Alexander G. Murzin

Application of the photon average trajectories method to real-time reconstruction of tissue inhomogeneities in diffuse optical tomography of strongly scattering media

The possibility of application of the photon average trajectories (PAT) method to real-time reconstruction of tissue inhomogeneities in diffuse optical tomography of strongly scattering media has been substantiated. By this method, the inverse problem is reduced to solution of the integral equation with integration along a conditional PAT. Such an approach allows the standard fast algebraic algorithms commonly used in projection computed tomography to be applied to diffuse optical image reconstruction. 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 done. Relative shadows caused by inhomogeneities are simulated via numerical solution of the non-stationary diffusion equation. To solve the inverse problem, the QR-factorization least-squares algorithm and the multiplicative algebraic reconstruction technique are used. The results are compared with those obtained by a well-known software package for temporal optical absorption and scattering tomography based on multiple solution of the diffusion equation. It is shown that the PAT method allows reconstruction of the optical structure of objects with comparable accuracy while saving reconstruction time considerably.

Application of transform algorithms to high-resolution image reconstruction in optical diffusion tomography of strongly scattering media

The applicability of transform algorithms generally used in projection-computed tomography is substantiated for the case of medical optical diffusion tomography (ODT). 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 ODT is reduced to a solution of an integral equation with integration along a PAT. Within the internal zone of the object, 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 low-contrast absorbing inhomogeneities is conducted. To solve the time-domain ODT inverse problem, two filtered backprojection algorithms (of Radon and Vainberg) are 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 solutions of a diffusion equation. It is shown that in important cases of low-contrast absorbing inhomogeneities, the PAT method using the Vainberg algorithm allows reconstruction of tissue optical inhomogeneities with a 20% gain in spatial resolution.

The possibility of increasing the spatial resolution in diffusion optical tomography

This paper discusses the possibility of increasing the resolution of diffusion optical tomography, using the method of average photon trajectories. It is shown that this method makes it possible to use fast reconstruction algorithms based on both iterative algebraic procedures and integral transformations with filtering of projections. The latter case not only suppresses the discretization noise but also substantially compensates the diffusion smearing of the reconstructed images.

Physical mechanisms of laser-induced shockwave lithotripsy in the microsecond range of laser pulse durations

Analysis of possible ways for organic minerals destruction by laser-induced shockwave is presented. Physical mechanisms describing lithotripsy with microsecond laser pulses are discussed. Theoretical considerations show that the most probable fragmentation mechanisms are connected with the existence of absorptive inclusions in the stone volume. We have shown that surface plasma flash may be considered as attendant phenomenon which does not necessarily play an important fragmentation role under our conditions of observation.

Application of photon average trajectories method for separate mapping of absorbing and scattering macroinhomogeneities using time-domain measurements technique

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.

Calculation of shadows induced by macroinhomogeneities located inside a strongly scattering object using integration over the average photon path

The trajectory approach to the problem of the optical imaging through the strongly scattering media with given macroinhomogeneities was considered. It was shown, that the shadow inside an object with any shape can be calculated by the representation of the photon mean path integrals. The influence of the objects boundary to the photon path statistical characteristics was investigated. The corresponding graphical dependencies conveniently illustrating trajectory alterations were represented. A comparative study of the three basic boundary geometry such as semi-infinite medium, flat layer and rectangular sector showed that the trajectory R((tau) ) of the photon statistical distribution center can be approximated by the three-segment polygonal line and the photon path root-mean- square deviation (Delta) ((tau) ) and the value d(tau) /dl ((tau) ), which is in inverse proportion to the speed of the distribution center movement can be replaced by the simplified functions in general case.

Statistical characteristics of photon paths and optimization of the tomography algorithms for the case of strongly scattering media

The theoretical and experimental studies were carried out for statistical characteristics of photon paths in strongly scattering media dependently on type of inhomogeneities, boundary conditions and method of measurements. The possibility to represent the signal perturbations due to the macroinhomogeneities as an integral along the mean photon path is used to solve the tomography reconstruction problem in terms of volume quantization. The optimum quantization scale is chosen on the basis of area across which the macroinhomogeneity characteristics are averaged.

Influence of fast reconstruction algorithms on spatial resolution of optical diffuse tomography by photon average trajectories method

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.

Application of integral transform algorithms to high-resolution reconstruction of tissue inhomogeneities in medical diffuse optical tomography

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.

Optical diffuse tomography reconstruction using photon average trajectory

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.