very actively using computer simulations of light transport to guide clinical protocols and develop optical tools for medicine and biology.
The MC method uses statistical sampling to obtain numerical results, making it well-suited for simulating stochastic processes such as photon transport. Its application in modeling light propagation in tissues has been extensively reviewed, providing valuable insights into light-tissue interactions [2]. The basic principle consist in tracing the paths of photon packets as they travel through tissue layers, incorporating scattering, absorption, and reflection events [3]. Multilayer biotissues present unique challenges due to their heterogeneous nature. The MC method can effectively simulate photon trajectories by approximating tissue layers as planar structures with distinct optical properties. Recent studies have optimized these simulations by incorporating realistic geometrical and optical properties of tissues, improving their accuracy and predictive power [4]. Advances in computational resources have further enhanced the feasibility of such simulations [5].
Simulating a large number of photon packets necessitates substantial computational power, which has been addressed by modern parallel computing techniques and optimized algorithms [6]. Graphics processing unit (GPU) acceleration and cloud computing resources have significantly decreased computation time, making it feasible to simulate millions of photons in a reasonable time frame [7]. Moreover, recent developments in variance reduction techniques have improved the efficiency of simulations, reducing the required number of photon packets for achieving statistical significance [8].
The MC simulations of photon trajectories have critical implications in areas such as diffuse optical tomography, photothermal therapy, and laser-based diagnostics [9]. By accurately modeling of light
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propagation through tissues, these simulations aid in optimizing device design and improving the accuracy of diagnostic techniques. For instance, enhanced simulation models have contributed to better understanding and diagnosis of skin cancer, brain imaging, and other medical conditions that require precise optical measurements [10].
MATERIALS AND METHODS
The study employs a computer program implemented in Python to simulate photon paths and calculate photon absorption in multilayer biotissues. The program uses a random number generator to generate photon paths and calculate the probability of photon absorption using the Beer-Lambert law. The program simulates the trajectories of photon packets through a multi-layered medium, taking into account absorption, scattering, and transmission processes. The photon energy and scattering coefficients are varied to investigate their effects on photon paths and absorption.
Program Functionality
1. Layer Definition
The program defines a multi-layered medium with specific optical and geometrical properties for each layer, including thickness, refractive index (n), absorption coefficient (^a), scattering coefficient (^s), and anisotropy factor (g).
2. Photon Initialization
Each photon packet is initialized at the center of the first layer with an initial direction along the z-axis.
3. Trajectory Simulation
The trajectory of each photon packet is simulated by iteratively calculating its step size, determining whether it is absorbed, scattered, or transmitted, and updating its position and direction accordingly.
4. Position Recording
The positions of each photon packet are recorded and stored in a list for further analysis or visualization.
5. Termination Conditions
The simulation of a photon packet's trajectory is terminated if the photon is absorbed, leaves the defined spatial boundaries, or exits the multi-layered medium.
Table 1. Optical and geometric parameters used in modeling skin biotissue at a wavelength of 633 nm [11].
Layer Thickness, Mm Refractive index (n) Absorption coefficient (^a), cm-1 Scattering coefficient (Ms), cm-1 Anisotropy factor (g)
Air 10 1 0.0001 0.0001 0.001
Stratum corneum 20 1.50 0.15 175.0 0.90
Living epidermis 100 1.34 2.47 87.5 0.80
Dermis 500 1.40 0.28 80.6 0.82
Air 50 1 0.0001 0.0001 0.001
VISUALIZATION OF THE RESULTS
In Figure 1, a three-dimensional graph illustrates the simulation results of the trajectories of 10 000 photon packets using the MC simulation, along with their projections onto the two-dimensional XY, XZ, and YZ planes. Despite the limitation that this number of photon packets is insufficient for an adequate assessment of the model's overall performance, the individual trajectories of photon packets are clearly visible. This provides insights into their path dynamics. Moreover, the simulation's relatively quick processing time demonstrates the program's efficiency and potential for larger-scale computations, enabling rapid preliminary studies and iterative model refinement.
Figure 1: Simulate the trajectories of10 000 photon packets (a) 3D Plot of Photon Trajectories, 2D Plots of Photon Trajectories: (b) in the XYplane, (c) in the XZplane, (d) in the YZplane. The x, y, and z coordinates of the photon packets, represented as semi-transparent black lines. Lines and planes to separate the layers, with the z-coordinates corresponding to the cumulative thicknesses of the layers
By studying individual trajectories in detail, it is possible to identify specific patterns and behaviors that may not be obvious in large datasets. This can be useful for diagnosing problems within a model or for better understanding specific interactions or processes.
However, for comprehensive evaluations and to ensure robustness in varied conditions, a significantly larger number of photon packets is recommended. This would improve statistical reliability and ensure that the results are not scrambled by anomalies present in smaller sample sizes.
Figure 2 presents a three-dimensional visualization of the simulation results for the trajectories of 100 000 photon packets generated using the MC simulation within a multilayer biotissue model. Additionally, the figure includes projections of these trajectories onto the two-dimensional XY, XZ, and YZ planes, facilitating a comprehensive examination of photon behavior across different spatial orientations.
The substantial increase to 100,000 photon packets markedly enhances the simulation's capability to capture subtle variations in photon pathways, which are internally linked to the biotissue's optical properties as detailed in Table 1. With this increased number of photon packets, the differences in trajectories become distinctly observable. This allows for a more precise assessment of the effect of optical parameters on the tissue passing through the layers. This level of detail is critical for validating the model's accuracy and
reliability, as it ensures that the simulated photon behavior closely mirrors the complex interactions occurring in actual biological tissues.
(a)
100 200 300 400 500 600 z (microns)
(b)
(c)
(d)
Figure 2: Simulate the trajectories of100 000 photon packets (a) 3D Plot of Photon Trajectories, 2D Plots of Photon Trajectories: (b) in the XYplane, (c) in the XZplane, (d) in the YZplane. The x, y, and z coordinates of the photon packets, represented as semi-transparent black lines. Lines and planes to separate the layers, with the z-coordinates corresponding to the cumulative thicknesses of the layers
Simulating one million photon packets using the MC method presents significant challenges in terms of computational power and time investment. Figure 3 Three-dimensional visualization of the trajectories of one million photon packets, along with their projections onto the XY, XZ, and YZ planes.
Figure 3: Simulate the trajectories of1 000 000 photon packets (a) 3D Plot of Photon Trajectories, 2D Plots
of Photon Trajectories: (b) in the XYplane, (c) in the XZplane, (d) in the YZplane. The x, y, and z coordinates of the photon packets, represented as semi-transparent black lines. Lines and planes to separate the layers, with the z-coordinates corresponding to the cumulative thicknesses of the layers
While modeling one million photon packets using the MC simulation offers enhanced accuracy and a more comprehensive understanding of light transport in multilayer biotissues, it simultaneously imposes substantial demands on computational infrastructure and extends simulation times.
The exponential increase in the number of photon interactions necessitates high-performance computing resources to manage the extensive data processing and storage requirements effectively. Each photon packet must be individually tracked through multiple layers of biotissue, accounting for complex interactions such as scattering, absorption, and anisotropic reflections, which exponentially escalate the computational load as the photon count rises. Additionally, the increased memory requirements for storing the trajectories and interaction data of one million photon packets demand optimized memory management strategies to prevent inefficiencies and ensure smooth execution.
DISCUSSION
Achieving a balance between computational efficiency and simulation fidelity remains a persistent challenge, particularly as the demand for higher photon counts continues to grow in pursuit of more detailed and accurate modeling of light-tissue interactions.
The temporal aspect of large-scale modeling should not be overlooked. Conducting simulations using a large number of photon packets can increase processing time from several hours to several days, depending on the complexity of the tissue model and the available computing infrastructure. Increasing the simulation time not only impacts the feasibility of conducting extensive parametric studies but also limits the ability to perform iterative model refinements in a timely manner. Consequently, researchers must weigh the benefits of
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increased photon counts against the practical constraints of available computational resources and time, often necessitating compromises or the strategic allocation of resources to critical simulation phases.
Addressing these challenges requires continuous advancements in computational technologies, algorithm optimization, and efficient resource management to fully leverage the potential of high-photon-count simulations in biomedical research and clinical applications.
CONCLUSION
The study highlights the importance of modeling photon trajectories in biological tissues. The MC simulation provides a powerful tool to achieve this goal by accurately predicting the trajectories of photons in complex biological tissues. The study also discusses the limitations of the MC simulation, including computational complexity and uncertainty in modeling the photon trajectory. Future research should be aimed at improving the accuracy and effectiveness of the MC simulation in order to further improve and optimize its application in practice. The MC simulation remains a cornerstone for simulating photon trajectories in multilayer biotissues, offering unparalleled versatility and accuracy. With continuous advancements in computational techniques and resources, the scope and applicability of these simulations are likely to expand, further bridging the gap between theoretical models and practical biomedical applications.
ACKNOWLEDGEMENT
The work has been funded by the grant (23-14-00287) from the Russian Science Foundation, National Natural Science Foundation of China (NSFC) (Grant Nos. 32361133552).
REFERENCES
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