Abstract

The 360° rotation geometry of the hybrid fluorescence molecular tomography/x-ray computed tomography modality allows for acquisition of very large datasets, which pose numerical limitations on the reconstruction. We propose a compression method that takes advantage of the correlation of the Born-normalized signal among sources in spatially formed clusters to reduce the size of system model. The proposed method has been validated using an ex vivo study and an in vivo study of a nude mouse with a subcutaneous 4T1 tumor, with and without inclusion of a priori anatomical information. Compression rates of up to two orders of magnitude with minimum distortion of reconstruction have been demonstrated, resulting in large reduction in weight matrix size and reconstruction time.

© 2013 Optical Society of America

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  1. A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
    [CrossRef]
  2. R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
    [CrossRef]
  3. A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, Opt. Lett. 37, 4326 (2012).
    [CrossRef]
  4. J. Ripoll, Opt. Lett. 35, 688 (2010).
    [CrossRef]
  5. N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
    [CrossRef]
  6. X. Cao, X. Wang, B. Zhang, F. Liu, J. W. Luo, and J. Bai, Biomed. Opt. Express 4, 1 (2013).
    [CrossRef]
  7. X. Liu, B. Zhang, J. Luo, and J. Bai, Phys. Med. Biol. 57, 2727 (2012).
    [CrossRef]
  8. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
    [CrossRef]
  9. J. A. Hartigan, Clustering Algorithms (Wiley, 1975).
  10. C. C. Paige and M. A. Saunders, ACM Trans. Math. Softw. 8, 43 (1982).
    [CrossRef]
  11. A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
    [CrossRef]
  12. A. Sarantopoulos, G. Themelis, and V. Ntziachristos, Mol. Imag. Biol. 13, 874 (2011).
    [CrossRef]

2013 (2)

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

X. Cao, X. Wang, B. Zhang, F. Liu, J. W. Luo, and J. Bai, Biomed. Opt. Express 4, 1 (2013).
[CrossRef]

2012 (3)

X. Liu, B. Zhang, J. Luo, and J. Bai, Phys. Med. Biol. 57, 2727 (2012).
[CrossRef]

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, Opt. Lett. 37, 4326 (2012).
[CrossRef]

2011 (1)

A. Sarantopoulos, G. Themelis, and V. Ntziachristos, Mol. Imag. Biol. 13, 874 (2011).
[CrossRef]

2010 (3)

A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
[CrossRef]

J. Ripoll, Opt. Lett. 35, 688 (2010).
[CrossRef]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef]

1982 (1)

C. C. Paige and M. A. Saunders, ACM Trans. Math. Softw. 8, 43 (1982).
[CrossRef]

Ale, A.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, Opt. Lett. 37, 4326 (2012).
[CrossRef]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
[CrossRef]

Arridge, S.

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

Arridge, S. R.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef]

Bai, J.

Bassi, A.

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

Canti, G.

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

Cao, X.

Cohrs, C.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

D’Andrea, C.

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

de Angelis, M. H.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef]

Ducros, N.

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

Ermolayev, V.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

Freyer, M.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

Hartigan, J. A.

J. A. Hartigan, Clustering Algorithms (Wiley, 1975).

Herzog, E.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef]

Jin, A.

Liu, F.

Liu, X.

X. Liu, B. Zhang, J. Luo, and J. Bai, Phys. Med. Biol. 57, 2727 (2012).
[CrossRef]

Luo, J.

X. Liu, B. Zhang, J. Luo, and J. Bai, Phys. Med. Biol. 57, 2727 (2012).
[CrossRef]

Luo, J. W.

Ntziachristos, V.

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, Opt. Lett. 37, 4326 (2012).
[CrossRef]

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

A. Sarantopoulos, G. Themelis, and V. Ntziachristos, Mol. Imag. Biol. 13, 874 (2011).
[CrossRef]

A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
[CrossRef]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

Paige, C. C.

C. C. Paige and M. A. Saunders, ACM Trans. Math. Softw. 8, 43 (1982).
[CrossRef]

Ripoll, J.

Sarantopoulos, A.

A. Sarantopoulos, G. Themelis, and V. Ntziachristos, Mol. Imag. Biol. 13, 874 (2011).
[CrossRef]

A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
[CrossRef]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

Saunders, M. A.

C. C. Paige and M. A. Saunders, ACM Trans. Math. Softw. 8, 43 (1982).
[CrossRef]

Schulz, R. B.

A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
[CrossRef]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef]

Soehngen, E.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

Themelis, G.

A. Sarantopoulos, G. Themelis, and V. Ntziachristos, Mol. Imag. Biol. 13, 874 (2011).
[CrossRef]

Valentini, G.

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

Wang, X.

Yazici, B.

Zhang, B.

Zientkowska, M.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

ACM Trans. Math. Softw. (1)

C. C. Paige and M. A. Saunders, ACM Trans. Math. Softw. 8, 43 (1982).
[CrossRef]

Biomed. Opt. Express (1)

IEEE Trans. Med. Imaging (1)

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 465 (2010).
[CrossRef]

J. Biomed. Opt. (1)

N. Ducros, A. Bassi, G. Valentini, G. Canti, S. Arridge, and C. D’Andrea, J. Biomed. Opt. 18, 020503 (2013).
[CrossRef]

Med. Phys. (2)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef]

A. Ale, R. B. Schulz, A. Sarantopoulos, and V. Ntziachristos, Med. Phys. 37, 1976 (2010).
[CrossRef]

Mol. Imag. Biol. (1)

A. Sarantopoulos, G. Themelis, and V. Ntziachristos, Mol. Imag. Biol. 13, 874 (2011).
[CrossRef]

Nat. Methods (1)

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, Nat. Methods 9, 615 (2012).
[CrossRef]

Opt. Lett. (2)

Phys. Med. Biol. (1)

X. Liu, B. Zhang, J. Luo, and J. Bai, Phys. Med. Biol. 57, 2727 (2012).
[CrossRef]

Other (1)

J. A. Hartigan, Clustering Algorithms (Wiley, 1975).

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Figures (2)

Fig. 1.
Fig. 1.

Results for the ex vivo case: (a) an axial slice of the original reconstruction; (b)–(f) slices for compression parameter β=95, 80, 60, 20, and 0 (compression rates of 16, 58, 86, 136, and 270); (g) ht(X), hb(X), and the compression rate versus average number of retained components per cluster and versus β; (h) clusters shown on the animal surface. Arrow in (f) points to the tube.

Fig. 2.
Fig. 2.

Results for the in vivo case: (a) an axial slice of the original reconstruction; (b)–(e) slices for β=90, 80, 20, and 0 (compression rates of 25, 41, 104, and 209); (f)–(j) corresponding results using anatomical priors; (k) ex vivo validation; (l) ht(X), hb(X), and the compression rate versus average number of retained components per cluster and versus β (dotted curves correspond to reconstructions using anatomical priors); (m) clusters on the animal surface.

Equations (9)

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

WX=M,
X0=minX(WXM+λΓX),
Cka setSk:F(Sk,Ck)1/(|Sk|×|Ck|)1.
UkΣUk=QkQkTQk=(Bkmean(Bk)1|Ck|)F(Sk,Ck).
Nk(β)=mini{i|Ei/E|Sk|β/100}.
Mk=Uk(1:Nk(β),:)Bk.
Wk(i,j,v)=sSkUk(i,s)F(s,j)G(s,v)G(j,v)G(s,j).
WpX=Mp,
ht(X)=100X(I)X0(I)/X0(I)hb(X)=100(X(Ic)X0/X0(Ic)X1).

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