SignificanceFluorescence 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.AimThe 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.ApproachThe 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.Results3D 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.ConclusionsEven 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.
The paper is devoted to a new method of time-domain lifetime fluorescence molecular tomography. It is based on the use of early arriving diffuse photons and original measurement data, which are determined for the individual time gates of the diffuse temporal responses for fluorescence and exiting radiation. The paper presents in short the theoretical foundation of the method and describes a numerical experiment on the separate reconstruction of fluorophore absorption coefficient and fluorescence lifetime for 3D reflectance geometry that is suitable for small animal imaging. We show our first reconstruction results for the 3D scattering object region 11×11×8 mm3 in size with two spherical fluorescent inclusions 1 mm in diameter. The ways how to improve these results in the future are discussed.
The paper presents an original hybrid image reconstruction algorithm ART-TVS for few-views computed tomography of strongly absorbing media. It is based on the well-known algebraic reconstruction technique (ART), regularization of interim results through minimization of the total variation norm (TV-regularization), and a method of adaptive segmentation, which is a modernization of the known region growing algorithm. It is shown that the ART-TVS algorithm does not give stripe artifacts even if the number of views is very small (eight or less). ART-TVS reconstruction results for two numerical models of metal shells are compared with those obtained with the ART-TV algorithm (ART with TV-regularization and without adaptive segmentation), the iterative Potts minimization algorithm (IPMA), and our MART-AP algorithm (multiplicative ART with a priori information) we developed earlier for few-views discrete tomography. It is shown that ART-TVS outperforms ART-TV and IPMA and is comparable with MART-AP in reconstruction accuracy. Also, ART-TVS converges markedly faster than IRMA in cases where strongly underdetermined systems are treated. The algorithm we propose also demonstrates quite satisfactory resistance to projection data noise that is inherent in tomography of strongly absorbing media.
The important advantage of diffuse optical tomography (DOT) is the possibility of tissue functional diagnosis. However the possibility implements if only we separately reconstruct the spatial distributions of optical parameters, specifically the absorption and scattering coefficients. We have recently demonstrated that time-domain DOT based on the perturbation model by Lyubimov is capable of reconstructing absorbing inhomogeneities in tissue with a DOT high spatial resolution (better than 3 mm at a depth of 4 cm). This paper continues our research and focuses on the reconstruction of scattering inhomogeneities. We consider the flat layer transmission geometry which is traditional for optical mammography, and use diffusion approximation to derive analytical expressions for weight functions responsible for the reconstruction of scattering inhomogeneities. To confirm that our calculations are correct we perform a numerical experiment where we reconstruct a rectangular scattering object 10×8 cm in size with 4 circular scattering macroinhomogeneities 4 mm in diameter each, and a randomly inhomogeneous scattering structure. The inverse DOT problem is solved with a multiplicative algebraic reconstruction technique where interim iterations are processed through total variation norm minimization. The results suggest that our DOT method reliably resolves the scattering macroinhomogeneities of mentioned size against a randomly inhomogeneous structure.
We estimate a limit to spatial resolution in time-domain diffuse optical tomography (DOT) based on a perturbation
model by Lyubimov. In the context of structure reconstruction accuracy we consider and compare three approaches to
the inverse DOT problem. The first reconstructs diffuse tomograms from straight lines; the second does it from
curvilinear average trajectories of photons; and the third uses the total banana-like distributions of photon trajectories.
For getting estimates to resolution, we derive analytical expressions for the point spread function and the modulation
transfer function, and perform a numerical experiment to reconstruct rectangular scattering objects with circular
absorbing inhomogeneities. It is shown that reconstruction with photon trajectory distributions instead of straight lines
gives a gain of about order of magnitude in resolution and attains the accuracy of multistep nonlinear DOT algorithms.
This paper proposes a perturbation model for time-domain diffuse optical tomography in the flat layer transmission
geometry. We derive an analytical representation of the weighting function that models the imaging operator by using the
diffusion approximation of the radiative transfer equation and the perturbation theory by Born. To evaluate the weighing
function for the flat layer geometry, the Green's function of the diffusion equation for a semi-infinite scattering medium
with the Robin boundary condition is used. For time-domain measurement data we use the time-resolved optical projections
defined as relative disturbances in the photon fluxes, which are caused by optical inhomogeneities. To demonstrate the
efficiency of the proposed model, a numerical experiment was conducted, wherein the rectangular scattering objects with
two absorbing inhomogeneities and a randomly inhomogeneous component were reconstructed. Test tomograms are
recovered by means of the multiplicative algebraic reconstruction technique modified by us. It is shown that nonstandard
interpretation of the time-domain measurement data makes it possible to use different time-gating delays for
regularization of the reconstruction procedure. To regularize the solution, we state the reconstruction problem for an
augmented system of linear algebraic equations. At the recent stage of study the time-gating delays for regularization are
selected empirically.
The photon average trajectory method has been recently investigated as a fast reconstruction technique for time-domain
diffuse optical tomography. The main disadvantage of this method is that it reconstructs the tomograms blurred due to
averaging over the spatial distributions of photons. To get information about actual boundary and shape of optical
inhomogeneities being reconstructed, we propose the segmentation approach based on the generation of nonlinear
analytical and statistical functions of correspondence between image intensity and color space. It is shown that for simple
models (absorbing macro-inhomogeneities in a homogeneous scattering medium) the proposed approach allows the true
structure of inhomogeneities to be reproduced almost completely. If a medium contains randomly inhomogeneous
component, our segmentation method may give artifacts which should be removed on the basis of a priori information.
The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method is substantiated. The PAT method is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT). The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the standard filtered back projection algorithm can be used for fast reconstruction of diffuse optical tomograms. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons, which form the signal measured by the receiver. To improve the resolution, I apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small sub-regions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations: the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm are used for deblurring. It is shown that the restoration procedure enhances the tomogram profiles and allows an obvious gain in spatial resolution to be obtained.
Possibility is investigated to enhance spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method. The PAT method is based on a concept of average statistical trajectory of light energy transfer from point source to point detector. The inverse problem of diffuse optical tomography reduces to solution of an integral equation with integration by conventional PAT. In the result for reconstruction of diffuse optical images the conventional algorithms of projection tomography can be applied, including filtered backprojection algorithm. The shortcoming of the PAT method is that it reconstructs images blurred in the result of averaging by photons spatial distribution contributing into the signal measured by a detector. To enhance resolution we apply a spatially variant blur model based on interpolation of spatially invariant point spread functions simulated for different image regions. To restore tomograms two iterative algorithms for solution of system of linear algebraic equations are used: conjugate gradient algorithm for least squares problems and modified residual norm steepest descent algorithm. It is shown that one can achieve 27% enhancement of spatial resolution.
The possibility of improving the spatial resolution of diffuse optical images reconstructed by the photon average trajectories (PAT) method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT). The inverse problem of diffuse optical tomography (DOT) is reduced to solution of integral equation with integration along a conditional PAT. As a result the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. In our recent works we have shown that the application of the backprojection algorithms with special filtration of shadows allows a 20%-gain in spatial resolution to be obtained. But the shortcoming of the backprojection algorithm is that they can not reconstruct accurately the object regions located close to the boundary. In the present paper we consider alternative approach to improve the spatial reconstruction, which may be applied to images reconstructed with the use of algebraic techniques. It is based on post-reconstruction restoration of images blurred due to averaging over spatial distributions of photons, which form the signal measured by the receiver. We suggest a spatially invariant blurring model to restore local regions of a diffuse image with the use of standard deconvolution algorithms. Two iterative non-linear algorithms: the maximum-likelihood algorithm and the Lucy-Richardson algorithm are considered. It is shown that both of them allow the spatial resolution to be improved. The effect of the improvement is identical to that obtained with the use of the backprojection algorithms.
The applicability of the transform algorithms generally used in projection computed tomography is substantiated for the case of medical diffuse optical tomography (DOT). To reconstruct tissue optical inhomogeneities, a new method based on a concept of an average statistical trajectory for transfer of light energy (photon average trajectory, PAT) is proposed. By this method, the inverse problem of DOT is reduced to solution of integral equation with integration along a PAT. Within the internal zone of the object, remote well away from the boundaries, PATs tend to a straight line, and standard integral algorithms based on the inverse Radon transform may be used to restore diffuse optical images. To demonstrate the capabilities of the PAT method, a numerical experiment on cross-sectional reconstruction of cylindrical strongly scattering objects with absorbing inhomogeneities has been conducted. To solve the DOT inverse problem, two filtered backprojection algorithms (of Radon and of Vainberg) were used. The reconstruction results are compared with those obtained by a well-known software package for temporal optical absorption and scattering tomography, based on multiple solution of diffusion equation. It is shown that the PAT method using the Vainberg algorithm allows reconstruction of tissue optical structure with a 20%-gain in spatial resolution.
Vladimir Lyubimov, Alexander Konovalov, Igor Kutuzov, Olga Kravtsenyuk, Alexander Kalintsev, Alexander Murzin, Olga Golubkina, Leonid Soms, Lyudmila Yavorskaya
The influence of three reconstruction algorithms on spatial resolution of optical diffuse tomography by Photon Average Trajecotries (PAT) method was investigated. The resolution was estimated using the model of spatially invariant linear filter by the conventient procedure usually used in CT. The resolution of absorbing inhomogeneities of model objects is shown to go for a theoretical limit of PAT method and the algorithms considered appears to reconstruct optical diffuse images without complementary limitations on spatial resolution.
The applicability of backprojection algorithms of filtered shadows that have been earlier developed for computer tomography is shown for the case of optical tomography of strongly scattering media. This opportunity is based on the presence of a long rectilinear part in the approximation of the statistical Photon Average Trajectories of photons propagating through the scattering medium. The results of numerical experiments showed that the quality of reconstruction using filtered backprojection algorithms do not surrender to that for multi-iterative algorithms, at much shorter reconstruction time.
Olga Golubkina, Alexander Kalintsev, Alexander Konovalov, Olga Kravtsenyuk, Oleg Lyamtsev, Vladimir Lyubimov, Gennadiy Mordvinov, Alexander Murzin, Leonid Soms, Natalie Tokareva, Lyudmila Yavorskaya
Theoretical analysis and numerical experiments show a significant difference in a temporal dynamics of shadows caused by absorbing and scattering macroinhomogeneities. This difference is especially noticeable at the leading front of the pulse passed through the scattering medium. This makes it possible to image absorbing and scattering inhomogeneities separately using shadows obtained at subsequent time moments.
Olga Kravtsenyuk, Vladimir Lyubimov, Alexander Murzin, Alexander Kalintsev, Olga Golubkina, Alexander Konovalov, Oleg Lyamtsev, Gennadiy Mordvinov, Peter Volegov, Lyudmila Yavorskaya
Simulation of tomography reconstruction of several absorbing macro-inhomogeneities in a strongly scattering cylindrical body was carried out not using any prior information on the structure of macro-inhomogeneities. The data of time-domain measurements were simulated using a diffusion equation solving by FEM. For the reconstruction procedure the method based on curvilinear photon average trajectories (PAT) was used. This method allows solving the inverse problem of optical tomography in terms of a set of linear equations with a sparse coefficient matrix. Special methods for sparse matrix processing permit to decrease sufficiently the computing time for image reconstruction. The comparison was carried out for the results of application of the several matrix solvers used in conventional CT (such as MART, NNLS, LSQR, and their combinations) to PAT method. In order to estimate the computing time and the quality of reconstruction, a comparison was carried out between the images restored using PAT method and using multi-iterative program MMTOAST10, which employs FEM solving of the diffusion equation. It was shown that the trajectory method, being much faster, gives the comparable quality of the restored images.
Alexander Kalintsev, Olga Kravtsenyuk, Vladimir Lyubimov, Alexander Murzin, Olga Golubkina, Alexander Konovalov, Oleg Lyamtsev, Gennadiy Mordvinov, Peter Volegov
A simulation for a tomography reconstruction of an internal structure of the strongly scattering cylindrical body was carried out. For this purpose Photon Average Trajectories method was applied with several conventional CT algorithms such as the Max-Entropy algorithm MART and the least square algorithms NNLS and LSQR. The comparison of the reconstruction results obtained using these algorithms with ones obtained using MMTOAST10 program package based on diffuse equation Finite Element Method solver was carried out. It was shown that a satisfactory quality of the reconstruction was attainable already after few seconds of calculations at PC Pentium III for trajectory algorithms. The same quality of reconstruction with MMTOAST10 was achieved after about 1000 seconds.
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