Article

Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems.

Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA.
Medical Physics (Impact Factor: 3.01). 06/2008; 35(5):1682-97. DOI: 10.1118/1.2889778
Source: PubMed

ABSTRACT Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

0 Bookmarks
 · 
62 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper proposes a new reconstruction method for diffuse optical tomography using reduced-order models of light transport in tissue. The models, which directly map optical tissue parameters to optical flux measurements at the detector locations, are derived based on data generated by numerical simulation of a reference model. The reconstruction algorithm based on the reduced-order models is a few orders of magnitude faster than the one based on a finite element approximation on a fine mesh incorporating a priori anatomical information acquired by magnetic resonance imaging. We demonstrate the accuracy and speed of the approach using a phantom experiment and through numerical simulation of brain activation in a rat's head. The applicability of the approach for real-time monitoring of brain hemodynamics is demonstrated through a hypercapnic experiment. We show that our results agree with the expected physiological changes and with results of a similar experimental study. However, by using our approach, a three-dimensional tomographic reconstruction can be performed in ∼3 s per time point instead of the 1 to 2 h it takes when using the conventional finite element modeling approach.
    Journal of Biomedical Optics 02/2014; 19(2):26008. · 2.75 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Laser immunotherapy (LIT) is an in situ autologous cancer vaccine (inCVAX) that induces a systemic immune responses through a local intervention. The effect of LIT depends on two major interactions: a selective photothermal interaction and an active immunological stimulation. The selective photothermal interaction can help release tumor antigens, which can stimulate specific antitumor immunity in the host. The elevated expression of heat-shock protein and the local application of immunoadjuvant further enhance the immune responses. The safety and effectiveness of LIT have been tested in preclinical studies and in preliminary clinical trials. Tumor samples from breast cancer patients treated by LIT were analyzed using histochemical methods. Preliminary results showed a change in T cells after LIT treatment, indicating strong induced immune responses. LIT may be proven to be a feasible treatment modality for metastatic cancers.
    IEEE Journal of Selected Topics in Quantum Electronics 07/2012; 18(4):1434-1438. · 3.47 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The image reconstruction problem encountered in diffuse optical tomographic imaging is ill-posed in nature, necessitating the usage of regularization to result in stable solutions. This regularization also results in loss of resolution in the reconstructed images. A frame work, that is attributed by model-resolution, to improve the reconstructed image characteristics using the basis pursuit deconvolution method is proposed here. The proposed method performs this deconvolution as an additional step in the image reconstruction scheme. It is shown, both in numerical and experimental gelatin phantom cases, that the proposed method yields better recovery of the target shapes compared to traditional method, without the loss of quantitativeness of the results.
    IEEE Transactions on Medical Imaging 04/2014; 33(4):891-901. · 3.80 Impact Factor

Preview

Download
1 Download
Available from