Abstract

Bioluminescence imaging is a very sensitive imaging modality, used in preclinical molecular imaging. However, in its planar projection form, it is non-quantitative and has poor spatial resolution. In contrast, bioluminescence tomography (BLT) promises to provide three dimensional quantitative source information. Currently, nearly all BLT reconstruction algorithms in use employ the diffusion approximation theory to determine light propagation in tissues. In this process, several approximations and assumptions that are made severely affect the reconstruction quality of BLT. It is therefore necessary to develop novel reconstruction methods using high-order approximation models to the radiative transfer equation (RTE) as well as more complex geometries for the whole-body of small animals. However, these methodologies introduce significant challenges not only in terms of reconstruction speed but also for the overall reconstruction strategy. In this paper, a novel fully-parallel reconstruction framework is proposed which uses a simplified spherical harmonics approximation (SPN). Using this framework, a simple linear relationship between the unknown source distribution and the surface measured photon density can be established. The distributed storage and parallel operations of the finite element-based matrix make SPN-based spectrally resolved reconstruction feasible at the small animal whole body level. Performance optimization of the major steps of the framework remarkably improves reconstruction speed. Experimental reconstructions with mouse-shaped phantoms and real mice show the effectiveness and potential of this framework. This work constitutes an important advance towards developing more precise BLT reconstruction algorithms that utilize high-order approximations, particularly second-order self-adjoint forms to the RTE for in vivo small animal experiments.

© 2009 Optical Society of America

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Y. Lu and A. F. Chatziioannou, "A parallel adaptive finite element method for the simulation of photon migration with the radiative-transfer-based model," Commun. Numer. Methods Eng. 25,751-770 (2009).
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2007

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007 (2007).
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S. Wright, M. Schweiger, and S. R. Arridge, "Reconstruction in optical tomography using the PN approximations," Meas. Sci. Technol. 18,79-86 (2007).
[CrossRef]

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Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

2006

2005

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef] [PubMed]

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

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," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

2004

2002

R. Weissleder, "Scaling down imaging: Molecular mapping of cancer in mice," Nat. Rev. Cancer 2,11-18 (2002).
[CrossRef] [PubMed]

M. Benzi, "Preconditioning techniques for large linear systems: a survey," J. Comput. Phys. 182,418-477 (2002).
[CrossRef]

R. D. Falgout and U. M. Yang, "hypre: A library of high performance preconditioners," in Proceedings of the International Conference on Computational Science-Part III, p. 632-641 (2002).

1998

G. Karypis and V. Kumar, "Multilevel k-way partitioning scheme for irregular graphs," J. Parallel Distrib. Comput. 48,96-129 (1998).
[CrossRef]

1994

1993

1986

C. R. E. de Oliveira, "An arbitrary geometry finite element method for multigroup neutron transport with anisotropic scattering," Progr. Nucl. Energ. 18,227-236 (1986).
[CrossRef]

Alexandrakis, G.

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," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

Arridge, S. R.

S. Wright, M. Schweiger, and S. R. Arridge, "Reconstruction in optical tomography using the PN approximations," Meas. Sci. Technol. 18,79-86 (2007).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef] [PubMed]

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Benzi, M.

M. Benzi, "Preconditioning techniques for large linear systems: a survey," J. Comput. Phys. 182,418-477 (2002).
[CrossRef]

Carey, G. F.

B. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey, "libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations," Eng. Comput. 22,237-254 (2006).
[CrossRef]

Chatziioannou, A. F.

Y. Lu and A. F. Chatziioannou, "A parallel adaptive finite element method for the simulation of photon migration with the radiative-transfer-based model," Commun. Numer. Methods Eng. 25,751-770 (2009).
[CrossRef]

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," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

Chaudhari, A. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Cong, A.

Cong, W.

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Coquoz, O.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007 (2007).
[CrossRef] [PubMed]

Darvas, F.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Davis, S. C.

de Oliveira, C. R. E.

C. R. E. de Oliveira, "An arbitrary geometry finite element method for multigroup neutron transport with anisotropic scattering," Progr. Nucl. Energ. 18,227-236 (1986).
[CrossRef]

Dehghani, H.

Falgout, R. D.

R. D. Falgout and U. M. Yang, "hypre: A library of high performance preconditioners," in Proceedings of the International Conference on Computational Science-Part III, p. 632-641 (2002).

Feng, T.

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef] [PubMed]

Gu, X.

Haskell, R. C.

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef] [PubMed]

Hoffman, E. A.

Jansen, E. D.

Jiang, H.

Jiang, M.

Jiang, S.

Karypis, G.

G. Karypis and V. Kumar, "Multilevel k-way partitioning scheme for irregular graphs," J. Parallel Distrib. Comput. 48,96-129 (1998).
[CrossRef]

Kirk, B.

B. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey, "libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations," Eng. Comput. 22,237-254 (2006).
[CrossRef]

Klose, A. D.

A. D. Klose, "Transport-theory-based stochastic image reconstruction of bioluminescent sources," J. Opt. Soc. Am. A 24,1601-1608 (2007), http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-6-1601.
[CrossRef]

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220,441-470 (2006).
[CrossRef]

Kumar, D.

Kumar, V.

G. Karypis and V. Kumar, "Multilevel k-way partitioning scheme for irregular graphs," J. Parallel Distrib. Comput. 48,96-129 (1998).
[CrossRef]

Kuo, C.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007 (2007).
[CrossRef] [PubMed]

Larcom, L.

Larsen, E. W.

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220,441-470 (2006).
[CrossRef]

Leahy, R. M.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Li, H.

Li, Y.

G. Wang, Y. Li, and M. Jiang, "Uniqueness theorems in bioluminescence tomography," Med. Phys. 31,2289-2299 (2004).
[CrossRef] [PubMed]

Liu, Y.

Lu, Y.

Y. Lu and A. F. Chatziioannou, "A parallel adaptive finite element method for the simulation of photon migration with the radiative-transfer-based model," Commun. Numer. Methods Eng. 25,751-770 (2009).
[CrossRef]

Luo, J.

Lv, Y.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

McAdams, M. S.

McCray, P. B.

McLennan, G.

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

Patterson, M. S.

Paulsen, K. D.

Peterson, J. W.

B. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey, "libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations," Eng. Comput. 22,237-254 (2006).
[CrossRef]

Pogue, B. W.

Powers, A. C.

Prahl, S. A.

Qin, C.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Rannou, F. R.

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," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

Rice, B. W.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007 (2007).
[CrossRef] [PubMed]

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

Schweiger, M.

S. Wright, M. Schweiger, and S. R. Arridge, "Reconstruction in optical tomography using the PN approximations," Meas. Sci. Technol. 18,79-86 (2007).
[CrossRef]

Smith, D. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Stogner, R. H.

B. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey, "libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations," Eng. Comput. 22,237-254 (2006).
[CrossRef]

Svaasand, L. O.

Tian, J.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Tromberg, B. J.

Troy, T. L.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007 (2007).
[CrossRef] [PubMed]

Tsay, T.

van Gemert, M. J. C.

Virostko, J.

Wang, G.

Wang, L. V.

Weisslder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

Weissleder, R.

R. Weissleder, "Scaling down imaging: Molecular mapping of cancer in mice," Nat. Rev. Cancer 2,11-18 (2002).
[CrossRef] [PubMed]

Welch, A. J.

Wright, S.

S. Wright, M. Schweiger, and S. R. Arridge, "Reconstruction in optical tomography using the PN approximations," Meas. Sci. Technol. 18,79-86 (2007).
[CrossRef]

Xu, H.

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Figures (7)

Fig. 1.
Fig. 1.

The flowchart of the proposed fully parallel framework.

Fig. 2.
Fig. 2.

(a) Photograph of Caliper mouse-shaped phantom in a Maestro 2 system; (b) and (c) are the photon distribution at 580nm and 640nm corresponding to (a).

Fig. 3.
Fig. 3.

(a) shows the volumetric mesh and the mapped photon distribution at 640nm. (b) is the mesh partitioning results when 10 CPUs are used in BLT reconstruction.

Fig. 4.
Fig. 4.

BLT reconstructions with SPN approximations. (a), (b) and (c) are the reconstructed results corresponding to SP 1(DA), SP 3 and SP7 . Green dotted lines are used to align the boundaries of CT slices with those of reconstructed slices. Thin red lines pass through the center of the source in CT slices. (Unit: mm)

Fig. 5.
Fig. 5.

Performance comparison depending on CPU number in SPN -based BLT reconstruction. (a) is the total reconstruction time depending on CPU number; (b) and (c) are the reconstruction time of the major steps in the proposed framework and the percentages of the total reconstruction time respectively. Note that SP7 -based reconstruction becomes possible when at least 4 CPUs are used.

Fig. 6.
Fig. 6.

(a) shows the volumetric mesh and the mapped photon distribution at 660nm for real mouse experiments. (b) is the mesh partitioning results when 30 CPUs are used in BLT reconstruction.

Fig. 7.
Fig. 7.

BLT reconstructions with SPN approximations for real mouse experiments. (a), (b) and (c) are the reconstructed results corresponding to SP 1(DA), SP 3 and SP7 . Green dotted lines are used to align the boundaries of CT slices with those of reconstructed slices. Thin red lines pass through the center of the source in CT slices. (Unit: mm)

Tables (2)

Tables Icon

Table 1. Optical properties of a mouse-shaped phantom and actual mouse muscle

Tables Icon

Table 2. Performance comparison between direct and iterative inversions when 10 CPUs are used in reconstructions. DI is Direct Inversion; II denotes Iterative Inversion; and DI/II is the ratio of total time between DI and II.

Equations (29)

Equations on this page are rendered with MathJax. Learn more.

ŝ · ψ (r,ŝ,λ) + (μs(r,λ)+μa(r,λ))ψ(r,ŝ,λ)
= μs (r,λ)4πp(ŝ,ŝ)ψ(r,ŝ,λ)dŝ+S(r,ŝ,λ)
p (cosθ)=1g24π(1+g22gcosθ)32
R (cosθb)=12[sin2(θbθm)sin2(θb+θm)+tan2(θbθm)tan2(θb+θm)]
J+ (r,λ)=ŝ·v>0[1R(ŝ·v)](ŝ·v)ψ(r,ŝ,λ)dŝ
(n+12n+1)·1μa,n+1(λ)((n+22n+3)ϕn+2(λ)+(n+12n+3)ϕn(λ))
(12n+1) · 1μa,n1(λ) ((n2n1)ϕn(λ)+(n12n1)ϕn2)+μa,n(λ)ϕn(λ)=s(λ)
φ1 = ϕ0+2 ϕ2 ,
φ2 = 3ϕ2+4ϕ4,
,
φn = (2n1)ϕ2n2+(2n)ϕ2n,
,
φ(N+1)2 = N1 .
· 𝓒i,φi (λk)φi(λk)+j=1(N+1)2𝓒i,φj(λk)φj(λk)=𝓒i,S(λ)Si(λk)
j=1(N+1)2𝓒i,φjb(λk)v·φj(λk)=j=1(N+1)2𝓒i,φjb(λk)φj(λk)i[1,(N+1)2]
Ω{𝓒i,φi(λk)φi(λk)·υ+j=1(N+2)2𝓒i,φj(λk)φj(λk)·υ}dΩ
Ω𝓒i,φij=1(N+1)2fv·φi(φj)·υdΩ=Ω𝓒i,SSi(λk)·υdΩ
φi (r,λk)p=1N𝒫φi,p(λk)υp(r)
Si (r,λk)p=1N𝒫Si,p(λk)υp(r)
[m1φ1(λk)m1φ2(λk)m1φ(N+1)2(λk)m2φ1(λk)m2φ2(λk)m1φ(N+1)/2(λk)m(N+1)2φ1(λk)m(N+1)2φ2(λk)m(N+1)2φ(N+1)/2(λk)] [φ1,τe(λk)φ2,τe(λk)φ(N+1)2,τe(λk)]=
[b1φ1(λk)b2φ2(λk)b(N+1)2φ(N+1)2(λk)] [s1,τe(λk)S2,τe(λk)s(N+1)2,τe(λk)]
[M1φ1𝒯c(λk)M1φ2𝒯c(λk)M1φ(N+1)2𝒯c(λk)M2φ1𝒯c(λk)M2φ2𝒯c(λk)M2φ(N+1)2𝒯c(λk)M(N+1)2φ1𝒯c(λk)M(N+1)2φ2𝒯c(λk)M(N+1)2φ(N+1)2𝒯c(λk)] [φ1𝒯c(λk)φ2𝒯c(λk)φ(N+1)2𝒯c(λk)] =
[B𝒯cB𝒯cB𝒯c][S1𝒯c(λk)S2𝒯c(λk)S(N+1)2𝒯c(λk)]
[φ1𝒯c(λk)φ2𝒯c(λk)φ(N+1)2𝒯c(λk)] = [j=1(N+1)2𝓒j,SIM1φj𝒯c(λk)·B𝒯c·S𝒯c(λk)j=1(N+1)2𝓒j,SIM2φj𝒯c(λk)·B𝒯c·S𝒯c(λk)j=1(N+1)2𝓒j.SIM(N+1)2φj𝒯c(λk)·B𝒯c·S𝒯c(λk)]
J𝒯c,+,b (λk)=j=1(N+1)2βj(λk)φj𝒯c,b(λk)=j=1(N+1)2βj(λk)Gj𝒯c(λk)S𝒯c(λk)
= G𝒯c (λk)S𝒯c(λk)
J𝒯c,+,b=𝒜𝒯cS𝒯c
J𝒯c,+,b = [J𝒯c,+,b(λ1)J𝒯c,+,b(λk)J𝒯c,+,b(λK)] , 𝒜𝒯c = [γ1G𝒯c(λ1)γkG𝒯c(λk)γKG𝒯c(λK)]
min0<S𝒯c<Ssup Θ (S𝒯c):𝒜𝒯cS𝒯cJ𝒯c,+,m2+δη(S𝒯c)

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