Reconstructions for Continuous-Wave Diffuse Optical Tomography by a Globally Convergent Method

Jianzhong Su^1*, Yueming Liu¹, Zi-Jing Lin², Steven Teng¹, Aubrey Rhoden¹, Natee Pantong¹, Hanli Liu²

¹Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA.
²Department of Bioengineering, University of Texas at Arlington, Arlington, Texas, USA.

DOI: 10.4236/jamp.2014.25025                

Abstract

In this paper, a novel reconstruction method is presented for Near Infrared (NIR) 2-D imaging to recover optical absorption coefficients from laboratory phantom data. The main body of this work validates a new generation of highly efficient reconstruction algorithms called “Globally Convergent Method” (GCM) based upon actual measurements taken from brain-shape phantoms. It has been demonstrated in earlier studies using computer-simulated data that this type of reconstructions is stable for imaging complex distributions of optical absorption. The results in this paper demonstrate the excellent capability of GCM in working with experimental data measured from optical phantoms mimicking a rat brain with stroke.

Keywords

Inverse Problems, Diffuse Optical Tomography, Medical and Biological Imaging, Globally Convergence Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Srinivasan, S., Pogue, B.W., Brooksby, B., Jiang, S., Dehghani, H., Kogel, C., Poplack, S.P. and Paulsen, K.D. (2005) Near-Infrared Characterization of Breast Tumors in Vivo Using Spectrally-Constrained Reconstruction. Technology in Cancer Research & Treatment, 4, 513-526.
[2]	Xu, Y., Gu, X., Fajardo, L. and Jiang, H. (2003) In Vivo Breast Imaging with Diffuse Optical Tomography Based on Higher-Order Diffusion Equations. Applied Optics, 42, 3163-3169. http://dx.doi.org/10.1364/AO.42.003163
[3]	Godavarty, A., Thompson, A.B., Roy, R., Gurfinkel, M., Eppstein, M.J., Zhang, C. and Sevick-Muraka, E.M. (2004) Diagnostic of Breast Cancer Using Fluorescence-Enhanced Optical Tomography: Phantom Studies. Journal of Biomedical Optics, 9, 488-496. http://dx.doi.org/10.1117/1.1691027
[4]	Gopinath, S., Robertson, C.S., Grossman, R.G. and Chance, B. (1993) Near-Infrared Spectroscopic Localization of Intracranial Hematomas. Journal of Neurosurgery, 79, 43-47. http://dx.doi.org/10.3171/jns.1993.79.1.0043
[5]	Bluestone, A.Y., Stewart, M., Lasker, J., Abdoulaev, G.S. and Hielscher, A.H. (2004) Three-Dimensional Optical Tomographic Brain Imaging in Small Animals, Part 1: Hypercapnia. Journal of Biomedical Optics, 9, 1046-1062. http://dx.doi.org/10.1117/1.1784471
[6]	Zhang, G., Katz, A., Alfano, R.R., Kofinas, A.D., Stubblefield, P.G., Rosenfeld, W., Beyer, D., Maulik, D. and Stankovic, M.R. (2000) Brain Perfusion Monitoring with Frequency-Domain and Continuous-Wave Near-Infrared Spectroscopy: A Cross-Correlation Study in Newborn Piglets. Physics in Medicine and Biology, 45, 3143-3158. http://dx.doi.org/10.1088/0031-9155/45/11/303
[7]	Yodh, A.G. and Boas, D.A. (2003) Functional Imaging with Diffusing Light. In: Vo-Dinh, T., Ed., Biomedical Photonics Handbook, CRC Press, New York, 1-45.
[8]	Joseph, D.K., Huppert, T.J., Franceschini, M.A. and Boas, D.A. (2006) Diffuse Optical Tomography System to Image Brain Activation with Improved Spatial Resolution and Validation with Functional Magnetic Resonance Imaging. Applied Optics, 45, 8142-8151. http://dx.doi.org/10.1364/AO.45.008142
[9]	Boas, D.A., Gaudette, T., Strangman, G., Cheng, X., Marota, J.J.A. and Mandeville, J.B. (2001) The Accuracy of Near Infrared Spectroscopy and Imaging during Focal Changes in Cerebral Hemodynamics. NeuroImage, 13, 76-90. http://dx.doi.org/10.1006/nimg.2000.0674
[10]	Chance, B. anday, E., Nioka, S., Zhou, S., Hong, L., Worden, K., Li, C., Murray, T., Ovetsky, Y., Pidikiti, D. and Thomas, R. (1998) A Novel Method for Fast Imaging of Brain Function, Non-Invasively, with Light. Optics Express, 2, 411-423. http://dx.doi.org/10.1364/OE.2.000411
[11]	Boas, D.A., Gaudette, T., Strangman, G., Cheng, X., Marota, J.J.A. and Mandeville, J.B. (2001) The Accuracy of Near Infrared Spectroscopy and Imaging during Focal Changes in Cerebral Hemodynamics. NeuroImage, 13, 76-90. http://dx.doi.org/10.1006/nimg.2000.0674
[12]	Wang, K.K. and Zhu, T.C. (2009) Reconstruction of In-Vivo Optical Properties for Human Prostate Using Interstitial Diffuse Optical Tomography. Optics Express, 17, 11665-11672. http://dx.doi.org/10.1364/OE.17.011665
[13]	McBride, T.O., Pogue, B.W., Jiang, S., Österberg, U.L. and Paulsen, K.D. (2001) Initial Studies of in Vivo Absorbing and Scattering Heterogeneity in Near-Infrared Tomographic Breast Imaging. Optics Letters, 26, 822-824. http://dx.doi.org/10.1364/OL.26.000822
[14]	Kolehmainen, V., Prince, S., Arridge, S.R. and Kaipio, J.P. (2000) A State Estimation Approach to Non-Stationary Optical Tomography Problem. Journal of the Optical Society of America, 20, 876-884. http://dx.doi.org/10.1364/JOSAA.20.000876
[15]	Zhang, Q., Brooks, D.H. and Boas, D.A. (2005) A Haemodynamic Response Function Model in Spatio-Temporal Diffuse Optical Tomography. Physics in Medicine and Biology, 50, 4625-4644. http://dx.doi.org/10.1088/0031-9155/50/19/014
[16]	Arridge, S.R. and Schotland, J.C (2009) Optical Tomography: Forward and Inverse Problems. Inverse Problems, 25, 123010. http://dx.doi.org/10.1088/0266-5611/25/12/123010
[17]	Arridge, S.R. and Hebden, J.C. (1997) Optical Imaging in Medicine: II. Modeling and Reconstruction. Phys. Med. Boil., 42, 841-853. http://dx.doi.org/10.1088/0031-9155/42/5/008
[18]	Hielscher, A.H., Klose, A.D. and Hanson, K.M. (1999) Gradient-Based Iterative Reconstruction Scheme for Time- Resolved Optical Tomography. IEEE Transactions on Medical Imaging, 18, 262-271. http://dx.doi.org/10.1109/42.764902
[19]	Schotland, J.C. (1997) Continuous-Wave Diffusion Imaging. Journal of the Optical Society of America, 14, 275-279. http://dx.doi.org/10.1364/JOSAA.14.000275
[20]	O’Leary, M.A., Boas D.A., Chance, B. and Yodh, A.G. (1995) Experimental Images of Heterogeneous Turbid Media by Frequency-Domain Diffusion-Photon Tomography. Optics Letters, 20, 426-428. http://dx.doi.org/10.1364/OL.20.000426
[21]	Gryazin, Y.A., Klibanov, M.V. and Lucas, T.R. (2001) Numerical Solution of a Subsurface Imaging Inverse Problem. SIAM Journal on Applied Mathematics, 62, 664-683. http://dx.doi.org/10.1137/S0036139900377366
[22]	Klibanov, M.V. and Timonov, A. (2004) Carleman Estimates for Coefficient Inverse Problems and Numerical Applications. Brill Academic Publishers, VSP, Imprint Brill.
[23]	Klibanov, M.V. and Timonov, A. (2007) Numerical Studies on the Globally Convergent Convexification Algorithm in 2D. Inverse Problems, 23, 123-138. http://dx.doi.org/10.1088/0266-5611/23/1/006
[24]	Keller, H.B. and Perozzi, D.J. (1983) Fast Seismic Ray Tracing. SIAM Journal on Applied Mathematics, 43, 981-992. http://dx.doi.org/10.1137/0143064
[25]	Su, J., Shan, H., Liu, H. and Klibanov, M.V. (2006) Reconstruction Method with Data from a Multiple-Site Continuous-Wave Source for Three-Dimensional Optical Tomography. Journal of the Optical Society of America, 23, 2388- 2395. http://dx.doi.org/10.1364/JOSAA.23.002388
[26]	Shan, H., Klibanov, M.V., Liu, H., Pantong, N. and Su, J. (2008) Numerical Implementation of the Convexification Algorithm for an Optical Diffusion Tomograph. Inverse Problems, 24, 025006. http://dx.doi.org/10.1088/0266-5611/24/2/025006
[27]	Shan, H., Klibanov, M.V., Su, J., Pantong, N. and Liu, H. (2008) A Globally Accelerated Numerical Method for Optical Tomography with Continuous Wave Source. Journal of Inverse and III-posed Problems, 16, 763-790. http://dx.doi.org/10.1515/JIIP.2008.048
[28]	Beilina, L. and Klibanov, M.V. (2008) A Globally Convergent Numerical Method for a Coefficient Inverse Problem. SIAM Journal on Scientific Computing, 31, 478-509. http://dx.doi.org/10.1137/070711414
[29]	Beilina, L. and Klibanov, M.V. (2012) Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems. http://dx.doi.org/10.1007/978-1-4419-7805-9
[30]	Su, J., Klibanov, M.V., Liu, Y., Lin, Z., Pantong, N. and Liu, H. (2013) Optical Imaging of Phantoms from Real Data by an Approximately Globally Convergent Inverse Algorithm. Inverse Problems in Science and Engineering, 21, 1125-1150. http://dx.doi.org/10.1080/17415977.2012.743126
[31]	Pantong, N., Su, J., Shan, H., Klibanov, M.V. and Liu, H. (2009) A Globally Accelerated Reconstruction Algorithm for Diffusion Tomography with Continuous-Wave Source in Arbitrary Convex Shape Domain. Journal of the Optical Society of America, 26, 456-472. http://dx.doi.org/10.1364/JOSAA.26.000456
[32]	Klibanov, M.V., Su, J., Pantong, N., Shan, H. and Liu, H. (2010) A Globally Convergent Numerical Method for an Inverse Elliptic Problem of Optical Tomography. Appl. Anal., 6, 861-891. http://dx.doi.org/10.1080/00036811003649157
[33]	Niu, H., Tian, F., Lin, Z. and Liu H. (2010) Development of a Compensation Algorithm for Accurate Depth Localization in Diffuse Optical Tomography. Optics Letters, 35, 429-431. http://dx.doi.org/10.1364/OL.35.000429
[34]	Niu, H., Lin, Z., Tian, F., Dhamne, S. and Liu, H. (2010) Comprehensive Investigation of Three-Dimensional Diffuse Optical Tomography with Depth Compensation Algorithm. Journal of Biomedical Optics, 15, 046005. http://dx.doi.org/10.1117/1.3462986
[35]	Huppert, T.J., Diamond, S.G., Franceschini, M.A. and Boas, D.A. (2009) HomER: A Review of Time Series Analysis Methods for Near-Infrared Spectroscopy of the Brain. Applied Optics, 48, D280-D298. http://dx.doi.org/10.1364/AO.48.00D280