Abstract

In molecular imaging (MI), especially the optical molecular imaging, bioluminescence tomography (BLT) emerges as an effective imaging modality for small animal imaging. The finite element methods (FEMs), especially the adaptive finite element (AFE) framework, play an important role in BLT. The processing speed of the FEMs and the AFE framework still needs to be improved, although the multi-thread CPU technology and the multi CPU technology have already been applied. In this paper, we for the first time introduce a new kind of acceleration technology to accelerate the AFE framework for BLT, using the graphics processing unit (GPU). Besides the processing speed, the GPU technology can get a balance between the cost and performance. The CUBLAS and CULA are two main important and powerful libraries for programming on NVIDIA GPUs. With the help of CUBLAS and CULA, it is easy to code on NVIDIA GPU and there is no need to worry about the details about the hardware environment of a specific GPU. The numerical experiments are designed to show the necessity, effect and application of the proposed CUBLAS and CULA based GPU acceleration. From the results of the experiments, we can reach the conclusion that the proposed CUBLAS and CULA based GPU acceleration method can improve the processing speed of the AFE framework very much while getting a balance between cost and performance.

©2010 Optical Society of America

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2010 (1)

2009 (1)

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]

2008 (3)

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452, 580–589 (2008).
[Crossref] [PubMed]

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[Crossref] [PubMed]

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, “Galerkin-based meshless methods for photon transport in the biological tissue,” Opt. Express 16, 20317–20333 (2008), http://www.opticsinfobase. org/oe/abstract.cfm?URI=oe-16-25-20317.
[Crossref] [PubMed]

2006 (3)

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]

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, “Self-illuminating quantum dot conjugates for in vivo imaging,” Nat. Biotechnol. 24, 339–343 (2006).
[Crossref] [PubMed]

W. Cong and G. Wang, “Boundary integral method for bioluminescence tomography,” J. Biomed. Opt. 11, 020503 (2006).
[Crossref] [PubMed]

2005 (2)

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[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 (3)

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[Crossref]

X. Gu, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with modelbased reconstruction,” Opt. Express 12, 3996–4000 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-17-3996.
[Crossref] [PubMed]

2003 (1)

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[Crossref] [PubMed]

2002 (2)

1995 (2)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biomed. 47, 131–146 (1995).
[Crossref]

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,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

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.

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,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

Bachmann, M. H.

C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]

Boas, D.

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]

Cong, A.

W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[Crossref]

Cong, W.

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]

W. Cong and G. Wang, “Boundary integral method for bioluminescence tomography,” J. Biomed. Opt. 11, 020503 (2006).
[Crossref] [PubMed]

W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[Crossref]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

Contag, C.

C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]

Culver, J.

Delpy, D. T.

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,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

Dinkelborg, L. M.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[Crossref] [PubMed]

Duderstadt, J. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis, (Wiley, New York, 1976).

Dunn, A.

Feng, J.

Gambhir, S. S.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[Crossref] [PubMed]

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, “Self-illuminating quantum dot conjugates for in vivo imaging,” Nat. Biotechnol. 24, 339–343 (2006).
[Crossref] [PubMed]

Gu, X.

Hamilton, L. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis, (Wiley, New York, 1976).

Han, D.

B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18, 6477–6491 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-7-6477.
[Crossref] [PubMed]

B. Zhang, J. Tian, D. Liu, L. Sun, X. Yang, and D. Han, “A multithread based new sparse matrix method in bioluminescence tomography,” presented at Conference 7626 of SPIE on Medical Imaging, San Diego, USA, 13–18 February 2010.

Hiraoka, M.

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,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

Hoffman, E. A.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

Jacques, S. L.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biomed. 47, 131–146 (1995).
[Crossref]

Jiang, H.

Kumar, D.

W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[Crossref]

Larcom, L.

Li, H.

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]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

Li, X.

Liu, D.

B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18, 6477–6491 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-7-6477.
[Crossref] [PubMed]

B. Zhang, J. Tian, D. Liu, L. Sun, X. Yang, and D. Han, “A multithread based new sparse matrix method in bioluminescence tomography,” presented at Conference 7626 of SPIE on Medical Imaging, San Diego, USA, 13–18 February 2010.

Liu, K.

Liu, Y.

W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[Crossref]

Loening, A. M.

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, “Self-illuminating quantum dot conjugates for in vivo imaging,” Nat. Biotechnol. 24, 339–343 (2006).
[Crossref] [PubMed]

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.

Ma, X.

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[Crossref] [PubMed]

Pittet, M. J.

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452, 580–589 (2008).
[Crossref] [PubMed]

Qin, C.

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]

Rao, J. H.

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, “Self-illuminating quantum dot conjugates for in vivo imaging,” Nat. Biotechnol. 24, 339–343 (2006).
[Crossref] [PubMed]

Rao, S. S.

S. S. Rao, The finite element method in engineering, (Butterworth-Heinemann, Boston, 1999).

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

Schweiger, M.

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,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

So, M. K.

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, “Self-illuminating quantum dot conjugates for in vivo imaging,” Nat. Biotechnol. 24, 339–343 (2006).
[Crossref] [PubMed]

Stott, J.

Sun, L.

B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18, 6477–6491 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-7-6477.
[Crossref] [PubMed]

B. Zhang, J. Tian, D. Liu, L. Sun, X. Yang, and D. Han, “A multithread based new sparse matrix method in bioluminescence tomography,” presented at Conference 7626 of SPIE on Medical Imaging, San Diego, USA, 13–18 February 2010.

Tian, J.

van Bruggen, N.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[Crossref] [PubMed]

Wang, G.

W. Cong and G. Wang, “Boundary integral method for bioluminescence tomography,” J. Biomed. Opt. 11, 020503 (2006).
[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]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[Crossref]

Wang, L. H.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biomed. 47, 131–146 (1995).
[Crossref]

Wang, L. H. V.

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

Wang, L. V.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

Weissleder, R.

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452, 580–589 (2008).
[Crossref] [PubMed]

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[Crossref] [PubMed]

Willmann, J. K.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[Crossref] [PubMed]

Xu, C. J.

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, “Self-illuminating quantum dot conjugates for in vivo imaging,” Nat. Biotechnol. 24, 339–343 (2006).
[Crossref] [PubMed]

Xu, M.

Yan, G.

Yang, W.

Yang, X.

Zhang, B.

B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18, 6477–6491 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-7-6477.
[Crossref] [PubMed]

B. Zhang, J. Tian, D. Liu, L. Sun, X. Yang, and D. Han, “A multithread based new sparse matrix method in bioluminescence tomography,” presented at Conference 7626 of SPIE on Medical Imaging, San Diego, USA, 13–18 February 2010.

Zhang, Q.

Zhang, X.

Zheng, L. Q.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biomed. 47, 131–146 (1995).
[Crossref]

Zhong, J.

Zhu, F.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

Zhu, S.

Acad. Radiol. (1)

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method,” Acad. Radiol. 11, 1029–1038 (2004).
[Crossref] [PubMed]

Annu. Rev. Biomed. Eng. (1)

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Figures (6)

Fig. 1.
Fig. 1. The hardware model of GPU [11].

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Fig. 2.
Fig. 2. The execution flow chart of matrix inversion and multiplication using GPU.

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Fig. 3.
Fig. 3. Sub figure (a) is the heterogeneous cylindrical numerical phantom with single source, consisted of muscle (white), bone (black), heart (pink), lungs (green), liver (yellow) and a ball source (blue) in the right lung. Sub figure (b) is the surface light power distribution of the phantom in sub figure (a), which is generated by MOSE.

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Fig. 4.
Fig. 4. The �� in each case in Ex. 1. The horizontal axis in the figure was the case order and the vertical axis was ��.

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Fig. 5.
Fig. 5. GPU speed up to CPU. Sub figures (a) to (d) were SU Cpu8GpuInv , SU Cpu8GpuMul , UC puGpuInv and SU CpuGpuMul for each case of Ex. 2, respectively. The horizontal axis in all the sub figures was the case order. The vertical axis of sub figures (a) to (d) were SU Cpu8GpuInv , SU Cpu8GpuMul , UC puGpuInv and SU CpuGpuMul , respectively.

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Fig. 6.
Fig. 6. Reconstruction results of single source numerical experiment. Sub figures (a) to (d) were the 3D views, front views, side views and top views, respectively. The blue ball in each sub figure denoted the real source and the red tetrahedron denoted the reconstructed source with the maximum density. For concision, only the real source and the reconstructed source were displayed.

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Tables (4)

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Table 1. Optical parameters of different tissues of the heterogeneous cylindrical phantom

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Table 2. Statistics of main time consuming modules in the AFE framework

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Table 3. Comparisons between multi-thread CPU acceleration and GPU acceleration on matrix inversion and multiplication

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Table 4. Time cost of GPU acceleration on matrix inversion and multiplication for single source reconstruction experiment in every mesh refinement procedure of the AFE framework

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Equations (8)

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

∇ · ( D ( x ) ∇ Φ ( x ) ) + μ a ( x ) Φ ( x ) = S ( x ) ( x ∈ Ω )
Φ ( x ) + 2 A ( x ; n , n ′ ) D ( x ) ( v ( x ) · ∇ Φ ( x ) ) = 0 ( x ∈ ∂ Ω )
∫ Ω ( D ( x ) ( ∇ Φ ( x ) ) · ( ∇ Ψ ( x ) ) + μ a ( x ) Φ ( x ) Ψ ( x ) ) d x +
∫ ∂ Ω 1 2 A ( x ; n , n ′ ) Φ ( x ) Ψ ( x ) d x = ∫ Ω S ( x ) Ψ ( x ) d x ( ∀ Ψ ( x ) ∈ H 1 ( Ω ) )
( [ K l ] + [ C l ] + [ B l ] ) Φ l = M l Φ l = F l S l
Φ l = M l − 1 F l S l = A l S l
Φ l meas = A l ps S l P
f l ( S l P ) = ∣∣ A l ps S l P − Φ l meas ∣∣ 2 2

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