Incorporating reflection boundary conditions in the Neumann series radiative transport equation: Application to photon propagation and reconstruction in diffuse optical imaging

We propose a formalism to incorporate boundary conditions in a Neumann-series-based radiative transport equation. The formalism accurately models the reflection of photons at the tissue-external medium interface using Fresnel’s equations. The formalism was used to develop a gradient descent-based image reconstruction technique. The proposed methods were implemented for 3D diffuse optical imaging. In computational studies, it was observed that the average root-mean-square error (RMSE) for the output images and the estimated absorption coefficients reduced by 38% and 84%, respectively, when the reflection boundary conditions were incorporated. These results demonstrate the importance of incorporating boundary conditions that model the reflection of photons at the tissue-external medium interface

ValoMC: a Monte Carlo software and MATLAB toolbox for simulating light transport in biological tissue

A Monte Carlo method for photon transport has gained wide popularity in biomedical optics for studying light behaviour in tissue. Nowadays, typical computation times range from a few minutes to hours. Although various implementations of the Monte Carlo algorithm exist, there is only a limited number of free software available. In addition, these packages may require substantial learning efforts. To address these issues, we present a new Monte Carlo software with a user-friendly interface. The simulation geometry is defined using an unstructured (triangular or tetrahedral) mesh. The program solves the photon fluence in the computation domain and the exitance at the domain boundary. It is capable of simulating complex measurement geometries with spatially varying optical parameter distributions and supports several types of light sources as well as intensity modulated light. Furthermore, attention is given to ease of use and fast problem set up with a MATLAB (The MathWorks Inc., Natick, MA) interface. The simulation code is written in C++ and parallelized using OpenMP. The simulation code has been validated against analytical and numerical solutions of radiative transfer equation and other Monte Carlo software in good agreement. The software is available for download from the homepage https://inverselight.github.io/ValoMC/ and the source code from GitHub https://github.com/InverseLight/ValoMC

GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography

We introduce a GPU-accelerated finite element forward solver for the computation of light transport in scattering media. The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation. We present solutions for both time-domain and frequency-domain problems. A comparison with a CPU-based implementation shows significant performance gains of the graphics accelerated solution, with improvements of approximately a factor of 10 for double-precision computations, and factors beyond 20 for single-precision computations. The gains are also shown to be dependent on the mesh complexity, where the largest gains are achieved for high mesh resolutions

A Born-type approximation method for bioluminescence tomography

In this paper, we present a Born-type approximation method for bioluminescence tomography (BLT), which is to reconstruct an internal bioluminescent source from the measured bioluminescent signal on the external surface of a small animal. Based on the diffusion approximation for the photon propagation in biological tissue, this BLT method utilizes the Green function to establish a linear relationship between the measured bioluminescent signal and the internal bioluminescent source distribution. The Green function can be modified to describe a heterogeneous medium with an arbitrary boundary using the Born approximation. The BLT reconstruction is formulated in a linear least-squares optimization framework with simple bounds constraint. The performance of this method is evaluated in numerical simulation and phantom experiments

A Bayesian approach for energy-based estimation of acoustic aberrations in high intensity focused ultrasound treatment

High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of the biological medium can defocus the ultrasound beam. Here we reduce the problem of refocusing the beam to the inverse problem of estimating the acoustic aberration due to the biological tissue from acoustic radiative force imaging data. We solve this inverse problem using a Bayesian framework with a hierarchical prior and solve the inverse problem using a Metropolis-within-Gibbs algorithm. The framework is tested using both synthetic and experimental datasets. We demonstrate that our approach has the ability to estimate the aberrations using small datasets, as little as 32 sonication tests, which can lead to significant speedup in the treatment process. Furthermore, our approach is compatible with a wide range of sonication tests and can be applied to other energy-based measurement techniques

Deep learning acceleration of iterative model-based light fluence correction for photoacoustic tomography

Photoacoustic tomography (PAT) is a promising imaging technique that can visualize the distribution of chromophores within biological tissue. However, the accuracy of PAT imaging is compromised by light fluence (LF), which hinders the quantification of light absorbers. Currently, model-based iterative methods are used for LF correction, but they require significant computational resources due to repeated LF estimation based on differential light transport models. To improve LF correction efficiency, we propose to use Fourier neural operator (FNO), a neural network specially designed for solving differential equations, to learn the forward projection of light transport in PAT. Trained using paired finite-element-based LF simulation data, our FNO model replaces the traditional computational heavy LF estimator during iterative correction, such that the correction procedure is significantly accelerated. Simulation and experimental results demonstrate that our method achieves comparable LF correction quality to traditional iterative methods while reducing the correction time by over 30 times

SIGNAL AND NOISE CORRELATIONS IN DIAGNOSTIC X-RAY IMAGING DETECTORS

X-ray detectors are an integral part of any x-ray imaging system. In order to maximize system performance, and hence image quality, signal and noise must be efficiently transferred from input to output. Ideally, an x-ray detector should preserve the input signal-to-noise ratio (SNR). However, in reality, various physical processes within the x-ray detector degrade SNR, which consequently results in lower image quality for a given x-ray imaging dose. The goal of this work is to understand how signal and noise correlations limit the performance of diagnostic x-ray detectors, especially those used in high-resolution imaging applications, such as mammography and micro computed tomography (CT). The fundamental spatial resolution and SNR limits caused by signal and noise correlations associated with x-ray interactions was determined using Monte Carlo simulations of the absorbed energy in common x-ray detector materials as a function of incident energy and converter thickness. These fundamental limits help identify potential performance bottlenecks in existing detectors and also serve as target benchmarks for future designs. Theoretical models of signal and noise transfer through the photoelectric effect and CT filtered backprojection algorithm were developed using a cascaded systems analysis to analytically predict how signal and noise correlations affect detector performance and CT image quality, respectively. This work provides x-ray detector manufacturers and imaging scientists (i) a priori knowledge of the fundamental barriers of detector performance, and (ii) “tools” necessary for the design and optimization of radiography and CT based imaging systems. These contributions will not only save time, money and resources, but will ultimately lead to x-ray detectors with higher SNR efficiency, which in turn, may lead to better image quality (greater diagnostic accuracy) and/or lower patient dose (lower cancer risk)