Abstract

Light may traverse a turbid material, such as blood, without encountering any of its pigment containing structures, a phenomenon known as sieve effect. This phenomenon may result in a decrease in the amount of light absorbed by the material. Accordingly, the corresponding sieve factor needs to be accounted for in optical investigations aimed at the derivation of blood biophysical properties from light transmittance measurements. The existing procedures used for its estimation either lack the flexibility required for practical applications or are based on general formulas that incorporate other light and matter interaction phenomena such as detour (scattering) effects. In this paper, a ray optics framework is proposed to estimate the sieve factor for blood samples. It employs a first principles approach to account for the distribution, orientation and shape of the cells that contain hemoglobin, the essential (oxygen-carrying) pigment found in human blood. Within this framework, ray-casting techniques are used to determine the probability that light can traverse a blood sample without encountering any of these cells. The predictive capabilities of the proposed framework are demonstrated through a series of in silico experiments. Its effectiveness is further illustrated by visualizations depicting the different blood parameterizations considered in the simulations.

© 2010 Optical Society of America

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2009 (1)

2008 (2)

Y. M. Serebrennikova, J. M. Smith, D. E. Huffman, G. F. Leparc, and L. H. García-Rubio, "Quantitative interpretations of visible-nir reflectance spectra of blood," Opt. Express 16, 18215-18229 (2008).
[CrossRef] [PubMed]

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

2007 (5)

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range," J. Biomed. Opt. 12, 014024 (2007).
[CrossRef] [PubMed]

J. Laufer, D. T. Delpy, C. Elwell, and P. Beard, "Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration," Phys. Med. Biol. 52, 141-168 (2007).
[CrossRef]

D. Eng and G. Baranoski, "The application of photoacoustic absorption spectral data to the modeling of leaf optical properties in the visible range," IEEE Trans. Geosci. Remote Sens. 45, 4077-4086 (2007).
[CrossRef]

G. Baranoski and D. Eng, "An investigation on sieve and detour effects affecting the interaction of collimated and diffuse infrared radiation (750 to 2500 nm) with plant leaves," IEEE Trans. Geosci. Remote Sens. 45, 2593-2599 (2007).
[CrossRef]

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Empirical model functions to calculate hematocritdependent optical properties of human blood," Appl. Opt. 46, 1742-1753 (2007).
[CrossRef] [PubMed]

2006 (2)

B. D. Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, "From in vivo to in silico biology and back," Nature 443, 527-533 (2006).
[CrossRef] [PubMed]

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh. "Light scattering by single erythrocyte: Comparison of different methods", J. Quant. Spectrosc. Radiat. Transfer 100, 444456 (2006).
[CrossRef]

2004 (1)

L. Orf, "Scientific visualizations with pov-ray," Linux J. 2004, 2 (2004).

1999 (2)

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H. J. Schwarzmaier, "Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

1998 (1)

1997 (1)

W. M. Star, "Light dosimetry in vivo," Phys. Med. Biol. 42, 763-787 (1997).
[CrossRef] [PubMed]

1994 (1)

S. J. Matcher, M. Cope, and D. T. Delpy, "Use of the water absorption spectrum to quantify tissue chromophore concentration changes in near-infrared spectroscopy," Phys. Med. Biol. 39, 177-196 (1994).
[CrossRef] [PubMed]

1993 (1)

T. C. Vogelmann, "Plant Tissue Optics," Annu. Rev. Plant Physiol. Mol. Biol. 44, 231-251 (1993).
[CrossRef]

1990 (1)

J. H. McClendon and L. Fukshansky, "On the interpretation of absorption spectra of leaves - ii. The non-absorbed ray of the sieve effect and the mean optical pathlength in the remainder of the leaf," Photochem. Photobiol. 51, 211-216 (1990).
[CrossRef]

1989 (1)

F. Garlaschi, G. Zucchelli, and R. Jennings, "Studies on light absorption and photochemical activity changes in chloroplast suspensions and leaves due to light scattering and light filtration across chloroplasts and vegetation layers," Photosynthesis Research 20, 207-220 (1989).

1988 (2)

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

J. M. Steinke and A. P. Shepherd, "Comparison of Mie theory and the light scattering of red blood cells," Appl. Opt. 27, 4027-4033 (1988).
[CrossRef] [PubMed]

1987 (1)

S. T. Flock, B. C. Wilson, and M. S. Patterson, "Total attenuation coefficient and scattering phase function of tissues and phantom materials at 633nm," Med. Phys. 14, 1742-1753 (1987).
[CrossRef]

1986 (1)

R. N. Pittman, "In vivo photometric analysis of hemoglobin," Ann. Biomed. Eng. 14, 1416-1432 (1986).
[CrossRef]

1979 (1)

W. Rühle and A. Wild, "The intensification of absorbance changes in leaves by light dispersion," Planta 146, 551-557 (1979).
[CrossRef]

1978 (2)

L. Fukshansky, "On the theory of light absorption in non-homogeneous objects," J. Math. Biol. 6, 1416-1432 (1978).
[CrossRef]

E. G. Popov, "Orientation of nonspherical cells in blood flowing through a vessel," Bull. Exp. Biol. Med. 86, 1556-1557 (1978).
[CrossRef]

1969 (1)

R. Skalak and P. I. Branemark, "Deformation of Red Blood Cells in Capillaries," Science 164, 717-719 (1969).
[CrossRef] [PubMed]

1967 (2)

N. M. Anderson and P. Sekelj, "Light-absorbing and scattering properties of nonhaemolysed blood," Phys. Med. Biol. 12, 173-184 (1967).
[CrossRef] [PubMed]

N. M. Anderson and P. Sekelj, "Reflection and transmission of light by thin films of nonhaemolysed blood," Phys. Med. Biol. 12, 185-192 (1967).
[CrossRef] [PubMed]

1964 (1)

W. L. Butler, "Absorption spectroscopy in vivo: Theory and applications," Ann. Rev. Plant Physiol. 15, 451-470 (1964).
[CrossRef]

1956 (1)

L. N. M. Duysens, "The flattening of the absorption spectrum of suspensions as compared to that of solutions," Biochim. Biophys. Acta 19 (1956).
[PubMed]

1951 (1)

K. Kramer, J. Elam, G. Saxton, and W. E. Jr., "Influence of oxygen saturation, concentration and optical depth upon the red and near-infrared light transmittance of whole blood," Am. J. Physiology 165, 229-246 (1951).

Amelink, A.

Anderson, N. M.

N. M. Anderson and P. Sekelj, "Light-absorbing and scattering properties of nonhaemolysed blood," Phys. Med. Biol. 12, 173-184 (1967).
[CrossRef] [PubMed]

N. M. Anderson and P. Sekelj, "Reflection and transmission of light by thin films of nonhaemolysed blood," Phys. Med. Biol. 12, 185-192 (1967).
[CrossRef] [PubMed]

Arridge, S.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

Baranoski, G.

D. Eng and G. Baranoski, "The application of photoacoustic absorption spectral data to the modeling of leaf optical properties in the visible range," IEEE Trans. Geosci. Remote Sens. 45, 4077-4086 (2007).
[CrossRef]

G. Baranoski and D. Eng, "An investigation on sieve and detour effects affecting the interaction of collimated and diffuse infrared radiation (750 to 2500 nm) with plant leaves," IEEE Trans. Geosci. Remote Sens. 45, 2593-2599 (2007).
[CrossRef]

Beard, P.

J. Laufer, D. T. Delpy, C. Elwell, and P. Beard, "Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration," Phys. Med. Biol. 52, 141-168 (2007).
[CrossRef]

Boyer, M.

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

Branemark, P. I.

R. Skalak and P. I. Branemark, "Deformation of Red Blood Cells in Capillaries," Science 164, 717-719 (1969).
[CrossRef] [PubMed]

Butler, W. L.

W. L. Butler, "Absorption spectroscopy in vivo: Theory and applications," Ann. Rev. Plant Physiol. 15, 451-470 (1964).
[CrossRef]

Chei, S.

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

Christiaanse, T.

Cope, M.

S. J. Matcher, M. Cope, and D. T. Delpy, "Use of the water absorption spectrum to quantify tissue chromophore concentration changes in near-infrared spectroscopy," Phys. Med. Biol. 39, 177-196 (1994).
[CrossRef] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

Delpy, D. T.

J. Laufer, D. T. Delpy, C. Elwell, and P. Beard, "Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration," Phys. Med. Biol. 52, 141-168 (2007).
[CrossRef]

S. J. Matcher, M. Cope, and D. T. Delpy, "Use of the water absorption spectrum to quantify tissue chromophore concentration changes in near-infrared spectroscopy," Phys. Med. Biol. 39, 177-196 (1994).
[CrossRef] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

Doershel, K.

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Duysens, L. N. M.

L. N. M. Duysens, "The flattening of the absorption spectrum of suspensions as compared to that of solutions," Biochim. Biophys. Acta 19 (1956).
[PubMed]

Elam, J.

K. Kramer, J. Elam, G. Saxton, and W. E. Jr., "Influence of oxygen saturation, concentration and optical depth upon the red and near-infrared light transmittance of whole blood," Am. J. Physiology 165, 229-246 (1951).

Elwell, C.

J. Laufer, D. T. Delpy, C. Elwell, and P. Beard, "Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration," Phys. Med. Biol. 52, 141-168 (2007).
[CrossRef]

Eng, D.

D. Eng and G. Baranoski, "The application of photoacoustic absorption spectral data to the modeling of leaf optical properties in the visible range," IEEE Trans. Geosci. Remote Sens. 45, 4077-4086 (2007).
[CrossRef]

G. Baranoski and D. Eng, "An investigation on sieve and detour effects affecting the interaction of collimated and diffuse infrared radiation (750 to 2500 nm) with plant leaves," IEEE Trans. Geosci. Remote Sens. 45, 2593-2599 (2007).
[CrossRef]

Eremina, E.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh. "Light scattering by single erythrocyte: Comparison of different methods", J. Quant. Spectrosc. Radiat. Transfer 100, 444456 (2006).
[CrossRef]

Flock, S. T.

S. T. Flock, B. C. Wilson, and M. S. Patterson, "Total attenuation coefficient and scattering phase function of tissues and phantom materials at 633nm," Med. Phys. 14, 1742-1753 (1987).
[CrossRef]

Friebel, M.

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range," J. Biomed. Opt. 12, 014024 (2007).
[CrossRef] [PubMed]

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Empirical model functions to calculate hematocritdependent optical properties of human blood," Appl. Opt. 46, 1742-1753 (2007).
[CrossRef] [PubMed]

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Fukshansky, L.

J. H. McClendon and L. Fukshansky, "On the interpretation of absorption spectra of leaves - ii. The non-absorbed ray of the sieve effect and the mean optical pathlength in the remainder of the leaf," Photochem. Photobiol. 51, 211-216 (1990).
[CrossRef]

L. Fukshansky, "On the theory of light absorption in non-homogeneous objects," J. Math. Biol. 6, 1416-1432 (1978).
[CrossRef]

García-Rubio, L. H.

Garlaschi, F.

F. Garlaschi, G. Zucchelli, and R. Jennings, "Studies on light absorption and photochemical activity changes in chloroplast suspensions and leaves due to light scattering and light filtration across chloroplasts and vegetation layers," Photosynthesis Research 20, 207-220 (1989).

Goldbach, T.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H. J. Schwarzmaier, "Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Hahn, A.

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Hammer, M.

Helfmann, J.

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Empirical model functions to calculate hematocritdependent optical properties of human blood," Appl. Opt. 46, 1742-1753 (2007).
[CrossRef] [PubMed]

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range," J. Biomed. Opt. 12, 014024 (2007).
[CrossRef] [PubMed]

Hellmers, J.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh. "Light scattering by single erythrocyte: Comparison of different methods", J. Quant. Spectrosc. Radiat. Transfer 100, 444456 (2006).
[CrossRef]

Huffman, D. E.

Jennings, R.

F. Garlaschi, G. Zucchelli, and R. Jennings, "Studies on light absorption and photochemical activity changes in chloroplast suspensions and leaves due to light scattering and light filtration across chloroplasts and vegetation layers," Photosynthesis Research 20, 207-220 (1989).

Jr, W. E.

K. Kramer, J. Elam, G. Saxton, and W. E. Jr., "Influence of oxygen saturation, concentration and optical depth upon the red and near-infrared light transmittance of whole blood," Am. J. Physiology 165, 229-246 (1951).

Kolb, A.

Kramer, K.

K. Kramer, J. Elam, G. Saxton, and W. E. Jr., "Influence of oxygen saturation, concentration and optical depth upon the red and near-infrared light transmittance of whole blood," Am. J. Physiology 165, 229-246 (1951).

Laufer, J.

J. Laufer, D. T. Delpy, C. Elwell, and P. Beard, "Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration," Phys. Med. Biol. 52, 141-168 (2007).
[CrossRef]

Lemerle, C.

B. D. Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, "From in vivo to in silico biology and back," Nature 443, 527-533 (2006).
[CrossRef] [PubMed]

Leparc, G. F.

Matcher, S. J.

S. J. Matcher, M. Cope, and D. T. Delpy, "Use of the water absorption spectrum to quantify tissue chromophore concentration changes in near-infrared spectroscopy," Phys. Med. Biol. 39, 177-196 (1994).
[CrossRef] [PubMed]

McClendon, J. H.

J. H. McClendon and L. Fukshansky, "On the interpretation of absorption spectra of leaves - ii. The non-absorbed ray of the sieve effect and the mean optical pathlength in the remainder of the leaf," Photochem. Photobiol. 51, 211-216 (1990).
[CrossRef]

Meinke, M.

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Empirical model functions to calculate hematocritdependent optical properties of human blood," Appl. Opt. 46, 1742-1753 (2007).
[CrossRef] [PubMed]

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range," J. Biomed. Opt. 12, 014024 (2007).
[CrossRef] [PubMed]

Meng, J.

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

Michalodimitrakis, K.

B. D. Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, "From in vivo to in silico biology and back," Nature 443, 527-533 (2006).
[CrossRef] [PubMed]

Michel, B.

Mueller, G.

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Müller, G.

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range," J. Biomed. Opt. 12, 014024 (2007).
[CrossRef] [PubMed]

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Empirical model functions to calculate hematocritdependent optical properties of human blood," Appl. Opt. 46, 1742-1753 (2007).
[CrossRef] [PubMed]

Orf, L.

L. Orf, "Scientific visualizations with pov-ray," Linux J. 2004, 2 (2004).

Patterson, M. S.

S. T. Flock, B. C. Wilson, and M. S. Patterson, "Total attenuation coefficient and scattering phase function of tissues and phantom materials at 633nm," Med. Phys. 14, 1742-1753 (1987).
[CrossRef]

Pittman, R. N.

R. N. Pittman, "In vivo photometric analysis of hemoglobin," Ann. Biomed. Eng. 14, 1416-1432 (1986).
[CrossRef]

Popov, E. G.

E. G. Popov, "Orientation of nonspherical cells in blood flowing through a vessel," Bull. Exp. Biol. Med. 86, 1556-1557 (1978).
[CrossRef]

Roggan, A.

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

Rühle, W.

W. Rühle and A. Wild, "The intensification of absorbance changes in leaves by light dispersion," Planta 146, 551-557 (1979).
[CrossRef]

Saxton, G.

K. Kramer, J. Elam, G. Saxton, and W. E. Jr., "Influence of oxygen saturation, concentration and optical depth upon the red and near-infrared light transmittance of whole blood," Am. J. Physiology 165, 229-246 (1951).

Schuh, R.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh. "Light scattering by single erythrocyte: Comparison of different methods", J. Quant. Spectrosc. Radiat. Transfer 100, 444456 (2006).
[CrossRef]

Schwarzmaier, H. J.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H. J. Schwarzmaier, "Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Schweitzer, D.

Sekelj, P.

N. M. Anderson and P. Sekelj, "Reflection and transmission of light by thin films of nonhaemolysed blood," Phys. Med. Biol. 12, 185-192 (1967).
[CrossRef] [PubMed]

N. M. Anderson and P. Sekelj, "Light-absorbing and scattering properties of nonhaemolysed blood," Phys. Med. Biol. 12, 173-184 (1967).
[CrossRef] [PubMed]

Serebrennikova, Y. M.

Serrano, L.

B. D. Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, "From in vivo to in silico biology and back," Nature 443, 527-533 (2006).
[CrossRef] [PubMed]

Sheaffer, J.W.

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

Shepherd, A. P.

Skadron, K.

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

Skalak, R.

R. Skalak and P. I. Branemark, "Deformation of Red Blood Cells in Capillaries," Science 164, 717-719 (1969).
[CrossRef] [PubMed]

Smith, J. M.

Star, W. M.

W. M. Star, "Light dosimetry in vivo," Phys. Med. Biol. 42, 763-787 (1997).
[CrossRef] [PubMed]

Steinke, J. M.

Sterenborg, H. J. C. M.

Tarjan, D.

S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

Thamm, E.

van der Zee, P.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

Ventura, B. D.

B. D. Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, "From in vivo to in silico biology and back," Nature 443, 527-533 (2006).
[CrossRef] [PubMed]

Vogelmann, T. C.

T. C. Vogelmann, "Plant Tissue Optics," Annu. Rev. Plant Physiol. Mol. Biol. 44, 231-251 (1993).
[CrossRef]

Wild, A.

W. Rühle and A. Wild, "The intensification of absorbance changes in leaves by light dispersion," Planta 146, 551-557 (1979).
[CrossRef]

Wilson, B. C.

S. T. Flock, B. C. Wilson, and M. S. Patterson, "Total attenuation coefficient and scattering phase function of tissues and phantom materials at 633nm," Med. Phys. 14, 1742-1753 (1987).
[CrossRef]

Wray, S.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

Wriedt, T.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh. "Light scattering by single erythrocyte: Comparison of different methods", J. Quant. Spectrosc. Radiat. Transfer 100, 444456 (2006).
[CrossRef]

Wyatt, J.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

Yaroslavsky, A. N.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H. J. Schwarzmaier, "Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Yaroslavsky, I. V.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H. J. Schwarzmaier, "Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Zucchelli, G.

F. Garlaschi, G. Zucchelli, and R. Jennings, "Studies on light absorption and photochemical activity changes in chloroplast suspensions and leaves due to light scattering and light filtration across chloroplasts and vegetation layers," Photosynthesis Research 20, 207-220 (1989).

Am. J. Physiology (1)

K. Kramer, J. Elam, G. Saxton, and W. E. Jr., "Influence of oxygen saturation, concentration and optical depth upon the red and near-infrared light transmittance of whole blood," Am. J. Physiology 165, 229-246 (1951).

Ann. Biomed. Eng. (1)

R. N. Pittman, "In vivo photometric analysis of hemoglobin," Ann. Biomed. Eng. 14, 1416-1432 (1986).
[CrossRef]

Ann. Rev. Plant Physiol. (1)

W. L. Butler, "Absorption spectroscopy in vivo: Theory and applications," Ann. Rev. Plant Physiol. 15, 451-470 (1964).
[CrossRef]

Annu. Rev. Plant Physiol. Mol. Biol. (1)

T. C. Vogelmann, "Plant Tissue Optics," Annu. Rev. Plant Physiol. Mol. Biol. 44, 231-251 (1993).
[CrossRef]

Appl. Opt. (3)

Biochim. Biophys. Acta (1)

L. N. M. Duysens, "The flattening of the absorption spectrum of suspensions as compared to that of solutions," Biochim. Biophys. Acta 19 (1956).
[PubMed]

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E. G. Popov, "Orientation of nonspherical cells in blood flowing through a vessel," Bull. Exp. Biol. Med. 86, 1556-1557 (1978).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

G. Baranoski and D. Eng, "An investigation on sieve and detour effects affecting the interaction of collimated and diffuse infrared radiation (750 to 2500 nm) with plant leaves," IEEE Trans. Geosci. Remote Sens. 45, 2593-2599 (2007).
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D. Eng and G. Baranoski, "The application of photoacoustic absorption spectral data to the modeling of leaf optical properties in the visible range," IEEE Trans. Geosci. Remote Sens. 45, 4077-4086 (2007).
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J. Biomed. Opt. (3)

M. Meinke, G. Müller, J. Helfmann, and M. Friebel, "Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range," J. Biomed. Opt. 12, 014024 (2007).
[CrossRef] [PubMed]

A. Roggan, M. Friebel, K. Doershel, A. Hahn, and G. Mueller, "Optical properties of circulating human blood in the wavelength range 400-2500nm," J. Biomed. Opt. 4, 36-46 (1999).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H. J. Schwarzmaier, "Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

J. Math. Biol. (1)

L. Fukshansky, "On the theory of light absorption in non-homogeneous objects," J. Math. Biol. 6, 1416-1432 (1978).
[CrossRef]

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S. Chei, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron, "A performance study of general-purpose applications on graphics processors using cuda," J. Parallel Distrib. Comput. 68, 1370-1380 (2008).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh. "Light scattering by single erythrocyte: Comparison of different methods", J. Quant. Spectrosc. Radiat. Transfer 100, 444456 (2006).
[CrossRef]

Linux J. (1)

L. Orf, "Scientific visualizations with pov-ray," Linux J. 2004, 2 (2004).

Med. Phys. (1)

S. T. Flock, B. C. Wilson, and M. S. Patterson, "Total attenuation coefficient and scattering phase function of tissues and phantom materials at 633nm," Med. Phys. 14, 1742-1753 (1987).
[CrossRef]

Nature (1)

B. D. Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, "From in vivo to in silico biology and back," Nature 443, 527-533 (2006).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Photochem. Photobiol. (1)

J. H. McClendon and L. Fukshansky, "On the interpretation of absorption spectra of leaves - ii. The non-absorbed ray of the sieve effect and the mean optical pathlength in the remainder of the leaf," Photochem. Photobiol. 51, 211-216 (1990).
[CrossRef]

Photosynthesis Research (1)

F. Garlaschi, G. Zucchelli, and R. Jennings, "Studies on light absorption and photochemical activity changes in chloroplast suspensions and leaves due to light scattering and light filtration across chloroplasts and vegetation layers," Photosynthesis Research 20, 207-220 (1989).

Phys. Med. Biol. (6)

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, "Estimation of optical pathlength through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
[CrossRef] [PubMed]

S. J. Matcher, M. Cope, and D. T. Delpy, "Use of the water absorption spectrum to quantify tissue chromophore concentration changes in near-infrared spectroscopy," Phys. Med. Biol. 39, 177-196 (1994).
[CrossRef] [PubMed]

J. Laufer, D. T. Delpy, C. Elwell, and P. Beard, "Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration," Phys. Med. Biol. 52, 141-168 (2007).
[CrossRef]

W. M. Star, "Light dosimetry in vivo," Phys. Med. Biol. 42, 763-787 (1997).
[CrossRef] [PubMed]

N. M. Anderson and P. Sekelj, "Light-absorbing and scattering properties of nonhaemolysed blood," Phys. Med. Biol. 12, 173-184 (1967).
[CrossRef] [PubMed]

N. M. Anderson and P. Sekelj, "Reflection and transmission of light by thin films of nonhaemolysed blood," Phys. Med. Biol. 12, 185-192 (1967).
[CrossRef] [PubMed]

Planta (1)

W. Rühle and A. Wild, "The intensification of absorbance changes in leaves by light dispersion," Planta 146, 551-557 (1979).
[CrossRef]

Science (1)

R. Skalak and P. I. Branemark, "Deformation of Red Blood Cells in Capillaries," Science 164, 717-719 (1969).
[CrossRef] [PubMed]

Other (9)

L. Northam, "A ray optics framework for the computation of the sieve effect factor for blood," Master’s thesis, University of Waterloo, Waterloo, Ontario (2010).

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A. N. Yaroslavsky, A. V. Priezzhev, J. Rodriquez, I. V. Yaroslavsky, and H. Battarbee, Optics of Blood (SPIE Press, Bellingham, 2002).

V. V. Tuchin, Tissue Optics Light Scattering Methods and Instruments for Medical Diagnosis (The International Society for Optical Engineering, Bellingham, 2000).

L. Fukshansky, Optical properties of plants (Academic Press, London, 1981).

V. V. Barun and A. P. Ivanov, "Effect of hemoglobin localization in erythrocytes on optical absorption by human blood," in "Tenth International Conference on Light Scattering by Non-spherical Particles," (Bodrun, Turkey, 2007), pp. 5-8.

E. I. Rabinowitch, Light absorption by pigments in the living cell (Interscience Publishers Inc., New York, 1951), vol. II, chap. 22.

J. Evans, T. Vogelmann, and W. Williams, "Chloroplast to leaf," in "Photosynthetic Adaptation Chloroplast to Landscape,", W. Smith, T. Vogelmann, and C. Critchley, eds. (Springer, NY, USA, 2004), chap. 2, pp. 15-41. Part 2: Sunlight Capture, Ecological Studies, Vol. 178.

A. T. Lovell, J. C. Hebden, J. C. Goldstone, and M. Cope, "Determination of the transport scattering coefficient of red blood cells [3597-121]," in "Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series,", vol. 3597, B. Chance, R. R. Alfano, and B. J. Tromberg, eds. (1999), vol. 3597, p. 175.

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Figures (9)

Fig. 1.
Fig. 1.

Light traversing a medium may not encounter any of the pigment containing structures present in this medium, a phenomenon known as sieve effect.

Fig. 2.
Fig. 2.

Dimensions of a TUC-cell. On the left, raytraced views of the final shape. On the right, a cross-section of the TUC-cell showing the dimensions of the torus and cylinder. Cylinder has radius R = 2.62μm, and height h = 0.81μm. Torus has major radius R = 2.62μm, and minor radius r = 1.29μm (diameter 2r = 2.58μm). The radius of the TUC-cell is given by R+r = 3.91μm.

Fig. 3.
Fig. 3.

Images describing the “sphere pack” bounding shape used to detect collisions between TUC-cells. On the left, 12 spheres are used; in the middle, 20 spheres; and on the right, 100 spheres. Top and bottom images represent the same object viewed from different angles. Note that by increasing the number of spheres forming the ring, the smoother the bounding shape becomes. However, increasing sphere count decreases the performance of the collision detection procedure.

Fig. 4.
Fig. 4.

Plots of sieve effect factors computed for blood samples with thickness equal to 0.1mm. Three representation for the erythrocites were considered in these experiments: volume equivalent spheres, randomly oriented TUC-cells and flow oriented TUC-cells.

Fig. 5.
Fig. 5.

Plots of sieve effect factors computed for blood samples with thickness equal to 0.5mm. Three representation for the erythrocites were considered in these experiments: volume equivalent spheres, randomly oriented TUC-cells and flow oriented TUC-cells.

Fig. 6.
Fig. 6.

Plots of sieve effect factors computed for blood samples with thickness equal to 1.0mm. Three representation for the erythrocites were considered in these experiments: volume equivalent spheres, randomly oriented TUC-cells and flow oriented TUC-cells.

Fig. 7.
Fig. 7.

Images illustrating different TUC-cell profiles as observed from viewing direction coincident with the light incidence direction. Left: flow oriented TUC-cells. Right: randomly oriented TUC-cells. These images correspond to simulations involving samples with a thickness equal to 0.1mm and hematocrit equal to 5%.

Fig. 8.
Fig. 8.

Images illustrating the different cell geometries considered in the computation of the sieve effect factor. Left column: volume-equivalent spheres. Middle column: randomly-oriented TUC-cells. Right column: flow-oriented TUC-cells. Hematocrit of top row is 1%; middle row, 5%; and bottom row, 10%. These images correspond to simulations involving samples with a thickness equal to 0.1mm and assuming the light incidence direction to be perpendicular to the top face of the testing volume, which was removed to facilitate the visualization of the different cell geometries.

Fig. 9.
Fig. 9.

Ortographic projections (perpendicular to the light incidence direction) of three blood samples with different thicknesses and the same hematocrit (1%). Left: 0.1mm. Middle: 0.5mm. Right: 1.0mm.

Tables (1)

Tables Icon

Table 1. Summary of biophysical parameters employed to describe the different in silico experimental conditions considered in this investigation.

Equations (11)

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

T ( λ ) = Φ t ( λ ) Φ i ( λ ) = e ε ( λ ) cd ,
D ( λ ) = ln ( Φ i ( λ ) Φ t ( λ ) ) = ε ( λ ) cd .
D ( λ ) = ln ( Φ i ( λ ) Φ t ( λ ) ) = β ( λ ) ε ( λ ) cd ,
β S = D sus ( λ ) D sol ( λ ) ,
D sus ( λ ) = m log 10 [ 1 aH ( 1 10 ε ( λ ) c h b ) ] ,
D sol ( λ ) = ε ( λ ) c h Hd ,
β s = D sol ( λ ) D sus ( λ ) D sol ( λ ) ,
D sus ( λ ) = ln ( ( 1 γ ) + γ e 1 γ D ( λ ) sol ) ,
V TUC = 2 π 2 R r 2 + 2 π [ r R 2 sin x r 2 R ( 1 2 x + 1 4 sin ( 2 x ) ) + r 3 ( 1 3 ( 2 + cos 2 x ) sin x ) ] ,
x = sin 1 ( h / 2 r ) .
K = H V prism V TUC .

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