Abstract

Recent technological advancements in optical spectroscopy allow for the construction of hyperspectral (broadband) portable tissue oximeters. In a series of our recent papers we have shown that hyperspectral NIRS (hNIRS) has similar or better capabilities in the absolute tissue oximetry as frequency-domain NIRS, and that hNIRS is also very efficient in measuring temporal changes in tissue hemoglobin concentration and oxygenation. In this paper, we extend the application of hNIRS to the measurement of event-related hemodynamic and metabolic functional cerebral responses during simulated driving. In order to check if hNIRS can detect event-related changes in the brain, we measured the concentration changes of oxygenated (HbO2) and deoxygenated (HHb) hemoglobin and of the oxidized state of cytochrome c oxidase, on the right and left prefrontal cortices (PFC) simultaneously during simulated driving on sixteen healthy right-handed participants (aged between 22–32). We used our in-house hNIRS system based on a portable spectrometer with cooled CCD detector and a driving simulator with a fully functional steering wheel and foot pedals. Each participant performed different driving tasks and participants were distracted during some driving conditions by asking general knowledge true/false questions. Our findings suggest that more complex driving tasks (non-distracted) deactivate PFC while distractions during driving significantly activate PFC, which is in agreement with previous fMRI results. Also, we found the changes in the redox state of the cytochrome C oxidase to be very consistent with those in the concentrations of HbO2 and HHb. Overall our findings suggest that in addition to the suitability of absolute tissue oximetry, hyperspectral NIRS may also offer advantages in functional brain imaging. In particular, it can be used to measure the metabolic functional brain activity during actual driving.

© 2016 Optical Society of America

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References

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2014 (4)

M. Diop, E. Wright, V. Toronov, T. Y. Lee, and K. St Lawrence, “Improved light collection and wavelet de-noising enable quantification of cerebral blood flow and oxygen metabolism by a low-cost, off-the-shelf spectrometer,” J. Biomed. Opt. 19(5), 057007 (2014).
[Crossref] [PubMed]

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

M. Mason, P. Nicholls, and C. Cooper, “Re-evaluation of the near infrared spectra of mitochondrial cytochrome c oxidase: Implications for non-invasive in vivo monitoring of tissues,” Biochimica Biophysica Acta 1837(11), 1882–1891 (2014).
[Crossref]

G. Bale, S. Mitra, J. Meek, N. Robertson, and I. Tachtsidis, “A new broadband near-infrared spectroscopy system for in-vivo measurements of cerebral cytochrome-c-oxidase changes in neonatal brain injury,” Biomed. Opt. Express 5(10), 3450–3466 (2014).
[Crossref] [PubMed]

2013 (2)

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

G. Derosière, K. Mandrick, G. Dray, T. E. Ward, and S. Perrey, “NIRS-measured prefrontal cortex activity in neuroergonomics: strengths and weaknesses,” Front. Hum. Neurosci. 7, 583–595 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (1)

M. Smith, “Shedding light on the adult brain: a review of the clinical applications of near-infrared spectroscopy,” Philos Trans A Math Phys Eng. Sci. 3694452–4469 (2011).

2010 (1)

2008 (1)

M. M. Tisdall, I. Tachtsidis, T. S. Leung, C. E. Elwell, and M. Smith, “Increase in cerebral aerobic metabolism by normobaric hyperoxia after traumatic brain injury,” J. Neurosurg. 109(3), 424–432 (2008).
[Crossref] [PubMed]

2006 (1)

M. Banaji, “A generic model of electron transport in mitochondria,” J. Theor. Biol. 243(4), 501–516 (2006).
[Crossref] [PubMed]

2001 (1)

E. K. Miller and J. D. Cohen, “An integrative theory of prefrontal cortex function,” Annu. Rev. Neurosci. 24(1), 167–202 (2001).
[Crossref] [PubMed]

1999 (1)

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

1997 (1)

J. W. Taanman, “Human cytochrome c oxidase: structure, function, and deficiency,” J. Bioenerg. Biomembr. 29(2), 151–163 (1997).
[Crossref] [PubMed]

1994 (1)

1977 (1)

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[Crossref] [PubMed]

Bale, G.

Banaji, M.

M. Banaji, “A generic model of electron transport in mitochondria,” J. Theor. Biol. 243(4), 501–516 (2006).
[Crossref] [PubMed]

Cohen, J. D.

E. K. Miller and J. D. Cohen, “An integrative theory of prefrontal cortex function,” Annu. Rev. Neurosci. 24(1), 167–202 (2001).
[Crossref] [PubMed]

Cooper, C.

M. Mason, P. Nicholls, and C. Cooper, “Re-evaluation of the near infrared spectra of mitochondrial cytochrome c oxidase: Implications for non-invasive in vivo monitoring of tissues,” Biochimica Biophysica Acta 1837(11), 1882–1891 (2014).
[Crossref]

Cooper, C. E.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

C. Kolyva, I. Tachtsidis, A. Ghosh, T. Moroz, C. E. Cooper, M. Smith, and C. E. Elwell, “Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults,” Biomed. Opt. Express 3(10), 2550–2566 (2012).
[Crossref] [PubMed]

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Derosière, G.

G. Derosière, K. Mandrick, G. Dray, T. E. Ward, and S. Perrey, “NIRS-measured prefrontal cortex activity in neuroergonomics: strengths and weaknesses,” Front. Hum. Neurosci. 7, 583–595 (2013).
[Crossref] [PubMed]

Diop, M.

M. Diop, E. Wright, V. Toronov, T. Y. Lee, and K. St Lawrence, “Improved light collection and wavelet de-noising enable quantification of cerebral blood flow and oxygen metabolism by a low-cost, off-the-shelf spectrometer,” J. Biomed. Opt. 19(5), 057007 (2014).
[Crossref] [PubMed]

H. Z. Yeganeh, V. Toronov, J. T. Elliott, M. Diop, T. Y. Lee, and K. St Lawrence, “Broadband continuous-wave technique to measure baseline values and changes in the tissue chromophore concentrations,” Biomed. Opt. Express 3(11), 2761–2770 (2012).
[Crossref] [PubMed]

Dirnagl, U.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Dray, G.

G. Derosière, K. Mandrick, G. Dray, T. E. Ward, and S. Perrey, “NIRS-measured prefrontal cortex activity in neuroergonomics: strengths and weaknesses,” Front. Hum. Neurosci. 7, 583–595 (2013).
[Crossref] [PubMed]

Elliott, J. T.

Elwell, C.

A. Ghosh, C. Elwell, and M. Smith, “Review Article: Cerebral Near-Infrared Spectroscopy in Adults: A Work in Progress,” Anesth. Analg. 115(6), 1373–1383 (2012).
[Crossref] [PubMed]

Elwell, C. E.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

C. Kolyva, I. Tachtsidis, A. Ghosh, T. Moroz, C. E. Cooper, M. Smith, and C. E. Elwell, “Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults,” Biomed. Opt. Express 3(10), 2550–2566 (2012).
[Crossref] [PubMed]

M. M. Tisdall, I. Tachtsidis, T. S. Leung, C. E. Elwell, and M. Smith, “Increase in cerebral aerobic metabolism by normobaric hyperoxia after traumatic brain injury,” J. Neurosurg. 109(3), 424–432 (2008).
[Crossref] [PubMed]

Fantini, S.

Franceschini, M.

Ghosh, A.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

A. Ghosh, C. Elwell, and M. Smith, “Review Article: Cerebral Near-Infrared Spectroscopy in Adults: A Work in Progress,” Anesth. Analg. 115(6), 1373–1383 (2012).
[Crossref] [PubMed]

C. Kolyva, I. Tachtsidis, A. Ghosh, T. Moroz, C. E. Cooper, M. Smith, and C. E. Elwell, “Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults,” Biomed. Opt. Express 3(10), 2550–2566 (2012).
[Crossref] [PubMed]

Graham, S. J.

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

Gratton, E.

Heekeren, H. R.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Highton, D.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

Hung, Y.

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

Jöbsis, F. F.

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[Crossref] [PubMed]

Kan, K.

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

Kato, T.

K. Yoshino and T. Kato, “Vector-based phase classification of initial dips during word listening using near-infrared spectroscopy,” Neuroreport 23(16), 947–951 (2012).
[Crossref] [PubMed]

Kohl, M.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Kolyva, C.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

C. Kolyva, I. Tachtsidis, A. Ghosh, T. Moroz, C. E. Cooper, M. Smith, and C. E. Elwell, “Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults,” Biomed. Opt. Express 3(10), 2550–2566 (2012).
[Crossref] [PubMed]

Lee, T. Y.

M. Diop, E. Wright, V. Toronov, T. Y. Lee, and K. St Lawrence, “Improved light collection and wavelet de-noising enable quantification of cerebral blood flow and oxygen metabolism by a low-cost, off-the-shelf spectrometer,” J. Biomed. Opt. 19(5), 057007 (2014).
[Crossref] [PubMed]

H. Z. Yeganeh, V. Toronov, J. T. Elliott, M. Diop, T. Y. Lee, and K. St Lawrence, “Broadband continuous-wave technique to measure baseline values and changes in the tissue chromophore concentrations,” Biomed. Opt. Express 3(11), 2761–2770 (2012).
[Crossref] [PubMed]

Leung, T. S.

M. M. Tisdall, I. Tachtsidis, T. S. Leung, C. E. Elwell, and M. Smith, “Increase in cerebral aerobic metabolism by normobaric hyperoxia after traumatic brain injury,” J. Neurosurg. 109(3), 424–432 (2008).
[Crossref] [PubMed]

Mandrick, K.

G. Derosière, K. Mandrick, G. Dray, T. E. Ward, and S. Perrey, “NIRS-measured prefrontal cortex activity in neuroergonomics: strengths and weaknesses,” Front. Hum. Neurosci. 7, 583–595 (2013).
[Crossref] [PubMed]

Mason, M.

M. Mason, P. Nicholls, and C. Cooper, “Re-evaluation of the near infrared spectra of mitochondrial cytochrome c oxidase: Implications for non-invasive in vivo monitoring of tissues,” Biochimica Biophysica Acta 1837(11), 1882–1891 (2014).
[Crossref]

Matcher, S. J.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Meek, J.

Miller, E. K.

E. K. Miller and J. D. Cohen, “An integrative theory of prefrontal cortex function,” Annu. Rev. Neurosci. 24(1), 167–202 (2001).
[Crossref] [PubMed]

Mitra, S.

Moroz, T.

Naglie, G.

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

Nicholls, P.

M. Mason, P. Nicholls, and C. Cooper, “Re-evaluation of the near infrared spectra of mitochondrial cytochrome c oxidase: Implications for non-invasive in vivo monitoring of tissues,” Biochimica Biophysica Acta 1837(11), 1882–1891 (2014).
[Crossref]

Obrig, H.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Perrey, S.

G. Derosière, K. Mandrick, G. Dray, T. E. Ward, and S. Perrey, “NIRS-measured prefrontal cortex activity in neuroergonomics: strengths and weaknesses,” Front. Hum. Neurosci. 7, 583–595 (2013).
[Crossref] [PubMed]

Pucci, O.

Robertson, N.

Schelkanova, I.

Schweizer, T. A.

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

Smith, M.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

C. Kolyva, I. Tachtsidis, A. Ghosh, T. Moroz, C. E. Cooper, M. Smith, and C. E. Elwell, “Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults,” Biomed. Opt. Express 3(10), 2550–2566 (2012).
[Crossref] [PubMed]

A. Ghosh, C. Elwell, and M. Smith, “Review Article: Cerebral Near-Infrared Spectroscopy in Adults: A Work in Progress,” Anesth. Analg. 115(6), 1373–1383 (2012).
[Crossref] [PubMed]

M. Smith, “Shedding light on the adult brain: a review of the clinical applications of near-infrared spectroscopy,” Philos Trans A Math Phys Eng. Sci. 3694452–4469 (2011).

M. M. Tisdall, I. Tachtsidis, T. S. Leung, C. E. Elwell, and M. Smith, “Increase in cerebral aerobic metabolism by normobaric hyperoxia after traumatic brain injury,” J. Neurosurg. 109(3), 424–432 (2008).
[Crossref] [PubMed]

St Lawrence, K.

Taanman, J. W.

J. W. Taanman, “Human cytochrome c oxidase: structure, function, and deficiency,” J. Bioenerg. Biomembr. 29(2), 151–163 (1997).
[Crossref] [PubMed]

Tachtsidis, I.

C. Kolyva, A. Ghosh, I. Tachtsidis, D. Highton, C. E. Cooper, M. Smith, and C. E. Elwell, “Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin,” Neuroimage 85(Pt 1), 234–244 (2014).
[Crossref] [PubMed]

G. Bale, S. Mitra, J. Meek, N. Robertson, and I. Tachtsidis, “A new broadband near-infrared spectroscopy system for in-vivo measurements of cerebral cytochrome-c-oxidase changes in neonatal brain injury,” Biomed. Opt. Express 5(10), 3450–3466 (2014).
[Crossref] [PubMed]

C. Kolyva, I. Tachtsidis, A. Ghosh, T. Moroz, C. E. Cooper, M. Smith, and C. E. Elwell, “Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults,” Biomed. Opt. Express 3(10), 2550–2566 (2012).
[Crossref] [PubMed]

M. M. Tisdall, I. Tachtsidis, T. S. Leung, C. E. Elwell, and M. Smith, “Increase in cerebral aerobic metabolism by normobaric hyperoxia after traumatic brain injury,” J. Neurosurg. 109(3), 424–432 (2008).
[Crossref] [PubMed]

Tam, F.

T. A. Schweizer, K. Kan, Y. Hung, F. Tam, G. Naglie, and S. J. Graham, “Brain activity during driving with distraction: an immersive fMRI study,” Front. Hum. Neurosci. 7(7), 53 (2013).
[PubMed]

Tisdall, M. M.

M. M. Tisdall, I. Tachtsidis, T. S. Leung, C. E. Elwell, and M. Smith, “Increase in cerebral aerobic metabolism by normobaric hyperoxia after traumatic brain injury,” J. Neurosurg. 109(3), 424–432 (2008).
[Crossref] [PubMed]

Toronov, V.

Villringer, A.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

von Pannwitz, W.

H. R. Heekeren, M. Kohl, H. Obrig, R. Wenzel, W. von Pannwitz, S. J. Matcher, U. Dirnagl, C. E. Cooper, and A. Villringer, “Noninvasive Assessment of Changes in Cytochrome-c Oxidase Oxidation in Human Subjects During Visual Stimulation,” J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
[Crossref] [PubMed]

Ward, T. E.

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Figures (9)

Fig. 1
Fig. 1 (a) Driving simulator and fNIRS measurement apparatus; (b) event-related driving scenario design.
Fig. 2
Fig. 2 Diagram of the employed dual channel hNIRS setup.
Fig. 3
Fig. 3 (a) the raw hNIRS signal (at a single time point) and the standard deviation of the raw signal measured on tissue mimicking phantom and human head; (b) the absorption spectra of tissue chromophores.
Fig. 4
Fig. 4 hNIRS data processing algorithm.
Fig. 5
Fig. 5 The average changes during straight driving with distraction a) HbO2; b) HHb; c) ox-CCO.
Fig. 6
Fig. 6 Average traces of concentration changes in right PFC during a) right turn; b) distracted right turn; I: HbO2 ; II: HHb and III: ox-CCO.
Fig. 7
Fig. 7 Average traces of concentration changes in right PFC during a) left turn in traffic; b) distracted left turn in traffic; I: HbO2; II: HHb and III: ox-CCO.
Fig. 8
Fig. 8 Individual event-related changes during different tasks in a single random participant in right PFC; induced changes due to: a) right turn; b) distracted right turn; c) left turn in traffic; d) distracted left turn in traffic and e) distracted straight driving.
Fig. 9
Fig. 9 Group mean analysis based on one-way ANOVA (details are presented in Table 2).

Tables (2)

Tables Icon

Table 1 Average event-related changes in concentrations of HbO2, HHb and ox-CCO and calculated p-value from paired-sample t-tests (performed between the initial moment of each event and the maximum induced changes); arrows show the direction of the average changes that were statistically significant and the changes that were not statistically significant are shown by ≈.

Tables Icon

Table 2 Average concentration changes and one-way ANOVA results of all distracted conditions vs. average changes of all non-distracted conditions; positive means reflect an overall increase and negative means represent an overall decrease.

Equations (4)

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

Φ(ρ)= 2 (4π) 2 S D exp[ ρ ( μ a D ) 1/2 ] ρ 3 [ 1+ρ ( μ a D ) 1/2 ]( z 0 + z b )×[ z b +3D[ 1 ( z 0 + z b ) 2 +3 z b 2 2 ρ 2 [ 3+ ρ 2 μ a D 1+ρ ( μ a D ) 1/2 ] ] ]
ln ψ λ,t ( μ a +Δ μ a , μ s ) ψ λ, t 0 ( μ a , μ s ) nonlinearfit ln[ Data(λ,t) Data(λ, t 0 ) ]
μ a (t)=Δ [Hb O 2 ] t ε (λ) Hb O 2 +Δ [HHb] t ε (λ) HHb +Δ [oxCCO] t ε (λ) CCO
μ s (λ)= μ s,800nm ( λ 800 ) α

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