Machine learning estimation of tissue optical properties

Reconstruction of Optical Properties in Turbid Media: Omitting the Need of the Collimated Transmission for an Integrating Sphere Setup

Currently, the most reliable approach to reconstruct optical properties, namely absorption coefficient, reduced scattering coefficient, scattering coefficient and asymmetry factor, of turbid media is through inverse Monte Carlo simulation. To determine these optical properties, three measurements are required: total transmission, total reflection and collimated transmission. However, the accurate determination of the collimated transmission is very difficult. To overcome the difficulty of measuring the collimated transmission, it is proposed to measure the total transmission and total reflection of the same sample with two different thicknesses instead. To prove this alternative solution, machine learning is used to prove that the repeated measurement for two different thicknesses carries all the necessary information. As a result, all four optical properties can be measured with high accuracy, particularly for interpolation problems where the test data fall within the range of the training data. For extrapolation problems, high accuracy can be achieved in the determination of at least the absorption coefficient, reduced scattering coefficient and scattering coefficient. Hence, these results allow that in the future, an easier and therefore more precise reconstruction of the optical properties is possible, potentially even with inverse Monte Carlo simulations as the current standard.

Designing a use-error robust machine learning model for quantitative analysis of diffuse reflectance spectra

Significance

Machine learning (ML)-enabled diffuse reflectance spectroscopy (DRS) is increasingly used as an alternative to the computation-intensive inverse Monte Carlo (MCI) simulation to predict tissue's optical properties, including the absorption coefficient, μ a and reduced scattering coefficient, μ s ' .

Aim

We aim to develop a use-error-robust ML algorithm for optical property prediction from DRS spectra.

Approach

We developed a wavelength-independent regressor (WIR) to predict optical properties from DRS data. For validation, we generated 1520 simulated DRS spectra with the forward Monte Carlo model, where μ a = 0.44 to 2.45    cm - 1 , and μ s ' = 6.53 to 9.58    cm - 1 . We introduced common use-errors, such as wavelength miscalibrations and intensity fluctuations. Finally, we collected 882 experimental DRS images from 170 tissue-mimicking phantoms and compared performances of the WIR model, a dense neural network, and the MCI model.

Results

When compounding all use-errors on simulated data, the WIR model best balanced accuracy and speed, yielding errors of 1.75% for μ a and 1.53% for μ s ' , compared to the MCI's 50.9% for μ a and 24.6% for μ s ' . Regarding experimental data, WIR model had mean errors of 13.2% and 6.1% for μ a and μ s ' , respectively. The errors for MCI were about eight times higher.

Conclusions

The WIR model presents reliable use-error-robust optical property predictions from DRS data.

Neural network-based inverse model for diffuse reflectance spectroscopy

In diffuse reflectance spectroscopy, the retrieval of the optical properties of a target requires the inversion of a measured reflectance spectrum. This is typically achieved through the use of forward models such as diffusion theory or Monte Carlo simulations, which are iteratively applied to optimize the solution for the optical parameters. In this paper, we propose a novel neural network-based approach for solving this inverse problem, and validate its performance using experimentally measured diffuse reflectance data from a previously reported phantom study. Our inverse model was developed from a neural network forward model that was pre-trained with data from Monte Carlo simulations. The neural network forward model then creates a lookup table to invert the diffuse reflectance to the optical coefficients. We describe the construction of the neural network-based inverse model and test its ability to accurately retrieve optical properties from experimentally acquired diffuse reflectance data in liquid optical phantoms. Our results indicate that the developed neural network-based model achieves comparable accuracy to traditional Monte Carlo-based inverse model while offering improved speed and flexibility, potentially providing an alternative for developing faster clinical diagnosis tools. This study highlights the potential of neural networks in solving inverse problems in diffuse reflectance spectroscopy.

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.

Real-time and accurate estimation ex vivo of four basic optical properties from thin tissue based on a cascade forward neural network

Double integrating sphere measurements obtained from thin ex vivo tissues provides more spectral information and hence allows full estimation of all basic optical properties (OPs) theoretically. However, the ill-conditioned nature of the OP determination increases excessively with the reduction in tissue thickness. Therefore, it is crucial to develop a model for thin ex vivo tissues that is robust to noise. Herein, we present a deep learning solution to precisely extract four basic OPs in real-time from thin ex vivo tissues, leveraging a dedicated cascade forward neural network (CFNN) for each OP with an additional introduced input of the refractive index of the cuvette holder. The results show that the CFNN-based model enables accurate and fast evaluation of OPs, as well as robustness to noise. Our proposed method overcomes the highly ill-conditioned restriction of OP evaluation and can distinguish the effects of slight changes in measurable quantities without any a priori knowledge.

Machine Learning Diffuse Optical Tomography Using Extreme Gradient Boosting and Genetic Programming

Diffuse optical tomography (DOT) is a non-invasive method for detecting breast cancer; however, it struggles to produce high-quality images due to the complexity of scattered light and the limitations of traditional image reconstruction algorithms. These algorithms can be affected by boundary conditions and have a low imaging accuracy, a shallow imaging depth, a long computation time, and a high signal-to-noise ratio. However, machine learning can potentially improve the performance of DOT by being better equipped to solve inverse problems, perform regression, classify medical images, and reconstruct biomedical images. In this study, we utilized a machine learning model called "XGBoost" to detect tumors in inhomogeneous breasts and applied a post-processing technique based on genetic programming to improve accuracy. The proposed algorithm was tested using simulated DOT measurements from complex inhomogeneous breasts and evaluated using the cosine similarity metrics and root mean square error loss. The results showed that the use of XGBoost and genetic programming in DOT could lead to more accurate and non-invasive detection of tumors in inhomogeneous breasts compared to traditional methods, with the reconstructed breasts having an average cosine similarity of more than 0.97 ± 0.07 and average root mean square error of around 0.1270 ± 0.0031 compared to the ground truth.

Estimation of optical properties of turbid media using spatially resolved diffuse reflectance combined with LSTM-attention network

The accurate estimation of the optical properties of turbid media by using a spatially resolved (SR) technique remains a challenging task due to measurement errors in the acquired spatially resolved diffuse reflectance (SRDR) and challenges in inversion model implementation. In this study, what we believe to be a novel data-driven model based on a long short-term memory network and attention mechanism (LSTM-attention network) combined with SRDR is proposed for the accurate estimation of the optical properties of turbid media. The proposed LSTM-attention network divides the SRDR profile into multiple consecutive and partially overlaps sub-intervals by using the sliding window technique, and uses the divided sub-intervals as the input of the LSTM modules. It then introduces an attention mechanism to evaluate the output of each module automatically and form a score coefficient, finally obtaining an accurate estimation of the optical properties. The proposed LSTM-attention network is trained with Monte Carlo (MC) simulation data to overcome the difficulty in preparing training (reference) samples with known optical properties. Experimental results of the MC simulation data showed that the mean relative error (MRE) with 5.59% for the absorption coefficient [with the mean absolute error (MAE) of 0.04 cm^-1, coefficient of determination (R²) of 0.9982, and root mean square error (RMSE) of 0.058 cm^-1] and 1.18% for the reduced scattering coefficient (with an MAE of 0.208 cm^-1, R² of 0.9996, and RMSE of 0.237 cm^-1), which were significantly better than those of the three comparative models. The SRDR profiles of 36 liquid phantoms, collected using a hyperspectral imaging system that covered a wavelength range of 530-900 nm, were used to test the performance of the proposed model further. The results showed that the LSTM-attention model achieved the best performance (with the MRE of 14.89%, MAE of 0.022 cm^-1, R² of 0.9603, and RMSE of 0.026 cm^-1 for the absorption coefficient; and the MRE of 9.76%, MAE of 0.732 cm^-1, R² of 0.9701, and RMSE of 1.470 cm^-1for the reduced scattering coefficient). Therefore, SRDR combined with the LSTM-attention model provides an effective method for improving the estimation accuracy of the optical properties of turbid media.

Coronary artery properties in atherosclerosis: A deep learning predictive model

In this work an Artificial Neural Network (ANN) was developed to help in the diagnosis of plaque vulnerability by predicting the Young modulus of the core (E _core ) and the plaque (E _plaque ) of atherosclerotic coronary arteries. A representative in silico database was constructed to train the ANN using Finite Element simulations covering the ranges of mechanical properties present in the bibliography. A statistical analysis to pre-process the data and determine the most influential variables was performed to select the inputs of the ANN. The ANN was based on Multilayer Perceptron architecture and trained using the developed database, resulting in a Mean Squared Error (MSE) in the loss function under 10^-7, enabling accurate predictions on the test dataset for E _core and E _plaque . Finally, the ANN was applied to estimate the mechanical properties of 10,000 realistic plaques, resulting in relative errors lower than 3%.

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.