Abstract

A refined model for the photon energy distribution in a living artery is established by solving the radiative transfer equation in a cylindrical geometry, using the Monte Carlo method. Combining this model with the most recent experimental values for the optical properties of flowing blood and the biomechanics of a blood-filled artery subject to a pulsatile pressure, we find that the optical intensity transmitted through large arteries decreases linearly with increasing arterial distension. This finding provides a solid theoretical foundation for measuring photoplethysmograms.

© 2013 Optical Society of America

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    [CrossRef]
  30. R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
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    [CrossRef]

2013 (1)

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

2008 (2)

A. Reisner, P. A. Shaltis, D. McCombie, and H. Asada, “Utility of the Photoplethysmogram in circulatory monitoring,” Anesthesiology108, 950–958 (2008).
[CrossRef] [PubMed]

R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
[CrossRef]

2007 (3)

P. V. Stroev, P. R. Hoskins, and W. J. Easson, “Distribution of wall shear rate throughout the arterial tree: A case study,” Atherosclerosis191(2), 276–280 (2007).
[CrossRef]

J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas.28, R1–R39 (2007).
[CrossRef] [PubMed]

M. Friebel, J. Helfmann, G. Mueller, and M. Meinke, “Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm,” J. Biomed. Opt.12(5), 1–8 (2007).
[CrossRef]

2006 (1)

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

2003 (2)

1997 (1)

L. Wang, S. L. Jacques, and L. Zheng, “CONV - convolution for responses to a finite diameter photon beam incident on multi-layered tissues,” Computer Meth. Prog. Biomed.54, 141–150 (1997).
[CrossRef]

1995 (1)

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

1990 (1)

W. -F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

1989 (3)

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surgery Med.9, 148–154 (1989).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, 5, 102–111 (1989).

A. A. R. Kamal, J. B. Harness, G. Irving, and A. J. Mearns, ”Skin photoplethysmography - a review,” Computer Methods and Programs in Biomedicine, 28, 257–269 (1989).
[CrossRef]

1988 (1)

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

1979 (1)

G. B. Thurston, “Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood,” Biorheology16, 149–162 (1979).

1972 (1)

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

1968 (1)

R. H. Cox, “Wave propagation through a newtonian fluid contained within a thick-walled, viscoelastic tube,” Biophys. J.8, 691–709 (1968).
[CrossRef]

1967 (1)

I. Mirsky, “Wave propagation in a viscous fluid contained in an orthotropic elastic tube,” Biophys. J.7, 165–186 (1967).
[CrossRef] [PubMed]

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.93, 70–83 (1941).
[CrossRef]

Allen, J.

J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas.28, R1–R39 (2007).
[CrossRef] [PubMed]

Allison, R. R.

R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
[CrossRef]

Andersson-Engels, S.

Arkuszewski, M.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Aruna, P.

Asada, H.

A. Reisner, P. A. Shaltis, D. McCombie, and H. Asada, “Utility of the Photoplethysmogram in circulatory monitoring,” Anesthesiology108, 950–958 (2008).
[CrossRef] [PubMed]

Bagnato, V. S.

R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
[CrossRef]

Barkhuysen, R.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Beyersdorf, F.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

Bingger, P.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

Born, M.

M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge University Press, 1999), pp. 40–43.

Brands, P. J.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Brechtelsbauer, H.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

Cheong, W. -F.

W. -F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

Cox, R. H.

R. H. Cox, “Wave propagation through a newtonian fluid contained within a thick-walled, viscoelastic tube,” Biophys. J.8, 691–709 (1968).
[CrossRef]

Cucchiara, B. L.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Easson, W. J.

P. V. Stroev, P. R. Hoskins, and W. J. Easson, “Distribution of wall shear rate throughout the arterial tree: A case study,” Atherosclerosis191(2), 276–280 (2007).
[CrossRef]

Enejder, A. M. K.

Fiala, J.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

Fine, I.

L. D. Shvartsman and I. Fine, “Optical transmission of blood: Effect of erythrocyte aggregation,” IEEE Trans. Biomed. Eng.50(8), 1026–1033 (2003).
[CrossRef] [PubMed]

Foerster, K.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

Friebel, M.

M. Friebel, J. Helfmann, G. Mueller, and M. Meinke, “Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm,” J. Biomed. Opt.12(5), 1–8 (2007).
[CrossRef]

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.93, 70–83 (1941).
[CrossRef]

Harness, J. B.

A. A. R. Kamal, J. B. Harness, G. Irving, and A. J. Mearns, ”Skin photoplethysmography - a review,” Computer Methods and Programs in Biomedicine, 28, 257–269 (1989).
[CrossRef]

Heilmann, C.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

Heinich, L.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

Helfmann, J.

M. Friebel, J. Helfmann, G. Mueller, and M. Meinke, “Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm,” J. Biomed. Opt.12(5), 1–8 (2007).
[CrossRef]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.93, 70–83 (1941).
[CrossRef]

Hoeks, A. P. G.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Hoskins, P. R.

P. V. Stroev, P. R. Hoskins, and W. J. Easson, “Distribution of wall shear rate throughout the arterial tree: A case study,” Atherosclerosis191(2), 276–280 (2007).
[CrossRef]

Hurst, R. W.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Irving, G.

A. A. R. Kamal, J. B. Harness, G. Irving, and A. J. Mearns, ”Skin photoplethysmography - a review,” Computer Methods and Programs in Biomedicine, 28, 257–269 (1989).
[CrossRef]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “CONV - convolution for responses to a finite diameter photon beam incident on multi-layered tissues,” Computer Meth. Prog. Biomed.54, 141–150 (1997).
[CrossRef]

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

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, 5, 102–111 (1989).

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surgery Med.9, 148–154 (1989).
[CrossRef]

Kamal, A. A. R.

A. A. R. Kamal, J. B. Harness, G. Irving, and A. J. Mearns, ”Skin photoplethysmography - a review,” Computer Methods and Programs in Biomedicine, 28, 257–269 (1989).
[CrossRef]

Kasner, S. E.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, 5, 102–111 (1989).

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surgery Med.9, 148–154 (1989).
[CrossRef]

Kitslaar, P. J. E. H. M.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Klose, H. J.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

Krejza, J.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Letokhov, V. S.

V. S. Letokhov, “Laser light in biomedicine and the life sciences: From the present to the future,” in Biomedical Photonics Handbook, T. Vo-Dinh, ed. (CRC Press, 2003), pp. 1–16.

McCombie, D.

A. Reisner, P. A. Shaltis, D. McCombie, and H. Asada, “Utility of the Photoplethysmogram in circulatory monitoring,” Anesthesiology108, 950–958 (2008).
[CrossRef] [PubMed]

Mearns, A. J.

A. A. R. Kamal, J. B. Harness, G. Irving, and A. J. Mearns, ”Skin photoplethysmography - a review,” Computer Methods and Programs in Biomedicine, 28, 257–269 (1989).
[CrossRef]

Meinke, M.

M. Friebel, J. Helfmann, G. Mueller, and M. Meinke, “Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm,” J. Biomed. Opt.12(5), 1–8 (2007).
[CrossRef]

Messe, S. R.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Mirsky, I.

I. Mirsky, “Wave propagation in a viscous fluid contained in an orthotropic elastic tube,” Biophys. J.7, 165–186 (1967).
[CrossRef] [PubMed]

Mobley, J.

J. Mobley and T. Vo-Dinh, “Optical properties of tissue,” in Biomedical Photonics Handbook, T. Vo-Dinh, ed. (CRC Press, 2003), pp. 1–75.

Mota, H. C.

R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
[CrossRef]

Moyle, J. T. B.

J. T. B. Moyle, “Optical principles,” in Pulse Oximetry (BMJ Books, 2003), pp. 7–14.

Mueller, G.

M. Friebel, J. Helfmann, G. Mueller, and M. Meinke, “Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm,” J. Biomed. Opt.12(5), 1–8 (2007).
[CrossRef]

Nichols, W. W.

W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, “Properties of the arterial wall: practice,” in McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, eds. (Hodder Arnold Publishers, 2011), pp. 77–109.

O’Rourke, M. F.

W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, “Properties of the arterial wall: practice,” in McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, eds. (Hodder Arnold Publishers, 2011), pp. 77–109.

Prahl, S. A.

W. -F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, 5, 102–111 (1989).

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surgery Med.9, 148–154 (1989).
[CrossRef]

Reisner, A.

A. Reisner, P. A. Shaltis, D. McCombie, and H. Asada, “Utility of the Photoplethysmogram in circulatory monitoring,” Anesthesiology108, 950–958 (2008).
[CrossRef] [PubMed]

Reith, P.

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

Reneman, R. S.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Ruh, D.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

D. Ruh, S. Sherman, H. Zappe, and A. Seifert, “Optoelectronics on flexible substrates for biomedical applications,” in Optical MEMS and Nanophotonics (OMN), 2012 International Conference on, pp. 186–187 (2012).

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

Ruhhammer, J.

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

Samijo, S. K.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Schmid-Schoenbein, H.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

Seifert, A.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

D. Ruh, S. Sherman, H. Zappe, and A. Seifert, “Optoelectronics on flexible substrates for biomedical applications,” in Optical MEMS and Nanophotonics (OMN), 2012 International Conference on, pp. 186–187 (2012).

Shaltis, P. A.

A. Reisner, P. A. Shaltis, D. McCombie, and H. Asada, “Utility of the Photoplethysmogram in circulatory monitoring,” Anesthesiology108, 950–958 (2008).
[CrossRef] [PubMed]

Sherman, S.

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

D. Ruh, S. Sherman, H. Zappe, and A. Seifert, “Optoelectronics on flexible substrates for biomedical applications,” in Optical MEMS and Nanophotonics (OMN), 2012 International Conference on, pp. 186–187 (2012).

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

Shvartsman, L. D.

L. D. Shvartsman and I. Fine, “Optical transmission of blood: Effect of erythrocyte aggregation,” IEEE Trans. Biomed. Eng.50(8), 1026–1033 (2003).
[CrossRef] [PubMed]

Sibata, C. H.

R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
[CrossRef]

Stroev, P. V.

P. V. Stroev, P. R. Hoskins, and W. J. Easson, “Distribution of wall shear rate throughout the arterial tree: A case study,” Atherosclerosis191(2), 276–280 (2007).
[CrossRef]

Swartling, J.

Theodor, M.

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

Thurston, G. B.

G. B. Thurston, “Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood,” Biorheology16, 149–162 (1979).

Tuchin, V. V.

V. V. Tuchin, “Part I: An introduction to tissue optics,” in Tissue optics: Light Scattering Methods and Instruments for Medical Diagnosis, V. V. Tuchin, ed. (SPIE, 2007), pp. 3–142.

Ustymowicz, A.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Vlachopoulos, C.

W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, “Properties of the arterial wall: practice,” in McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, eds. (Hodder Arnold Publishers, 2011), pp. 77–109.

Vo-Dinh, T.

J. Mobley and T. Vo-Dinh, “Optical properties of tissue,” in Biomedical Photonics Handbook, T. Vo-Dinh, ed. (CRC Press, 2003), pp. 1–75.

Volger, E.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “CONV - convolution for responses to a finite diameter photon beam incident on multi-layered tissues,” Computer Meth. Prog. Biomed.54, 141–150 (1997).
[CrossRef]

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

Weigele, J.

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Welch, A. J.

W. -F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, 5, 102–111 (1989).

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surgery Med.9, 148–154 (1989).
[CrossRef]

Willigers, J. M.

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Witzig, K.

K. Witzig, “Ueber erzwungene Wellenbewegungen zaeher, inkompressibler Fluessigkeiten in elastischen Roehren,” Inaugural Dissertation, University of Bern, Bern, (1914).

Wolf, E.

M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge University Press, 1999), pp. 40–43.

Womersley, J. R.

J. R. Womersley, “Section III: The equations of motion of the freely-moving elastic tube and the derivation of the pulse-velocity,” in An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mammalian Arteries, J. R. Womersley, ed. (Wright Air Development Center, 1957), pp. 19–29.

Zappe, H.

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

D. Ruh, S. Sherman, H. Zappe, and A. Seifert, “Optoelectronics on flexible substrates for biomedical applications,” in Optical MEMS and Nanophotonics (OMN), 2012 International Conference on, pp. 186–187 (2012).

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “CONV - convolution for responses to a finite diameter photon beam incident on multi-layered tissues,” Computer Meth. Prog. Biomed.54, 141–150 (1997).
[CrossRef]

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

Anesthesiology (1)

A. Reisner, P. A. Shaltis, D. McCombie, and H. Asada, “Utility of the Photoplethysmogram in circulatory monitoring,” Anesthesiology108, 950–958 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.93, 70–83 (1941).
[CrossRef]

Atherosclerosis (1)

P. V. Stroev, P. R. Hoskins, and W. J. Easson, “Distribution of wall shear rate throughout the arterial tree: A case study,” Atherosclerosis191(2), 276–280 (2007).
[CrossRef]

Biomed. Microdev. (1)

J. Fiala, P. Bingger, D. Ruh, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “An implantable optical blood pressure sensor based on pulse transit time,” Biomed. Microdev.15(1), 73–81 (2013).
[CrossRef]

Biophys. J. (2)

I. Mirsky, “Wave propagation in a viscous fluid contained in an orthotropic elastic tube,” Biophys. J.7, 165–186 (1967).
[CrossRef] [PubMed]

R. H. Cox, “Wave propagation through a newtonian fluid contained within a thick-walled, viscoelastic tube,” Biophys. J.8, 691–709 (1968).
[CrossRef]

Biorheology (1)

G. B. Thurston, “Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood,” Biorheology16, 149–162 (1979).

Cardiovascular Res. (1)

S. K. Samijo, J. M. Willigers, R. Barkhuysen, P. J. E. H. M. Kitslaar, R. S. Reneman, P. J. Brands, and A. P. G. Hoeks, “Wall shear stress in the human common carotid artery as function of age and gender,” Cardiovascular Res.39, 515–522 (1988).
[CrossRef]

Computer Meth. Prog. Biomed. (2)

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

L. Wang, S. L. Jacques, and L. Zheng, “CONV - convolution for responses to a finite diameter photon beam incident on multi-layered tissues,” Computer Meth. Prog. Biomed.54, 141–150 (1997).
[CrossRef]

Computer Methods and Programs in Biomedicine (1)

A. A. R. Kamal, J. B. Harness, G. Irving, and A. J. Mearns, ”Skin photoplethysmography - a review,” Computer Methods and Programs in Biomedicine, 28, 257–269 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. -F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

L. D. Shvartsman and I. Fine, “Optical transmission of blood: Effect of erythrocyte aggregation,” IEEE Trans. Biomed. Eng.50(8), 1026–1033 (2003).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

M. Friebel, J. Helfmann, G. Mueller, and M. Meinke, “Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm,” J. Biomed. Opt.12(5), 1–8 (2007).
[CrossRef]

Lasers Surgery Med. (1)

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surgery Med.9, 148–154 (1989).
[CrossRef]

Pfluegers Arch. (1)

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, and H. Schmid-Schoenbein, “Microrheology and light transmission of blood I. The photometric effects of red cell aggregation and red cell orientation,” Pfluegers Arch.333, 126–139 (1972).
[CrossRef]

Photodiagnosis and Photodynamic Therapy (1)

R. R. Allison, H. C. Mota, V. S. Bagnato, and C. H. Sibata, “Bio-nanotechnology and photodynamic therapyState of the art review,” Photodiagnosis and Photodynamic Therapy5, 19–28, (2008).
[CrossRef]

Physiol. Meas. (1)

J. Allen, “Photoplethysmography and its application in clinical physiological measurement,” Physiol. Meas.28, R1–R39 (2007).
[CrossRef] [PubMed]

SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology (1)

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, 5, 102–111 (1989).

Stroke (1)

J. Krejza, M. Arkuszewski, S. E. Kasner, J. Weigele, A. Ustymowicz, R. W. Hurst, B. L. Cucchiara, and S. R. Messe, “Carotid artery diameter in men and women and the relation to body and neck size,” Stroke, 37, 1103–1105 (2006).
[CrossRef] [PubMed]

Other (11)

J. Mobley and T. Vo-Dinh, “Optical properties of tissue,” in Biomedical Photonics Handbook, T. Vo-Dinh, ed. (CRC Press, 2003), pp. 1–75.

D. Ruh, S. Sherman, M. Theodor, J. Ruhhammer, K. Foerster, C. Heilmann, F. Beyersdorf, H. Zappe, and A. Seifert, “Determination of vessel wall dynamics by optical microsensors,” in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, pp. 2359–2362 (2012).

K. Witzig, “Ueber erzwungene Wellenbewegungen zaeher, inkompressibler Fluessigkeiten in elastischen Roehren,” Inaugural Dissertation, University of Bern, Bern, (1914).

J. R. Womersley, “Section III: The equations of motion of the freely-moving elastic tube and the derivation of the pulse-velocity,” in An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mammalian Arteries, J. R. Womersley, ed. (Wright Air Development Center, 1957), pp. 19–29.

D. Ruh, S. Sherman, H. Zappe, and A. Seifert, “Optoelectronics on flexible substrates for biomedical applications,” in Optical MEMS and Nanophotonics (OMN), 2012 International Conference on, pp. 186–187 (2012).

D. Ruh, P. Reith, S. Sherman, M. Theodor, J. Ruhhammer, A. Seifert, and H. Zappe, “Stretchable optoelectronic circuits embedded in a polymer network, Adv. Mater. DOI: , (2013).
[CrossRef]

V. V. Tuchin, “Part I: An introduction to tissue optics,” in Tissue optics: Light Scattering Methods and Instruments for Medical Diagnosis, V. V. Tuchin, ed. (SPIE, 2007), pp. 3–142.

M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge University Press, 1999), pp. 40–43.

W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, “Properties of the arterial wall: practice,” in McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, W. W. Nichols, M. F. O’Rourke, and C. Vlachopoulos, eds. (Hodder Arnold Publishers, 2011), pp. 77–109.

V. S. Letokhov, “Laser light in biomedicine and the life sciences: From the present to the future,” in Biomedical Photonics Handbook, T. Vo-Dinh, ed. (CRC Press, 2003), pp. 1–16.

J. T. B. Moyle, “Optical principles,” in Pulse Oximetry (BMJ Books, 2003), pp. 7–14.

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Figures (8)

Fig. 1
Fig. 1

Comparison of the simulation geometry between a) MCML and b) extMCML. a) In MCML, a stack of infinitely extended planes is illuminated by a Dirac beam in the z-direction. b) In extMCML, the Dirac beam strikes an infinitely long multilayered cylinder in the lateral direction.

Fig. 2
Fig. 2

Simulations by extMCML and MCML. The left plot shows the radiative flux obtained by MCML, the plot on the right presents the radiative flux determined by extMCML. The two different detectors are sketched in red, both detector areas are 1 mm2.

Fig. 3
Fig. 3

Simulation geometry used to calculate the photon energy distribution inside a static, large artery. The 3D plot of the simulation geometry introduces the thicknesses of the various layers forming the arterial wall, adventitia ta, media tm and intima ti; the length of the investigated arterial segment l; inner and outer radii of the arterial wall ri and ro; the Cartesian coordinate system x,y,z; and the Dirac beam striking the arterial wall in z direction.

Fig. 4
Fig. 4

Decay of the radiative flux inside the model artery at rest. left: normalized radiative flux at y = 0μm as a function of z calculated by integrating along the x direction. The blood layer is marked between the two arterial walls. The three different arterial layers forming the arterial wall are labeled as adventitia ta, media tm, and intima ti (dashed, black). right: Normalized radiative flux in x direction integrated over z at y = 0μm. Since there are no optical boundaries in direction of x, the plot shows no discontinuities. The insets in both graphs show the location of the plotted radiative flux inside the cylinder.

Fig. 5
Fig. 5

Schematic of the arrangement for calculating the photoplethysmograms in large, distending arteries. The upper part shows two photon energy distributions in a cross-sectional view for two different points in time t0 and t1. The cross-sectional view at t0 is to scale while the cross-sectional view at t1 is magnified to point out the change in diameter. The exact change in diameter is presented in the lower part of this figure. Here, the temporal behavior of the inner (red, dashed) and outer (red, dotted) arterial wall distensions ur are plotted. The dotted vertical lines indicate the two states above, where t0 and t1 represent the arterial state at the diastole and systole, respectively.

Fig. 6
Fig. 6

Measured pressure waveform p(t) and calculated inner (red, dashed) and outer (red, dotted) arterial displacements. The displacement waveforms are calculated according to Equation 10 with respect to the biomechanical parameters of Table 5.

Fig. 7
Fig. 7

Normalized transmission mode photoplethysmograms (blue, circle) versus arterial strain ε(%). left: data based on the intrinsic optical parameters of blood given by Friebel et al. [8]; right: data based on the intrinsic optical parameters reported by Enejder et al. [9]. The red error bars show the standard deviations of the normalized transmission photoplethysmograms with respect to variations of the intrinsic optical parameters in the wall shear rate range of 200 s−1WSR ≤ 1000 s−1.

Fig. 8
Fig. 8

Derived photoplethysmogram and the corresponding intra-arterial pressure. The PPG is inverted as per common clinical practice.

Tables (6)

Tables Icon

Table 1 Optical parameters to compare extMCML with the original MCML code.

Tables Icon

Table 2 Verification of the extMCML code by comparison of total transmittance and diffuse reflectance with the MCML code provided by [11]. Input power is 1 W, detector area is 1 mm2.

Tables Icon

Table 3 Relative error between MCML and extMCML for various anisotropy factors.

Tables Icon

Table 4 Optical properties [19,20] of the three different layers of the arterial wall and blood at a wavelength of 633 nm.

Tables Icon

Table 5 Biomechanical parameters of the arterial wall defining the linear viscoelastic behavior given in Equation 8 optimized to yield arterial strains of roughly 5 %.

Tables Icon

Table 6 Intrinsic optical parameters of flowing blood for shear rates ranging from 200 s−1 to 1000 s−1. Bold values are taken from literature [8, 9], the other values are linearly interpolated.

Equations (12)

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

( s ) I ν ( r , s ) + ( μ a + μ s ) μ t I ν ( r , s ) = μ t 4 π 4 π I ν ( r , s ) p s ( s , s ) ) d Ω ,
p s ( θ ) = 1 4 π 1 g 2 ( 1 + g 2 2 g cos θ ) 3 / 2
g = 0 π p s ( θ ) cos θ 2 π sin θ d θ .
p r = 2 ( p i r ) p i + p i ,
p t = n i n t p i + ( 1 n i n t 1 ( p i r ) 2 n i p i r ) r
A ( x , y , z ) = N p h Δ W i N p h d V
Φ ( x , y , z ) = A ( x , y , z ) μ a .
μ * = μ 0 1 + i ω λ 2 1 + i ω λ 1 ,
p ( r , x , t ) = n N P n ( r ) exp [ i ( n ω t γ n x ) ] ,
u r = N n γ n P n n ω ρ ( Δ 13 Δ 11 J 1 ( k n r ) + Δ 14 Δ 11 Y 1 ( k n r ) + Δ 15 Δ 11 J 1 ( i γ n r ) + Δ 16 Δ 11 Y 1 ( i γ n r ) ) exp [ i ( n ω t γ n x ) ] ,
k n 2 = n 2 ω 2 ρ w μ * γ n 2 ,
WSR = v x r | r = r i .

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