Abstract

We present a dynamic microcirculation PIPE model for functional neuroimaging, non-neuroimaging, and coherent hemodynamics spectroscopy. The temporal evolution of the concentration and oxygen saturation of hemoglobin in tissue, comprised of the contributions from the arterioles, capillaries, and venules of microvasculature, is determined by time-resolved hemodynamic and metabolic variations in blood volume, flow velocity, and oxygen consumption with a fluid mechanics treatment. Key parameters regarding microcirculation can be assessed, including the effective blood transit times through the capillaries and the venules, and the rate constant of oxygen release from hemoglobin to tissue. The vascular autoregulation can further be quantified from the relationship between the resolved blood volume and flow velocity variations. The PIPE model shows excellent agreement with the experimental cerebral and cutaneous coherent hemodynamics spectroscopy (CHS) and fMRI-BOLD data. It further identifies the impaired cerebral autoregulation distinctively in hemodialysis patients compared to healthy subjects measured by CHS. This new dynamic microcirculation PIPE model provides a valuable tool for brain and other functional studies with hemodynamic-based techniques. It is instrumental in recovering physiological parameters from analyzing and interpreting the signals measured by hemodynamic-based neuroimaging and non-neuroimaging techniques such as functional near-infrared spectroscopy (fNIRS) and functional magnetic resonance imaging (fMRI) in response to brain activation, physiological challenges, or physical maneuvers.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  14. M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
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    [Crossref]
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    [Crossref]
  32. B. Klitzman and P. C. Johnson, “Capillary network geometry and red cell distribution in hamster cremaster muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 242(2), H211–H219 (1982).
    [Crossref]
  33. I. Kida, D. L. Rothman, and F. Hyder, “Dynamics of changes in blood flow, volume, and oxygenation: Implications for dynamic functional magnetic resonance imaging calibration,” J. Cereb. Blood Flow Metab. 27(4), 690–696 (2007).
    [Crossref]
  34. F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
    [Crossref]
  35. A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
    [Crossref]
  36. W. Lin, B. Zeng, Z. Cao, X. Chen, and M. Xu, “Quantitative diagnosis of tissue microstructure with wide-field high spatial frequency domain imaging,” Biomed. Opt. Express 9(7), 2905–2916 (2018).
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2019 (1)

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “Dynamic measurements of absolute cerebral blood flow with coherent hemodynamics spectroscopy,” Proc. SPIE 10874, 49 (2019).
[Crossref]

2018 (1)

2017 (3)

2016 (3)

M. Xu, Z. Cao, W. Lin, X. Chen, L. Zheng, and B. Zeng, “Single snapshot multiple frequency modulated imaging of subsurface optical properties of turbid media with structured light,” AIP Adv. 6(12), 125208 (2016).
[Crossref]

C. Francis, L. Frederic, F. Céline, P. Steffen, and L. C. Valerie, “A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex,” Microcirculation 13(1), 1–18 (2016).
[Crossref]

M. Xu, “Diagnosis of the phase function of random media from light reflectance,” Sci. Rep. 6(1), 22535 (2016).
[Crossref]

2015 (2)

J. M. Kainerstorfer, A. Sassaroli, K. T. Tgavalekos, and S. Fantini, “Dynamic cerebral autoregulation measured with coherent hemodynamics spectroscopy (CHS),” Proc. SPIE 9319, 931901 (2015).
[Crossref]

M. Reilly and M. Xu, “Analytical model for sub-diffusive light reflection and the application to spatial frequency-domain imaging,” Proc. SPIE 9319, 93191A (2015).
[Crossref]

2014 (3)

S. Fantini, “Dynamic model for the tissue concentration and oxygen saturation of hemoglobin in relation to blood volume, flow velocity, and oxygen consumption: Implications for functional neuroimaging and coherent hemodynamics spectroscopy (CHS),” NeuroImage 85, 202–221 (2014).
[Crossref]

M. L. Pierro, B. Hallacoglu, A. Sassaroli, J. M. Kainerstorfer, and S. Fantini, “Validation of a novel hemodynamic model for coherent hemodynamics spectroscopy (CHS) and functional brain studies with fNIRS and fMRI,” NeuroImage 85, 222–233 (2014).
[Crossref]

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

2012 (1)

M. L. Pierro, A. Sassaroli, P. R. Bergethon, B. L. Ehrenberg, and S. Fantini, “Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects,” NeuroImage 63(3), 1571–1584 (2012).
[Crossref]

2011 (2)

A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
[Crossref]

F. N. van de Vosse and N. Stergiopulos, “Pulse wave propagation in the arterial tree,” Annu. Rev. Fluid Mech. 43(1), 467–499 (2011).
[Crossref]

2009 (2)

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

C. Jurgen A H R, L. Benjamin D, and Z. Rong, “Dynamic cerebral autoregulation during repeated squat-stand maneuvers,” J. Appl. Physiol. 106(1), 153–160 (2009).
[Crossref]

2008 (2)

M. Xu, “Low-coherence enhanced backscattering beyond diffusion,” Opt. Lett. 33(11), 1246–1248 (2008).
[Crossref]

A. H. E. A. Van Beek, J. A. H. R. Claassen, M. G. M. O. Rikkert, and R. W. M. M. Jansen, “Cerebral autoregulation: An overview of current concepts and methodology with special focus on the elderly,” J. Cereb. Blood Flow Metab. 28(6), 1071–1085 (2008).
[Crossref]

2007 (3)

I. Kida, D. L. Rothman, and F. Hyder, “Dynamics of changes in blood flow, volume, and oxygenation: Implications for dynamic functional magnetic resonance imaging calibration,” J. Cereb. Blood Flow Metab. 27(4), 690–696 (2007).
[Crossref]

A. Rune, B. Martin, S. Gill, M. Douville Colleen, and W. Newell David, “Asymmetric dynamic cerebral autoregulatory response to cyclic stimuli,” Stroke 38(5), 1465–1469 (2007).
[Crossref]

F. Michael D and R. Marcus E, “Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging,” Nat. Rev. Neurosci. 8(9), 700–711 (2007).
[Crossref]

2006 (1)

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

2003 (1)

M. Reinhard, T. Muller, B. Guschlbauer, J. Timmer, and A. Hetzel, “Transfer function analysis for clinical evaluation of dynamic cerebral autoregulation-a comparison between spontaneous and respiratory-induced oscillations,” Physiol. Meas. 24(1), 27–43 (2003).
[Crossref]

2001 (2)

L. Hughson R, R. Edwards M, D. O’Leary D, and K. Shoemaker J, “Critical analysis of cerebrovascular autoregulation during repeated head-up tilt,” Stroke 32(10), 2403–2408 (2001).
[Crossref]

F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
[Crossref]

2000 (1)

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
[Crossref]

1999 (1)

B. Mandeville, J. J. A. Marota, M. A. Moskowitz, R. Rosen, and M. Weisskoff, “Evidence of a cerebrovascular postarteriole Windkessel with delayed compliance,” J. Cereb. Blood Flow Metab. 19(6), 679–689 (1999).
[Crossref]

1998 (2)

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: The balloon model,” Magn. Reson. Med. 39(6), 855–864 (1998).
[Crossref]

R. R. Diehl, D. Linden, D. Lücke, and P. Berlit, “Spontaneous blood pressure oscillations and cerebral autoregulation,” Clin. Auton. Res. 8(1), 7–12 (1998).
[Crossref]

1997 (1)

M. Ursino and A. Lodi C, “A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics,” J. Appl. Physiol. 82(4), 1256–1269 (1997).
[Crossref]

1996 (1)

R. B. King, G. M. Raymond, and J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24(3), 352–372 (1996).
[Crossref]

1982 (1)

B. Klitzman and P. C. Johnson, “Capillary network geometry and red cell distribution in hamster cremaster muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 242(2), H211–H219 (1982).
[Crossref]

1977 (1)

C. R. Honig, M. L. Feldstein, and J. L. Frierson, “Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 233(1), H122–H129 (1977).
[Crossref]

1931 (1)

R. Fahraeus and T. Lindqvist, “The viscosity of the blood in narrow capillary tubes,” Am. J. Physiol. 96(3), 562–568 (1931).
[Crossref]

Akons, K.

Bassingthwaighte, J. B.

R. B. King, G. M. Raymond, and J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24(3), 352–372 (1996).
[Crossref]

Behar, K. L.

F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
[Crossref]

Benjamin D, L.

C. Jurgen A H R, L. Benjamin D, and Z. Rong, “Dynamic cerebral autoregulation during repeated squat-stand maneuvers,” J. Appl. Physiol. 106(1), 153–160 (2009).
[Crossref]

Bergethon, P. R.

M. L. Pierro, A. Sassaroli, P. R. Bergethon, B. L. Ehrenberg, and S. Fantini, “Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects,” NeuroImage 63(3), 1571–1584 (2012).
[Crossref]

A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
[Crossref]

Berlit, P.

R. R. Diehl, D. Linden, D. Lücke, and P. Berlit, “Spontaneous blood pressure oscillations and cerebral autoregulation,” Clin. Auton. Res. 8(1), 7–12 (1998).
[Crossref]

Blaney, G.

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “Dynamic measurements of absolute cerebral blood flow with coherent hemodynamics spectroscopy,” Proc. SPIE 10874, 49 (2019).
[Crossref]

Buxton, R. B.

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: The balloon model,” Magn. Reson. Med. 39(6), 855–864 (1998).
[Crossref]

Cao, Z.

W. Lin, B. Zeng, Z. Cao, X. Chen, and M. Xu, “Quantitative diagnosis of tissue microstructure with wide-field high spatial frequency domain imaging,” Biomed. Opt. Express 9(7), 2905–2916 (2018).
[Crossref]

M. Xu, Z. Cao, W. Lin, X. Chen, L. Zheng, and B. Zeng, “Single snapshot multiple frequency modulated imaging of subsurface optical properties of turbid media with structured light,” AIP Adv. 6(12), 125208 (2016).
[Crossref]

Céline, F.

C. Francis, L. Frederic, F. Céline, P. Steffen, and L. C. Valerie, “A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex,” Microcirculation 13(1), 1–18 (2016).
[Crossref]

Chen, S.

Chen, X.

Civiletto, A.

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

Claassen, J. A. H. R.

A. H. E. A. Van Beek, J. A. H. R. Claassen, M. G. M. O. Rikkert, and R. W. M. M. Jansen, “Cerebral autoregulation: An overview of current concepts and methodology with special focus on the elderly,” J. Cereb. Blood Flow Metab. 28(6), 1071–1085 (2008).
[Crossref]

Cohen, A. L.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

Culver, J. P.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

Dann, E. J.

de Voorde, J.

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
[Crossref]

De Vriese, A. S.

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
[Crossref]

Diehl, R. R.

R. R. Diehl, D. Linden, D. Lücke, and P. Berlit, “Spontaneous blood pressure oscillations and cerebral autoregulation,” Clin. Auton. Res. 8(1), 7–12 (1998).
[Crossref]

Douville Colleen, M.

A. Rune, B. Martin, S. Gill, M. Douville Colleen, and W. Newell David, “Asymmetric dynamic cerebral autoregulatory response to cyclic stimuli,” Stroke 38(5), 1465–1469 (2007).
[Crossref]

Edwards M, R.

L. Hughson R, R. Edwards M, D. O’Leary D, and K. Shoemaker J, “Critical analysis of cerebrovascular autoregulation during repeated head-up tilt,” Stroke 32(10), 2403–2408 (2001).
[Crossref]

Ehrenberg, B. L.

M. L. Pierro, A. Sassaroli, P. R. Bergethon, B. L. Ehrenberg, and S. Fantini, “Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects,” NeuroImage 63(3), 1571–1584 (2012).
[Crossref]

Fahraeus, R.

R. Fahraeus and T. Lindqvist, “The viscosity of the blood in narrow capillary tubes,” Am. J. Physiol. 96(3), 562–568 (1931).
[Crossref]

Fantini, S.

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “Dynamic measurements of absolute cerebral blood flow with coherent hemodynamics spectroscopy,” Proc. SPIE 10874, 49 (2019).
[Crossref]

J. M. Kainerstorfer, A. Sassaroli, K. T. Tgavalekos, and S. Fantini, “Dynamic cerebral autoregulation measured with coherent hemodynamics spectroscopy (CHS),” Proc. SPIE 9319, 931901 (2015).
[Crossref]

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

S. Fantini, “Dynamic model for the tissue concentration and oxygen saturation of hemoglobin in relation to blood volume, flow velocity, and oxygen consumption: Implications for functional neuroimaging and coherent hemodynamics spectroscopy (CHS),” NeuroImage 85, 202–221 (2014).
[Crossref]

M. L. Pierro, B. Hallacoglu, A. Sassaroli, J. M. Kainerstorfer, and S. Fantini, “Validation of a novel hemodynamic model for coherent hemodynamics spectroscopy (CHS) and functional brain studies with fNIRS and fMRI,” NeuroImage 85, 222–233 (2014).
[Crossref]

M. L. Pierro, A. Sassaroli, P. R. Bergethon, B. L. Ehrenberg, and S. Fantini, “Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects,” NeuroImage 63(3), 1571–1584 (2012).
[Crossref]

A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
[Crossref]

Feldstein, M. L.

C. R. Honig, M. L. Feldstein, and J. L. Frierson, “Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 233(1), H122–H129 (1977).
[Crossref]

Francis, C.

C. Francis, L. Frederic, F. Céline, P. Steffen, and L. C. Valerie, “A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex,” Microcirculation 13(1), 1–18 (2016).
[Crossref]

Frank, L. R.

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: The balloon model,” Magn. Reson. Med. 39(6), 855–864 (1998).
[Crossref]

Frederic, L.

C. Francis, L. Frederic, F. Céline, P. Steffen, and L. C. Valerie, “A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex,” Microcirculation 13(1), 1–18 (2016).
[Crossref]

Frierson, J. L.

C. R. Honig, M. L. Feldstein, and J. L. Frierson, “Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 233(1), H122–H129 (1977).
[Crossref]

Gill, S.

A. Rune, B. Martin, S. Gill, M. Douville Colleen, and W. Newell David, “Asymmetric dynamic cerebral autoregulatory response to cyclic stimuli,” Stroke 38(5), 1465–1469 (2007).
[Crossref]

Grabiak, D.

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
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M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

M. Reinhard, T. Muller, B. Guschlbauer, J. Timmer, and A. Hetzel, “Transfer function analysis for clinical evaluation of dynamic cerebral autoregulation-a comparison between spontaneous and respiratory-induced oscillations,” Physiol. Meas. 24(1), 27–43 (2003).
[Crossref]

Hallacoglu, B.

M. L. Pierro, B. Hallacoglu, A. Sassaroli, J. M. Kainerstorfer, and S. Fantini, “Validation of a novel hemodynamic model for coherent hemodynamics spectroscopy (CHS) and functional brain studies with fNIRS and fMRI,” NeuroImage 85, 222–233 (2014).
[Crossref]

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

Hetzel, A.

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

M. Reinhard, T. Muller, B. Guschlbauer, J. Timmer, and A. Hetzel, “Transfer function analysis for clinical evaluation of dynamic cerebral autoregulation-a comparison between spontaneous and respiratory-induced oscillations,” Physiol. Meas. 24(1), 27–43 (2003).
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C. R. Honig, M. L. Feldstein, and J. L. Frierson, “Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 233(1), H122–H129 (1977).
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Hughson R, L.

L. Hughson R, R. Edwards M, D. O’Leary D, and K. Shoemaker J, “Critical analysis of cerebrovascular autoregulation during repeated head-up tilt,” Stroke 32(10), 2403–2408 (2001).
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Hyder, F.

I. Kida, D. L. Rothman, and F. Hyder, “Dynamics of changes in blood flow, volume, and oxygenation: Implications for dynamic functional magnetic resonance imaging calibration,” J. Cereb. Blood Flow Metab. 27(4), 690–696 (2007).
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F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
[Crossref]

Jansen, R. W. M. M.

A. H. E. A. Van Beek, J. A. H. R. Claassen, M. G. M. O. Rikkert, and R. W. M. M. Jansen, “Cerebral autoregulation: An overview of current concepts and methodology with special focus on the elderly,” J. Cereb. Blood Flow Metab. 28(6), 1071–1085 (2008).
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B. Klitzman and P. C. Johnson, “Capillary network geometry and red cell distribution in hamster cremaster muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 242(2), H211–H219 (1982).
[Crossref]

Jurgen A H R, C.

C. Jurgen A H R, L. Benjamin D, and Z. Rong, “Dynamic cerebral autoregulation during repeated squat-stand maneuvers,” J. Appl. Physiol. 106(1), 153–160 (2009).
[Crossref]

Kainerstorfer, J. M.

J. M. Kainerstorfer, A. Sassaroli, K. T. Tgavalekos, and S. Fantini, “Dynamic cerebral autoregulation measured with coherent hemodynamics spectroscopy (CHS),” Proc. SPIE 9319, 931901 (2015).
[Crossref]

M. L. Pierro, B. Hallacoglu, A. Sassaroli, J. M. Kainerstorfer, and S. Fantini, “Validation of a novel hemodynamic model for coherent hemodynamics spectroscopy (CHS) and functional brain studies with fNIRS and fMRI,” NeuroImage 85, 222–233 (2014).
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M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
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F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
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I. Kida, D. L. Rothman, and F. Hyder, “Dynamics of changes in blood flow, volume, and oxygenation: Implications for dynamic functional magnetic resonance imaging calibration,” J. Cereb. Blood Flow Metab. 27(4), 690–696 (2007).
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F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
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R. B. King, G. M. Raymond, and J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24(3), 352–372 (1996).
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B. Klitzman and P. C. Johnson, “Capillary network geometry and red cell distribution in hamster cremaster muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 242(2), H211–H219 (1982).
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Lameire, N. H.

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
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Lin, W.

Linden, D.

R. R. Diehl, D. Linden, D. Lücke, and P. Berlit, “Spontaneous blood pressure oscillations and cerebral autoregulation,” Clin. Auton. Res. 8(1), 7–12 (1998).
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R. Fahraeus and T. Lindqvist, “The viscosity of the blood in narrow capillary tubes,” Am. J. Physiol. 96(3), 562–568 (1931).
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M. Ursino and A. Lodi C, “A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics,” J. Appl. Physiol. 82(4), 1256–1269 (1997).
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R. R. Diehl, D. Linden, D. Lücke, and P. Berlit, “Spontaneous blood pressure oscillations and cerebral autoregulation,” Clin. Auton. Res. 8(1), 7–12 (1998).
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F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
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A. Rune, B. Martin, S. Gill, M. Douville Colleen, and W. Newell David, “Asymmetric dynamic cerebral autoregulatory response to cyclic stimuli,” Stroke 38(5), 1465–1469 (2007).
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Michael D, F.

F. Michael D and R. Marcus E, “Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging,” Nat. Rev. Neurosci. 8(9), 700–711 (2007).
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B. Mandeville, J. J. A. Marota, M. A. Moskowitz, R. Rosen, and M. Weisskoff, “Evidence of a cerebrovascular postarteriole Windkessel with delayed compliance,” J. Cereb. Blood Flow Metab. 19(6), 679–689 (1999).
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M. Reinhard, T. Muller, B. Guschlbauer, J. Timmer, and A. Hetzel, “Transfer function analysis for clinical evaluation of dynamic cerebral autoregulation-a comparison between spontaneous and respiratory-induced oscillations,” Physiol. Meas. 24(1), 27–43 (2003).
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A. Rune, B. Martin, S. Gill, M. Douville Colleen, and W. Newell David, “Asymmetric dynamic cerebral autoregulatory response to cyclic stimuli,” Stroke 38(5), 1465–1469 (2007).
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L. Hughson R, R. Edwards M, D. O’Leary D, and K. Shoemaker J, “Critical analysis of cerebrovascular autoregulation during repeated head-up tilt,” Stroke 32(10), 2403–2408 (2001).
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B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
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T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “Dynamic measurements of absolute cerebral blood flow with coherent hemodynamics spectroscopy,” Proc. SPIE 10874, 49 (2019).
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A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
[Crossref]

Pierro, M. L.

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

M. L. Pierro, B. Hallacoglu, A. Sassaroli, J. M. Kainerstorfer, and S. Fantini, “Validation of a novel hemodynamic model for coherent hemodynamics spectroscopy (CHS) and functional brain studies with fNIRS and fMRI,” NeuroImage 85, 222–233 (2014).
[Crossref]

M. L. Pierro, A. Sassaroli, P. R. Bergethon, B. L. Ehrenberg, and S. Fantini, “Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects,” NeuroImage 63(3), 1571–1584 (2012).
[Crossref]

Raichle, M. E.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
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R. B. King, G. M. Raymond, and J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24(3), 352–372 (1996).
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M. Reilly and M. Xu, “Analytical model for sub-diffusive light reflection and the application to spatial frequency-domain imaging,” Proc. SPIE 9319, 93191A (2015).
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M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

M. Reinhard, T. Muller, B. Guschlbauer, J. Timmer, and A. Hetzel, “Transfer function analysis for clinical evaluation of dynamic cerebral autoregulation-a comparison between spontaneous and respiratory-induced oscillations,” Physiol. Meas. 24(1), 27–43 (2003).
[Crossref]

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A. H. E. A. Van Beek, J. A. H. R. Claassen, M. G. M. O. Rikkert, and R. W. M. M. Jansen, “Cerebral autoregulation: An overview of current concepts and methodology with special focus on the elderly,” J. Cereb. Blood Flow Metab. 28(6), 1071–1085 (2008).
[Crossref]

Rong, Z.

C. Jurgen A H R, L. Benjamin D, and Z. Rong, “Dynamic cerebral autoregulation during repeated squat-stand maneuvers,” J. Appl. Physiol. 106(1), 153–160 (2009).
[Crossref]

Rosen, R.

B. Mandeville, J. J. A. Marota, M. A. Moskowitz, R. Rosen, and M. Weisskoff, “Evidence of a cerebrovascular postarteriole Windkessel with delayed compliance,” J. Cereb. Blood Flow Metab. 19(6), 679–689 (1999).
[Crossref]

Roth, M.

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
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I. Kida, D. L. Rothman, and F. Hyder, “Dynamics of changes in blood flow, volume, and oxygenation: Implications for dynamic functional magnetic resonance imaging calibration,” J. Cereb. Blood Flow Metab. 27(4), 690–696 (2007).
[Crossref]

F. Hyder, I. Kida, K. L. Behar, R. P. Kennan, P. K. Maciejewski, and D. L. Rothman, “Quantitative functional imaging of the brain: Towards mapping neuronal activity by BOLD fMRI,” NMR Biomed. 14(7-8), 413–431 (2001).
[Crossref]

Rune, A.

A. Rune, B. Martin, S. Gill, M. Douville Colleen, and W. Newell David, “Asymmetric dynamic cerebral autoregulatory response to cyclic stimuli,” Stroke 38(5), 1465–1469 (2007).
[Crossref]

Sassaroli, A.

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “Dynamic measurements of absolute cerebral blood flow with coherent hemodynamics spectroscopy,” Proc. SPIE 10874, 49 (2019).
[Crossref]

J. M. Kainerstorfer, A. Sassaroli, K. T. Tgavalekos, and S. Fantini, “Dynamic cerebral autoregulation measured with coherent hemodynamics spectroscopy (CHS),” Proc. SPIE 9319, 931901 (2015).
[Crossref]

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

M. L. Pierro, B. Hallacoglu, A. Sassaroli, J. M. Kainerstorfer, and S. Fantini, “Validation of a novel hemodynamic model for coherent hemodynamics spectroscopy (CHS) and functional brain studies with fNIRS and fMRI,” NeuroImage 85, 222–233 (2014).
[Crossref]

M. L. Pierro, A. Sassaroli, P. R. Bergethon, B. L. Ehrenberg, and S. Fantini, “Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects,” NeuroImage 63(3), 1571–1584 (2012).
[Crossref]

A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
[Crossref]

Schlaggar, B. L.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

Sheng, J.

Shoemaker J, K.

L. Hughson R, R. Edwards M, D. O’Leary D, and K. Shoemaker J, “Critical analysis of cerebrovascular autoregulation during repeated head-up tilt,” Stroke 32(10), 2403–2408 (2001).
[Crossref]

Snyder, A. Z.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
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F. N. van de Vosse and N. Stergiopulos, “Pulse wave propagation in the arterial tree,” Annu. Rev. Fluid Mech. 43(1), 467–499 (2011).
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J. M. Kainerstorfer, A. Sassaroli, K. T. Tgavalekos, and S. Fantini, “Dynamic cerebral autoregulation measured with coherent hemodynamics spectroscopy (CHS),” Proc. SPIE 9319, 931901 (2015).
[Crossref]

Timmer, J.

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

M. Reinhard, T. Muller, B. Guschlbauer, J. Timmer, and A. Hetzel, “Transfer function analysis for clinical evaluation of dynamic cerebral autoregulation-a comparison between spontaneous and respiratory-induced oscillations,” Physiol. Meas. 24(1), 27–43 (2003).
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M. Ursino and A. Lodi C, “A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics,” J. Appl. Physiol. 82(4), 1256–1269 (1997).
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Valerie, L. C.

C. Francis, L. Frederic, F. Céline, P. Steffen, and L. C. Valerie, “A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex,” Microcirculation 13(1), 1–18 (2016).
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A. H. E. A. Van Beek, J. A. H. R. Claassen, M. G. M. O. Rikkert, and R. W. M. M. Jansen, “Cerebral autoregulation: An overview of current concepts and methodology with special focus on the elderly,” J. Cereb. Blood Flow Metab. 28(6), 1071–1085 (2008).
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F. N. van de Vosse and N. Stergiopulos, “Pulse wave propagation in the arterial tree,” Annu. Rev. Fluid Mech. 43(1), 467–499 (2011).
[Crossref]

Vanhoutte, P. M.

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
[Crossref]

Verbeuren, T. J.

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
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Wang, C.

Wehrle-Wieland, E.

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

Weiller, C.

M. Reinhard, E. Wehrle-Wieland, D. Grabiak, M. Roth, B. Guschlbauer, J. Timmer, C. Weiller, and A. Hetzel, “Oscillatory cerebral hemodynamics—the macro- vs. microvascular level,” J. Neurol. Sci. 250(1-2), 103–109 (2006).
[Crossref]

Weiner, D. E.

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
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Weisskoff, M.

B. Mandeville, J. J. A. Marota, M. A. Moskowitz, R. Rosen, and M. Weisskoff, “Evidence of a cerebrovascular postarteriole Windkessel with delayed compliance,” J. Cereb. Blood Flow Metab. 19(6), 679–689 (1999).
[Crossref]

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B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
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Xu, M.

Yelin, D.

Zeng, B.

Zheng, F.

A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
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Zheng, L.

M. Xu, Z. Cao, W. Lin, X. Chen, L. Zheng, and B. Zeng, “Single snapshot multiple frequency modulated imaging of subsurface optical properties of turbid media with structured light,” AIP Adv. 6(12), 125208 (2016).
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AIP Adv. (1)

M. Xu, Z. Cao, W. Lin, X. Chen, L. Zheng, and B. Zeng, “Single snapshot multiple frequency modulated imaging of subsurface optical properties of turbid media with structured light,” AIP Adv. 6(12), 125208 (2016).
[Crossref]

Am. J. Physiol. (1)

R. Fahraeus and T. Lindqvist, “The viscosity of the blood in narrow capillary tubes,” Am. J. Physiol. 96(3), 562–568 (1931).
[Crossref]

Am. J. Physiol. - Hear. Circ. Physiol. (2)

C. R. Honig, M. L. Feldstein, and J. L. Frierson, “Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 233(1), H122–H129 (1977).
[Crossref]

B. Klitzman and P. C. Johnson, “Capillary network geometry and red cell distribution in hamster cremaster muscle,” Am. J. Physiol. - Hear. Circ. Physiol. 242(2), H211–H219 (1982).
[Crossref]

Ann. Biomed. Eng. (1)

R. B. King, G. M. Raymond, and J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24(3), 352–372 (1996).
[Crossref]

Annu. Rev. Fluid Mech. (1)

F. N. van de Vosse and N. Stergiopulos, “Pulse wave propagation in the arterial tree,” Annu. Rev. Fluid Mech. 43(1), 467–499 (2011).
[Crossref]

Biomed. Opt. Express (4)

Br. J. Pharmacol. (1)

A. S. De Vriese, T. J. Verbeuren, J. de Voorde, N. H. Lameire, and P. M. Vanhoutte, “Endothelial dysfunction in diabetes,” Br. J. Pharmacol. 130(5), 963–974 (2000).
[Crossref]

Clin. Auton. Res. (1)

R. R. Diehl, D. Linden, D. Lücke, and P. Berlit, “Spontaneous blood pressure oscillations and cerebral autoregulation,” Clin. Auton. Res. 8(1), 7–12 (1998).
[Crossref]

J. Appl. Physiol. (2)

C. Jurgen A H R, L. Benjamin D, and Z. Rong, “Dynamic cerebral autoregulation during repeated squat-stand maneuvers,” J. Appl. Physiol. 106(1), 153–160 (2009).
[Crossref]

M. Ursino and A. Lodi C, “A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics,” J. Appl. Physiol. 82(4), 1256–1269 (1997).
[Crossref]

J. Biomed. Opt. (1)

M. L. Pierro, J. M. Kainerstorfer, A. Civiletto, D. E. Weiner, A. Sassaroli, B. Hallacoglu, and S. Fantini, “Reduced speed of microvascular blood flow in hemodialysis patients versus healthy controls: a coherent hemodynamics spectroscopy study,” J. Biomed. Opt. 19(2), 026005 (2014).
[Crossref]

J. Cereb. Blood Flow Metab. (3)

B. Mandeville, J. J. A. Marota, M. A. Moskowitz, R. Rosen, and M. Weisskoff, “Evidence of a cerebrovascular postarteriole Windkessel with delayed compliance,” J. Cereb. Blood Flow Metab. 19(6), 679–689 (1999).
[Crossref]

A. H. E. A. Van Beek, J. A. H. R. Claassen, M. G. M. O. Rikkert, and R. W. M. M. Jansen, “Cerebral autoregulation: An overview of current concepts and methodology with special focus on the elderly,” J. Cereb. Blood Flow Metab. 28(6), 1071–1085 (2008).
[Crossref]

I. Kida, D. L. Rothman, and F. Hyder, “Dynamics of changes in blood flow, volume, and oxygenation: Implications for dynamic functional magnetic resonance imaging calibration,” J. Cereb. Blood Flow Metab. 27(4), 690–696 (2007).
[Crossref]

J. Innov. Opt. Health Sci. (1)

A. Sassaroli, F. Zheng, M. Pierro, P. R. Bergethon, and S. Fantini, “Phase difference between low-frequency oscillations of cerebral deoxy- and oxyhemoglobin concentrations during a mental task,” J. Innov. Opt. Health Sci. 04(02), 151–158 (2011).
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Figures (16)

Fig. 1.
Fig. 1. The schematic diagram for the hemodynamics PIPE model.
Fig. 2.
Fig. 2. Coherent hemodynamics spectra (CHS) measured on the forehead of five hemodialysis patients (Subjects 1 to 5 from top to bottom) fitted by the PIPE model (blue lines) and the Fantini model (red lines).
Fig. 3.
Fig. 3. Coherent hemodynamics spectra (CHS) measured on the forehead of six healthy subjects (Subjects 6 to 11 from top to bottom) fitted by the PIPE model (blue lines) and the Fantini model (red lines).
Fig. 4.
Fig. 4. Flow chart of the procedure for cutaneous coherent hemodynamics spectroscopy.
Fig. 5.
Fig. 5. Hemodynamic characteristics (tc: capillary blood transit time, tv: venous blood transit time, $\omega_c^{(autoReg)}/2\pi$: autoregulation cutoff frequency) for the five hemodialysis patients (subjects 1-5) and the six healthy subjects (subjects 6-11) fitted by the PIPE model (the blue lines and the blue diamond points) and the Fantini model (the red lines and the red square points). Horizontal lines represent the respective average values.
Fig. 6.
Fig. 6. The blood volume oscillation from the Fantini model (top row) and the PIPE model (bottom row). ΔCBV(v) is the cerebral blood oscillation phasor defined in the Fantini model. Ov, Dv, and Tv represent oxy-, deoxy-, and total hemoglobin volume oscillation phasors, respectively. Red arrows represent healthy subjects and blue arrows represent hemodialysis patients.
Fig. 7.
Fig. 7. The blood flow velocity oscillation for the Fantini model (top row) and the PIPE model (bottom row). OF, DF and TF represent oxy-, deoxy- and total hemoglobin flow oscillations, respectively. Red arrows represent healthy subjects and blue arrows represent hemodialysis patients.
Fig. 8.
Fig. 8. Cerebral autoregulation OF/OV and TF/TV from the Fantini model (top row) and the PIPE model (bottom row). The ratio TF/TV reduces to zero in the Fantini model (the top right panel). Red arrows represent healthy subjects and blue arrows represent hemodialysis patients.
Fig. 9.
Fig. 9. Cutaneous hemodynamic characteristics (tc: capillary blood transit time, tv: venous blood transit time, $\omega_c^{(autoReg)}/2\pi$: autoregulation cutoff frequency) for four healthy subjects fitted by the PIPE model (the blue lines and the blue diamond points) and the Fantini model (the red lines and the red square points). Horizontal lines represent the respective average values.
Fig. 10.
Fig. 10. The cutaneous blood volume oscillation from the Fantini model (top row) and the PIPE model (bottom row). OV, DV, and TV represent oxy-, deoxy-, and total hemoglobin volume oscillations, respectively.
Fig. 11.
Fig. 11. The cutaneous blood flow velocity oscillation for the Fantini model (top row) and the PIPE model (bottom row). OF, DF and TF represent oxy-, deoxy- and total hemoglobin flow oscillations, respectively.
Fig. 12.
Fig. 12. Cutaneous autoregulation OF/OV and TF/TV from the Fantini model (top row) and the PIPE model (bottom row). OF/OV and TF/TV reflect the subject's opisthenar autoregulation.
Fig. 13.
Fig. 13. BOLD fMRI study on rats. Left: 4s forepaw stimulation; Right: 16s forepaw stimulation. The top three panels are the relative changes in cerebral blood flow (ΔCBF/CBF), the metabolic rate of oxygen (ΔCMRO2/CMRO2), and cerebral blood volume (ΔCBV/CBV) derived from the data reported by Kida et al. [33] as described in the text. The bottom panel shows the BOLD fMRI signal measured by Kida et al. [33] using fMRI (solid line), and those predicted by the PIPE model (short dash lines) and the Fantini model (long dash lines).
Fig. 14.
Fig. 14. Mean capillary oxygen saturation in (a) brain and (b)opisthenar by the PIPE model (the blue lines and the blue diamond points) and the Fantini model (the red lines and the red square points).
Fig. 15.
Fig. 15. The baseline oxygen extraction efficiency E/T0 in (a) brain (the blue diamond points) and (b) opisthenar (the red square points) from the PIPE model.
Fig. 16.
Fig. 16. The oxygen extraction efficiency enhancement δE/T0 in (a) brain (the blue diamond points) and (b) opisthenar (the red square points) from the PIPE model.

Tables (5)

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Table 1. Expressions for Oxy-, Deoxy-, and Total Hemoglobin Volume and Velocity Oscillation Phasors. Here the Auto-regulation Factor v 1 exp ( i θ ) / v 0 is Specified by υ R ( ω ) = υ / ( 1 + i ω c / ω ) and β is Given by ω / ( 1 + ω / 2 π f h e a r t ) . The Rules of (28-30) Should be Applied to Account for the Capillary and Venule Transit Time Distributions. The Temporal Dependence on the Angular Frequency ω Takes the Form of exp(-iωt).

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Table 2. Average Capillary Blood Transit Time, Venous Blood Transit Time, and Autoregulation Cutoff Frequency and Their p-Values from t-Tests Comparing Hemodialysis Patients and Healthy Subjects.

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Table 3. Cerebral Autoregulation of Hemodialysis Patients vs Healthy Subjects.

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Table 4. |OF|/|OV| and |TF|/|TV| in Brain and Opisthenar for Healthy Subjects

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Table 5. tc, tv, ScO2 of Hemodialysis Patients

Equations (35)

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Q y + O t = α O ( y , t ) , 0 y L c
Q y + O t = 0 , L c y L c + L v .
O 0 ( y , t ) = S 0 f ( t y v 0 ) exp ( α y v 0 ) , 0 y L c = S 0 f ( t y v 0 ) exp ( α t c ) , L c y L c + L v ,
T ( y , t ) = f ( t y v 0 ) , 0 y L c + L v
δ O y v 0 + δ O t + α δ O = ( O 0 δ v ) y O 0 δ α , 0 y L c
δ O y v 0 + δ O t = ( O 0 δ v ) y , L c y L c + L v
δ O ( y , t ) = v 0 1 exp ( α v 0 y ) 0 y exp ( α v 0 ξ ) a ( ξ , t y ξ v 0 ) d ξ , 0 y L c = δ O ( L c , t y L c v 0 ) v 0 1 L c y b ( ξ , t y ξ v 0 ) d ξ , L c y L c + L v
a ( y , t ) ( O 0 δ v ) y + O 0 δ α
b ( y , t ) ( O 0 δ v ) y
O 0 ( t ) = S 0 ϕ ( a ) f ( t ) + S 0 ϕ ( c ) t c 0 t c f ( t τ ) exp ( α τ ) d τ + S 0 ϕ ( v ) t v exp ( α t c ) t c t c + t v f ( t τ ) d τ
δ O ( t ) = δ O δ v ( t ) + δ O δ α ( t )
δ O δ v ( t ) = S 0 ϕ ( c ) v 0 t c 0 t c d τ [ exp ( α t c ) f ( t t c ) δ v ( v 0 t c v 0 τ , t τ ) exp ( α τ ) f ( t τ ) δ v ( 0 , t τ ) ] + S 0 ϕ ( v ) v 0 t v exp ( α t c ) [ 0 t c d τ f ( t t c ) δ v ( v 0 t c v 0 τ , t τ ) + t c t c + t v d τ f ( t τ ) δ v ( 0 , t τ ) ] S 0 ϕ ( v ) v 0 t v exp ( α t c ) [ 0 t v exp ( α ( t v τ ) ) + t v t c  +  t v ] f ( t t c t v ) δ v ( v 0 t c + v 0 t v v 0 τ , t τ ) d τ + S 0 ϕ ( v ) v 0 t v α exp ( α t c ) t c t c + t v d τ f ( t τ ) 0 t c δ v ( v 0 τ , t τ + τ ) d τ
δ O δ α ( t ) = S 0 ϕ ( c ) t c 0 t c d τ exp ( α τ ) f ( t τ ) 0 τ d τ δ α ( v 0 τ , t τ + τ ) S 0 ϕ ( v ) t v exp ( α t c ) t c t c + t v d τ f ( t τ ) 0 t c d τ δ α ( v 0 τ , t τ + τ )
T ( t ) = ϕ ( a ) f ( t ) + ϕ ( c ) t c 0 t c f ( t τ ) d τ + ϕ ( v ) t v t c t c + t v f ( t τ ) d τ
δ T ( t ) = ϕ ( c ) v 0 t c 0 t c d τ [ f ( t t c ) δ v ( v 0 t c v 0 τ , t τ ) f ( t τ ) δ v ( 0 , t τ ) ] + ϕ ( v ) v 0 t v [ 0 t c d τ f ( t t c ) δ v ( v 0 t c v 0 τ , t τ ) + t c t c + t v d τ f ( t τ ) δ v ( 0 , t τ ) ] ϕ ( v ) v 0 t v 0 t c + t v f ( t t c t v ) δ v ( v 0 t c + v 0 t v v 0 τ , t τ ) d τ
O 0 ( y , t ) = S 0 T 0 exp ( α v 0 y ) + S 0 T 1 exp ( α v 0 y ) exp ( i ω t + i ω v 0 y ) , 0 y L c = S 0 T 0 exp ( α t c ) + S 0 T 1 exp ( α t c ) exp ( i ω t + i ω v 0 y ) , L c y L c + L v
T ( y , t ) = T 0 + T 1 exp ( i ω t + i ω v 0 y ) , 0 y L c + L v
δ O ( y , t ) = S 0 T 0 v 1 v 0 ( α v 0 i k ) exp [ α v 0 y i ω ( t y v 0 ) + i θ ] exp [ ( i k i ω v 0 ) y ] 1 i k i ω v 0 + 1 2 S 0 T 1 v 1 v 0 ( α i ω v 0 i k ) exp [ α v 0 y i 2 ω ( t y v 0 ) + i θ ] exp [ ( i k i ω v 0 ) y ] 1 i k i ω v 0 1 2 S 0 T 1 v 1 v 0 ( i k + α i ω v 0 ) exp ( α v 0 y i θ ) exp [ ( i k i ω v 0 ) y ] 1 i k i ω v 0 .
δ O ( y , t ) = δ O ( L c , t y L c v 0 ) S 0 T 0 v 1 v 0 k k ω v 0 exp [ i ω ( t y v 0 ) + i θ α t c + ( i k i ω v 0 ) L c ] { exp [ ( i k i ω v 0 ) ( y L c ) ] 1 } 1 2 S 0 T 1 v 1 v 0 k + ω v 0 k ω v 0 exp [ i 2 ω ( t y v 0 ) + i θ α t c + ( i k i ω v 0 ) L c ] { exp [ ( i k i ω v 0 ) ( y L c ) ] 1 } 1 2 S 0 T 1 v 1 v 0 exp [ i θ α t c ( i k i ω v 0 ) L c ] { exp [ ( i k i ω v 0 ) ( y L c ) ] 1 } .
E = α S 0 T 0 1 exp ( α t c ) α t c
δ E = t c 1 1 2 S 0 T 1 v 1 v 0 exp ( i θ ) [ 1 exp ( α t c ) + i α k v 0 ω ( 1 exp ( i ( k v 0 ω ) t c ) ) exp ( α t c ) ]
δ O ( y , t ) = S 0 T 0 v 1 v 0 β + i α β ω exp [ i ω t + i θ ] { exp [ ( α i β ) y v 0 ] exp [ ( α i ω ) y v 0 ] } , 0 y L c = S 0 T 0 v 1 v 0 β + i α β ω exp [ i ω t + i θ α t c + i ω y v 0 ] { exp [ i ( β ω ) t c ] 1 } S 0 T 0 v 1 v 0 β β ω exp [ i ω t + i θ α t c + i β t c ] { exp [ i β y v 0 i β t c ] exp [ i ω y v 0 i ω t c ] } , L c y L c + L v
δ T ( y , t ) = T 0 v 1 v 0 β β ω exp [ i ω ( t y v 0 ) + i θ ] { exp [ i ( β ω ) y v 0 ] 1 } , 0 y L c = T 0 v 1 v 0 β β ω exp [ i ω ( t y v 0 ) + i θ ] { exp [ i ( β ω ) t c ] 1 } T 0 v 1 v 0 β β ω exp [ i ω ( t y v 0 ) + i θ ] { exp [ i ( β ω ) y v 0 ] exp [ i ( β ω ) t c ] } , L c y L c + L v
O 0 ( t ) = S 0 T 0 [ ϕ ( a ) + ϕ ( c ) exp ( α t c ) 1 α t c + ϕ ( v ) exp ( α t c ) ]  +  S 0 T 1 exp ( i ω t ) [ ϕ ( a ) + ϕ ( c ) exp ( α t c + i ω t c ) 1 α t c + i ω t c + ϕ ( v ) exp ( i ω t v ) 1 i ω t v exp ( α t c + i ω t c ) ]
T ( t ) = T 0 ( ϕ ( a ) + ϕ ( c ) + ϕ ( v ) ) + T 1 exp ( i ω t ) [ ϕ ( a ) + ϕ ( c ) exp ( i ω t c ) 1 i ω t c + ϕ ( v ) exp ( i ω t v ) 1 i ω t v exp ( i ω t c ) ] ,
δ O ( t ) = ϕ ( c ) S 0 T 0 v 1 v 0 β + i α β ω exp [ i ω t + i θ ] { exp [ ( i β α ) t c ] 1 ( i β α ) t c exp [ ( i ω α ) t c ] 1 ( i ω α ) t c } ϕ ( v ) S 0 T 0 v 1 v 0 β + i α β ω exp [ i ω t + i θ α t c ] exp ( i ω t v ) 1 i ω t v [ exp ( i β t c ) exp ( i ω t c ) ] ϕ ( v ) S 0 T 0 v 1 v 0 β β ω exp [ i ω t + i θ α t c + i β t c ] { exp ( i β t v ) 1 i β t v exp ( i ω t v ) 1 i ω t v } ,
δ T ( t ) = ϕ ( c ) T 0 v 1 v 0 β β ω exp [ i ω t + i θ ] { exp ( i β t c ) 1 i β t c exp ( i ω t c ) 1 i ω t c } ϕ ( v ) T 0 v 1 v 0 β β ω exp [ i ω t + i θ ] { exp ( i β t c ) exp ( i β t v ) 1 i β t v exp ( i ω t c ) exp ( i ω t v ) 1 i ω t v } .
exp ( β t ) = ( a a + β μ ) a
exp ( β t ) β t = β μ ( a a + β μ ) a + 1
exp ( β t ) 1 β t = a ( a + 1 ) β μ [ ( a a + β μ ) a 1 1 ] .
δ v ( t ) v 0 = k g 0 R ( τ ) δ T ( t τ ) T 0 d τ
R ( t ) = 1 τ c exp ( t / τ c ) + δ ( t )
R ( ω ) = 1 1 + i ω c / ω
error = 1 3 n i = 1 n ( | OT i o t i | 2 | o t | ¯ 2 + | DT i d t i | 2 | d t | ¯ 2 + | DO i d o i | 2 | d o | ¯ 2 )
error = i = 1 3 [ ( MT F AC ( λ i ) mt f AC ( λ i ) ) 2 + ( MT F DC ( λ i ) mt f DC ( λ i ) ) 2 ]