×

A parallel adaptive finite element method for the simulation of photon migration with the radiative-transfer-based model. (English) Zbl 1165.78307

Summary: Whole-body optical molecular imaging of mouse models in preclinical research is rapidly developing in recent years. In this context, it is essential and necessary to develop novel simulation methods of light propagation for optical imaging, especially when a priori knowledge, large-volume domain and a wide-range of optical properties need to be considered in the reconstruction algorithm. In this paper, we propose a 3D parallel adaptive finite element method with simplified spherical harmonics \((SP_N)\) approximation to simulate optical photon propagation in large volumes of heterogeneous tissues. The simulation speed is significantly improved by a posteriori parallel adaptive mesh refinement and dynamic mesh repartitioning. Compared with the diffusion equation and the Monte Carlo methods, the \(SP_N\) method shows improved performance and the necessity of high-order approximation in heterogeneous domains. Optimal solver selection and time-costing analysis in real mouse geometry further improve the performance of the proposed algorithm and show the superiority of the proposed parallel adaptive framework for whole-body optical molecular imaging in murine models.

MSC:

78A40 Waves and radiation in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
92C55 Biomedical imaging and signal processing
65Y05 Parallel numerical computation
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Weissleder, Scaling down imaging: molecular mapping of cancer in mice, Nature Reviews Cancer 2 pp 11– (2002)
[2] Ntziachristos, Looking and listening to light: the evolution of whole body photonic imaging, Nature Biotechnology 23 (3) pp 313– (2005)
[3] Cherry, In vivo molecular and genomic imaging: new challenges for imaging physics, Physics in Medicine and Biology 49 pp R13– (2004)
[4] Massoud, Molecular imaging in living subjects: seeing fundamental biological processes in a new light, Genes and Development 17 pp 545– (2003)
[5] Wang, Development of the first bioluminescence ct scanner, Radiology 566 pp 229– (2003)
[6] Schulz, Experimental fluorescence tomography of tissues with noncontact measurements, IEEE Transactions on Medical Imaging 23 pp 492– (2004)
[7] Gibson, Recent advances in diffuse optical imaging, Physics in Medicine and Biology 50 pp R1– (2005)
[8] Arridge, Optical tomography in medical imaging, Inverse Problems 15 pp R41– (1999) · Zbl 0926.35155
[9] Klose, Light transport in biological tissue based on the simplified spherical harmonics equations, Journal of Computational Physics 220 (1) pp 441– (2006) · Zbl 1122.78015
[10] Lewis, Computational Methods of Neutron Transport (1984)
[11] Rasmussen, Radiative transport in fluorescence-enhanced frequency domain photon migration, Medical Physics 33 (12) pp 4685– (2006)
[12] Aydin, A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method, Medical Physics 29 (9) pp 2013– (2002)
[13] Cong, Flux vector formulation for photon propagation in the biological tissue, Optics Letters 32 (19) pp 2837– (2007)
[14] Wang, Uniqueness theorems in bioluminescence tomography, Medical Physics 31 (8) pp 2289– (2004)
[15] Cong, Practical reconstruction method for bioluminescence tomography, Optics Express 13 (18) pp 6756– (2005)
[16] Alexandrakis, Tomographic bioluminescence imaging by use of a combined optical-pet (opet) system: a computer simulation feasibility study, Physics in Medicine and Biology 50 pp 4225– (2005)
[17] Chaudhari, Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging, Physics in Medicine and Biology 50 pp 5421– (2005)
[18] Joshi, Adaptive finite element based tomography for fluorescence optical imaging in tissue, Optics Express 12 (22) pp 5402– (2004)
[19] Lv, Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation, Physics in Medicine and Biology 52 pp 4497– (2007)
[20] Joshi, Non-contact fluorescence optical tomography with scanning patterned illumination, Optics Express 14 (14) pp 6516– (2006)
[21] Vo-Dinh, Biomedical Photonics Handbook (2002)
[22] Klose, The inverse source problem based on the radiative transfer equation in optical molecular imaging, Journal of Computational Physics 202 (1) pp 323– (2005) · Zbl 1061.65143
[23] Ishimaru, Wave Propagation and Scattering in Random Media (1997) · Zbl 0873.65115
[24] Haskell, Boundary conditions for the diffusion equation in radiative transfer, Journal of the Optical Society of America A 11 (10) pp 2727– (1994)
[25] Saad, Iterative Methods for Sparse Linear Systems (2003) · Zbl 1031.65046 · doi:10.1137/1.9780898718003
[26] Henson, Boomeramg: a parallel algebraic multigrid solver and preconditioner, Applied Numerical Mathematics 41 (1) pp 155– (2002) · Zbl 0995.65128
[27] Benzi, Preconditioning techniques for large linear systems: a survey, Journal of Computational Physics 182 (2) pp 418– (2002) · Zbl 1015.65018
[28] Saad, Iterative solution of linear systems in the 20th century, Journal of Computational and Applied Mathematics 123 pp 1– (2000) · Zbl 0965.65051
[29] Hysom, A scalable parallel algorithm for incomplete factor preconditioning, SIAM Journal on Scientific Computing 22 (6) pp 2194– (2000) · Zbl 0986.65048
[30] Chow, A priori sparsity patterns for parallel sparse approximate inverse preconditioners, SIAM Journal on Scientific Computing 21 (5) pp 1804– (2000) · Zbl 0957.65023
[31] Smith, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations (1996) · Zbl 0857.65126
[32] Kelly, A posteriori error analysis and adaptive processes in the finite element method: Part i-error analysis, International Journal for Numerical Methods in Engineering 19 (11) pp 1593– (1983) · Zbl 0534.65068
[33] Kirk BS. Adaptive finite element simulation of flow and transport applications on parallel computers. Ph.D. Thesis, The University of Texas, Austin, 2007.
[34] Carey, Computational Grids: Generation, Adaptation, and Solution Strategies (1997) · Zbl 0955.74001
[35] Bey, Tetrahedral grid refinement, Computing 55 pp 355– (1995) · Zbl 0839.65135
[36] Karypis, Multilevel k-way partitioning scheme for irregular graphs, Journal of Parallel and Distributed Computing 48 (1) pp 96– (1998) · Zbl 0918.68073
[37] Kirk, libMesh: a C + + library for parallel adaptive mesh refinement/coarsening simulations, Engineering with Computers 22 pp 237– (2006)
[38] Balay S, Buschelman K, Gropp WD, Kaushik D, Knepley MG, McInnes LC, Smith BF, Zhang H. PETSc Web page, 2001. http://www.mcs.anl.gov/petsc.
[39] Segars, Development of a 4d digital mouse phantom for molecular imaging research, Molecular Imaging and Biology 6 pp 149– (2004)
[40] Wang, Mcml-Monte Carlo modeling of photon transport in multi-layered tissues, Computer Methods and Programs in Biomedicine 47 pp 131– (1995)
[41] Falgout RD, Yang UM. Hypre: a library of high performance preconditioners. ICCS’02: Proceedings of the International Conference on Computational Science-Part III, Amsterdam, Netherlands, vol. 40, 2002; 632-641. · Zbl 1056.65046
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.