## Three-Dimensional Simulation of Near-Infrared Diffusion in Tissue: Boundary Condition and Geometry Analysis for Finite-Element Image Reconstruction

Applied Optics, Vol. 40, Issue 4, pp. 588-600 (2001)

http://dx.doi.org/10.1364/AO.40.000588

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### Abstract

Imaging of tissue with near-infrared spectral tomography is emerging as a practicable method to map hemoglobin concentrations within tissue. However, the accurate recovery of images by using modeling methods requires a good match between experiments and the model prediction of light transport in tissue. We illustrate the potential for a match between (i) three-dimensional (3-D) frequency-domain diffusion theory, (ii) two-dimensional diffusion theory, (iii) Monte Carlo simulations, and (iv) experimental data from tissue-simulating phantoms. Robin-type boundary conditions are imposed in the 3-D model, which can be implemented with a scalar coupling coefficient relating the flux through the surface to the diffuse fluence rate at the same location. A comparison of 3-D mesh geometries for breast imaging indicates that relative measurements are sufficiently similar when calculated on either cylindrical or female breast shapes, suggesting that accurate reconstruction may be achieved with the simpler cylindrical mesh. Simulation studies directly assess the effects from objects extending out of the image plane, with results suggesting that spherically shaped objects reconstruct at lower contrast when their diameters are less than 15–20 mm. The algorithm presented here illustrates that a 3-D forward diffusion model can be used with circular tomographic measurements to reconstruct two-dimensional images of the interior absorption coefficient.

© 2001 Optical Society of America

**OCIS Codes**

(110.6880) Imaging systems : Three-dimensional image acquisition

(110.7050) Imaging systems : Turbid media

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.3830) Medical optics and biotechnology : Mammography

(170.5270) Medical optics and biotechnology : Photon density waves

(170.5280) Medical optics and biotechnology : Photon migration

**Citation**

Brian W. Pogue, Shireen Geimer, Troy O. McBride, Shudong Jiang, Ulf L. Österberg, and Keith D. Paulsen, "Three-Dimensional Simulation of Near-Infrared Diffusion in Tissue: Boundary Condition and Geometry Analysis for Finite-Element Image Reconstruction," Appl. Opt. **40**, 588-600 (2001)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-4-588

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### References

- G. J. Mueller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, and P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).
- B. Chance, Q. Luo, S. Nioka, D. C. Alsop, and J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Philos. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
- S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, and B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
- H. Jess, H. Erdl, T. Moesta, S. Fantini, M. A. Francecshini, E. Gratton, and M. Kaschke, “Intensity modulated breast imaging: technology and clinical pilot study results, in Advances in Optical Imaging and Photon Migration,” Vol. 2 of 1996 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996).
- B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Express. 1, 391–403 (1997).
- B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
- K. D. Paulsen, and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
- K. D. Paulsen, and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35, 3447–3458 (1996).
- 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).
- B. W. Pogue, T. McBride, U. Osterberg, and K. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Exp. 4, 270–286 (1999).
- T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, and K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygenation in tissue,” Appl. Opt. 38, 5480–5490 (1999).
- B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, O. K. S., U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared light: initial pilot results in the breast,” Radiology 218, 261–266 (2001).
- M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittances for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
- M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1990).
- D. T. Delpy and M. Cope, “Quantification in tissue near-infrared spectroscopy,” Philos. Trans. R. Soc. London Ser. B. 352, 649–659 (1997).
- S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, R41–R93 (1999).
- W. Zhu, Y. Wang, Y. Yao, J. Chang, H. L. Graber, and R. L. Barbour, “Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method,” J. Opt. Soc. Am. A 14, 799–807 (1997).
- J. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997).
- M. J. Eppstein, D. E. Dougherty, T. L. Troy, and E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
- A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
- B. C. Wilson, M. S. Patterson, S. T. Flock, and J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, M. D. Dall’Acqua, ed. (Plenum, New York, 1988), pp. 45–52.
- W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
- T. J. Farrell, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties,” Med. Phys. 19, 879–888 (1992).
- R. A. J. Groenhuis, H. A. Ferwerda, and J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. I. Theory,” Appl. Opt. 22, 2456–2462 (1983).
- M. S. Patterson, S. J. Madsen, J. D. Moulton, and B. C. Wilson, “Diffusion equation representation of photon migration in tissue,” in Microwave Theory and Techniques Symposium Digest (IEEE, New York, 1991), pp. 905–908.
- J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal-reflection of diffusive light in random-media,” Phys. Rev. A. 44, 3948–3959 (1991).
- I. Freund, “Surface reflections and boundary-conditions for diffusive photon transport,” Phys. Rev. A 45, 8854–8858 (1992).
- C. P. Gonatas, M. Miwa, M. Ishii, J. Schotland, B. Chance, and J. S. Leigh, “Effects due to geometry and boundary conditions in multiple light scattering,” Phys. Rev. E 48, 2212–2216 (1993).
- R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
- A. H. Hielscher, L. Wang, K. Tittel, and S. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
- R. Aronson, “Boundary-conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
- J. C. J. Paasschens and G. W. ’t Hooft, “Influence of boundaries on the imaging of objects in turbid media,” J. Opt. Soc. Am. A 15, 1797–1812 (1998).
- K. D. Paulsen and H. B. Jiang, “Spatially varying optical property reconstruction using a finite-element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
- M. Schweiger and S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
- B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
- B. W. Pogue and M. S. Patterson, “Frequency domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
- J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976), pp. 133–138.
- J. B. Fishkin, S. Fantini, M. J. VandeVen, and E. Gratton, “Gigahertz photon density waves in a turbid medium: theory and experiments,” Phys. Rev. E. 53, 2307–2319 (1996).
- J. D. Moulton, “Diffusion theory modeling of picosecond laser pulse propagation in turbid media” (Physics Department, McMaster University, Hamilton, Canada, 1990).
- L. L. Lapidus and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering (Wiley, New York, 1999).
- R. Saxena, T. S. Keller, and J. M. Sullivan, “A three-dimensional finite element scheme to investigate apparent mechanical properties of trabecular bone,” Comp. Meth. Biomech. Biomed. Eng. 2, 285–294 (1999).
- K. D. Paulsen, X. Jia, and J. M. Sullivan, “Finite element computations of specific absorption rates in anatomically conforming full-body models for hyperthermia treatment analysis,” IEEE Trans. Biomed. Eng. 40, 933–945 (1993).
- B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
- T. O. McBride, S. Jiang, B. W. Pogue, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near-infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. (to be published).
- G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
- H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
- B. W. Pogue, “Frequency-domain optical spectroscopy and imaging of tissue and tissue-simulating media” (Physics Department, McMaster University, Hamilton, Canada, 1996).
- M. Testorf, U. L. Osterberg, B. W. Pogue, and K. D. Paulsen, “Sampling of time and frequency domain signals in Monte Carlo simulations of photon migration,” Appl. Opt. 38, 236–245 (1999).
- B. W. Pogue, T. Momma, H. Wu, and T. Hasan are preparing a manuscript to be called “Investigation of transient absorption in vivo during photodynamic therapy with pulsed laser light.”
- S. J. Madsen, M. S. Patterson, and B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
- T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, “Strategies for absolute calibration of near infrared tomographic tissue imaging,” in Oxygen Transport to Tissue XXII, J. Dunn and H. Swartz, eds. (Pabst, Lengerich, Germany, 2001).
- B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 182–193 (2000).
- B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, and L. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
- M. Schweiger and S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (Springer, New York, 1997), pp. 71–84.
- M. Schweiger and S. R. Arridge, “Direct calculation with a finite-element method of the Laplace transform of the distribution of photon time of flight in tissue,” Appl. Opt. 36, 9042–9049 (1997).

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