Share This Article:

Models and Algorithms for Diffuse Optical Tomographic System

Abstract Full-Text HTML XML Download Download as PDF (Size:1399KB) PP. 489-496
DOI: 10.4236/ijcns.2013.612052    2,677 Downloads   4,012 Views   Citations

ABSTRACT

Diffuse optical tomography (DOT) using near-infrared (NIR) light is a promising tool for noninvasive imaging of deep tissue. The approach is capable of reconstructing the quantitative optical parameters (absorption coefficient and scattering coefficient) of a soft tissue. The motivation for reconstructing the optical property variation is that it and, in particular, the absorption coefficient variation, can be used to diagnose different metabolic and disease states of tissue. In DOT, like any other medical imaging modality, the aim is to produce a reconstruction with good spatial resolution and in contrast with noisy measurements. The parameter recovery known as inverse problem in highly scattering biological tissues is a nonlinear and ill-posed problem and is generally solved through iterative methods. The algorithm uses a forward model to arrive at a prediction flux density at the tissue boundary. The forward model uses light transport models such as stochastic Monte Carlo simulation or deterministic methods such as radioactive transfer equation (RTE) or a simplified version of RTE namely the diffusion equation (DE). The finite element method (FEM) is used for discretizing the diffusion equation. The frequently used algorithm for solving the inverse problem is Newton-based Model based Iterative Image Reconstruction (N-MoBIIR). Many Variants of Gauss-Newton approaches are proposed for DOT reconstruction. The focuses of such developments are 1) to reduce the computational complexity; 2) to improve spatial recovery; and 3) to improve contrast recovery. These algorithms are 1) Hessian based MoBIIR; 2) Broyden-based MoBIIR; 3) adjoint Broyden-based MoBIIR; and 4) pseudo-dynamic approaches.

 

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Biswas, R. Kanhirodan and R. Vasu, "Models and Algorithms for Diffuse Optical Tomographic System," International Journal of Communications, Network and System Sciences, Vol. 6 No. 12, 2013, pp. 489-496. doi: 10.4236/ijcns.2013.612052.

References

[1] S. R. Arridge, “Optical Tomography in Medical Imaging,” Inverse Problems, Vol. 15, No. 2, 1999, pp. R41-R93.
[2] S. R. Arridge, M. Schweiger, M. Hiraoka and D. T. Delpy, “Finite Element Approach for Modelling Photon Transport in Tissue,” Medical Physics, Vol. 20, 1993, pp. 299-309.
http://dx.doi.org/10.1118/1.597069
[3] B. Kanmani and R. M. Vasu, “Noise-Tolerance Analysis for Detection and Reconstruction of Absorbing Inhomogeneities with Diffuse Optical Tomography Using Singleand Phase-Correlated Dual-Source Schemes,” Physics in Medicine and Biology, Vol. 52, 2007, p. 1409.
http://dx.doi.org/10.1088/0031-9155/52/5/013
[4] B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani and K. D. Paulsen, “Image Analysis Methods for Diffuse Optical Tomography,” Journal of Biomedical Optics, Vol. 11, 2006, Article ID: 1033001.
http://dx.doi.org/10.1117/1.2209908
[5] S. K. Biswas, K. Rajan, R. M. Vasu and D. Roy, “Accelerated Gradient Based Diffuse Optical Tomographic Image Reconstruction,” Medical Physics, Vol. 38, 2011, p. 539.
http://dx.doi.org/10.1118/1.3531572
[6] S. K. Biswas, K. Rajan and R. M. Vasu, “Practical Fully 3-D Reconstruction Algorithm for Diffuse Optical Tomography,” Journal of the Optical Society of America A, Vol. 29, 2012, p. 1017.
http://dx.doi.org/10.1364/JOSAA.29.001017
[7] D. A. Boas, J. P. Culver, J. J. Stott and A. K. Dunn, “Three Dimensional Monte Carlo Code for Photon Migration through Complex Heterogeneous Media Including the Adult Human Head,” Optics Express, Vol. 10, No. 3, 2002, pp. 159-170.
http://dx.doi.org/10.1364/OE.10.000159
[8] G. S. Abdoulaev and A. H. Hielscher, “Three-Dimensional Optical Tomography with the Equation of Radiative Transfer,” Journal of Electronic Imaging, Vol. 12, No. 4, 2003, pp. 594-601.
http://dx.doi.org/10.1117/1.1587730
[9] M. Schweiger, S. R. Arridge and I. Nissila, “GaussNewton Method for Image Reconstruction in Diffuse Optical Tomography,” Physics in Medicine and Biology, Vol. 50, No. 10, 2005, pp. 2365-2386.
http://dx.doi.org/10.1088/0031-9155/50/10/013
[10] C. K. Hayakawa and J. Spanier, F. Bevilacqua, A. K. Dunn, J. S. You, B. J. Tromberg and V. Venugopalan “Perturbation Monte Carlo Methods to Solve Inverse Photon Migration Problems in Heterogeneous Tissues,” Optics Letters, Vol. 26, No. 17, 2001, pp. 1335-1337.
[11] P. K. Yalavarthy, K. Karlekar, H. S. Patel, R. M. Vasu, M. Pramanik, P. C. Mathias, B. Jain and P. K. Gupta, “Experimental Investigation of Perturbation Monte-Carlo Based Derivative Estimation for Imaging Low-Scattering Tissue,” Optics Express, Vol. 13, No. 3, 2005, pp. 985-988.
[12] A. Sassaroli, “Fast Perturbation Monte Carlo Method for Photon Migration in Heterogeneous Turbid Media,” Optics Letters, Vol. 36, No. 11, 2011, pp. 2095-2097.
http://dx.doi.org/10.1364/OL.36.002095
[13] B. W. Pogue, M. S. Patterson, H. Jiang and K. D. Paulsen, “Initial Assessment of a Simple System for Frequency Domain Diffuse Optical Tomography,” Physics in Medicine and Biology, Vol. 40, 1995, pp. 1709-1729.
http://dx.doi.org/10.1088/0031-9155/40/10/011
[14] T. Tarvainen, M. Vauhkonen, V. Kolemainen, S. R. Arridge and J. P. Kaipio, “Coupled Radiative Transfer Equation and Diffusion Approximation Model for Photon Migration in Turbid Medium with Low-Scattering and Non-Scattering Regions,” Physics in Medicine and Biology, Vol. 50, 2005, pp. 4913-4930.
http://dx.doi.org/10.1088/0031-9155/50/20/011
[15] K. Levenburg, “A Method for the Solution of Certain Non-Linear Problems in Least-Squares,” Quarterly of Applied Mathematics, Vol. 2, 1944, p. 164.
[16] D. W. Marquardt, “An Algorithm for the Least-Square Estimation of Non-Linear Parameters,” SIAM Journal on Applied Mathematics, Vol. 11, 1963, p. 431.
http://dx.doi.org/10.1137/0111030
[17] C. G. Broyden, “On the Discovery of the Good Broyden Method,” Mathematical Programming, Vol. 87, No. 2, 2000, p. 209.
[18] C. G. Broyden, “A Class of Methods for Solving Nonlinear Simultaneous Equations,” Mathematics of Computation, Vol. 19, 1965, pp. 577-593.
[19] H. Wang and R. P. Tewakson, “Quasi-Gauss-Newton Method for Solving Non-Linear Algebraic Equations,” Computers & Mathematics with Applications, Vol. 25, 1993, pp. 53-63.
[20] R. H. Byrd, H. Khalfan and R. B. Schnabel, “A Theoretical and Experimental Study of the Symmetric Rank One Update,” Technical Report CU-CS-489-90, University of Colorado, 2002
[21] J. Branes, “An Algorithm for Solving Nonlinear Equations Based on the Secant Method,” Computer Journal, Vol. 8, No. 1, 1965, pp. 66-72.
[22] J. E. Dennis Jr. and R. B. Schnabel, “Numerical Methods for Unconstrained Optimization and Nonlinear Equations,” Prentice-Hall, Englewood Cliffs, 1983.
[23] S. Schlenkrich, A. Griewank and A. Walther, “On the Local Convergence of Adjoint Broyden Methods,” Mathematical Programming, Vol. 121, No. 2, 2010, pp. 221-247.
[24] B. W. Pogue, T. McBride, J. Prewitt, U. L. Osterberg and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Applied Optics, Vol. 38, 1999, pp. 2950-2961.
http://dx.doi.org/10.1364/AO.38.002950
[25] B. Banerjee and D. Roy and R. M. Vasu, “A PseudoDynamical Systems Approach to a Class of Inverse Problems in Engineering,” Proceedings of the Royal Society A, Vol. A465, 2009, pp. 1561-1579.
[26] B. Banerjee and D. Roy and R. M. Vasu, “A PseudoDynamic Sub-Optimal Filter for Elastography under Static Loading and Measurement,” Physics in Medicine and Biology, Vol. 54, 2009, pp. 285-305.
http://dx.doi.org/10.1088/0031-9155/54/2/008

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.