A tetrahedron-based inhomogeneous Monte Carlo optical simulator

MCOCT: an experimentally and numerically validated, open-source Monte Carlo simulator for optical coherence tomography

Here, we present MCOCT, a Monte Carlo simulator for optical coherence tomography (OCT), incorporating a Gaussian illumination scheme and bias to increase backscattered event collection. MCOCT optical fluence was numerically compared and validated to an established simulator (MCX) and showed concordance at the focus while diverging slightly with distance to it. MCOCT OCT signals were experimentally compared and validated to OCT signals acquired in tissue-mimicking phantoms with known optical properties and showed a similar attenuation pattern with increasing depth while diverging beyond 1.5 mm and proximal to layer interfaces. MCOCT may help in the design of OCT systems for a wide range of applications.

Physics-guided neural network for tissue optical properties estimation

Finding the optical properties of tissue is essential for various biomedical diagnostic/therapeutic applications such as monitoring of blood oxygenation, tissue metabolism, skin imaging, photodynamic therapy, low-level laser therapy, and photo-thermal therapy. Hence, the research for more accurate and versatile optical properties estimation techniques has always been a primary interest of researchers, especially in the field of bioimaging and bio-optics. In the past, most of the prediction methods were based on physics-based models such as the pronounced diffusion approximation method. In more recent years, with the advancement and growing popularity of machine learning techniques, most of the prediction methods are data-driven. While both methods have been proven to be useful, each of them suffers from several shortcomings that could be complemented by their counterparts. Thus, there is a need to bring the two domains together to obtain superior prediction accuracy and generalizability. In this work, we proposed a physics-guided neural network (PGNN) for tissue optical properties regression which integrates physics prior and constraint into the artificial neural network (ANN) model. With this method, we have demonstrated superior generalizability of PGNN compared to its pure ANN counterpart. The prediction accuracy and generalizability of the network were evaluated on single-layered tissue samples simulated with Monte Carlo simulation. Two different test datasets, the in-domain test dataset and out-domain dataset were used to evaluate in-domain generalizability and out-domain generalizability, respectively. The physics-guided neural network (PGNN) showed superior generalizability for both in-domain and out-domain prediction compared to pure ANN.

Lawrence K, Tachtsidis I, Tong Y, Torricelli A, Urner T, Wabnitz H, Wolf M, Wolf U, Xu S, Yang C, Yodh AG, Yücel MA, Zhou W. Optical imaging and spectroscopy for the study of the human brain: status report

This report is the second part of a comprehensive two-part series aimed at reviewing an extensive and diverse toolkit of novel methods to explore brain health and function. While the first report focused on neurophotonic tools mostly applicable to animal studies, here, we highlight optical spectroscopy and imaging methods relevant to noninvasive human brain studies. We outline current state-of-the-art technologies and software advances, explore the most recent impact of these technologies on neuroscience and clinical applications, identify the areas where innovation is needed, and provide an outlook for the future directions.

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.

A review of advances in imaging methodology in fluorescence molecular tomography

Objective. Fluorescence molecular tomography (FMT) is a promising non-invasive optical molecular imaging technology with strong specificity and sensitivity that has great potential for preclinical and clinical studies in tumor diagnosis, drug development and therapeutic evaluation. However, the strong scattering of photons and insufficient surface measurements make it very challenging to improve the quality of FMT image reconstruction and its practical application for early tumor detection. Therefore, continuous efforts have been made to explore more effective approaches or solutions in the pursuit of high-quality FMT reconstructions. Approach. This review takes a comprehensive overview of advances in imaging methodology for FMT, mainly focusing on two critical issues in FMT reconstructions: improving the accuracy of solving the forward physical model and mitigating the ill-posed nature of the inverse problem from a methodological point of view. More importantly, numerous impressive and practical strategies and methods for improving the quality of FMT reconstruction are summarized. Notably, deep learning methods are discussed in detail to illustrate their advantages in promoting the imaging performance of FMT thanks to large datasets, the emergence of optimized algorithms and the application of innovative networks. Main results. The results demonstrate that the imaging quality of FMT can be effectively promoted by improving the accuracy of optical parameter modeling, combined with prior knowledge, and reducing dimensionality. In addition, the traditional regularization-based methods and deep neural network-based methods, especially end-to-end deep networks, can enormously alleviate the ill-posedness of the inverse problem and improve the quality of FMT image reconstruction. Significance. This review aims to illustrate a variety of effective and practical methods for the reconstruction of FMT images that may benefit future research. Furthermore, it may provide some valuable research ideas and directions for FMT in the future, and could promote, to a certain extent, the development of FMT and other methods of optical tomography.

Two-step verification method for Monte Carlo codes in biomedical optics applications

SIGNIFICANCE

Code verification is an unavoidable step prior to using a Monte Carlo (MC) code. Indeed, in biomedical optics, a widespread verification procedure for MC codes is still missing. Analytical benchmarks that can be easily used for the verification of different MC routines offer an important resource.

AIM

We aim to provide a two-step verification procedure for MC codes enabling the two main tasks of an MC simulator: (1) the generation of photons' trajectories and (2) the intersections of trajectories with boundaries separating the regions with different optical properties. The proposed method is purely based on elementary analytical benchmarks, therefore, the correctness of an MC code can be assessed with a one-sample t-test.

APPROACH

The two-step verification is based on the following two analytical benchmarks: (1) the exact analytical formulas for the statistical moments of the spatial coordinates where the scattering events occur in an infinite medium and (2) the exact invariant solutions of the radiative transfer equation for radiance, fluence rate, and mean path length in media subjected to a Lambertian illumination.

RESULTS

We carried out a wide set of comparisons between MC results and the two analytical benchmarks for a wide range of optical properties (from non-scattering to highly scattering media, with different types of scattering functions) in an infinite non-absorbing medium (step 1) and in a non-absorbing slab (step 2). The deviations between MC results and exact analytical values are usually within two standard errors (i.e., t-tests not rejected at a 5% level of significance). The comparisons show that the accuracy of the verification increases with the number of simulated trajectories so that, in principle, an arbitrary accuracy can be obtained.

CONCLUSIONS

Given the simplicity of the verification method proposed, we envision that it can be widely used in the field of biomedical optics.

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.

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.

A Monte Carlo study of near infrared light propagation in the human head with lesions-a time-resolved approach

Several clinical conditions leading to traumatic brain injury can cause hematomas or edemas inside the cerebral tissue. If these are not properly treated in time, they are prone to produce long-term neurological disabilities, or even death. Low-cost, portable and easy-to-handle devices are desired for continuous monitoring of these conditions and Near Infrared Spectroscopy (NIRS) techniques represent an appropriate choice. In this work, we use Time-Resolved (TR) Monte Carlo simulations to present a study of NIR light propagation over a digital MRI phantom. Healthy and injured (hematoma/edema) situations are considered. TR Diffuse Reflectance simulations for different lesion volumes and interoptode distances are performed in the frontal area and the left parietal area. Results show that mean partial pathlengths, photon measurement density functions and time dependent contrasts are sensitive to the presence of lesions, allowing their detection mainly for intermediate optodes separations, which proves that these metrics represent robust means of diagnose and monitoring. Conventional Continuous Wave (CW) contrasts are also presented as a particular case of the time dependent ones, but they result less sensitive to the lesions, and have higher associated uncertainties.

MCX Cloud-a modern, scalable, high-performance and in-browser Monte Carlo simulation platform with cloud computing

SIGNIFICANCE

Despite the ample progress made toward faster and more accurate Monte Carlo (MC) simulation tools over the past decade, the limited usability and accessibility of these advanced modeling tools remain key barriers to widespread use among the broad user community.

AIM

An open-source, high-performance, web-based MC simulator that builds upon modern cloud computing architectures is highly desirable to deliver state-of-the-art MC simulations and hardware acceleration to general users without the need for special hardware installation and optimization.

APPROACH

We have developed a configuration-free, in-browser 3D MC simulation platform-Monte Carlo eXtreme (MCX) Cloud-built upon an array of robust and modern technologies, including a Docker Swarm-based cloud-computing backend and a web-based graphical user interface (GUI) that supports in-browser 3D visualization, asynchronous data communication, and automatic data validation via JavaScript Object Notation (JSON) schemas.

RESULTS

The front-end of the MCX Cloud platform offers an intuitive simulation design, fast 3D data rendering, and convenient simulation sharing. The Docker Swarm container orchestration backend is highly scalable and can support high-demand GPU MC simulations using MCX over a dynamically expandable virtual cluster.

CONCLUSION

MCX Cloud makes fast, scalable, and feature-rich MC simulations readily available to all biophotonics researchers without overhead. It is fully open-source and can be freely accessed at http://mcx.space/cloud.

Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans' migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically "solving" the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.

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.

Compton-camera-based SPECT for thyroid cancer imaging

Thyroid cancer is the most common type of endocrine-related cancer and the most common cancer in young women. Currently, single photon emission computed tomography (SPECT) and computed tomography (CT) are used with radioiodine scintigraphy to evaluate patients with thyroid cancer. The gamma camera for SPECT contains a mechanical collimator that greatly compromises dose efficiency and limits diagnostic sensitivity. Fortunately, the Compton camera is emerging as an ideal approach for mapping the distribution of radiopharmaceuticals inside the thyroid. In this preliminary study, based on the state-of-the-art readout chip Timepix3, we investigate the feasibility of using Compton camera for radiotracer SPECT imaging in thyroid cancer. A thyroid phantom is designed to mimic human neck, the mechanism of Compton camera-based event detection is simulated to generate realistic list-mode data, and a weighted back-projection method is developed to reconstruct the original distribution of the emission source. Study results show that the Compton camera can improve the detection efficiency for two or higher orders of magnitude comparing with the conventional gamma cameras. The thyroid gland regions can be reconstructed from the Compton camera measurements in terms of radiotracer distribution. This makes the Compton-camera-based SPECT imaging a promising modality for future clinical applications with significant benefits for dose reduction, scattering artifact reduction, temporal resolution enhancement, scan throughput increment, and others.

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/.

Graphics processing unit-accelerated mesh-based Monte Carlo photon transport simulations

The mesh-based Monte Carlo (MMC) algorithm is increasingly used as the gold-standard for developing new biophotonics modeling techniques in 3-D complex tissues, including both diffusion-based and various Monte Carlo (MC)-based methods. Compared to multilayered and voxel-based MCs, MMC can utilize tetrahedral meshes to gain improved anatomical accuracy but also results in higher computational and memory demands. Previous attempts of accelerating MMC using graphics processing units (GPUs) have yielded limited performance improvement and are not publicly available. We report a highly efficient MMC-MMCL-using the OpenCL heterogeneous computing framework and demonstrate a speedup ratio up to 420× compared to state-of-the-art single-threaded CPU simulations. The MMCL simulator supports almost all advanced features found in our widely disseminated MMC software, such as support for a dozen of complex source forms, wide-field detectors, boundary reflection, photon replay, and storing a rich set of detected photon information. Furthermore, this tool supports a wide range of GPUs/CPUs across vendors and is freely available with full source codes and benchmark suites at http://mcx.space/#mmc.

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.

Smart Toolkit for Fluorescence Tomography: Simulation, Reconstruction, and Validation

OBJECTIVE

Fluorescence molecular tomography (FMT) can provide valuable molecular information by mapping the bio-distribution of fluorescent reporter molecules in the intact organism. Various prototype FMT systems have been introduced during the past decade. However, none of them has evolved as a standard tool for routine biomedical research. The goal of this paper is to develop a software package that can automate the complete FMT reconstruction procedure.

METHODS

We present smart toolkit for fluorescence tomography (STIFT), a comprehensive platform comprising three major protocols: 1) virtual FMT, i.e., forward modeling and reconstruction of simulated data; 2) control of actual FMT data acquisition; and 3) reconstruction of experimental FMT data.

RESULTS

Both simulation and phantom experiments have shown robust reconstruction results for homogeneous and heterogeneous tissue-mimicking phantoms containing fluorescent inclusions.

CONCLUSION

STIFT can be used for optimization of FMT experiments, in particular for optimizing illumination patterns.

SIGNIFICANCE

This paper facilitates FMT experiments by bridging the gaps between simulation, actual experiments, and data reconstruction.

Tissue-Specific Optical Mapping Models of Swine Atria Informed by Optical Coherence Tomography

Computational models and experimental optical mapping of cardiac electrophysiology serve as powerful tools to investigate the underlying mechanisms of arrhythmias. Modeling can also aid the interpretation of optical mapping signals, which may have different characteristics with respect to the underlying electrophysiological signals they represent. However, despite the prevalence of atrial arrhythmias such as atrial fibrillation, models of optical electrical mapping incorporating realistic structure of the atria are lacking. Therefore, we developed image-based models of atrial tissue using structural information extracted from optical coherence tomography (OCT), which can provide volumetric tissue characteristics in high resolution. OCT volumetric data of four swine atrial tissue samples were used to develop models incorporating tissue geometry, tissue-specific myofiber orientation, and ablation lesion regions. We demonstrated the use of these models through electrophysiology and photon scattering simulations. Changes in transmural electrical conduction were observed with the inclusion of OCT-derived, depth-resolved fiber orientation. Additionally, the amplitude of optical mapping signals were not found to correspond with lesion transmurality because of lesion geometry and electrical propagation occurring beyond excitation light penetration. This work established a framework for the development of tissue-specific models of atrial tissue derived from OCT imaging data, which can be useful in future investigations of electrophysiology and optical mapping signals with respect to realistic atrial tissue structure.

Accurate Monte Carlo simulation of frequency-domain optical coherence tomography

Optical coherence tomography (OCT) relies on optical interferometry to provide noninvasive imaging of living tissues. In addition to its 3D imaging capacity for medical diagnosis, its potential use for recovering optical parameters of biological tissues for biological and pathological analyses has also been explored by researchers, as pathological changes in tissue alter the microstructure of the tissue and therefore its optical properties. We aim to develop a new approach to OCT data analysis by estimating optical properties of tissues from OCT scans, which are invisible in the scans. This is an inverse problem. Solving an inverse problem involves a forward modeling step to simulate OCT scans of the tissues with hypothesized optical parameter values and an inverse step to estimate the real optical par1meters values by matching the simulated scans to real scans. In this paper, we present a Monte Carlo (MC)-based approach for simulating the frequency-domain OCT. We incorporated a focusing Gaussian light beam rather than an infinitesimally thin light beam for accurate simulations. A new and more accurate photon detection scheme is also implemented. We compare our MC model to an analytical OCT model based on the extended Huygens-Fresnel principle (EHF) to demonstrate the consistency between the two models. We show that the two models are in good agreement for tissues with high scattering and high anisotropy factors.

Dual-grid mesh-based Monte Carlo algorithm for efficient photon transport simulations in complex three-dimensional media

The mesh-based Monte Carlo (MMC) method is an efficient algorithm to model light propagation inside tissues with complex boundaries, but choosing appropriate mesh density can be challenging. A fine mesh improves the spatial resolution of the output but requires more computation. We propose an improved MMC-dual-grid mesh-based Monte Carlo (DMMC)-to accelerate photon simulations using a coarsely tessellated tetrahedral mesh for ray-tracing computation and an independent voxelated grid for output data storage. The decoupling between ray-tracing and data storage grids allows us to simultaneously achieve faster simulations and improved output spatial accuracy. Furthermore, we developed an optimized ray-tracing technique to eliminate unnecessary ray-tetrahedron intersection tests in optically thick mesh elements. We validate the proposed algorithms using a complex heterogeneous domain and compare the solutions with those from MMC and voxel-based Monte Carlo. We found that DMMC with an unrefined constrained Delaunay tessellation of the boundary nodes yielded the highest speedup, ranging from 1.3  ×   to 2.9  ×   for various scattering settings, with nearly no loss in accuracy. In addition, the optimized ray-tracing technique offers excellent acceleration in high-scattering media, reducing the ray-tetrahedron test count by over 100-fold. Our DMMC software can be downloaded at http://mcx.space/mmc.

Direct approach to compute Jacobians for diffuse optical tomography using perturbation Monte Carlo-based photon "replay"

Perturbation Monte Carlo (pMC) has been previously proposed to rapidly recompute optical measurements when small perturbations of optical properties are considered, but it was largely restricted to changes associated with prior tissue segments or regions-of-interest. In this work, we expand pMC to compute spatially and temporally resolved sensitivity profiles, i.e. the Jacobians, for diffuse optical tomography (DOT) applications. By recording the pseudo random number generator (PRNG) seeds of each detected photon, we are able to "replay" all detected photons to directly create the 3D sensitivity profiles for both absorption and scattering coefficients. We validate the replay-based Jacobians against the traditional adjoint Monte Carlo (aMC) method, and demonstrate the feasibility of using this approach for efficient 3D image reconstructions using in vitro hyperspectral wide-field DOT measurements. The strengths and limitations of the replay approach regarding its computational efficiency and accuracy are discussed, in comparison with aMC, for point-detector systems as well as wide-field pattern-based and hyperspectral imaging systems. The replay approach has been implemented in both of our open-source MC simulators - MCX and MMC (http://mcx.space).

Recent methodology advances in fluorescence molecular tomography

Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.

Particle-beam-dependent optimization for Monte Carlo simulation in hadrontherapy using tetrahedral geometries

The use of tetrahedral-based phantoms in conjunction with Monte Carlo dose calculation techniques has shown high capabilities in radiation therapy. However, the generation of a precise dose distribution can be very time-consuming since a fine tetrahedral mesh is required. In this work, we propose a new method that defines the density distribution of patient-specific tetrahedral phantoms, based upon the CT-scans and the direction of the particle beam. The final purpose is to coarsen the tetrahedral mesh to improve computational performance in Monte Carlo simulations while guaranteeing a precise dose distribution in the target volume. Contrarily to the state of the art methods that calculate the density value of a tetrahedron, locally based only on the CT-scans, our approach also takes into account the direction of the beam to minimize the error of the water equivalent thickness of the tetrahedrons before the tumor volume. In this study, the experiments carried out on a multi-layer computational phantom, and a thorax geometry, show that by applying our method on a coarse mesh, we offer a better dose distribution inside the tumor compared to other density mapping methods, in the same level of detail. This is due to the reduction of the water equivalent path length error from 9.65 mm to 0.62 mm in the case of the multi-layer phantom, and from 2.42 mm to 0.48 mm for the thorax geometry. Moreover, a similar dose coverage is obtained with refined tetrahedral meshes. As a consequence of the reduction of the number of tetrahedrons, computational time is found to be 25% shorter than both the refined tetrahedral mesh and the voxel-based structure in most cases. Using a coarse tetrahedral mesh to have accurate dose distributions on a given target is feasible as long as the water equivalent path length in the direction of the beam is respected.

Parallelized Monte Carlo software to efficiently simulate the light propagation in arbitrarily shaped objects and aligned scattering media

A GPU-based Monte Carlo software (MCtet) was developed to calculate the light propagation in arbitrarily shaped objects, like a human tooth, represented by a tetrahedral mesh. A unique feature of MCtet is a concept to realize different kinds of light-sources illuminating the complex-shaped surface of an object, for which no preprocessing step is needed. With this concept, it is also possible to consider photons leaving a turbid media and reentering again in case of a concave object. The correct implementation was shown by comparison with five other Monte Carlo software packages. A hundredfold acceleration compared with central processing units-based programs was found. MCtet can simulate anisotropic light propagation, e.g., by accounting for scattering at cylindrical structures. The important influence of the anisotropic light propagation, caused, e.g., by the tubules in human dentin, is shown for the transmission spectrum through a tooth. It was found that the sensitivity to a change in the oxygen saturation inside the pulp for transmission spectra is much larger if the tubules are considered. Another "light guiding" effect based on a combination of a low scattering and a high refractive index in enamel is described.

Lens implementation on the GATE Monte Carlo toolkit for optical imaging simulation

Optical imaging techniques are widely used for in vivo preclinical studies, and it is well known that the Geant4 Application for Emission Tomography (GATE) can be employed for the Monte Carlo (MC) modeling of light transport inside heterogeneous tissues. However, the GATE MC toolkit is limited in that it does not yet include optical lens implementation, even though this is required for a more realistic optical imaging simulation. We describe our implementation of a biconvex lens into the GATE MC toolkit to improve both the sensitivity and spatial resolution for optical imaging simulation. The lens implemented into the GATE was validated against the ZEMAX optical simulation using an US air force 1951 resolution target. The ray diagrams and the charge-coupled device images of the GATE optical simulation agreed with the ZEMAX optical simulation results. In conclusion, the use of a lens on the GATE optical simulation could improve the image quality of bioluminescence and fluorescence significantly as compared with pinhole optics.

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.

Development of computational small animal models and their applications in preclinical imaging and therapy research

The development of multimodality preclinical imaging techniques and the rapid growth of realistic computer simulation tools have promoted the construction and application of computational laboratory animal models in preclinical research. Since the early 1990s, over 120 realistic computational animal models have been reported in the literature and used as surrogates to characterize the anatomy of actual animals for the simulation of preclinical studies involving the use of bioluminescence tomography, fluorescence molecular tomography, positron emission tomography, single-photon emission computed tomography, microcomputed tomography, magnetic resonance imaging, and optical imaging. Other applications include electromagnetic field simulation, ionizing and nonionizing radiation dosimetry, and the development and evaluation of new methodologies for multimodality image coregistration, segmentation, and reconstruction of small animal images. This paper provides a comprehensive review of the history and fundamental technologies used for the development of computational small animal models with a particular focus on their application in preclinical imaging as well as nonionizing and ionizing radiation dosimetry calculations. An overview of the overall process involved in the design of these models, including the fundamental elements used for the construction of different types of computational models, the identification of original anatomical data, the simulation tools used for solving various computational problems, and the applications of computational animal models in preclinical research. The authors also analyze the characteristics of categories of computational models (stylized, voxel-based, and boundary representation) and discuss the technical challenges faced at the present time as well as research needs in the future.

Multi-atlas registration and adaptive hexahedral voxel discretization for fast bioluminescence tomography

Bioluminescence tomography (BLT) has been a valuable optical molecular imaging technique to non-invasively depict the cellular and molecular processes in living animals with high sensitivity and specificity. Due to the inherent ill-posedness of BLT, a priori information of anatomical structure is usually incorporated into the reconstruction. The structural information is usually provided by computed tomography (CT) or magnetic resonance imaging (MRI). In order to obtain better quantitative results, BLT reconstruction with heterogeneous tissues needs to segment the internal organs and discretize them into meshes with the finite element method (FEM). It is time-consuming and difficult to handle the segmentation and discretization problems. In this paper, we present a fast reconstruction method for BLT based on multi-atlas registration and adaptive voxel discretization to relieve the complicated data processing procedure involved in the hybrid BLT/CT system. A multi-atlas registration method is first adopted to estimate the internal organ distribution of the imaged animal. Then, the animal volume is adaptively discretized into hexahedral voxels, which are fed into FEM for the following BLT reconstruction. The proposed method is validated in both numerical simulation and an in vivo study. The results demonstrate that the proposed method can reconstruct the bioluminescence source efficiently with satisfactory accuracy.

Fractal propagation method enables realistic optical microscopy simulations in biological tissues

Current simulation methods for light transport in biological media have limited efficiency and realism when applied to three-dimensional microscopic light transport in biological tissues with refractive heterogeneities. We describe here a technique which combines a beam propagation method valid for modeling light transport in media with weak variations in refractive index, with a fractal model of refractive index turbulence. In contrast to standard simulation methods, this fractal propagation method (FPM) is able to accurately and efficiently simulate the diffraction effects of focused beams, as well as the microscopic heterogeneities present in tissue that result in scattering, refractive beam steering, and the aberration of beam foci. We validate the technique and the relationship between the FPM model parameters and conventional optical parameters used to describe tissues, and also demonstrate the method's flexibility and robustness by examining the steering and distortion of Gaussian and Bessel beams in tissue with comparison to experimental data. We show that the FPM has utility for the accurate investigation and optimization of optical microscopy methods such as light-sheet, confocal, and nonlinear microscopy.

Generalized mesh-based Monte Carlo for wide-field illumination and detection via mesh retessellation

Monte Carlo methods are commonly used as the gold standard in modeling photon transport through turbid media. With the rapid development of structured light applications, an accurate and efficient method capable of simulating arbitrary illumination patterns and complex detection schemes over large surface area is in great need. Here we report a generalized mesh-based Monte Carlo algorithm to support a variety of wide-field illumination methods, including spatial-frequency-domain imaging (SFDI) patterns and arbitrary 2-D patterns. The extended algorithm can also model wide-field detectors such as a free-space CCD camera. The significantly enhanced flexibility of source and detector modeling is achieved via a fast mesh retessellation process that combines the target domain and the source/detector space in a single tetrahedral mesh. Both simulations of complex domains and comparisons with phantom measurements are included to demonstrate the flexibility, efficiency and accuracy of the extended algorithm. Our updated open-source software is provided at http://mcx.space/mmc.

OptogenSIM: a 3D Monte Carlo simulation platform for light delivery design in optogenetics

Optimizing light delivery for optogenetics is critical in order to accurately stimulate the neurons of interest while reducing nonspecific effects such as tissue heating or photodamage. Light distribution is typically predicted using the assumption of tissue homogeneity, which oversimplifies light transport in heterogeneous brain. Here, we present an open-source 3D simulation platform, OptogenSIM, which eliminates this assumption. This platform integrates a voxel-based 3D Monte Carlo model, generic optical property models of brain tissues, and a well-defined 3D mouse brain tissue atlas. The application of this platform in brain data models demonstrates that brain heterogeneity has moderate to significant impact depending on application conditions. Estimated light density contours can show the region of any specified power density in the 3D brain space and thus can help optimize the light delivery settings, such as the optical fiber position, fiber diameter, fiber numerical aperture, light wavelength and power. OptogenSIM is freely available and can be easily adapted to incorporate additional brain atlases.

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.

Lensed fiber-optic probe design for efficient photon collection in scattering media

Measurement of bioluminescent or fluorescent optical reporters with an implanted fiber-optic probe is a promising approach to allow real-time monitoring of molecular and cellular processes in conscious behaving animals. Technically, this approach relies on sensitive light detection due to the relatively limited light signal and inherent light attenuation in scattering tissue. In this paper, we show that specific geometries of lensed fiber probes improve photon collection in turbid tissue such as brain. By employing Monte Carlo simulation and experimental measurement, we demonstrate that hemispherical- and axicon-shaped lensed fibers increase collection efficiency by up to 2-fold when compared with conventional bare fiber. Additionally we provide theoretical evidence that axicon lenses with specific angles improve photon collection over a wider axial range while conserving lateral collection when compared to hemispherical lensed fiber. These findings could guide the development of a minimally-invasive highly sensitive fiber optic-based light signal monitoring technique and may have broad implications such as fiber-based detection used in diffuse optical spectroscopy.

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.

Simulating photon scattering effects in structurally detailed ventricular models using a Monte Carlo approach

Light scattering during optical imaging of electrical activation within the heart is known to significantly distort the optically-recorded action potential (AP) upstroke, as well as affecting the magnitude of the measured response of ventricular tissue to strong electric shocks. Modeling approaches based on the photon diffusion equation have recently been instrumental in quantifying and helping to understand the origin of the resulting distortion. However, they are unable to faithfully represent regions of non-scattering media, such as small cavities within the myocardium which are filled with perfusate during experiments. Stochastic Monte Carlo (MC) approaches allow simulation and tracking of individual photon “packets” as they propagate through tissue with differing scattering properties. Here, we present a novel application of the MC method of photon scattering simulation, applied for the first time to the simulation of cardiac optical mapping signals within unstructured, tetrahedral, finite element computational ventricular models. The method faithfully allows simulation of optical signals over highly-detailed, anatomically-complex MR-based models, including representations of fine-scale anatomy and intramural cavities. We show that optical action potential upstroke is prolonged close to large subepicardial vessels than further away from vessels, at times having a distinct “humped” morphology. Furthermore, we uncover a novel mechanism by which photon scattering effects around vessels cavities interact with “virtual-electrode” regions of strong de-/hyper-polarized tissue surrounding cavities during shocks, significantly reducing the apparent optically-measured epicardial polarization. We therefore demonstrate the importance of this novel optical mapping simulation approach along with highly anatomically-detailed models to fully investigate electrophysiological phenomena driven by fine-scale structural heterogeneity.

Extension of the GATE Monte-Carlo simulation package to model bioluminescence and fluorescence imaging

The Geant4 Application for Emission Tomography (GATE) is an advanced open-source software dedicated to Monte-Carlo (MC) simulations in medical imaging involving photon transportation (Positron emission tomography, single photon emission computed tomography, computed tomography) and in particle therapy. In this work, we extend the GATE to support simulations of optical imaging, such as bioluminescence or fluorescence imaging, and validate it against the MC for multilayered media standard simulation tool for biomedical optics in simple geometries. A full simulation set-up for molecular optical imaging (bioluminescence and fluorescence) is implemented in GATE, and images of the light distribution emitted from a phantom demonstrate the relevance of using GATE for optical imaging simulations.

Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media

We examine the relative error of Monte Carlo simulations of radiative transport that employ two commonly used estimators that account for absorption differently, either discretely, at interaction points, or continuously, between interaction points. We provide a rigorous derivation of these discrete and continuous absorption weighting estimators within a stochastic model that we show to be equivalent to an analytic model, based on the radiative transport equation (RTE). We establish that both absorption weighting estimators are unbiased and, therefore, converge to the solution of the RTE. An analysis of spatially resolved reflectance predictions provided by these two estimators reveals no advantage to either in cases of highly scattering and highly anisotropic media. However, for moderate to highly absorbing media or isotropically scattering media, the discrete estimator provides smaller errors at proximal source locations while the continuous estimator provides smaller errors at distal locations. The origin of these differing variance characteristics can be understood through examination of the distribution of exiting photon weights.

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.

Accelerating mesh-based Monte Carlo method on modern CPU architectures

In this report, we discuss the use of contemporary ray-tracing techniques to accelerate 3D mesh-based Monte Carlo photon transport simulations. Single Instruction Multiple Data (SIMD) based computation and branch-less design are exploited to accelerate ray-tetrahedron intersection tests and yield a 2-fold speed-up for ray-tracing calculations on a multi-core CPU. As part of this work, we have also studied SIMD-accelerated random number generators and math functions. The combination of these techniques achieved an overall improvement of 22% in simulation speed as compared to using a non-SIMD implementation. We applied this new method to analyze a complex numerical phantom and both the phantom data and the improved code are available as open-source software at http://mcx.sourceforge.net/mmc/.

Reconstruction of sectional images in frequency-domain based photoacoustic imaging

Photoacoustic (PA) imaging is based upon the generation of an ultrasound pulse arising from subsurface tissue absorption due to pulsed laser excitation, and measurement of its surface time-of-arrival. Expensive and bulky pulsed lasers with high peak fluence powers may provide shortcomings for applications of PA imaging in medicine and biology. These limitations may be overcome with the frequency-domain PA measurements, which employ modulated rather than pulsed light to generate the acoustic wave. In this contribution, we model the single modulation frequency based PA pressures on the measurement plane through the diffraction approximation and then employ a convolution approach to reconstruct the sectional image slices. The results demonstrate that the proposed method with appropriate data post-processing is capable of recovering sectional images while suppressing the defocused noise resulting from the other sections.

GPU computing in medical physics: a review

The graphics processing unit (GPU) has emerged as a competitive platform for computing massively parallel problems. Many computing applications in medical physics can be formulated as data-parallel tasks that exploit the capabilities of the GPU for reducing processing times. The authors review the basic principles of GPU computing as well as the main performance optimization techniques, and survey existing applications in three areas of medical physics, namely image reconstruction, dose calculation and treatment plan optimization, and image processing.

Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media

We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the "good" seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed.

Comment on "A study on tetrahedron-based inhomogeneous Monte-Carlo optical simulation"

The Monte Carlo (MC) method is a popular approach to modeling photon propagation inside general turbid media, such as human tissue. Progress had been made in the past year with the independent proposals of two mesh-based Monte Carlo methods employing ray-tracing techniques. Both methods have shown improvements in accuracy and efficiency in modeling complex domains. A recent paper by Shen and Wang [Biomed. Opt. Express 2, 44 (2011)] reported preliminary results towards the cross-validation of the two mesh-based MC algorithms and software implementations, showing a 3-6 fold speed difference between the two software packages. In this comment, we share our views on unbiased software comparisons and discuss additional issues such as the use of pre-computed data, interpolation strategies, impact of compiler settings, use of Russian roulette, memory cost and potential pitfalls in measuring algorithm performance. Despite key differences between the two algorithms in handling of non-tetrahedral meshes, we found that they share similar structure and performance for tetrahedral meshes. A significant fraction of the observed speed differences in the mentioned article was the result of inconsistent use of compilers and libraries.