Finite element model for the coupled radiative transfer equation and diffusion approximation

International Journal for Numerical Methods in Engineering

Volumn 65, Issue 3, 2006, Pages 383-405

  Tarvainen, Tanja ^a   Vauhkonen, M ^a   Kolehmainen, V ^a   Kaipio, J P ^a  

^a UNIVERSITY OF EASTERN FINLAND   (Finland)

Author keywords

Diffusion approximation; Finite element method; Photon migration; Radiative transfer equation

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFUSION; EQUATIONS OF MOTION; HEAT TRANSFER; LIGHT PROPAGATION; MATHEMATICAL MODELS; PHOTONS; TISSUE; TOMOGRAPHY;

COUPLED RADIATIVE TRANSFER EQUATION; OPTICAL TOMOGRAPHY; PHOTON MIGRATION;

FINITE ELEMENT METHOD;

MATHEMATICAL ANALYSIS;

EID: 30644469235     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1451     Document Type: Article

References (38)

1. Nissilä I, Noponen T, Kotilahti K, Tarvainen T, Schweiger M, Lipiäinen L, Arridge SR, Katila T. Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography. Review of Scientific Instruments 2005; 76(4):044302.
2. Pogue BW, Poplack SP, McBride TO, Wells WA, Osterman KS, Osterberg UL, Paulsen KD. Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast. Radiology 2001; 218:261-266.
3. Culver JP, Choe R, Holboke MJ, Zubkov L, Durduran T, Slemp A, Ntziachristos V, Chance B, Yodh AG. Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequancy doman/continuous wave clinical system for breast imaging. Medical Physics 2003; 30(2):235-247.
4. Hebden JC, Gibson A, Yusof RM, Everdell N, Hillman EMC, Delpy DT, Arridge SR, Austin T, Meek JH, Wyatt JS. Three-dimensional optical tomography of the premature infant brain. Physics in Medicine and Biology 2002; 47:4155-4166.
5. Franceschini MA, Toronov V, Filiaci ME, Gratton E, Fantini S. On-line optical imaging of the human brain with 160-ms temporal resolution. Optics Express 2000; 6(3):49-57.
6. Bluestone AV, Abdoulaev G, Schmitz CH, Barbour RL, Hielscher AH. Three-dimensional optical tomography of hemodynamics in the human head. Optics Express 2001; 9(6):272-286.
7. Prince S, Kolehmainen V, Kaipio JP, Franceschini MA, Boas D, Arridge SR. Time-series estimation of biological factors in optical diffusion tomography. Physics in Medicine and Biology 2003; 48:1491-1504.
8. Noponen T, Paloheimo M, Meriläinen P, Kajava T, Kotilahti K, Nissilä I, Katila T. Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia. In Biomedical Topical Meetings on CD-ROM. The Optical Society of America: Washington, DC, 2004; WF8.
9. Williams RA, Beck MS (eds). Process Tomography, Principles, Techniques and Applications. Butterworth-Heinemann: Oxford, 1995.
10. Kataja M (ed.). Multiphase Flows in Process Industry. ProMoni. VTT Research Notes, 2286, Espoo, Finland, 2005.
11. Chandrasekhar S. Radiative Transfer. Oxford University Press: London, 1950.
12. Case MC, Zweifel PF. Linear Transport Theory. Addison-Wesley: New York, 1967.
13. Ishimaru A. Wave Propagation and Scattering in Random Media, vol. 1. Academic Press: New York, 1978.
14. Cercignani C. The Boltzmann Equation and its Applications. Springer: New York, 1988.
15. Ackroyd RT. Finite Element Methods for Particle Transport: Applications to Reactor and Radiation Physics. Research Studies Press: Taunton, 1997.
16. Arridge SR. Optical tomography in medical imaging. Inverse Problems 1999; 15:R41-R93.
17. Dorn O. A transport-backtransport method for optical tomography. Inverse Problems 1998; 14(5):1107-1130.
18. Klose AD, Netz U, Beuthan J, Hielscher AH. Optical tomography using the time-independent equation of radiative transfer - Part 1: forward model. Journal of Quantitative Spectroscopy and Radiative Transfer 2002; 72:691-713.
19. Aydin ED, de Oliveira CRE, Goddard AJH. A finite element-spherical harmonics radiation transport model for photon migration in turbid media. Journal of Quantitative Spectroscopy and Radiative Transfer 2004; 84:247-260.
20. Boman E, Tervo J, Vauhkonen M. Modelling the transport of ionizing radiation using the finite element method. Physics in Medicine and Biology 2005; 50(2):265-280.
21. Richling S, Meinköhn E, Kryzhevoi N, Kanschat G. Radiative transfer with finite elements I. Basic method and tests. Astronomy and Astrophysics 2001; 380(2):776-788.
22. Hielscher AH, Alcouffe RE, Barbour RL. Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues. Physics in Medicine and Biology 1998; 43:1285-1302.
23. Arridge SR, Dehghani H, Schweiger M, Okada E. The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions. Medical Physics 2000: 27(1): 252-264.
24. Wang L, Jacques SL. Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media. Journal of the Optical Society of America A 1992; 10(8):1746-1752.
25. Alexandrakis G, Farrell TJ, Patterson MS. Monte Carlo diffusion hybrid model for photon migration in a two-layer medium in the frequency domain. Applied Optics 2000; 39(13):2235-2244.
26. Hayashi T, Kashio Y, Okada E. Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region. Applied Optics 2003; 42(16):2888-2896.
27. Bal G, Maday Y. Coupling of transport and diffusion models in linear transport theory. Mathematical Modelling and Numerical Analysis 2002; 36(1):69-86.
28. Tarvainen T, Vauhkonen M, Kolehmainen V, Kaipio JP. Hybrid radiative-transfer-diffusion model for optical tomography. Applied Optics 2005; 44(6):876-886.
29. Heino J, Somersalo E. Estimation of optical absorption in anisotropic background. Inverse Problems 2002; 18:559-573.
30. Henyey LG, Greenstein JL. Diffuse radiation in the galaxy. Astrophysical Journal 1941; 93:70-83.
31. Heino J, Arridge S, Sikora J, Somersalo E. Anisotropic effects in highly scattering media. Physical Review E 2003; 68:031908.
32. Tervo J, Kolmonen P, Vauhkonen M, Heikkinen LM, Kaipio JP. A finite-element model of electron transport in radiation therapy and a related inverse problem. Inverse Problems 1999; 15:1345-1361.
33. Arridge SR, Hebden JC. Optical imaging in medicine: II. Modelling and reconstruction. Physics in Medicine and Biology 1997; 42:841-853.
34. Groenhuis RAJ, Ferwerda HA, Ten Bosch JJ. Scattering and absorption of turbid materials determined from reflection measurements. 1: theory. Applied Optics 1983; 22(16):2456-2462.
35. Keijzer M, Star WM, Storchi PRM. Optical diffusion in layered media. Applied Optics 1988; 27(9):1820-1824.
36. Schweiger M, Arridge SR, Hiraoka M, Delpy DT. The finite element method for the propagation of light in scattering media: boundary and source conditions. Medical Physics 1995; 22(11):1779-1792.
37. Arridge SR, Schweiger M, Hiraoka M, Delpy DT. A finite element approach for modeling photon transport in tissue. Medical Physics 1993; 20(2):299-309.
38. Kolehmainen V. Novel approaches to image reconstruction in diffusion tomography. Ph.D. Thesis, University of Kuopio, Kuopio, Finland, 2001.