Abstract

Compared with commonly used analytical reconstruction methods, the frequency-domain finite element method (FEM) based approach has proven to be an accurate and flexible algorithm for photoacoustic tomography. However, the FEM-based algorithm is computationally demanding, especially for three-dimensional cases. To enhance the algorithm’s efficiency, in this work a parallel computational strategy is implemented in the framework of the FEM-based reconstruction algorithm using a graphic-processing-unit parallel frame named the “compute unified device architecture.” A series of simulation experiments is carried out to test the accuracy and accelerating effect of the improved method. The results obtained indicate that the parallel calculation does not change the accuracy of the reconstruction algorithm, while its computational cost is significantly reduced by a factor of 38.9 with a GTX 580 graphics card using the improved method.

© 2013 Optical Society of America

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  1. R. A. Kruger, P. Liu, and Y. Fang, “Photoacoustic ultrasound (PAUS)-reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
    [CrossRef]
  2. Z. Yuan, Q. Zhang, and H. Jiang, “Simultaneous reconstruction of acoustic and optical properties of heterogeneous media by quantitative photoacoustic tomography,” Opt. Express 14, 6749–6754 (2006).
    [CrossRef]
  3. Q. Zhang, Z. Liu, P. R. Carney, and H. Jiang, “Noninvasive imaging of epileptic seizures in vivo using photoacoustic tomography,” Phys. Med. Biol. 53, 1921–1931 (2008).
    [CrossRef]
  4. R. A. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography-technical considerations,” Med. Phys. 26, 1832–1837 (1999).
    [CrossRef]
  5. S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A. 20, 1859–1866 (2003).
    [CrossRef]
  6. M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E. 71, 016706 (2005).
    [CrossRef]
  7. Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-based photoacoustic tomography,” Opt. Lett. 30, 3054–3056 (2005).
    [CrossRef]
  8. Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88, 231101 (2006).
    [CrossRef]
  9. H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. 23, 878–888 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol. 54, 5457–5467 (2009).
    [CrossRef]
  13. J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
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    [CrossRef]
  16. X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
    [CrossRef]

2012

2010

J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
[CrossRef]

2009

Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol. 54, 5457–5467 (2009).
[CrossRef]

2008

Q. Zhang, Z. Liu, P. R. Carney, and H. Jiang, “Noninvasive imaging of epileptic seizures in vivo using photoacoustic tomography,” Phys. Med. Biol. 53, 1921–1931 (2008).
[CrossRef]

2007

Z. Yuan and H. Jiang, “Three-dimensional finite element-based photoacoustic tomography: reconstruction algorithm and simulations,” Med. Phys. 34, 538–546 (2007).
[CrossRef]

2006

Z. Yuan, Q. Zhang, and H. Jiang, “Simultaneous reconstruction of acoustic and optical properties of heterogeneous media by quantitative photoacoustic tomography,” Opt. Express 14, 6749–6754 (2006).
[CrossRef]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88, 231101 (2006).
[CrossRef]

H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. 23, 878–888 (2006).
[CrossRef]

Z. Yuan, H. Zhao, C. Wu, Q. Zhang, and H. Jiang, “Finite-element-based photoacoustic tomography: phantom and chicken bone experiments,” Appl. Opt. 45, 3177–3183 (2006).
[CrossRef]

2005

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E. 71, 016706 (2005).
[CrossRef]

Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-based photoacoustic tomography,” Opt. Lett. 30, 3054–3056 (2005).
[CrossRef]

2003

S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A. 20, 1859–1866 (2003).
[CrossRef]

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[CrossRef]

1999

R. A. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography-technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef]

1995

R. A. Kruger, P. Liu, and Y. Fang, “Photoacoustic ultrasound (PAUS)-reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef]

Carney, P. R.

Q. Zhang, Z. Liu, P. R. Carney, and H. Jiang, “Noninvasive imaging of epileptic seizures in vivo using photoacoustic tomography,” Phys. Med. Biol. 53, 1921–1931 (2008).
[CrossRef]

Chandrasekharan, V.

J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
[CrossRef]

Dehnavi, M. M.

D. M. Fernandez, M. M. Dehnavi, W. J. Gross, and D. Giannacopoulos, “Alternate parallel processing approach for FEM,” IEEE Trans. Magn. 48, 399–402 (2012).
[CrossRef]

Fan, Y.

Fang, Y.

R. A. Kruger, P. Liu, and Y. Fang, “Photoacoustic ultrasound (PAUS)-reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef]

Fernandez, D. M.

D. M. Fernandez, M. M. Dehnavi, W. J. Gross, and D. Giannacopoulos, “Alternate parallel processing approach for FEM,” IEEE Trans. Magn. 48, 399–402 (2012).
[CrossRef]

Giannacopoulos, D.

D. M. Fernandez, M. M. Dehnavi, W. J. Gross, and D. Giannacopoulos, “Alternate parallel processing approach for FEM,” IEEE Trans. Magn. 48, 399–402 (2012).
[CrossRef]

Gross, W. J.

D. M. Fernandez, M. M. Dehnavi, W. J. Gross, and D. Giannacopoulos, “Alternate parallel processing approach for FEM,” IEEE Trans. Magn. 48, 399–402 (2012).
[CrossRef]

Gu, X.

H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. 23, 878–888 (2006).
[CrossRef]

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[CrossRef]

Jiang, H.

Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol. 54, 5457–5467 (2009).
[CrossRef]

Q. Zhang, Z. Liu, P. R. Carney, and H. Jiang, “Noninvasive imaging of epileptic seizures in vivo using photoacoustic tomography,” Phys. Med. Biol. 53, 1921–1931 (2008).
[CrossRef]

Z. Yuan and H. Jiang, “Three-dimensional finite element-based photoacoustic tomography: reconstruction algorithm and simulations,” Med. Phys. 34, 538–546 (2007).
[CrossRef]

Z. Yuan, H. Zhao, C. Wu, Q. Zhang, and H. Jiang, “Finite-element-based photoacoustic tomography: phantom and chicken bone experiments,” Appl. Opt. 45, 3177–3183 (2006).
[CrossRef]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88, 231101 (2006).
[CrossRef]

H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. 23, 878–888 (2006).
[CrossRef]

Z. Yuan, Q. Zhang, and H. Jiang, “Simultaneous reconstruction of acoustic and optical properties of heterogeneous media by quantitative photoacoustic tomography,” Opt. Express 14, 6749–6754 (2006).
[CrossRef]

Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-based photoacoustic tomography,” Opt. Lett. 30, 3054–3056 (2005).
[CrossRef]

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[CrossRef]

Kruger, G.

R. A. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography-technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef]

Kruger, R. A.

R. A. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography-technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef]

R. A. Kruger, P. Liu, and Y. Fang, “Photoacoustic ultrasound (PAUS)-reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef]

Li, D.

Liu, P.

R. A. Kruger, P. Liu, and Y. Fang, “Photoacoustic ultrasound (PAUS)-reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef]

Liu, Z.

Q. Zhang, Z. Liu, P. R. Carney, and H. Jiang, “Noninvasive imaging of epileptic seizures in vivo using photoacoustic tomography,” Phys. Med. Biol. 53, 1921–1931 (2008).
[CrossRef]

Norton, S. J.

S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A. 20, 1859–1866 (2003).
[CrossRef]

Prakash, J.

J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
[CrossRef]

Qiao, H.

Reinecke, D.

R. A. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography-technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef]

Song, X.

Sun, Y.

Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol. 54, 5457–5467 (2009).
[CrossRef]

Upendra, V.

J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
[CrossRef]

Vo-Dinh, T.

S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A. 20, 1859–1866 (2003).
[CrossRef]

Wang, D.

Wang, L. V.

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E. 71, 016706 (2005).
[CrossRef]

Wu, C.

Xu, M.

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E. 71, 016706 (2005).
[CrossRef]

Xu, Y.

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[CrossRef]

Yalavarthy, P. K.

J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
[CrossRef]

Yuan, Z.

Z. Yuan and H. Jiang, “Three-dimensional finite element-based photoacoustic tomography: reconstruction algorithm and simulations,” Med. Phys. 34, 538–546 (2007).
[CrossRef]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88, 231101 (2006).
[CrossRef]

H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. 23, 878–888 (2006).
[CrossRef]

Z. Yuan, H. Zhao, C. Wu, Q. Zhang, and H. Jiang, “Finite-element-based photoacoustic tomography: phantom and chicken bone experiments,” Appl. Opt. 45, 3177–3183 (2006).
[CrossRef]

Z. Yuan, Q. Zhang, and H. Jiang, “Simultaneous reconstruction of acoustic and optical properties of heterogeneous media by quantitative photoacoustic tomography,” Opt. Express 14, 6749–6754 (2006).
[CrossRef]

Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-based photoacoustic tomography,” Opt. Lett. 30, 3054–3056 (2005).
[CrossRef]

Zhang, Q.

Zhao, H.

Appl. Opt.

Appl. Phys. Lett.

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88, 231101 (2006).
[CrossRef]

IEEE Trans. Magn.

D. M. Fernandez, M. M. Dehnavi, W. J. Gross, and D. Giannacopoulos, “Alternate parallel processing approach for FEM,” IEEE Trans. Magn. 48, 399–402 (2012).
[CrossRef]

J. Biomed. Opt.

J. Prakash, V. Chandrasekharan, V. Upendra, and P. K. Yalavarthy, “Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units,” J. Biomed. Opt. 15, 066009 (2010).
[CrossRef]

J. Opt. Soc. Am.

H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. 23, 878–888 (2006).
[CrossRef]

J. Opt. Soc. Am. A.

S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A. 20, 1859–1866 (2003).
[CrossRef]

Med. Phys.

R. A. Kruger, P. Liu, and Y. Fang, “Photoacoustic ultrasound (PAUS)-reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef]

R. A. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography-technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef]

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[CrossRef]

Z. Yuan and H. Jiang, “Three-dimensional finite element-based photoacoustic tomography: reconstruction algorithm and simulations,” Med. Phys. 34, 538–546 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

Q. Zhang, Z. Liu, P. R. Carney, and H. Jiang, “Noninvasive imaging of epileptic seizures in vivo using photoacoustic tomography,” Phys. Med. Biol. 53, 1921–1931 (2008).
[CrossRef]

Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol. 54, 5457–5467 (2009).
[CrossRef]

Phys. Rev. E.

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E. 71, 016706 (2005).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Flow diagram of the FEM-based PAT reconstruction algorithm.

Fig. 2.
Fig. 2.

Flow diagram of the GPU-based MA.

Fig. 3.
Fig. 3.

Decomposition of the matrix multiplication.

Fig. 4.
Fig. 4.

Flow diagram of the block, which is employed to calculate the submatrix of the ith row and jth column in the product.

Fig. 5.
Fig. 5.

Flow diagram of the GPU-based reduced LDLT factorization.

Fig. 6.
Fig. 6.

Flow diagram of the parallel mesh mapping.

Fig. 7.
Fig. 7.

Geometrical information of the cylindrical phantom. (a) Lateral view. (b) Sectional view.

Fig. 8.
Fig. 8.

Reconstruction results of different excitation schemes on the plane of x=0mm. (a) Real distribution. (b) Reconstructed distribution of top surface illumination. (c) Reconstructed distribution of bottom surface illumination. (d) Average of (b) and (c).

Fig. 9.
Fig. 9.

Comparisons of the CPU-based reconstruction results and GPU-based reconstruction results on the planes of z=±2.5, y=3, and x=0. (a) Real distribution of absorption coefficient on these four planes. (b) CPU-based reconstruction results. (c) GPU-based reconstruction results.

Tables (7)

Tables Icon

Table 1. Optical and Acoustic Parameters of the Phantom

Tables Icon

Table 2. Information of Spatial Discrete Meshes

Tables Icon

Table 3. Information of Frequency Sets

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Table 4. RRMSE between GPU- and CPU-based Reconstruction Results

Tables Icon

Table 5. Calculation Time on CPU with Different Spatial Discrete Meshes and Frequency Sets in Simulationsa

Tables Icon

Table 6. Calculation Time on GPU with Different Spatial Discrete Meshes and Frequency Sets in Simulationsa

Tables Icon

Table 7. Acceleration Ratio of Different Modules of Calculation

Equations (15)

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

2P(r,ω)+k0(1+O)P(r,ω)=k0v0βΦ(r)/Cp,
Ae,ωPe,ω=Be,ωΦωe=1,2.Ne,
AωPω=BωΦ.
TcoΔΦco=(Jco)T(PcPo),
Jco=[JR,co1,1JR,co1,NconJI,co1,1JI,co1,NconJR,coNw,1JR,coNw,NconJI,coNw,1JI,coNw,Ncon],
JR/I,coω,n=(Ψω)TBωΦfiΦR/I,con,
AωΨω=Q,
Qi,j={1,ifdj=i0,elsei=1,2,Nfin;j=1,2,,Nd.
χ=[χ1,,χNfin]T=[k=14ψcoc1,kχcoc1,k,,k=14ψcocNfin,kχcocNfin,k]T,
μa=1Nii=1Niμai,
L1i,j={1ifAi,j0andij0elseFori=1:NnL1k,i=sign(l=m1i1L1i,lL1k,l),withk=i,i+1,,m2;m1=max(1,i+1bandwidth);m2=min(i+bandwidth1,Nn).endSSL={(i,j)|L1i,j=1}.
L1j,iω={Aj,iω ifAi,j0andij0,elseFori=1:NnL1b(k),iω=L1b(k),iωl=1HLb(k)L1b(k),c(l)ωL1i,c(l)ωL1c(l),c(l)ω;withk=1,2,,LLi;(b(k),i)SSL;(b(k),c(l))SSL;c(l)i.endLi,jω={L1i,jω/L1j,jω,if(i,j)SSL,0,else.,
fori=1:Nnyiω=biωj=1HLi1Li,c(j)ωbc(j)ω;with(i,c(j))SSL;c(j)i.endfori=Nn:1Piω=yiωj=2LLiL1c(j),iωxc(j)ωL1c(1),iω;with(c(j),i)SSL;c(j)i.end,
fori=1:Nnyiω,d=biω,dj=1HLi1Li,c(j)ωbc(j)ω,d;with(i,c(j))SSL;c(j)i.endfori=Nn:1Ψiω,d=yiω,dj=2LLiL1c(j),iωxc(j)ω,dL1c(1),iω;with(c(j),i)SSL;c(j)i.end,
Eimc={j|minj=1Ncoe(Vj,i)}={j|minj=1Ncoe(k=14Vj,ikVj)},

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