Light Propagation In Turbid Media Research Articles

Unwrapping non-locality in the image transmission through turbid media

Achieving high-fidelity image transmission through turbid media is a significant challenge facing both the AI and photonic/optical communities. While this capability holds promise for a variety of applications, including data transfer, neural endoscopy, and multi-mode optical fiber-based imaging, conventional deep learning methods struggle to capture the nuances of light propagation, leading to weak generalization and limited reconstruction performance. To address this limitation, we investigated the non-locality present in the reconstructed images and discovered that conventional deep learning methods rely on specific features extracted from the training dataset rather than meticulously reconstructing each pixel. This suggests that they fail to effectively capture long-range dependencies between pixels, which are crucial for accurate image reconstruction. Inspired by the physics of light propagation in turbid media, we developed a global attention mechanism to approach this problem from a broader perspective. Our network harnesses information redundancy generated by peculiar non-local features across the input and output fiber facets. This mechanism enables a two-order-of-magnitude performance boost and high fidelity to the data context, ensuring an accurate representation of intricate details in a pixel-to-pixel reconstruction rather than mere loss minimization.

MCDataset: a public reference dataset of Monte Carlo simulated quantities for multilayered and voxelated tissues computed by massively parallel PyXOpto Python package.

.Significance: Current open-source Monte Carlo (MC) method implementations for light propagation modeling are many times tedious to build and require third-party licensed software that can often discourage prospective researchers in the biomedical optics community from fully utilizing the light propagation tools. Furthermore, the same drawback also limits rigorous cross-validation of physical quantities estimated by various MC codes.Aim: Proposal of an open-source tool for light propagation modeling and an easily accessible dataset to encourage fruitful communications amongst researchers and pave the way to a more consistent comparison between the available implementations of the MC method.Approach: The PyXOpto implementation of the MC method for multilayered and voxelated tissues based on the Python programming language and PyOpenCL extension enables massively parallel computation on numerous OpenCL-enabled devices. The proposed implementation is used to compute a large dataset of reflectance, transmittance, energy deposition, and sampling volume for various source, detector, and tissue configurations.Results: The proposed PyXOpto agrees well with the original MC implementation. However, further validation reveals a noticeable bias introduced by the random number generator used in the original MC implementation.Conclusions: Establishing a common dataset is highly important for the validation of existing and development of MC codes for light propagation in turbid media.

Retrieval of Absorption or Scattering Coefficient Spectrum (RASCS) Program: A Tool to Monitor Optical Properties in Real Time.

Optical properties characterize light propagation in turbid media, such as tissue. Recovery of optical properties is of great importance in a wide variety of biomedical applications, including both therapeutic treatments and diagnosis. Most of the available methodologies are well established, however, these are not optimized for real-time measurements. Optical properties are recovered using the Inverse Adding Doubling program from reflectance measurements measured with an integrating sphere and light in the visible range. A user-friendly interface was programmed inVisual Studio and the libraries of aparticular spectrophotometer were used. To achieve real-time measurements, a parallel computing routine was implemented, splitting the whole spectra in threads to be computed independently. Several tests using living tissue and inorganic materials were carried out to validate the proposed algorithm. Recovery of absorption/scattering coefficient spectrum in the visible range with high precision in a couple of seconds was achieved, demonstrating its capabilities for real-time monitoring in biomedical applications. The absorption coefficient spectrum shows the expected characteristics according to the different melanin and blood concentration of various volunteers, also showing the expected changes during a thermoregulation process. A real-time monitoring of optical properties algorithm was developed, including parallel computing and a user-friendly interface. The proposed algorithm would be of help in biomedical applications, where real-time monitoring optical properties is required. Lasers Surg. Med. © 2019 Wiley Periodicals, Inc.

FullMonteCUDA: a fast, flexible, and accurate GPU-accelerated Monte Carlo simulator for light propagation in turbid media.

Optimizing light delivery for photodynamic therapy, quantifying tissue optical properties or reconstructing 3D distributions of sources in bioluminescence imaging and absorbers in diffuse optical imaging all involve solving an inverse problem. This can require thousands of forward light propagation simulations to determine the parameters to optimize treatment, image tissue or quantify tissue optical properties, which is time-consuming and computationally expensive. Addressing this problem requires a light propagation simulator that produces results quickly given modelling parameters. In previous work, we developed FullMonteSW: currently the fastest, tetrahedral-mesh, Monte Carlo light propagation simulator written in software. Additional software optimizations showed diminishing performance improvements, so we investigated hardware acceleration methods. This work focuses on FullMonteCUDA: a GPU-accelerated version of FullMonteSW which targets NVIDIA GPUs. FullMonteCUDA has been validated across several benchmark models and, through various GPU-specific optimizations, achieves a 288-936x speedup over the single-threaded, non-vectorized version of FullMonteSW and a 4-13x speedup over the highly optimized, hand-vectorized and multi-threaded version. The increase in performance allows inverse problems to be solved more efficiently and effectively.

Transmission model and characteristics of focused laser beam in turbid phantom verified by numerical simulation and beam profile analysis

The study of light propagation in turbid media is of great importance for tissue imaging, component measurement and laser therapy. A geometric model for simulating Gaussian laser beam has been presented and proved by Monte Carlo method and experiment with sample of turbid suspension. The beam expansion ratio (BER) and total power attenuation have been used to evaluate the scattering and absorption characteristics of the samples. BER is a useful indicator to distinguish scattering medium and absorbing medium, and is sensitive to the position of focus plane. The power attenuation is sensitive to different suspensions and independent to focus position. The transmission measurement need be combined with method of reflection or refraction, which can give more information of the contribution of each optical parameter to power attenuation and beam expansion.

Comparative evaluations of the Monte Carlo-based light propagation simulation packages for optical imaging

Monte Carlo simulation of light propagation in turbid medium has been studied for years. A number of software packages have been developed to handle with such issue. However, it is hard to compare these simulation packages, especially for tissues with complex heterogeneous structures. Here, we first designed a group of mesh datasets generated by Iso2Mesh software, and used them to cross-validate the accuracy and to evaluate the performance of four Monte Carlo-based simulation packages, including Monte Carlo model of steady-state light transport in multi-layered tissues (MCML), tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIMOS), Molecular Optical Simulation Environment (MOSE), and Mesh-based Monte Carlo (MMC). The performance of each package was evaluated based on the designed mesh datasets. The merits and demerits of each package were also discussed. Comparative results showed that the TIMOS package provided the best performance, which proved to be a reliable, efficient, and stable MC simulation package for users.

Lookup table-based sampling of the phase function for Monte Carlo simulations of light propagation in turbid media.

Analytical expressions for sampling the scattering angle from a phase function in Monte Carlo simulations of light propagation are available only for a limited number of phase functions. Consequently, numerical sampling methods based on tabulated values are often required instead. By using Monte Carlo simulated reflectance, we compare two existing and propose an improved numerical sampling method and show that both the number of the tabulated values and the numerical sampling method significantly influence the accuracy of the simulated reflectance. The provided results and guidelines should serve as a good starting point for conducting computationally efficient Monte Carlo simulations with numerical phase function sampling.

Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam.

Spatially resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of an infinitely small light beam. The method is, however, prone to error in measurement because the actual boundary condition and light beam often deviate from that used in deriving the analytical solutions. It is therefore important to quantify the effect of different boundary conditions and light beams on spatially resolved diffuse reflectance in order to improve the measurement accuracy of the technique. This research was aimed at using finite element method (FEM) to model light propagation in turbid media, subjected to normal illumination by a continuous-wave beam of infinitely small or finite size. Three types of boundary conditions [i.e., partial current (PCBC), extrapolated (EBC), and zero (ZBC)] were evaluated and compared against Monte Carlo (MC) simulations, since MC could provide accurate fluence rate and diffuse reflectance. The effect of beam size was also investigated. Overall results showed that FEM provided results as accurate as those of the analytical method when an appropriate boundary condition was applied. ZBC did not give satisfactory results in most cases. FEM-PCBC yielded a better fluence rate at the boundary than did FEM-EBC, while they were almost identical in predicting diffuse reflectance. Results further showed that FEM coupled with EBC effectively simulated spatially resolved diffuse reflectance under the illumination of a finite size beam. A large beam introduced more error, especially within the region of illumination. Research also confirmed an earlier finding that a light beam of less than 1 mm diameter should be used for estimation of optical parameters. FEM is effective for modeling light propagation in biological tissues and can be used for improving the optical property measurement by the spatially resolved technique.

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.

Monte Carlo methods for light propagation in biological tissues

Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis–Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang–Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg–Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.

Acceleration of Monte Carlo simulation of photon migration in complex heterogeneous media using Intel many-integrated core architecture.

Over two decades, the Monte Carlo technique has become a gold standard in simulation of light propagation in turbid media, including biotissues. Technological solutions provide further advances of this technique. The Intel Xeon Phi coprocessor is a new type of accelerator for highly parallel general purpose computing, which allows execution of a wide range of applications without substantial code modification. We present a technical approach of porting our previously developed Monte Carlo (MC) code for simulation of light transport in tissues to the Intel Xeon Phi coprocessor. We show that employing the accelerator allows reducing computational time of MC simulation and obtaining simulation speed-up comparable to GPU. We demonstrate the performance of the developed code for simulation of light transport in the human head and determination of the measurement volume in near-infrared spectroscopy brain sensing.

Modeling focusing Gaussian beams in a turbid medium with Monte Carlo simulations.

Monte Carlo techniques are the gold standard for studying light propagation in turbid media. Traditional Monte Carlo techniques are unable to include wave effects, such as diffraction; thus, these methods are unsuitable for exploring focusing geometries where a significant ballistic component remains at the focal plane. Here, a method is presented for accurately simulating photon propagation at the focal plane, in the context of a traditional Monte Carlo simulation. This is accomplished by propagating ballistic photons along trajectories predicted by Gaussian optics until they undergo an initial scattering event, after which, they are propagated through the medium by a traditional Monte Carlo technique. Solving a known problem by building upon an existing Monte Carlo implementation allows this method to be easily implemented in a wide variety of existing Monte Carlo simulations, greatly improving the accuracy of those models for studying dynamics in a focusing geometry.

Virtual-source diffusion approximation for enhanced near-field modeling of photon-migration in low-albedo medium.

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we herein report on an improved explicit model for a semi-infinite geometry, referred to as "Virtual Source" (VS) diffuse approximation (DA), to fit for low-albedo medium and short source-detector separation. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the near-field to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. This parameterized scheme is proved to inherit the mathematical simplicity of the DA approximation while considerably extending its validity in modeling the near-field photon migration in low-albedo medium. The superiority of the proposed VS-DA method to the established ones is demonstrated in comparison with Monte-Carlo simulations over wide ranges of the source-detector separation and the medium optical properties.

Breakdown of the continuum limit approximation to the discrete scattering events and its influence on the electric field autocorrelation functions of transmitted light

The complexity of modeling light propagation in turbid media can be significantly simplified if one assumes it to be diffusive. This is, however, only valid after the light has traveled a sufficient distance so that the diffusion equation can be employed. So far, there has been no reliable way to determine this distance, despite the fact that the assumption is often applied in optics. The discrete nature of scattering events plays an important role in modeling propagation of weakly scattered light, so a continuum equation such as the diffusion equation cannot be used to describe this process. Electric field autocorrelation functions ${g}_{1}(\ensuremath{\tau})$ of light transmitted through turbid colloidal samples are measured using diffusing wave spectroscopy and compared to Monte Carlo simulations in order to obtain a better estimation of the continuum limit. The two methods to calculate ${g}_{1}(\ensuremath{\tau})$ from the simulated photon trajectories are compared; the first assumes the continuum limit by using the path-length distributions of photon trajectories, while the second considers the square momentum transfers and therefore accurately calculates ${g}_{1}(\ensuremath{\tau})$ even if the detected signal is composed of weakly scattered light. The results of the two methods are used to determine the lengths of the shortest diffuse photon trajectories; they grow with the sample thickness and scattering anisotropy.

Higher order processes in random Raman lasing.

Random Raman lasers offer a unique opportunity to study many exciting dynamics of light propagation in turbid media. One of the most notable features observed to exist in the recently discovered random Raman laser are the presence of higher order stimulated Raman scattering (SRS) processes. The higher order Stokes generation likely comes from photons that have the longest pathlengths, thus have the most gain. This makes these photons particularly likely to offer interesting insight into wave propagation effects such as coherent backscattering and optical Anderson localization. In this work, we use Monte Carlo simulations to investigate how these higher order processes occur and what properties they are expected to exhibit when considering only transport equation dynamics. This knowledge will allow us to look for deviations from this theory in future experiments to determine if wavelike properties play an active role in random Raman lasing.

Multiple scattering of polarized light: influence of absorption

This work continues previous research about multiple scattering of polarized light propagation in turbid media, putting emphasis on the imaginary part of the scatterers’ complex refractive index. The whole angle-dependent Müller matrix is evaluated by comparing results of a polarization sensitive radiative transfer solution to Maxwell theory. Turbid media of defined scatterer concentrations are modelled in three dimensions by sphere ensembles kept inside a cubic or spherical simulation volume. This study addresses the impact of absorption on polarization characteristics for selected media from low to high absorption. Besides that, effects caused by multiple and dependent scattering are shown for increasing volume concentration. In this context some unique properties associated with multiple scattering and absorption are pointed out. Further, scattering results in two dimensions are compared for examples of infinite parallel cylinders of high absorption and perpendicularly incident plane waves.

New approach for absolute fluence distribution calculations in Monte Carlo simulations of light propagation in turbid media

A novel way to attain three dimensional fluence rate maps from Monte-Carlo simulations of photon propagation is presented in this work. The propagation of light in a turbid medium is described by the radiative transfer equation and formulated in terms of radiance. For many applications, particularly in biomedical optics, the fluence rate is a more useful quantity and directly derived from the radiance by integrating over all directions. Contrary to the usual way which calculates the fluence rate from absorbed photon power, the fluence rate in this work is directly calculated from the photon packet trajectory. The voxel based algorithm works in arbitrary geometries and material distributions. It is shown that the new algorithm is more efficient and also works in materials with a low or even zero absorption coefficient. The capabilities of the new algorithm are demonstrated on a curved layered structure, where a non-scattering, non-absorbing layer is sandwiched between two highly scattering layers.

Contactless and non-destructive differentiation of microstructures of sugar foams by hyperspectral scatter imaging

Abstract A hyperspectral scatter imaging system was developed for the contactless acquisition of spatially resolved diffuse reflectance profiles for the optical characterization of turbid food products in the wavelength range from 500 to 960 nm. To investigate the potential of this concept sugar foams with different microstructures, but with similar chemical compositions, have been prepared by applying different mixing times to the same mixtures of sugar and albumin. Hyperspectral scatter images have been acquired from these samples and the absorption and reduced scattering coefficients have been derived from spatially resolved reflectance profiles based on the diffusion approximation of the radiative transfer equation describing the light propagation in turbid media. The estimated reduced scattering coefficients μ s ′ spectra clearly reflected the effect of the different mixing times on the foam microstructure. On the other hand, similar absorption coefficient spectra were observed, confirming the identical chemical composition of the sugar–albumin matrix. These results indicate that the hyperspectral scatter imaging technique has potential as a non-contact and rapid method for online quality control and process monitoring of foamed food products. Industrial relevance The presented non-contact and non-destructive hyperspectral scatter imaging technique has potential for many applications in food industry domain. The technique is suitable for on-line scanning of food samples owing to the line-scanning operation in which all the wavebands are recorded simultaneously by the CCD camera. Such non-contact online screening ability makes the hyperspectral technique become highly desirable for industrial application in sorting and grading of food products by means of optical properties related to food quality attributes. A hyperspectral scatter imaging system can be easily integrated into industrial conveyor belt system for on-line food quality assessment and monitoring of industrial processes.

Molecular Optical Simulation Environment (MOSE): A Platform for the Simulation of Light Propagation in Turbid Media

The study of light propagation in turbid media has attracted extensive attention in the field of biomedical optical molecular imaging. In this paper, we present a software platform for the simulation of light propagation in turbid media named the “Molecular Optical Simulation Environment (MOSE)”. Based on the gold standard of the Monte Carlo method, MOSE simulates light propagation both in tissues with complicated structures and through free-space. In particular, MOSE synthesizes realistic data for bioluminescence tomography (BLT), fluorescence molecular tomography (FMT), and diffuse optical tomography (DOT). The user-friendly interface and powerful visualization tools facilitate data analysis and system evaluation. As a major measure for resource sharing and reproducible research, MOSE aims to provide freeware for research and educational institutions, which can be downloaded at http://www.mosetm.net.

Hybrid forward-peaked-scattering-diffusion approximations for light propagation in turbid media with low-scattering regions

Coupled light transport models which use forward-peaked scattering approximations of the radiative transport equation and the diffusion approximation to model light propagation in tissues are introduced. The forward-peaked Fokker–Planck–Eddington approximations are used in those parts of the domain in which the diffusion approximation is not valid, such as close to the source and boundary, and in low-scattering regions. The diffusion approximation is used elsewhere. The models are coupled through boundary conditions and the resulting system of equations is solved using a finite element method. The proposed coupled Fokker–Planck-diffusion and Fokker–Planck–Eddington-diffusion models are tested with simulations, and compared with the radiative transport equation, diffusion approximation and coupled radiative transport-diffusion model. The results show that the new coupled models give almost as accurate results as the radiative transport equation with reduced computational load.