## Biomedical Optical Tomography Using Dynamic Parameterization and Bayesian Conditioning on Photon Migration Measurements

Applied Optics, Vol. 38, Issue 10, pp. 2138-2150 (1999)

http://dx.doi.org/10.1364/AO.38.002138

Acrobat PDF (584 KB)

### Abstract

Stochastic reconstruction techniques are developed for mapping the interior optical properties of tissues from exterior frequency-domain photon migration measurements at the air–tissue interface. Parameter fields of absorption cross section, fluorescence lifetime, and quantum efficiency are accurately reconstructed from simulated noisy measurements of phase shift and amplitude modulation by use of a recursive, Bayesian, minimum-variance estimator known as the approximate extended Kalman filter. Parameter field updates are followed by data-driven zonation to improve the accuracy, stability, and computational efficiency of the method by moving the system from an underdetermined toward an overdetermined set of equations. These methods were originally developed by Eppstein and Dougherty [Water Resources Res. **32,** 3321 (1996)] for applications in geohydrology. Estimates are constrained to within feasible ranges by modeling of parameters as β-distributed random variables. No arbitrary smoothing, regularization, or interpolation is required. Results are compared with those determined by use of Newton–Raphson-based inversions. The speed and accuracy of these preliminary Bayesian reconstructions suggest the near-future application of this inversion technology to three-dimensional biomedical imaging with frequency-domain photon migration.

© 1999 Optical Society of America

**OCIS Codes**

(000.5490) General : Probability theory, stochastic processes, and statistics

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(100.6950) Image processing : Tomographic image processing

(110.4280) Imaging systems : Noise in imaging systems

(170.5280) Medical optics and biotechnology : Photon migration

**Citation**

Margaret J. Eppstein, David E. Dougherty, Tamara L. Troy, and Eva M. Sevick-Muraca, "Biomedical Optical Tomography Using Dynamic Parameterization and Bayesian Conditioning on Photon Migration Measurements," Appl. Opt. **38**, 2138-2150 (1999)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-10-2138

Sort: Year | Journal | Reset

### References

- J. R. Singer, F. A. Grunbaum, P. Kohn, and J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
- R. L. Barbour, H. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, and P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.
- S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance and A. Katzir, eds., Proc. SPIE 1431, 204–215 (1991).
- S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
- M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusion photon tomography,” Opt. Lett. 20, 426–428 (1995).
- H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
- M. A. O’Leary, D. A. Boas, D. X. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
- D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent lifetime and yield from multiple scattered light reemitted from tissues and other random media,” Appl. Opt. 36, 2260–2272 (1997).
- J. Chang, H. L. Graber, and R. L. Barbour, “Luminescence optical tomography of dense scattering media,” J. Opt. Soc. Am. A 14, 288–299 (1997).
- D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical heterogeneities with turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
- Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
- W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag. 9, 218–225 (1990).
- K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
- S. R. Arridge and M. Schweiger, “Image reconstruction in optical tomography,” Phil. Trans. R. Soc. London Series B 352, 717–726 (1997).
- H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt. 37, 5337–5343 (1998).
- N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, 2nd ed. (Wiley, New York, 1995), Vol. 1.
- V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source-detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
- M. J. Eppstein and D. E. Dougherty, “Simultaneous estimation of transmissivity values and zonation,” Water Resources Res. 32, 3321–3336 (1996).
- T. L. Troy, D. L. Page, and E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 1, 342–355 (1996).
- E. M. Sevick-Muraca, C. L. Hutchinson, and D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7(1), 25–28 (1996).
- E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
- E. M. Sevick and C. L. Burch, “Origin of phosphorescence signals re-emitted from tissues,” Opt. Lett. 19, 1928–1930 (1994).
- M. S. Patterson and B. W. Pogue, “Mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissues,” Appl. Opt. 33, 1963–1974 (1994).
- C. L. Hutchinson, T. L. Troy, and E. M. Sevick-Muraca, “Fluorescence-lifetime determination in tissues or other scattering media from measurement of excitation and emission kinetics,” Appl. Opt. 35, 2325–2332 (1996).
- J. C. Adams, “mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations,” Appl. Math. Comp. 34, 133–146 (1989).
- M. S. Patterson, B. Chance, and B. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
- M. J. Eppstein and D. E. Dougherty, “Optimal 3-D traveltime tomography,” Geophysics 63, 1053–1061 (1998).
- M. J. Eppstein and D. E. Dougherty, “Efficient three-dimensional data inversion: soil characterization and moisture monitoring from cross-well ground-penetrating radar at a Vermont test site,” Water Resources Res. 34, 1889–1900 (1998).
- M. J. Eppstein and D. E. Dougherty, “Three-dimensional stochastic tomography with upscaling,” U.S. patent application 09/110,506 (9 July 1998).
- R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. D 82, 35–45 (1960).
- G. L. Smith, S. F. Schmidt, and L. A. McGee, “Application of statistical filter theory to the optimal estimation of position and velocity on board a circumlunar vehicle,” NASA Tech. Rep. R-135 (U.S. Government Printing Office, Washington, D.C., 1962).
- A. Gelb, ed., Applied Optimal Estimation (MIT Press, Cambridge, Mass. 1974).
- J. S. Reynolds, T. L. Troy, and E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotech. Prog. 13, 669–680 (1997).
- N. Sun and W. W.-G. Yeh, “Identification of parameter structure in groundwater inverse problem,” Water Resources Res. 21, 869–883 (1985).
- F. Aschenbrenner and A. Ostin, “Automatic parameter estimation applied on a groundwater model: the problem of structure identification,” Environ. Geol. 25, 205–210 (1995).
- M. J. Eppstein and D. E. Dougherty, “Optimal 3-D geophysical tomography,” in 1998 Proceedings of the Symposium on the Application of Geophysics to Environmental and Engineering Problems (SAGEEP), R. S. Bell, M. H. Powers, and T. Larson, eds. (Environmental and Engineering Geophysical Society, Wheat Ridge, Colo. 1998), pp. 249–256.
- T. L. Troy, “Biomedical optical imaging using frequency domain photon migration measurements: experiments and numerical image reconstructions,” Ph.D. dissertation (Purdue University, Lafayette, Ind., 1997).
- J. S. Reynolds, T. L. Troy, R. H. Mayer, A. B. Thompson, D. J. Waters, K. K. Cornell, P. W. Snyder, and E. M. Sevick-Muraca, “Imaging of spontaneous mammary tumors using fluorescent contrast agents,” (submitted to Photochem. Photobiol).
- M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, and B. J. Tromberg, eds., Proc. SPIE 3597 (to be published).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.