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.

Monte Carlo fluorescence microtomography.

Fluorescence microscopy allows real-time monitoring of optical molecular probes for disease characterization, drug development, and tissue regeneration. However, when a biological sample is thicker than 1 mm, intense scattering of light would significantly degrade the spatial resolution of fluorescence microscopy. In this paper, we develop a fluorescence microtomography technique that utilizes the Monte Carlo method to image fluorescence reporters in thick biological samples. This approach is based on an l(0)-regularized tomography model and provides an excellent solution. Our studies on biomimetic tissue scaffolds have demonstrated that the proposed approach is capable of localizing and quantifying the distribution of optical molecular probe accurately and reliably.

Numerical study on the validity of the diffusion approximation for computational optical biopsy.

Currently, we are developing a computational optical biopsy technology for molecular sensing. We use the diffusion equation to model photon propagation but have a concern about the accuracy of diffusion approximation when the optical sensor is close to a bioluminescent source. We derive formulas to describe photon fluence for point and ball sources and measurement formulas for an idealized optical biopsy probe. Then, we numerically compare the diffusion approximation and the radiative transport as implemented by Monte Carlo simulation in the cases of point and ball sources. Our simulation results show that the diffusion approximation can be accurately applied if mu's>>mu(a) even if the sensor is very close to the source (>1mm). Furthermore, an approximate formula is given to describe the measurement of a cut-end fiber probe for a ball source.

A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method.

RATIONALE AND OBJECTIVES: As an important part of bioluminescence tomography, which is a newly developed optical imaging modality, mouse optical simulation environment (MOSE) is developed to simulate bioluminescent phenomena in the living mouse and to predict bioluminescent signals detectable outside the mouse. This simulator is dedicated to small animal optical imaging based on bioluminescence. MATERIALS AND METHODS: With the parameters of biological tissues, bioluminescent sources, and charge coupled device (CCD) detectors, the 2-dimensional/3-dimensional MOSE simulates the whole process of the light propagation in 2-dimensional/3-dimensional biological tissues using the Monte Carlo method. Both the implementation details and the software architecture are described in this article. RESULTS: The software system is implemented in the Visual C++ programming language with the OpenGL techniques and has a user-friendly interface facilitating interactions relevant to bioluminescent imaging. The accuracy of the system is verified by comparing the MOSE results with independent data from analytic solutions and commercial software. CONCLUSION: As shown in our simulation and analysis, the MOSE is accurate, flexible, and efficient to simulate the photon propagation for bioluminescence tomography. With graduate refinements and enhancements, it is hoped that the MOSE will become a standard tool for bioluminescence tomography.

Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium.

BACKGROUND: The bioluminescent enzyme firefly luciferase (Luc) or variants of green fluorescent protein (GFP) in transformed cells can be effectively used to reveal molecular and cellular features of neoplasia in vivo. Tumor cell growth and regression in response to various therapies can be evaluated by using bioluminescent imaging. In bioluminescent imaging, light propagates in highly scattering tissue, and the diffusion approximation is sufficiently accurate to predict the imaging signal around the biological tissue. The numerical solutions to the diffusion equation take large amounts of computational time, and the studies for its analytic solutions have attracted more attention in biomedical engineering applications. METHODS: Biological tissue is a turbid medium that both scatters and absorbs photons. An accurate model for the propagation of photons through tissue can be adopted from transport theory, and its diffusion approximation is applied to predict the imaging signal around the biological tissue. The solution to the diffusion equation is formulated by the convolution between its Green's function and source term. The formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium can be obtained to accelerate the forward simulation of bioluminescent phenomena. RESULTS: The closed form solutions have been derived for the time-dependent diffusion equation and the steady-state diffusion equation with solid and hollow spherical sources in a homogeneous medium, respectively. Meanwhile, the relationship between solutions with a solid sphere source and ones with a surface sphere source is obtained. CONCLUSION: We have formulated solutions for the diffusion equation with solid and hollow spherical sources in an infinite homogeneous medium. These solutions have been verified by Monte Carlo simulation for use in biomedical optical imaging studies. The closed form solution is highly accurate and more computationally efficient in biomedical engineering applications. By using our analytic solutions for spherical sources, we can better predict bioluminescent signals and better understand both the potential for, and the limitations of, bioluminescent tomography in an idealized case. The formulas are particularly valuable for furthering the development of bioluminescent tomography.