Abstract

As the most accurate model for simulating light propagation in heterogeneous tissues, Monte Carlo (MC) method has been widely used in the field of optical molecular imaging. However, MC method is time-consuming due to the calculations of a large number of photons propagation in tissues. The structural complexity of the heterogeneous tissues further increases the computational time. In this paper we present a parallel implementation for MC simulation of light propagation in heterogeneous tissues whose surfaces are constructed by different number of triangle meshes. On the basis of graphics processing units (GPU), the code is implemented with compute unified device architecture (CUDA) platform and optimized to reduce the access latency as much as possible by making full use of the constant memory and texture memory on GPU. We test the implementation in the homogeneous and heterogeneous mouse models with a NVIDIA GTX 260 card and a 2.40GHz Intel Xeon CPU. The experimental results demonstrate the feasibility and efficiency of the parallel MC simulation on GPU.

© 2010 OSA

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References

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    [PubMed]
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  24. B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009

2008

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[CrossRef] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008).
[CrossRef] [PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef]

2007

2006

N. S. Zołek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Meth. Prog. Biol. 84(1), 50–57 (2006).
[CrossRef]

2005

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

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

A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16(1), 79–88 (2005).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

2004

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

2002

2001

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6(4), 432–440 (2001).
[CrossRef] [PubMed]

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

1997

T. Möller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics Tools 2, 21–28 (1997).

1995

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biol. 47(2), 131–146 (1995).
[CrossRef]

1993

1983

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Adam, G.

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Alerstam, E.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008).
[CrossRef] [PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Andersson-Engels, S.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008).
[CrossRef] [PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Boas, D. A.

Cable, M. D.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6(4), 432–440 (2001).
[CrossRef] [PubMed]

Chatziioannou, A. F.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Cong, W. X.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Culver, J.

Dogdas, B.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[CrossRef] [PubMed]

Dunn, A.

Fang, Q.

French, P. J.

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16(1), 79–88 (2005).
[CrossRef] [PubMed]

Hoffman, E. A.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Jacques, S. L.

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biol. 47(2), 131–146 (1995).
[CrossRef]

L. V. Wang and S. L. Jacques, “Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10(8), 1746–1752 (1993).
[CrossRef]

Jiang, M.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

Leahy, R. M.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[CrossRef] [PubMed]

Li, H.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Li, Y.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

Liebert, A.

N. S. Zołek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Meth. Prog. Biol. 84(1), 50–57 (2006).
[CrossRef]

Mahmood, U.

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Maniewski, R.

N. S. Zołek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Meth. Prog. Biol. 84(1), 50–57 (2006).
[CrossRef]

Margallo-Balbás, E.

Möller, T.

T. Möller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics Tools 2, 21–28 (1997).

Nelson, M. B.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6(4), 432–440 (2001).
[CrossRef] [PubMed]

Ntziachristos, V.

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

Pittet, M. J.

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Rice, B. W.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6(4), 432–440 (2001).
[CrossRef] [PubMed]

Ripoll, J.

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

Stott, J.

Stout, D.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[CrossRef] [PubMed]

Svensson, T.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008).
[CrossRef] [PubMed]

Tian, J.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Trumbore, B.

T. Möller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics Tools 2, 21–28 (1997).

Wang, G.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Wang, L. V.

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

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biol. 47(2), 131–146 (1995).
[CrossRef]

L. V. Wang and S. L. Jacques, “Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10(8), 1746–1752 (1993).
[CrossRef]

Weissleder, R.

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[CrossRef] [PubMed]

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

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Wilson, B. C.

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Zheng, L. Q.

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biol. 47(2), 131–146 (1995).
[CrossRef]

Zhu, F.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Zolek, N. S.

N. S. Zołek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Meth. Prog. Biol. 84(1), 50–57 (2006).
[CrossRef]

Acad. Radiol.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Comput. Meth. Prog. Biol.

N. S. Zołek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Meth. Prog. Biol. 84(1), 50–57 (2006).
[CrossRef]

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biol. 47(2), 131–146 (1995).
[CrossRef]

Curr. Opin. Biotechnol.

A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16(1), 79–88 (2005).
[CrossRef] [PubMed]

J. Biomed. Opt.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6(4), 432–440 (2001).
[CrossRef] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008).
[CrossRef] [PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef]

J. Graphics Tools

T. Möller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics Tools 2, 21–28 (1997).

J. Opt. Soc. Am. A

Med. Phys.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Nat. Biotechnol.

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

Nature

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[CrossRef] [PubMed]

Opt. Express

Phys. Med. Biol.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Radiology

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Other

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

S. Prahl, “Optical Properties Spectra” (Oregon Medical Laser Clinic, 2001). http://omlc.ogi.edu/spectra/index.html .

H. Lensch, and R. Strzodka, “Massively Parallel Computing with CUDA” (2008). http://www.mpi-inf.mpg.de/~strzodka/lectures/ParCo08/ .

NVIDIA CUDA Compute Unified Device Architecture - Programming Guide, Version 2.3 (2009).

N. Ren, and J. Tian, gpu-Molecular Optical Simulation Environment (2010). http://www.mosetm.net .

J. Arenberg, “Re: Ray/Triangle Intersection with Barycentric Coordinates,” in Eric Haines, ed., Ray Tracing News, 1 (1988). http://tog.acm.org/resources/RTNews/html/rtnews5b.html#art3 .

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Figures (7)

Fig. 1
Fig. 1

Tissue structure in MOSE. Tissue 1 is the outermost tissue, Tissue 2 and 3 are both the internal tissues. Shape 1 is the boundary between Tissue 1 and ambient medium and corresponding to Tissue 1. Shape 2 is the boundary between Tissue 1 and Tissue 2 and corresponding to Tissue 2, so do Shape 3.

Fig. 2
Fig. 2

Flowchart of photon propagation in tissues based on MC method.

Fig. 3
Fig. 3

(a) 3D view of the tissue surface which is projected onto the 2D plane grid. Points A and B are the starting and end points of a step (marked with blue color), respectively. A is the external point of the tissue and B is internal point of the tissue. (b) 2D view of the grid and the projections of the tissue and the photon path, A´ and B´ are the projections of points A and B, respectively. The grid cells intersected with the projection of the photon path are marked with red color.

Fig. 4
Fig. 4

Flowchart of the parallel MC simulation based on CUDA.

Fig. 5
Fig. 5

Pseudocode description of MC simulation implemented on CPU and GPU, respectively.

Fig. 6
Fig. 6

3D surface rendering of the tissues used in the experiments. The bounding box of the mouse phantom is 38 × 99.2 × 20.8 (mm). The point light source is located near the stomach marked with green color and its coordinate is (20, 50, 15) (mm). The picture is obtained from MOSE.

Fig. 7
Fig. 7

(a) Speedup varies with the number of threads. (b) Speedup varies with the number of triangle meshes. (c) Speedup varies with the number of tissues. (d) Relative errors between the transmittances obtained from CPU and GPU.

Tables (5)

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Table 1 Simulation parameters of the phantom

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Table 2 The averages and the standard errors of the total reflectance and total transmittance

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Table 3 Simulation parameters of the phantom

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Table 4 The averages and the standard errors of the total reflectance

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Table 5 Simulation parameters of the tissues

Equations (2)

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T c p u = T 0 + T c p u = T 0 + i = 1 N p T i
{ T j = i = 1 N p / ( N b × N t ) T i T g p u = T 0 + T g p u = T 0 + ( T c + max ( T j ) + T c ) j = 1 , 2... N b × N t

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