Diffuse optical tomography using intensity measurements and the a priori acquired regions of interest: theory and simulations

A simple algorithm for diffuse optical tomography without Jacobian inversion

A computationally simpler algorithm to reconstruct the optical property distribution of turbid media using diffuse optical tomographic principles is presented. The proposed algorithm eliminates the requirement of large Jacobian matrix inversion which otherwise is essential for tomographic imaging. The most significant Jacobians are identified based on proper thresholding of the measurement and the intersection of these Jacobians gives the approximate spatial location of the inhomogeneity. The algorithm is tested and optimized using simulations and further validated using tissue-mimicking phantom-based experiments andin-vivosmall-animal experiments.

Localization of an absorber in a turbid semi-infinite medium by spatially resolved continuous-wave diffuse reflectance measurements

A method to locate an absorber embedded in a semi-infinite turbid medium by spatially-resolved continuous-wave (SRCW) diffuse reflectance measurements is introduced. The depth of the absorber is assessed by single wavelength SRCW diffuse reflectance measurements by two detectors in a radial row. The ratio of perturbations introduced by the defect at two detectors is used to be matched with the ratio-versus-depth curve, which are generated by approximate formulas of continuous wave diffuse reflectance. The error due to approximation and the error in depth assessment are studied for different cases revealing favorable source-detector placements with respect to planar position of the defect. The effect of lateral displacement of the source with respect to defect is studied. A strategy to overcome errors introduced by erroneous prediction of background medium optical properties is suggested. Theoretical results indicate that the depth of the absorber can be obtained with 0.1 mm precision independent of its absorption coefficient and its size for the values chosen in the study. The approach is tested experimentally and it is observed that theoretical results fit with experimental data.

Rapid convergence to the inverse solution regularized with Lorentzian distributed function for near-infrared continuous wave diffuse optical tomography

A promising method to achieve rapid convergence for image reconstruction is introduced for the continuous-wave near-infrared (NIR) diffuse optical tomography (DOT). Tomographic techniques are usually implemented off line and are time consuming to realize image reconstruction, especially for NIR DOT. Therefore, it is essential to both speed up reconstruction and achieve stable and convergent solutions. We propose an approach using a constraint based on a Lorentzian distributed function incorporated into Tikhonov regularization, thereby rapidly converging a stable solution. It is found in the study that using the proposed method with around five or six iterations leads to a stable solution. The result is compared to the primary method usually converging in approximately 25 iterations. Our algorithm rapidly converges to stable solution in the case of noisy (>20 dB) detected intensities.

Noise-tolerance analysis for detection and reconstruction of absorbing inhomogeneities with diffuse optical tomography using single- and phase-correlated dual-source schemes

An iterative reconstruction procedure is used to invert intensity data from both single- and phase-correlated dual-source illuminations for absorption inhomogeneities. The Jacobian for the dual source is constructed by an algebraic addition of the Jacobians estimated for the two sources separately. By numerical simulations, it is shown that the dual-source scheme performs superior to the single-source system in regard to (i) noise tolerance in data and (ii) ability to reconstruct smaller and lower contrast objects. The quality of reconstructions from single-source data, as indicated by mean-square error at convergence, is markedly poorer compared to their dual-source counterpart, when noise in data was in excess of 2%. With fixed contrast and decreasing inhomogeneity diameter, our simulations showed that, for diameters below 7 mm, the dual-source scheme has a higher percentage contrast recovery compared to the single-source scheme. Similarly, the dual-source scheme reconstructs to a higher percentage contrast recovery from lower contrast inhomogeneity, in comparison to the single-source scheme.

Image reconstruction of effective Mie scattering parameters of breast tissue in vivo with near-infrared tomography

A method for image reconstruction of the effective size and number density of scattering particles is discussed within the context of interpreting near-infrared (NIR) tomography images of breast tissue. An approach to use Mie theory to estimate the effective scattering parameters is examined and applied, given some assumptions about the index of refraction change expected in lipid membrane-bound scatterers. When using a limited number of NIR wavelengths in the reduced scattering spectra, the parameter extraction technique is limited to representing a continuous distribution of scatterer sizes, which is modeled as a simple exponentially decreasing distribution function. In this paper, image formation of effective scatterer size and number density is presented based on the estimation method. The method was evaluated with Intralipid phantom studies to demonstrate particle size estimation to within 9% of the expected value. Then the method was used in NIR patient images, and it indicates that for a cancer tumor, the effective scatterer size is smaller than the background breast values and the effective number density is higher. In contrast, for benign tumor patients, there is not a significant difference in effective scatterer size or number density between tumor and normal tissues. The method was used to interpret magnetic resonance imaging-coupled NIR images of adipose and fibroglandular tissues, and it indicated that the fibroglandular tissue has smaller effective scatterer size and larger effective number density than the adipose tissue does.

Diffuse optical tomography through solving a system of quadratic equations: theory and simulations

This paper discusses the iterative solution of the nonlinear problem of optical tomography. In the established forward model-based iterative image reconstruction (MOBIIR) method a linear perturbation equation containing the first derivative of the forward operator is solved to obtain the update vector for the optical properties. In MOBIIR, the perturbation equation is updated by recomputing the first derivative after each update of the optical properties. In the method presented here a nonlinear perturbation equation, containing terms up to the second derivative, is used to iteratively solve for the optical property updates. Through this modification, reconstructions with reasonable contrast recovery and accuracy are obtained without the need for updating the perturbation equation and therefore eliminating the outer iteration of the usual MOBIIR algorithm. To improve the performance of the algorithm the outer iteration is reintroduced in which the perturbation equation is recomputed without re-estimating the derivatives and with only updated computed data. The system of quadratic equations is solved using either a modified conjugate gradient descent scheme or a two-step linearized predictor-corrector scheme. A quick method employing the adjoint of the forward operator is used to estimate the derivatives. By solving the nonlinear perturbation equation it is shown that the iterative scheme is able to recover large contrast variations in absorption coefficient with improved noise tolerance in data. This ability has not been possible so far with linear algorithms. This is demonstrated by presenting results of numerical simulations from objects with inhomogeneous inclusions in absorption coefficient with different contrasts and shapes.