Monte Carlo modeling of temporal point spread functions and sensitivity functions for mesoscopic time-resolved fluorescence molecular tomography

The paper describes a TurbidMC code that implements a perturbative Monte Carlo method to model temporal point spread functions and sensitivity functions for time-resolved fluorescence molecular tomography (FMT). The code is aimed at working with a particular FMT method published earlier (Ref. [22]) which defines the specificity of sensitivity function calculation. The method solves the inverse problem first for a generalized fluorescence parameter distribution function and then calculates separate distributions for the fluorophore absorption coefficient and the fluorescence lifetime. The proper operation of the code was verified through a comparison between fluorescence temporal point spread functions from test calculations and data from experiments where a phantom with a fluorophore was scanned with a three-channel probe in the mesoscopic reflectance regime. An example is given on the reconstruction of fluorescence parameter distributions. It shows that the sensitivity functions are calculated correctly.

ASYMPTOTIC SOURCE FUNCTION APPROXIMATION BASED FLUORESCENCE MOLECULAR TOMOGRAPHY: CURRENT STATUS AND PROSPECTS

The paper is devoted to an original method of time-resolved fluorescence molecular tomog-raphy based on asymptotic approximation to the fluorescence source function. It analyzes re-sults the authors have obtained during last 4 years in their testing the method in numerical and physical experiments. The method is inferred to be quite promising and directions of fur-ther research for its verification as a sub-millimeter resolution method are outlined. As a modernization of the method, the authors propose an iterative approach where the fluoro-phore absorption coefficient and fluorescence lifetime are reconstructed successively using a posteriori knowledge on the object from previous iterations.

Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study

SIGNIFICANCE

Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons.

AIM

The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry.

APPROACH

The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method.

RESULTS

3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object.

CONCLUSIONS

Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.

Monte Carlo simulation of sensitivity functions for few-view computed tomography of strongly absorbing media

The paper describes a sensitivity function calculation method for few-view X-ray computed tomography of strongly absorbing objects. It is based on a probabilistic interpretation of energy transport through the object from a source to a detector. A PRIZMA code package is used to track photons. The code is developed at FSUE “RFNC–VNIITF named after Academ. E. I. Zababakhin” and implements a stochastic Monte Carlo method. The value of the sensitivity function in a discrete cell of the reconstruction region is assumed to be directly proportional to the fraction of photon trajectories which cross the cell from all those recorded by the detector. The method’s efficiency is validated through a numerical experiment on the reconstruction of a section of a spherical heavy-metal phantom with an air cavity and a density difference of 25 Ṫhe proposed method is shown to outperform the method based on projection approximation in case of reconstruction from 9 views.

Early-photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

The paper presents an original approach to time-domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state-of-the-art compressed-sensing-like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source-receiver separations which correspond to the macroscopic regime. Two compressed-sensing-like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage-thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.

Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography

Two algorithms of few-view tomography are compared, specifically, the iterative Potts minimization algorithm (IPMA) and the algebraic reconstruction technique with TV-regularization and adaptive segmentation (ART-TVS). Both aim to reconstruct piecewise-constant structures, use the compressed sensing theory, and combine image reconstruction and segmentation procedures. Using a numerical experiment, it is shown that either algorithm can exactly reconstruct the Shepp-Logan phantom from as small as 7 views with noise characteristic of the medical applications of X-ray tomography. However, if an object has a complicated high-frequency structure (QR-code), the minimal number of views required for its exact reconstruction increases to 17–21 for ART-TVS and to 32–34 for IPMA. The ART-TVS algorithm developed by the authors is shown to outperform IPMA in reconstruction accuracy and speed and in resistance to abnormally high noise as well. ART-TVS holds good potential for further improvement.

Spatial Resolution Analysis for Few-Views Discrete Tomography Based on MART-AP Algorithm

We study a new MART-AP algorithm of few-views discrete tomography. Its efficiency for high-frequency structure reproduction is investigated in a numerical experiment where we reconstruct a 2D model for the estimation of the spatial resolution limit. We estimate the modulation transfer function of the reconstruction algorithm and compare it with the modulation transfer function of projection distortions. Our results show that MART-AP weakly influences the contrast of spatial structures being reproduced and can be used for high-resolution reconstruction when only a few projections are registered.