×

zbMATH — the first resource for mathematics

Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging. (English) Zbl 1261.92030
Summary: An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP\(_N\)). In the XFEM scheme of SP\(_N\) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.
MSC:
92C55 Biomedical imaging and signal processing
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
Software:
XFEM
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nature Biotechnology, vol. 23, no. 3, pp. 313-320, 2005. · doi:10.1038/nbt1074
[2] M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Physics in Medicine and Biology, vol. 50, no. 12, pp. 2837-2858, 2005. · doi:10.1088/0031-9155/50/12/008
[3] A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Physics in Medicine and Biology, vol. 50, no. 4, pp. R1-R43, 2005. · doi:10.1088/0031-9155/50/4/R01
[4] W. Cong, G. Wang, D. Kumar et al., “Practical reconstruction method for bioluminescence tomography,” Optics Express, vol. 13, no. 18, pp. 6756-6771, 2005. · doi:10.1364/OPEX.13.006756
[5] A. E. Spinelli, C. Kuo, B. W. Rice et al., “Multispectral Cerenkov luminescence tomography for small animal optical imaging,” Optics Express, vol. 19, no. 13, pp. 12605-12618, 2011. · doi:10.1364/OE.19.012605
[6] A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” Journal of Computational Physics, vol. 220, no. 1, pp. 441-470, 2006. · Zbl 1122.78015 · doi:10.1016/j.jcp.2006.07.007
[7] M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Physics in Medicine and Biology, vol. 54, no. 8, pp. 2493-2509, 2009. · doi:10.1088/0031-9155/54/8/016
[8] A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” Journal of Computational Physics, vol. 202, no. 1, pp. 323-345, 2005. · Zbl 1061.65143 · doi:10.1016/j.jcp.2004.07.008
[9] M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Medical Physics, vol. 22, no. 11 I, pp. 1779-1792, 1995. · doi:10.1118/1.597634
[10] H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Applied Optics, vol. 37, no. 22, pp. 5337-5343, 1998.
[11] N. Moës, J. Dolbow, and T. Belytschko, “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, vol. 46, no. 1, pp. 131-150, 1999. · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[12] J. Chessa, P. Smolinski, and T. Belytschko, “The extended finite element method (XFEM) for solidification problems,” International Journal for Numerical Methods in Engineering, vol. 53, no. 8, pp. 1959-1977, 2002. · Zbl 1003.80004 · doi:10.1002/nme.386
[13] Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Physics in Medicine and Biology, vol. 55, no. 16, pp. 4625-4645, 2010. · doi:10.1088/0031-9155/55/16/002
[14] G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Physics in Medicine and Biology, vol. 50, no. 17, pp. 4225-4241, 2005. · doi:10.1088/0031-9155/50/17/021
[15] B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Physics in Medicine and Biology, vol. 52, no. 3, pp. 577-587, 2007. · doi:10.1088/0031-9155/52/3/003
[16] MOSE, http://www.mosetm.net/.
[17] Y. Lv, J. Tian, W. Cong et al., “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Optics Express, vol. 14, no. 18, pp. 8211-8223, 2006. · doi:10.1364/OE.14.008211
[18] A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Optics Express, vol. 12, no. 22, pp. 5402-5417, 2004. · doi:10.1364/OPEX.12.005402
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.