Vladimir V. Lyubimov

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.

Principles of fluorescence laser tomography of strongly scattering media

The propagation of laser radiation and fluorescence excited by it in a strongly scattering medium are analyzed in the diffusion equation approximation. The possibility of applying efficient algorithms of the tomographic reconstruction with the use of mean paths of photons in biotissues to fluorescence laser tomography is substantiated.

Space-varying iterative restoration of diffuse optical tomograms reconstructed by the photon average trajectories method

The possibility of improving the spatial resolution of diffuse optical tomograms 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 is reduced to a solution of an 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. 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, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions 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 a gain in spatial resolution can be obtained.

Superresolution in diffuse optical tomography

The possibility of applying image reconstruction methods used in optics to improve the resolution of the photon average trajectories method of diffuse optical tomography is demonstrated. The limit resolution determined by Nyquist’s consequence of the Kotel’nikov-Shannon theorem is achieved.

Physical foundations of the strongly scattering media laser tomography

The median photons path needed for the formulation of the tomographic problem is revealed in the photon diffusion equation solution as well as probability density distribution of single photons instantaneous position deviation from the median path. The mentioned distribution defines the resolution of the strongly scattering medium tomographic investigation.

A semi-analytical perturbation model for diffusion tomogram reconstruction from time-resolved optical projections

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.

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.