Perturbation and differential Monte Carlo methods for measurement of optical properties in a layered epithelial tissue model

Application limits of the scaling relations for Monte Carlo simulations in diffuse optics. Part 1: theory

Monte Carlo (MC) is a powerful tool to study photon migration in scattering media, yet quite time-consuming to solve inverse problems. To speed up MC-simulations, scaling relations can be applied to an existing initial MC-simulation to generate a new data-set with different optical properties. We named this approach trajectory-based since it uses the knowledge of the detected photon trajectories of the initial MC-simulation, in opposition to the slower photon-based approach, where a novel MC-simulation is rerun with new optical properties. We investigated the convergence and applicability limits of the scaling relations, both related to the likelihood that the sample of trajectories considered is representative also for the new optical properties. For absorption, the scaling relation contains smoothly converging Lambert-Beer factors, whereas for scattering it is the product of two quickly diverging factors, whose ratio, for NIRS cases, can easily reach ten orders of magnitude. We investigated such instability by studying the probability-distribution for the number of scattering events in trajectories of given length. We propose a convergence test of the scattering scaling relation based on the minimum-maximum number of scattering events in recorded trajectories. We also studied the dependence of MC-simulations on optical properties, most critical in inverse problems, finding that scattering derivatives are ascribed to small deviations in the distribution of scattering events from a Poisson distribution. This paper, which can also serve as a tutorial, helps to understand the physics of the scaling relations with the causes of their limitations and devise new strategies to deal with them.

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.

High-resolution three-dimensional blood flow tomography in the subdiffuse regime using laser speckle contrast imaging

SIGNIFICANCE

Visualizing high-resolution hemodynamics in cerebral tissue over a large field of view (FOV), provides important information in studying disease states affecting the brain. Current state-of-the-art optical blood flow imaging techniques either lack spatial resolution or are too slow to provide high temporal resolution reconstruction of flow map over a large FOV.

AIM

We present a high spatial resolution computational optical imaging technique based on principles of laser speckle contrast imaging (LSCI) for reconstructing the blood flow maps in complex tissue over a large FOV provided that the three-dimensional (3D) vascular structure is known or assumed.

APPROACH

Our proposed method uses a perturbation Monte Carlo simulation of the high-resolution 3D geometry for both accurately deriving the speckle contrast forward model and calculating the Jacobian matrix used in our reconstruction algorithm to achieve high resolution. Given the convex nature of our highly nonlinear problem, we implemented a mini-batch gradient descent with an adaptive learning rate optimization method to iteratively reconstruct the blood flow map. Specifically, we implemented advanced optimization techniques combined with efficient parallelization and vectorization of the forward and derivative calculations to make reconstruction of the blood flow map feasible with reconstruction times on the order of tens of minutes.

RESULTS

We tested our reconstruction algorithm through simulation of both a flow phantom model as well as an anatomically correct murine cerebral tissue and vasculature captured via two-photon microscopy. Additionally, we performed a noise study, examining the robustness of our inverse model in presence of 0.1% and 1% additive noise. In all cases, the blood flow reconstruction error was <2  %   for most of the vasculature, except for the peripheral vasculature which suffered from insufficient photon sampling. Descending vasculature and deeper structures showed slightly higher sensitivity to noise compared with vasculature with a horizontal orientation at the more superficial layers. Our results show high-resolution reconstruction of the blood flow map in tissue down to 500  μm and beyond.

CONCLUSIONS

We have demonstrated a high-resolution computational imaging technique for visualizing blood flow map in complex tissue over a large FOV. Once a high-resolution structural image is captured, our reconstruction algorithm only requires a few LSCI images captured through a camera to reconstruct the blood flow map computationally at a high resolution. We note that the combination of high temporal and spatial resolution of our reconstruction algorithm makes the solution well-suited for applications involving fast monitoring of flow dynamics over a large FOV, such as in functional neural imaging.

Recovery of layered tissue optical properties from spatial frequency-domain spectroscopy and a deterministic radiative transport solver

We present a method to recover absorption and reduced scattering spectra for each layer of a two-layer turbid media from spatial frequency-domain spectroscopy data. We focus on systems in which the thickness of the top layer is less than the transport mean free path   (  0.1  -  0.8l  *    )  . We utilize an analytic forward solver, based upon the N'th-order spherical harmonic expansion with Fourier decomposition   (  SHEFN  )   method in conjunction with a multistage inverse solver. We test our method with data obtained using spatial frequency-domain spectroscopy with 32 evenly spaced wavelengths within λ  =  450 to 1000 nm on six-layered tissue phantoms with distinct optical properties. We demonstrate that this approach can recover absorption and reduced scattering coefficient spectra for both layers with accuracy comparable with current Monte Carlo methods but with lower computational cost and potential flexibility to easily handle variations in parameters such as the scattering phase function or material refractive index. To our knowledge, this approach utilizes the most accurate deterministic forward solver used in such problems and can successfully recover properties from a two-layer media with superficial layer thicknesses.

Development of perturbation Monte Carlo methods for polarized light transport in a discrete particle scattering model

We present a polarization-sensitive, transport-rigorous perturbation Monte Carlo (pMC) method to model the impact of optical property changes on reflectance measurements within a discrete particle scattering model. The model consists of three log-normally distributed populations of Mie scatterers that approximate biologically relevant cervical tissue properties. Our method provides reflectance estimates for perturbations across wavelength and/or scattering model parameters. We test our pMC model performance by perturbing across number densities and mean particle radii, and compare pMC reflectance estimates with those obtained from conventional Monte Carlo simulations. These tests allow us to explore different factors that control pMC performance and to evaluate the gains in computational efficiency that our pMC method provides.

Pressure modulation algorithm to separate cerebral hemodynamic signals from extracerebral artifacts

We introduce and validate a pressure measurement paradigm that reduces extracerebral contamination from superficial tissues in optical monitoring of cerebral blood flow with diffuse correlation spectroscopy (DCS). The scheme determines subject-specific contributions of extracerebral and cerebral tissues to the DCS signal by utilizing probe pressure modulation to induce variations in extracerebral blood flow. For analysis, the head is modeled as a two-layer medium and is probed with long and short source-detector separations. Then a combination of pressure modulation and a modified Beer-Lambert law for flow enables experimenters to linearly relate differential DCS signals to cerebral and extracerebral blood flow variation without a priori anatomical information. We demonstrate the algorithm's ability to isolate cerebral blood flow during a finger-tapping task and during graded scalp ischemia in healthy adults. Finally, we adapt the pressure modulation algorithm to ameliorate extracerebral contamination in monitoring of cerebral blood oxygenation and blood volume by near-infrared spectroscopy.

Robust estimation of cerebral hemodynamics in neonates using multilayered diffusion model for normal and oblique incidences

The diffusion approximation is useful for many optical diagnostics modalities, such as near-infrared spectroscopy. However, the simple normal incidence, semi-infinite layer model may prove lacking in estimation of deep-tissue optical properties such as required for monitoring cerebral hemodynamics, especially in neonates. To answer this need, we present an analytical multilayered, oblique incidence diffusion model. Initially, the model equations are derived in vector-matrix form to facilitate fast and simple computation. Then, the spatiotemporal reflectance predicted by the model for a complex neonate head is compared with time-resolved Monte Carlo (TRMC) simulations under a wide range of physiologically feasible parameters. The high accuracy of the multilayer model is demonstrated in that the deviation from TRMC simulations is only a few percent even under the toughest conditions. We then turn to solve the inverse problem and estimate the oxygen saturation of deep brain tissues based on the temporal and spatial behaviors of the reflectance. Results indicate that temporal features of the reflectance are more sensitive to deep-layer optical parameters. The accuracy of estimation is shown to be more accurate and robust than the commonly used single-layer diffusion model. Finally, the limitations of such approaches are discussed thoroughly.

Verification of a two-layer inverse Monte Carlo absorption model using multiple source-detector separation diffuse reflectance spectroscopy

A two-layer Monte Carlo lookup table-based inverse model is validated with two-layered phantoms across physiologically relevant optical property ranges. Reflectance data for source-detector separations of 370 μm and 740 μm were collected from these two-layered phantoms and top layer thickness, reduced scattering coefficient and the top and bottom layer absorption coefficients were extracted using the inverse model and compared to the known values. The results of the phantom verification show that this method is able to accurately extract top layer thickness and scattering when the top layer thickness ranges from 0 to 550 μm. In this range, top layer thicknesses were measured with an average error of 10% and the reduced scattering coefficient was measured with an average error of 15%. The accuracy of top and bottom layer absorption coefficient measurements was found to be highly dependent on top layer thickness, which agrees with physical expectation; however, within appropriate thickness ranges, the error for absorption properties varies from 12-25%.

Perturbation Monte Carlo methods for tissue structure alterations

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.

A GAMOS plug-in for GEANT4 based Monte Carlo simulation of radiation-induced light transport in biological media

We describe a tissue optics plug-in that interfaces with the GEANT4/GAMOS Monte Carlo (MC) architecture, providing a means of simulating radiation-induced light transport in biological media for the first time. Specifically, we focus on the simulation of light transport due to the Čerenkov effect (light emission from charged particle's traveling faster than the local speed of light in a given medium), a phenomenon which requires accurate modeling of both the high energy particle and subsequent optical photon transport, a dynamic coupled process that is not well-described by any current MC framework. The results of validation simulations show excellent agreement with currently employed biomedical optics MC codes, [i.e., Monte Carlo for Multi-Layered media (MCML), Mesh-based Monte Carlo (MMC), and diffusion theory], and examples relevant to recent studies into detection of Čerenkov light from an external radiation beam or radionuclide are presented. While the work presented within this paper focuses on radiation-induced light transport, the core features and robust flexibility of the plug-in modified package make it also extensible to more conventional biomedical optics simulations. The plug-in, user guide, example files, as well as the necessary files to reproduce the validation simulations described within this paper are available online at http://www.dartmouth.edu/optmed/research-projects/monte-carlo-software.

Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities

We present a hybrid method that combines a multilayered scaling method and a perturbation method to speed up the Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with finite-size tumor-like heterogeneities. The proposed method consists of two steps. In the first step, a set of photon trajectory information generated from a baseline Monte Carlo simulation is utilized to scale the exit weight and exit distance of survival photons for the multilayered tissue model. In the second step, another set of photon trajectory information, including the locations of all collision events from the baseline simulation and the scaling result obtained from the first step, is employed by the perturbation Monte Carlo method to estimate diffuse reflectance from the multilayered tissue model with tumor-like heterogeneities. Our method is demonstrated to shorten simulation time by several orders of magnitude. Moreover, this hybrid method works for a larger range of probe configurations and tumor models than the scaling method or the perturbation method alone.

Analysis of single Monte Carlo methods for prediction of reflectance from turbid media

Starting from the radiative transport equation we derive the scaling relationships that enable a single Monte Carlo (MC) simulation to predict the spatially- and temporally-resolved reflectance from homogeneous semi-infinite media with arbitrary scattering and absorption coefficients. This derivation shows that a rigorous application of this single Monte Carlo (sMC) approach requires the rescaling to be done individually for each photon biography. We examine the accuracy of the sMC method when processing simulations on an individual photon basis and also demonstrate the use of adaptive binning and interpolation using non-uniform rational B-splines (NURBS) to achieve order of magnitude reductions in the relative error as compared to the use of uniform binning and linear interpolation. This improved implementation for sMC simulation serves as a fast and accurate solver to address both forward and inverse problems and is available for use at http://www.virtualphotonics.org/.

Role of optical spectroscopy using endogenous contrasts in clinical cancer diagnosis

Optical spectroscopy has been intensively studied for cancer management in the past two decades. This review paper first introduces the background of optical spectroscopy for cancer management, which includes the advantages of optical techniques compared to other established techniques, the principle of optical spectroscopy and the typical setup of instrumentation. Then the recent progress in optical spectroscopy for cancer diagnosis in the following organs is reviewed: the brain, breast, cervix, lung, stomach, colon, prostate and the skin. Reviewed papers were selected from the PubMed database with keywords combining the terms of individual optical spectroscopy techniques and cancers. The primary focus is on the in vivo applications of optical spectroscopy in clinical studies. Ex vivo studies are also included for some organs to highlight special applications or when there are few in vivo results in the literature. Practical considerations of applying optical spectroscopy in clinical settings such as the speed, cost, complexity of operation, accuracy and clinical value are discussed. A few commercially available clinical instruments that are based on optical spectroscopy techniques are presented. Finally several technical challenges and standard issues are discussed and firm conclusions are made.

Experimental and theoretical evaluation of a fiber-optic approach for optical property measurement in layered epithelial tissue

Improvements in measurement of epithelial tissue optical properties (OPs) in the ultraviolet and visible (UV-Vis) may lead to enhanced understanding of optical techniques for neoplasia detection. In this study, we investigated an approach based on fiber-optic measurement of reflectance to determine absorption and reduced scattering coefficients (μ(a) and μ(s)') in two-layer turbid media. Neural network inverse models were trained on simulation data for a wide variety of OP combinations (μ(a) = 1-22.5, μ(s)' = 5-42.5 cm(-1)). Experimental measurements of phantoms with top-layer thicknesses (D) ranging from 0.22 to 0.66 mm were performed at three UV-Vis wavelengths. OP estimation accuracy was calculated and compared to theoretical results. Mean prediction errors were strongly correlated with D and ranged widely, from 1.5 to 12.1 cm(-1). Theoretical analyses indicated the potential for improving accuracy with alternate probe geometries. Although numerous challenges remain, this initial experimental study of an unconstrained approach for fiber-optic-based OP determination in two-layer epithelial tissue indicates the potential to provide useful measurements.

Adaptive spectral window sizes for extraction of diagnostic features from optical spectra

We present an approach to adaptively adjust the spectral window sizes for optical spectra feature extraction. Previous studies extracted features from spectral windows of a fixed width. In our algorithm, piecewise linear regression is used to adaptively adjust the window sizes to find the maximum window size with reasonable linear fit with the spectrum. This adaptive windowing technique ensures the signal linearity in defined windows; hence, the adaptive windowing technique retains more diagnostic information while using fewer windows. This method was tested on a data set of diffuse reflectance spectra of oral mucosa lesions. Eight features were extracted from each window. We performed classifications using linear discriminant analysis with cross-validation. Using windowing techniques results in better classification performance than not using windowing. The area under the receiver-operating-characteristics curve for windowing techniques was greater than a nonwindowing technique for both normal versus mild dysplasia (MD) plus severe high-grade dysplasia or carcinama (SD) (MD+SD) and benign versus MD+SD. Although adaptive and fixed-size windowing perform similarly, adaptive windowing utilizes significantly fewer windows than fixed-size windows (number of windows per spectrum: 8 versus 16). Because adaptive windows retain most diagnostic information while reducing the number of windows needed for feature extraction, our results suggest that it isolates unique diagnostic features in optical spectra.

Quantification of the optical properties of two-layer turbid materials using a hyperspectral imaging-based spatially-resolved technique

Recent research has shown that a hyperspectral imaging-based spatially-resolved technique is useful for determining the optical properties of homogenous fruits and food products. To better characterize fruit properties and quality attributes, it is desirable to consider fruit to be composed of two homogeneous layers of skin and flesh. This research was aimed at developing a nondestructive method to determine the absorption and scattering properties of two-layer turbid materials with the characteristics of fruit. An inverse algorithm along with the sensitivity coefficient analysis for a two-layer diffusion model was developed for the extraction of optical properties from the spatially-resolved diffuse reflectance data acquired using a hyperspectral imaging system. The diffusion model and the inverse algorithm were validated with Monte Carlo simulations and experimental measurements from solid model samples of known optical properties. The average errors of determining two and four optical parameters were 6.8% and 15.3%, respectively, for Monte Carlo reflectance data. The optical properties of the first or top layer of the model samples were determined with errors of less than 23.0% for the absorption coefficient and 18.4% for the reduced scattering coefficient. The inverse algorithm did not give acceptable estimations for the second or lower layer of the model samples. While the hyperspectral imaging-based spatially-resolved technique has the potential to measure the optical properties of two-layer turbid materials like fruits and food products, further improvements are needed in determining the optical properties of the second layer.

Simultaneous multispectral reflectance imaging and laser speckle flowmetry of cerebral blood flow and oxygen metabolism in focal cerebral ischemia

Real-time investigation of cerebral blood flow (CBF), and oxy- and deoxyhemoglobin concentration (HbO, HbR) dynamics has been difficult until recently due to limited spatial and temporal resolution of techniques like laser Doppler flowmetry and magnetic resonance imaging (MRI). The combination of laser speckle flowmetry (LSF) and multispectral reflectance imaging (MSRI) yields high-resolution spatiotemporal maps of hemodynamic and metabolic changes in response to functional cortical activation. During acute focal cerebral ischemia, changes in HbO and HbR are much larger than in functional activation, resulting in the failure of the Beer-Lambert approximation to yield accurate results. We describe the use of simultaneous LSF and MSRI, using a nonlinear Monte Carlo fitting technique, to record rapid changes in CBF, HbO, HbR, and cerebral metabolic rate of oxygen (CMRO(2)) during acute focal cerebral ischemia induced by distal middle cerebral artery occlusion (dMCAO) and reperfusion. This technique captures CBF and CMRO(2) changes during hemodynamic and metabolic events with high temporal and spatial resolution through the intact skull and demonstrates the utility of simultaneous LSF and MSRI in mouse models of cerebrovascular disease.

Radiative transport in the delta-P1 approximation for semi-infinite turbid media

We have developed an analytic solution for spatially resolved diffuse reflectance within the deltaP1 approximation to the radiative transport equation for a semi-infinite homogeneous turbid medium. We evaluate the performance of this solution by comparing its predictions with those provided by Monte Carlo simulations and the standard diffusion approximation. We demonstrate that the delta-P1 approximation provides accurate estimates for spatially resolved diffuse reflectance in both low and high scattering media. We also develop a multi-stage nonlinear optimization algorithm in which the radiative transport estimates provided by the delta-P1 approximation are used to recover the optical absorption (microa), reduced scattering (micros'), and single-scattering asymmetry coefficients (g1) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the delta-P1 approximation can be used to recover microa, micros', and g1 with errors within +/- 22%, +/- 18%, and +/- 17%, respectively, for both intralipid-based and siloxane-based tissue phantoms. These phantoms span the optical property range 4 < (micros' /microa) < 117. Using these same measurements, application of the standard diffusion approximation resulted in the recovery of microa and micros' with errors o f +/- 29% and +/- 25%, respectively. Collectively, these results demonstrate that the delta-P1 approximation provides accurate radiative transport estimates that can be used to determine accurately the optical properties of biological tissues, particularly in spectral regions where tissue may display moderate/low ratios of reduced scattering to absorption (micros'/microa).