Estimation of optical properties by spatially resolved reflectance spectroscopy in the subdiffusive regime

Skin microcirculatory responses: A potential marker for early diabetic neuropathy assessment using a low-cost portable diffuse optical spectrometry device

Diffuse optical measurement is an evolving optical modality providing a fast and portable solution for microcirculation assessment. Diffuse optics in static and dynamic modalities are combined here in a system to assess hemodynamics in skin tissues of control and diabetic subjects. The in-house developed system consists of a laser source, fiber optic probe, a low-cost avalanche photodiode, a finite element model (FEM) derived static optical property estimator, and a software correlator for continuous flow monitoring through microvasculature. The studies demonstrated that the system quantifies the changes in blood flow rate in the immediate skin subsurface. The system is calibrated with in vitro flow models and a proof-of-concept was demonstrated on a limited number of subjects in a clinical environment. The flow changes in response to vasoconstrictive and vasodilative stimuli were analyzed and used to classify different stages of diabetes, including diabetic neuropathy.

First in human measurements of abscess cavity optical properties and methylene blue uptake prior to photodynamic therapy by in vivo diffuse reflectance spectroscopy

Significance

Efficacious photodynamic therapy (PDT) of abscess cavities requires personalized treatment planning. This relies on knowledge of abscess wall optical properties, which we report for the first time in human subjects.

Aim

The objective was to extract optical properties and photosensitizer concentration from spatially-resolved diffuse reflectance measurements of abscess cavities prior to methylene blue (MB) PDT, as part of a Phase 1 clinical trial.

Approach

Diffuse reflectance spectra were collected at the abscess wall of 13 human subjects using a custom fiber-optic probe and optical spectroscopy system, before and after MB administration. A Monte Carlo lookup table was used to extract optical properties.

Results

Pre-MB abscess wall absorption coefficients at 665 nm were 0.15±0.1 cm -1 (0.03-0.36 cm -1 ) and 10.74±15.81 cm -1 (0.08-49.3 cm -1 ) post-MB. Reduced scattering coefficients at 665 nm were 8.45±2.37 cm -1 (4.8-13.2 cm -1 ) and 5.6±2.26 cm -1 (1.6-9.9 cm -1 ) for pre-MB and post-MB, respectively. Oxygen saturations were found to be 58.83±35.78% (5.6-100%) pre-MB and 36.29±25.1% (0.0001-76.4%) post-MB. Determined MB concentrations were 71.83±108.22 µM (0-311 µM).

Conclusions

We observed substantial inter-subject variation in both native wall optical properties and methylene blue uptake. This underscores the importance of making these measurements for patient-specific treatment planning.

Photometric and Monte-Carlo modeling unified approach for the calculation of spatially-resolved correction coefficients linking simulated and experimental diffuse reflectance spectra

The estimation of skin optical properties by means of inverse problem solving from spatially resolved diffuse reflectance (SR-DR) spectra is one way to exploit the acquired clinical signals. This method requires the comparison between the experimental spectra collected with a medical device, and spectra generated by the photons transport numerical simulations. This comparison is usually limited to spectral shape due to the absence of intensity standardization of the experimental DR spectra. This study proposes to theoretically (using photometric calculation) and experimentally (from experimental spectra acquired on optical phantom) establish a corrective factor to obtain common intensity unit for experimental and simulated signals.

Neural network-based optimization of sub-diffuse reflectance spectroscopy for improved parameter prediction and efficient data collection

In this study, a general and systematical investigation of sub-diffuse reflectance spectroscopy is implemented. A Gegenbauer-kernel phase function-based Monte Carlo is adopted to describe photon transport more efficiently. To improve the computational efficiency and accuracy, two neural network algorithms, namely, back propagation neural network and radial basis function neural network are utilized to predict the absorption coefficient μ a , reduced scattering coefficient μ s ' and sub-diffusive quantifier γ , simultaneously, at multiple source-detector separations (SDS). The predicted results show that the three parameters can be predicated accurately by selecting five SDSs or above. Based on the simulation results, a four wavelength (520, 650, 785 and 830 nm) measurement system using five SDSs is designed by adopting phase-lock-in technique. Furtherly, the trained neural-network models are utilized to extract optical properties from the phantom and in vivo experimental data. The results verify the feasibility and effectiveness of our proposed system and methods in mucosal disease diagnosis.

Two-term scattering phase function for photon transport to model subdiffuse reflectance in superficial tissues

For Monte Carlo simulations of light transport in a variety of diffuse scattering applications, a single-scattering two-term phase function with five adjustable parameters is sufficiently flexible to separately control the forward and backward components of scattering. The forward component dominates light penetration into a tissue and the resulting diffuse reflectance. The backward component controls early subdiffuse scatter from superficial tissues. The phase function consists of a linear combination of two phase functions [Reynolds and McCormick, J. Opt. Soc. Am.70, 1206 (1980)10.1364/JOSA.70.001206] that were derived from the generating function for Gegenbauer polynomials. The two-term phase function (TT) accommodates strongly-forward anisotropic scattering with enhanced backscattering and is a generalization of the two-term, three-parameter Henyey-Greenstein phase function. An analytical inverse of the cumulative distribution function for scattering is provided for implementation in Monte Carlo simulations. Explicit TT equations are given for the single-scattering metrics g ₁, g ₂, γ, and δ. Scattering data from previously published bio-optical data are shown to fit better with the TT than other phase function models. Example Monte Carlo simulations illustrate the use of the TT and its independent control of subdiffuse scatter.

Phase function estimation from a diffuse optical image via deep learning

Objective. The phase function is a key element of a light propagation model for Monte Carlo (MC) simulation, which is usually fitted with an analytic function with associated parameters. In recent years, machine learning methods were reported to estimate the parameters of the phase function of a particular form such as the Henyey–Greenstein phase function but, to our knowledge, no studies have been performed to determine the form of the phase function. Approach. Here we design a convolutional neural network (CNN) to estimate the phase function from a diffuse optical image without any explicit assumption on the form of the phase function. Specifically, we use a Gaussian mixture model (GMM) as an example to represent the phase function generally and learn the model parameters accurately. The GMM is selected because it provides the analytic expression of phase function to facilitate deflection angle sampling in MC simulation, and does not significantly increase the number of free parameters. Main Results. Our proposed method is validated on MC-simulated reflectance images of typical biological tissues using the Henyey–Greenstein phase function with different anisotropy factors. The mean squared error of the phase function is 0.01 and the relative error of the anisotropy factor is 3.28%. Significance. We propose the first data-driven CNN-based inverse MC model to estimate the form of scattering phase function. The effects of field of view and spatial resolution are analyzed and the findings provide guidelines for optimizing the experimental protocol in practical applications.

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.

Optical property recovery with spatially-resolved diffuse reflectance at short source-detector separations using a compact fiber-optic probe

We describe a compact fiber-optic probe (2 mm outside diameter) that utilizes spatially-resolved diffuse reflectance for tissue optical property recovery. Validation was performed in phantoms containing Intralipid 20% as scatterer, and methylene blue (MB), MnTPPS, and/or India ink as absorbers. Over a range of conditions, the reduced scattering coefficient was recovered with a root mean square error (RMSE) of 0.86-2.7 cm^-1 (average error = 3.8%). MB concentration was recovered with RMSE = 0.26-0.52 µM (average error = 15.0%), which did not vary with inclusion of MnTPPS (p=0.65). This system will be utilized to determine optical properties in human abscesses, in order to generate treatment plans for photodynamic therapy.

Proposal for a Skin Layer-Wise Decomposition Model of Spatially-Resolved Diffuse Reflectance Spectra Based on Maximum Depth Photon Distributions: A Numerical Study

In the context of cutaneous carcinoma diagnosis based on in vivo optical biopsy, Diffuse Reflectance (DR) spectra, acquired using a Spatially Resolved (SR) sensor configuration, can be analyzed to distinguish healthy from pathological tissues. The present contribution aims at studying the depth distribution of SR-DR-detected photons in skin from the perspective of analyzing how these photons contribute to acquired spectra carrying local physiological and morphological information. Simulations based on modified Cuda Monte Carlo Modeling of Light transport were performed on a five-layer human skin optical model with epidermal thickness, phototype and dermal blood content as variable parameters using (i) wavelength-resolved scattering and absorption properties and (ii) the geometrical configuration of a multi-optical fiber probe implemented on an SR-DR spectroscopic device currently used in clinics. Through histograms of the maximum probed depth and their exploitation, we provide numerical evidence linking the characteristic penetration depth of the detected photons to their wavelengths and four source–sensor distances, which made it possible to propose a decomposition of the DR signals related to skin layer contributions.

Optical properties of PlatSil SiliGlass tissue-mimicking phantoms

In this work, we revise the preparation procedure and conduct an in depth characterization of optical properties for the recently proposed silicone-based tissue-mimicking optical phantoms in the spectral range from 475 to 925 nm. The optical properties are characterized in terms of refractive index and its temperature dependence, absorption and reduced scattering coefficients and scattering phase function related quantifiers. The scattering phase function and related quantifiers of the optical phantoms are first assessed within the framework of the Mie theory by using the measured refractive index of SiliGlass and size distribution of the hollow silica spherical particles that serve as scatterers. A set of purely absorbing optical phantoms in cuvettes is used to evaluate the linearity of the absorption coefficient with respect to the concentration of black pigment that serves as the absorber. Finally, the optical properties in terms of the absorption and reduced scattering coefficients and the subdiffusive scattering phase function quantifier γ are estimated for a subset of phantoms from spatially resolved reflectance using deep learning aided inverse models. To this end, an optical fiber probe with six linearly arranged optical fibers is used to collect the backscattered light at small and large distances from the source fiber. The underlying light propagation modeling is based on the stochastic Monte Carlo method that accounts for all the details of the optical fiber probe.

Fast and accurate Monte Carlo simulations of subdiffusive spatially resolved reflectance for a realistic optical fiber probe tip model aided by a deep neural network

In this work, we introduce a framework for efficient and accurate Monte Carlo (MC) simulations of spatially resolved reflectance (SRR) acquired by optical fiber probes that account for all the details of the probe tip including reflectivity of the stainless steel and the properties of the epoxy fill and optical fibers. While using full details of the probe tip is essential for accurate MC simulations of SRR, the break-down of the radial symmetry in the detection scheme leads to about two orders of magnitude longer simulation times. The introduced framework mitigates this performance degradation, by an efficient reflectance regression model that maps SRR obtained by fast MC simulations based on a simplified probe tip model to SRR simulated using the full details of the probe tip. We show that a small number of SRR samples is sufficient to determine the parameters of the regression model. Finally, we use the regression model to simulate SRR for a stainless steel optical probe with six linearly placed fibers and experimentally validate the framework through the use of inverse models for estimation of absorption and reduced scattering coefficients and subdiffusive scattering phase function quantifiers.

Determination of refractive index, size, and solid content of monodisperse polystyrene microsphere suspensions for the characterization of optical phantoms

Monodisperse polystyrene microspheres are often utilized in optical phantoms since optical properties such as the scattering coefficient and the scattering phase function can be calculated using the Mie theory. However, the calculated values depend on the inherent physical parameters of the microspheres which include the size, refractive index, and solid content. These parameters are often provided only approximately or can be affected by long shelf times. We propose a simple method to obtain the values of these parameters by measuring the collimated transmission of polystyrene microsphere suspensions from which the wavelength-dependent scattering coefficient can be calculated using the Beer-Lambert law. Since a wavelength-dependent scattering coefficient of a single suspension is insufficient to uniquely derive the size, refractive index and solid content by the Mie theory, the crucial and novel step involves suspending the polystyrene microspheres in aqueous sucrose solutions with different sucrose concentrations that modulates the refractive index of the medium and yields several wavelength-dependent scattering coefficients. With the proposed method, we are able to obtain the refractive index within 0.2% in the wavelength range from 500 to 800 nm, the microsphere size to approximately 15 nm and solid content within 2% of their respective reference values.

Methods of extraction of optical properties from diffuse reflectance measurements of ex-vivo human colon tissue using thin film silicon photodetector arrays

Spatially resolved diffuse reflectance spectroscopy (SRDRS) is a promising technique for characterization of colon tissue. Herein, two methods for extracting the reduced scattering and absorption coefficients ( μ s ' ( λ ) and μ a ( λ ) ) from SRDRS data using lookup tables of simulated diffuse reflectance are reported. Experimental measurements of liquid tissue phantoms performed with a custom multi-pixel silicon SRDRS sensor spanning the 450 - 750 nm wavelength range were used to evaluate the extraction methods, demonstrating that the combined use of spatial and spectral data reduces extraction error compared to use of spectral data alone. Additionally, SRDRS measurements of normal and tumor ex-vivo human colon tissue are presented along with μ s ' ( λ ) and μ a ( λ ) extracted from these measurements.

Efficient estimation of subdiffusive optical parameters in real time from spatially resolved reflectance by artificial neural networks

Subdiffusive reflectance captured at short source-detector separations provides increased sensitivity to the scattering phase function and hence allows superficial probing of the tissue ultrastructure. Consequently, estimation of subdiffusive optical parameters has been the subject of many recent studies focusing on lookup-table-based (LUT) inverse models. Since an adequate description of the subdiffusive reflectance requires additional scattering phase function related optical parameters, the LUT inverse models, which grow exponentially with the number of estimated parameters, become excessively large and computationally inefficient. Herein, we propose, to the best of our knowledge, the first artificial-neural-network-based inverse Monte Carlo model that overcomes the limitations of the LUT inverse models and thus allows efficient real-time estimation of optical parameters from subdiffusive spatially resolved reflectance. The proposed inverse model retains the accuracy, is about four orders of magnitude faster than the LUT inverse models, grows only linearly with the number of estimated optical parameters, and can be easily extended to estimate additional optical parameters.

Impact of the scattering phase function on the bulk reflectance of a turbid medium with large-scale inhomogeneities

We study the total bulk reflectance of a turbid medium with large (as compared to the light wavelength) inhomogeneities at grazing angles of light incidence. To model highly forward scattering in the medium, we take advantage of the Reynolds-McCormick scattering phase function. Using the scaling analysis for the small-angle radiative transfer equation, we derive simple analytical formulas for the total reflectance. For grazing incidence angles, we find a range of values of the medium transport coefficients where the total reflectance proves to be a universal function of a single parameter, which is expressed in terms of the incidence angle, the absorption coefficient, and the transport scattering one. The explicit form of this function is governed by the specific angular profile of the scattering phase function. The results obtained are verified by comparison with results of a direct numerical integration of the radiative transfer equation.

Virtually increased acceptance angle for efficient estimation of spatially resolved reflectance in the subdiffusive regime: a Monte Carlo study

Light propagation in biological tissues is frequently modeled by the Monte Carlo (MC) method, which requires processing of many photon packets to obtain adequate quality of the observed backscattered signal. The computation times further increase for detection schemes with small acceptance angles and hence small fraction of the collected backscattered photon packets. In this paper, we investigate the use of a virtually increased acceptance angle for efficient MC simulation of spatially resolved reflectance and estimation of optical properties by an inverse model. We devise a robust criterion for approximation of the maximum virtual acceptance angle and evaluate the proposed methodology for a wide range of tissue-like optical properties and various source configurations.

Determination of three optical properties from subdiffusive spatially resolved reflectance calculations

We report a theoretical study on the determination of three optical properties from spatially resolved reflectance calculations. In particular, the reduced scattering coefficient μs′, the absorption coefficient μa, and the recently defined phase function parameter σ are identified. The solution of the inverse problem is based on the principal component analysis of a large set of reflectance profiles that were calculated using an analytical solution of the radiative transfer equation. Different phase function types were studied to test the method in the range of 0.63  mm−1≤μs′≤4.2  mm−1 and 0.002  mm−1≤μa≤0.1  mm−1. For curves impaired with noise, we were able to reconstruct μs′ and μa with relative median errors of 2.5% and 12%, respectively, and σ with an absolute median error of 0.04.

Modeling subdiffusive light scattering by incorporating the tissue phase function and detector numerical aperture

To detect small-scale changes in tissue with optical techniques, small sampling volumes and, therefore, short source–detector separations are required. In this case, reflectance measurements are not adequately described by the diffusion approximation. Previous studies related subdiffusive reflectance to ? or ? , which parameterize the phase function. Recently, it was demonstrated that ? predicts subdiffusive reflectance better than ? , and that ? becomes less predictive for lower numerical apertures (NAs). We derive and evaluate the parameter R p NA , which incorporates the NA of the detector and the integral of the phase function over the NA in the backward and forward directions. Monte Carlo simulations are performed for overlapping source/detector geometries for a range of phase functions, reduced scattering coefficients, NAs, and source/detector diameters. R p NA improves prediction of the measured reflectance compared to ? and ? . It is, therefore, expected that R p NA will improve derivation of optical properties from subdiffusive measurements.

Adopting higher-order similarity relations for improved estimation of optical properties from subdiffusive reflectance

Estimation of optical properties from subdiffusive reflectance acquired at short source-detector separations is challenging due to the sensitivity to the underlying scattering phase function. In recent studies, a second-order similarity parameter γ has been increasingly used alongside the absorption and reduced scattering coefficients to account for some of the phase function variability. By using Monte Carlo simulations, we show that the influence of the scattering phase function on the subdiffusive reflectance for the biologically relevant variations can be captured sufficiently well by considering γ and a third-order similarity parameter δ. Utilizing this knowledge, we construct an inverse model that estimates the absorption and reduced scattering coefficients, γ and δ, from spatially resolved reflectance. Nearly an order of magnitude smaller errors of the estimated optical properties are obtained in comparison to the inverse model that only composes γ.