Light transport in tissue by 3D Monte Carlo: influence of boundary voxelization

The role of the light source in antimicrobial photodynamic therapy

Antimicrobial photodynamic therapy (APDT) is a promising approach to fight the growing problem of antimicrobial resistance that threatens health care, food security and agriculture. APDT uses light to excite a light-activated chemical (photosensitiser), leading to the generation of reactive oxygen species (ROS). Many APDT studies confirm its efficacy in vitro and in vivo against bacteria, fungi, viruses and parasites. However, the development of the field is focused on exploring potential targets and developing new photosensitisers. The role of light, a crucial element for ROS production, has been neglected. What are the main parameters essential for effective photosensitiser activation? Does an optimal light radiant exposure exist? And finally, which light source is best? Many reports have described the promising antibacterial effects of APDT in vitro, however, its application in vivo, especially in clinical settings remains very limited. The restricted availability may partially be due to a lack of standard conditions or protocols, arising from the diversity of selected photosensitising agents (PS), variable testing conditions including light sources used for PS activation and methods of measuring anti-bacterial activity and their effectiveness in treating bacterial infections. We thus sought to systematically review and examine the evidence from existing studies on APDT associated with the light source used. We show how the reduction of pathogens depends on the light source applied, radiant exposure and irradiance of light used, and type of pathogen, and so critically appraise the current state of development of APDT and areas to be addressed in future studies. We anticipate that further standardisation of the experimental conditions will help the field advance, and suggest key optical and biological parameters that should be reported in all APDT studies. More in vivo and clinical studies are needed and are expected to be facilitated by advances in light sources, leading to APDT becoming a sustainable, alternative therapeutic option for bacterial and other microbial infections in the future.

Meshless Monte Carlo radiation transfer method for curved geometries using signed distance functions

SIGNIFICANCE

Monte Carlo radiation transfer (MCRT) is the gold standard for modeling light transport in turbid media. Typical MCRT models use voxels or meshes to approximate experimental geometry. A voxel-based geometry does not allow for the precise modeling of smooth curved surfaces, such as may be found in biological systems or food and drink packaging. Mesh-based geometry allows arbitrary complex shapes with smooth curved surfaces to be modeled. However, mesh-based models also suffer from issues such as the computational cost of generating meshes and inaccuracies in how meshes handle reflections and refractions.

AIM

We present our algorithm, which we term signedMCRT (sMCRT), a geometry-based method that uses signed distance functions (SDF) to represent the geometry of the model. SDFs are capable of modeling smooth curved surfaces precisely while also modeling complex geometries.

APPROACH

We show that using SDFs to represent the problem's geometry is more precise than voxel and mesh-based methods.

RESULTS

sMCRT is validated against theoretical expressions, and voxel and mesh-based MCRT codes. We show that sMCRT can precisely model arbitrary complex geometries such as microvascular vessel network using SDFs. In comparison with the current state-of-the-art in MCRT methods specifically for curved surfaces, sMCRT is more precise for cases where the geometry can be defined using combinations of shapes.

CONCLUSIONS

We believe that SDF-based MCRT models are a complementary method to voxel and mesh models in terms of being able to model complex geometries and accurately treat curved surfaces, with a focus on precise simulation of reflections and refractions. sMCRT is publicly available at https://github.com/lewisfish/signedMCRT.

MCCL: an open-source software application for Monte Carlo simulations of radiative transport

The Monte Carlo Command Line application (MCCL) is an open-source software package that provides Monte Carlo simulations of radiative transport through heterogeneous turbid media. MCCL is available on GitHub through our virtualphotonics.org website, is actively supported, and carries extensive documentation. Here, we describe the main technical capabilities, the overall software architecture, and the operational details of MCCL.

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.

Hybrid mesh and voxel based Monte Carlo algorithm for accurate and efficient photon transport modeling in complex bio-tissues

Over the past decade, an increasing body of evidence has suggested that three-dimensional (3-D) Monte Carlo (MC) light transport simulations are affected by the inherent limitations and errors of voxel-based domain boundaries. In this work, we specifically address this challenge using a hybrid MC algorithm, namely split-voxel MC or SVMC, that combines both mesh and voxel domain information to greatly improve MC simulation accuracy while remaining highly flexible and efficient in parallel hardware, such as graphics processing units (GPU). We achieve this by applying a marching-cubes algorithm to a pre-segmented domain to extract and encode sub-voxel information of curved surfaces, which is then used to inform ray-tracing computation within boundary voxels. This preservation of curved boundaries in a voxel data structure demonstrates significantly improved accuracy in several benchmarks, including a human brain atlas. The accuracy of the SVMC algorithm is comparable to that of mesh-based MC (MMC), but runs 2x-6x faster and requires only a lightweight preprocessing step. The proposed algorithm has been implemented in our open-source software and is freely available at http://mcx.space.

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/.

Improving model-based functional near-infrared spectroscopy analysis using mesh-based anatomical and light-transport models

Significance: Functional near-infrared spectroscopy (fNIRS) has become an important research tool in studying human brains. Accurate quantification of brain activities via fNIRS relies upon solving computational models that simulate the transport of photons through complex anatomy. Aim: We aim to highlight the importance of accurate anatomical modeling in the context of fNIRS and propose a robust method for creating high-quality brain/full-head tetrahedral mesh models for neuroimaging analysis. Approach: We have developed a surface-based brain meshing pipeline that can produce significantly better brain mesh models, compared to conventional meshing techniques. It can convert segmented volumetric brain scans into multilayered surfaces and tetrahedral mesh models, with typical processing times of only a few minutes and broad utilities, such as in Monte Carlo or finite-element-based photon simulations for fNIRS studies. Results: A variety of high-quality brain mesh models have been successfully generated by processing publicly available brain atlases. In addition, we compare three brain anatomical models-the voxel-based brain segmentation, tetrahedral brain mesh, and layered-slab brain model-and demonstrate noticeable discrepancies in brain partial pathlengths when using approximated brain anatomies, ranging between - 1.5 % to 23% with the voxelated brain and 36% to 166% with the layered-slab brain. Conclusion: The generation and utility of high-quality brain meshes can lead to more accurate brain quantification in fNIRS studies. Our open-source meshing toolboxes "Brain2Mesh" and "Iso2Mesh" are freely available at http://mcx.space/brain2mesh.

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.

High-performance, robustly verified Monte Carlo simulation with FullMonte

We introduce the FullMonte tetrahedral 3-D Monte Carlo (MC) software package for simulation, visualization, and analysis of light propagation in heterogeneous turbid media including tissue. It provides the highest computational performance and richest set of input, output, and analysis facilities of any open-source tetrahedral-mesh MC light simulator. It also provides a robust framework for statistical verification. A scripting interface makes set-up of simulation runs simple, including parameter sweeps, while simultaneously providing customization options. Data formats shared with class-leading visualization tools, VTK and Paraview, facilitate interactive generation of publication-quality fluence and irradiance maps. The simulator can read and write file formats supported by other similar simulators, such as TIM-OS, MMC, COMSOL (finite-element simulations), and MCML to support comparison. Where simulator features permit, FullMonte can take a single test case, run it in multiple software packages, and load the results together for comparison. Example meshes, optical properties, set-up scripts, and output files are provided for user convenience. We demonstrate its use in several test cases, including photodynamic therapy of the brain, bioluminescence imaging (BLI) in a mouse phantom, and a comparison against MCML for layered geometries. Application domains that can benefit from use of FullMonte include photodynamic, photothermal, and photobiomodulation therapies, BLI, diffuse optical tomography, MC software development, and biophotonics education. Since MC results may be used for preclinical or even clinical experiments, a robust and rigorous verification process is essential. Being a stochastic numerical method, MC simulation has unique challenges associated with verification of output results since observed differences may be due simply to output variance or actual differences in expected output. We describe and have implemented a rigorous and statistically justified framework for comparing between simulators of the same class and for performing regression testing.

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.

Monte Carlo modelling of photodynamic therapy treatments comparing clustered three dimensional tumour structures with homogeneous tissue structures

We explore the effects of three dimensional (3D) tumour structures on depth dependent fluence rates, photodynamic doses (PDD) and fluorescence images through Monte Carlo radiation transfer modelling of photodynamic therapy. The aim with this work was to compare the commonly used uniform tumour densities with non-uniform densities to determine the importance of including 3D models in theoretical investigations. It was found that fractal 3D models resulted in deeper penetration on average of therapeutic radiation and higher PDD. An increase in effective treatment depth of 1 mm was observed for one of the investigated fractal structures, when comparing to the equivalent smooth model. Wide field fluorescence images were simulated, revealing information about the relationship between tumour structure and the appearance of the fluorescence intensity. Our models indicate that the 3D tumour structure strongly affects the spatial distribution of therapeutic light, the PDD and the wide field appearance of surface fluorescence images.

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

To adapt the complex tissue structure, laser propagation in a two-layered skin model is simulated to compare voxel-based Monte Carlo (VMC) and tetrahedron-based MC (TMC) methods with a geometry-based MC (GMC) method. In GMC, the interface is mathematically defined without any discretization. GMC is the most accurate but is not applicable to complicated domains. The implementation of VMC is simple because of its structured voxels. However, unavoidable errors are expected because of the zigzag polygonal interface. Compared with GMC and VMC, TMC provides a balance between accuracy and flexibility by the tetrahedron cells. In the present TMC, the body-fitted tetrahedra are generated in different tissues. No interface tetrahedral cells exist, thereby avoiding the photon reflection error in the interface cells in VMC. By introducing a distance threshold, the error caused by confused optical parameters between neighboring cells when photons are incident along the cell boundary can be avoided. The results show that the energy deposition error by TMC in the interfacial region is one-tenth to one-fourth of that by VMC, yielding more accurate computations of photon reflection, refraction, and energy deposition. The results of multilayered and n-shaped vessels indicate that a laser with a 1064-nm wavelength should be introduced to clean deep-buried vessels.

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 simulation of radiation transport in human skin with rigorous treatment of curved tissue boundaries

In three-dimensional (3-D) modeling of light transport in heterogeneous biological structures using the Monte Carlo (MC) approach, space is commonly discretized into optically homogeneous voxels by a rectangular spatial grid. Any round or oblique boundaries between neighboring tissues thus become serrated, which raises legitimate concerns about the realism of modeling results with regard to reflection and refraction of light on such boundaries. We analyze the related effects by systematic comparison with an augmented 3-D MC code, in which analytically defined tissue boundaries are treated in a rigorous manner. At specific locations within our test geometries, energy deposition predicted by the two models can vary by 10%. Even highly relevant integral quantities, such as linear density of the energy absorbed by modeled blood vessels, differ by up to 30%. Most notably, the values predicted by the customary model vary strongly and quite erratically with the spatial discretization step and upon minor repositioning of the computational grid. Meanwhile, the augmented model shows no such unphysical behavior. Artifacts of the former approach do not converge toward zero with ever finer spatial discretization, confirming that it suffers from inherent deficiencies due to inaccurate treatment of reflection and refraction at round tissue boundaries.

Mathematical modeling of the optimum pulse structure for safe and effective photo epilation using broadband pulsed light

The objective of this work is the investigation of intense pulsed light (IPL) photoepilation using Monte Carlo simulation to model the effect of the output dosimetry with millisecond exposure used by typical commercial IPL systems. The temporal pulse shape is an important parameter, which may affect the biological tissue response in terms of efficacy and adverse reactions. This study investigates the effect that IPL pulse structures, namely free discharge, square pulse, close, and spaced pulse stacking, has on hair removal. The relationship between radiant exposure distribution during the IPL pulse and chromophore heating is explored and modeled for hair follicles and the epidermis using a custom Monte Carlo computer simulation. Consistent square pulse and close pulse stacking delivery of radiant exposure across the IPL pulse is shown to generate the most efficient specific heating of the target chromophore, whilst sparing the epidermis, compared to free discharge and pulse stacking pulse delivery. Free discharge systems produced the highest epidermal temperature in the model. This study presents modeled thermal data of a hair follicle in situ, indicating that square pulse IPL technology may be the most efficient and the safest method for photoepilation. The investigation also suggests that the square pulse system design is the most efficient, as energy is not wasted during pulse exposure or lost through interpulse delay times of stacked pulses.

Highly parallel Monte-Carlo simulations of the acousto-optic effect in heterogeneous turbid media

The development of a highly parallel simulation of the acousto-optic effect is detailed. The simulation supports optically heterogeneous simulation domains under insonification by arbitrary monochromatic ultrasound fields. An adjoint method for acousto-optics is proposed to permit point-source/point-detector simulations. The flexibility and efficiency of this simulation code is demonstrated in the development of spatial absorption sensitivity maps which are in broad agreement with current experimental investigations. The simulation code has the potential to provide guidance in the feasibility and optimization of future studies of the acousto-optic technique, and its speed may permit its use as part of an iterative inversion model.

Mesh-based Monte Carlo method using fast ray-tracing in Plücker coordinates

We describe a fast mesh-based Monte Carlo (MC) photon migration algorithm for static and time-resolved imaging in 3D complex media. Compared with previous works using voxel-based media discretization, a mesh-based approach can be more accurate in modeling targets with curved boundaries or locally refined structures. We implement an efficient ray-tracing technique using Plücker Coordinates. The Barycentric coordinates computed from Plücker-formed ray-tracing enables us to use linear Lagrange basis functions to model both media properties and fluence distribution, leading to further improvement in accuracy. The Plücker-coordinate ray-polygon intersection test can be extended to hexahedral or high-order elements. Excellent agreement is found when comparing mesh-based MC with the analytical diffusion model and 3D voxel-based MC code in both homogeneous and heterogeneous cases. Realistic time-resolved imaging results are observed for a complex human brain anatomy using mesh-based MC. We also include multi-threading support in the software and will port it to a graphics processing unit platform in the near future.

A tetrahedron-based inhomogeneous Monte Carlo optical simulator

Optical imaging has been widely applied in preclinical and clinical applications. Fifteen years ago, an efficient Monte Carlo program 'MCML' was developed for use with multi-layered turbid media and has gained popularity in the field of biophotonics. Currently, there is an increasingly pressing need for simulating tools more powerful than MCML in order to study light propagation phenomena in complex inhomogeneous objects, such as the mouse. Here we report a tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIM-OS) to address this issue. By modeling an object as a tetrahedron-based inhomogeneous finite-element mesh, TIM-OS can determine the photon-triangle interaction recursively and rapidly. In numerical simulation, we have demonstrated the correctness and efficiency of TIM-OS.

Feasibility of Monte CarlO simulations in Quantitative Tissue Imaging

Purpose

The feasibility of Monte Carlo simulations as a tool to facilitate quantitative image analysis is investigated by means of simulating light transport in skin phantoms.

Methods

A Monte Carlo tool is used to compare if simulated fluorescent signals show agreement with measured data. The lipophilic fluorescent probe Nile Red and dedicated skin phantoms are also used in simulations to investigate the influence of the optical properties of the skin on the signal.

Results

It is shown that the simulated and measured fluorescence signals show linear behavior up to a certain concentration of Nile Red. The simulations of the skin phantoms show the varying influence of single skin layers on the fluorescence signal. A calibration factor for quantitative analysis can be determined for the different skin layers.

Conclusion

Characterizing the influence of different media on imaging signals is a primary task in developing quantitative analysis methods. Monte Carlo simulations are a useful tool to investigate imaging properties of biological specimen where quantifying signals is important. However, detailed models must be provided.

Full-field laser-Doppler imaging and its physiological significance for tissue blood perfusion

Using Monte Carlo simulations for a semi-infinite medium representing a skeletal muscle tissue, it is demonstrated that the zero- and first-order moments of the power spectrum for a representative pixel of a full-field laser-Doppler imager behave differently from classical laser-Doppler flowmetry. In particular, the zero-order moment has a very low sensitivity to tissue blood volume changes, and it becomes completely insensitive if the probability for a photon to interact with a moving red blood cell is above 0.05. It is shown that the loss in sensitivity is due to the strong forward scatter of the propagating photons in biological tissues (i.e., anisotropy factor g = 0.9). The first-order moment is linearly related to the root mean square of the red blood cell velocity (the Brownian component), and there is also a positive relationship with tissue blood volume. The most common physiological interpretation of the first-order moment is as tissue blood volume times expectation of the blood velocity (in probabilistic terms). In this sense, the use of the first-order moment appears to be a reasonable approach for qualitative real-time blood flow monitoring, but it does not allow us to obtain information on blood velocity or volume independently. Finally, it is shown that the spatial and temporal resolution trade-off imposed by the CMOS detectors, used in full-field laser-Doppler hardware, may lead to measurements that vary oppositely with the underlying physiological quantities. Further improvements on detectors' sampling rate will overcome this limitation.