Abstract

Spectral imaging requires rapid analysis of spectra associated with each pixel. A rapid algorithm has been developed that uses iterative matrix inversions to solve for the absorption spectra of a tissue using a lookup table for photon pathlength based on numerical simulations. The algorithm uses tissue water content as an internal standard to specify the strength of optical scattering. An experimental example is presented on the spectroscopy of portwine stain lesions. When implemented in MATLAB, the method is ~100-fold faster than using fminsearch().

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  1. S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
    [CrossRef] [PubMed]
  2. L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
    [CrossRef] [PubMed]
  3. K. G. Phillips and S. L. Jacques, “Solution of transport equations in layered media with refractive index mismatch using the PN-method,” J. Opt. Soc. Am. A 26(10), 2147–2162 (2009).
    [CrossRef] [PubMed]
  4. S. L. Jacques, Origins of tissue optical properties in the UVA, visible and NIR (1991). Optical Society of America Trends in Optics and Photonics, Vol. 2 Advances in Optical Imaging and Photon Migration, p. 364–371 (1996).
  5. C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
    [CrossRef] [PubMed]
  6. S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation,” Photochem. Photobiol. 53(6), 769–775 (1991).
    [PubMed]

2009 (1)

2008 (1)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[CrossRef] [PubMed]

1998 (1)

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
[CrossRef] [PubMed]

1995 (1)

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

1991 (1)

S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation,” Photochem. Photobiol. 53(6), 769–775 (1991).
[PubMed]

Cope, M.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
[CrossRef] [PubMed]

Essenpreis, M.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
[CrossRef] [PubMed]

Jacques, S. L.

K. G. Phillips and S. L. Jacques, “Solution of transport equations in layered media with refractive index mismatch using the PN-method,” J. Opt. Soc. Am. A 26(10), 2147–2162 (2009).
[CrossRef] [PubMed]

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation,” Photochem. Photobiol. 53(6), 769–775 (1991).
[PubMed]

Kohl, M.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
[CrossRef] [PubMed]

McAuliffe, D. J.

S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation,” Photochem. Photobiol. 53(6), 769–775 (1991).
[PubMed]

Phillips, K. G.

Pogue, B. W.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[CrossRef] [PubMed]

Simpson, C. R.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
[CrossRef] [PubMed]

Wang, L.-H.

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

Zheng, L.-Q.

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

Comput. Methods Programs Biomed. (1)

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Photochem. Photobiol. (1)

S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation,” Photochem. Photobiol. 53(6), 769–775 (1991).
[PubMed]

Phys. Med. Biol. (1)

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998) (as posted on website http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/skin/ skinoptprop.htm.).
[CrossRef] [PubMed]

Other (1)

S. L. Jacques, Origins of tissue optical properties in the UVA, visible and NIR (1991). Optical Society of America Trends in Optics and Photonics, Vol. 2 Advances in Optical Imaging and Photon Migration, p. 364–371 (1996).

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Figures (4)

Fig. 1
Fig. 1

The algorithm for spectral analysis. The measured spectrum specifies OD. The array A [see Eq. (5) is initially filled using Eq. (1)] to specify μa and using the lookup tables L(μa, μs’, Mμa.mel) and Lepia, μs’, Mμa.mel) based on Monte Carlo simulations to specify L and Lepi for each wavelength. An initial value μs500nm is assumed. The matrix inversion X = A−1OD yields values for B, S, W that are used to update μa. The predicted water W1 is used to update μs500nm: μs500nm = μs500nm(0.65/W1). Then μa, M and μs500nm are used to update L and Lepi. The A matrix is updated. The cycle is repeated. After 5 iterations, the values of X converge on stable values.

Fig. 2
Fig. 2

A hand-held spectral camera for measuring skin sites. Liquid crystal tunable filter scans to different wavelengths. Camera views reflected skin through cross-polarizer filter to reject surface glare. The open port contacting the skin does not compress the skin site and avoids blanching the vasculature.

Fig. 3
Fig. 3

Portwine stain lesion (PWS) spectra taken (A) before laser treatment and (B) 35 min after laser treatment (black circles). Red line shows fit by algorithm. Magenta lines show oxygenated blood (S = 0.6-1.0). Cyan lines show deoxygenated blood (S = 0-0.5). The blood content (B) increases and the oxygen saturation (S) decreases as thrombi are formed in the PWS by the laser treatment. The melanin content (M) and the constant (K) did not change significantly. The spectra for scatter only (black), + water (blue), + melanin (green) and + blood (red) are shown.

Fig. 4
Fig. 4

Time required for fitting spectra, using (A) the matrix method of this report, and (B) the fminsearch() function in MATLABTM. The histograms for computation time (ms) for fitting one spectrum is shown, based on fitting over 300 spectra. The mean time for the matrix method (1.2 ms) is 100-fold faster than the mean time for the fminsearch() method (120 ms).

Equations (10)

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g e t R ( μ a , μ s ' , n r ) = e μ a L ( μ a , μ ' s , n r )
μ a ( λ ) = B S μ a . o x y ( λ ) + B ( 1 S ) μ a . d e o x y ( λ ) + W μ a . w a t e r ( λ ) + i f i μ a . i ( λ )
μ s ' ( λ ) = μ s ' 500 n m ( f ( λ 500 n m ) 4 + ( 1 f ) ( λ 500 n m ) b )
R ( λ ) = K e M μ a . m e l L e p i e μ a L
O D ( λ ) = ln ( R ) = B S μ a . o x y ( λ ) L ( λ ) + B ( 1 S ) μ a . d e o x y ( λ ) L ( λ ) + W μ a . w a t e r ( λ ) L ( λ ) + M μ a . m e l ( λ ) L e p i ( λ ) ln ( K )
| O D λ 1 O D λ 2 O D λ 3 ... O D λ N | O D = = | μ a . o x y . λ 1 L λ 1 μ a . d e o x y . λ 1 L λ 1 μ a . w a t e r . λ 1 L λ 1 μ a . m e l . λ 1 L e p i . λ 1 1 μ a . o x y . λ 2 L λ 2 μ a . d e o x y . λ 2 L λ 2 μ a . w a t e r . λ 2 L λ 2 μ a . m e l . λ 2 L e p i . λ 2 1 μ a . o x y . λ 3 L λ 3 μ a . d e o x y . λ 3 L λ 3 μ a . w a t e r . λ 3 L λ 3 μ a . m e l . λ 3 L e p i . λ 3 1 ... ... ... ... ... μ a . o x y . λ N L λ N μ a . d e o x y . λ N L λ N μ a . w a t e r . λ N L λ N μ a . m e l . λ N L e p i . λ N 1 | A × | B S B ( 1 S ) W M ln ( K ) | X
X = A 1 O D
B = X ( 1 ) + X ( 2 ) S = X ( 1 ) / ( X ( 1 ) + X ( 2 ) ) W = X ( 3 ) B = X ( 4 ) K = exp ( X ( 1 ) )
L ( μ a , μ s ' , M μ a . m e l ) = 1 R ( μ a , μ s ' , M μ a . m e l ) R ( μ a , μ s ' , M μ a . m e l ) μ a
L e p i ( μ a , μ s ' , M μ a . m e l ) = 1 R ( μ a , μ s ' , M μ a . m e l ) R ( μ a , μ s ' , M μ a . m e l ) ( M μ a . m e l )

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