## Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain

Optics Express, Vol. 11, Issue 21, pp. 2717-2729 (2003)

http://dx.doi.org/10.1364/OE.11.002717

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### Abstract

Frequency-domain near-infrared spectro-imaging offers significant advantages over the continuous-wave method in human brain applications. However, the drawback of existing instruments is a low signal-to-noise ratio for measured phase and modulation depth changes caused by cerebral activation. In this paper we show that in the case of the geometry specific for the activated area in the human brain, the SNR can be significantly improved by increasing the modulation frequency. We present the results of two studies: one performed experimentally using a sub-nanosecond pulsed light source and a spherical absorbing inhomo geneity immersed in a highly scattering solution, and the other performed numerically using Monte Carlo simulations of light transport in an MRI-based digital phantom of the adult human head. We show that changes caused by the absorbing inhomogeneity in both phase and modulation depth increase with frequency and reach maximum values at frequencies between 400 and 1400 MHz, depending on the particular source-detector distance. We also show that for the human head geometry an increase of the modulation frequency from 100 to 500 MHz can increase the phase SNR 2–3 times, and the modulation depth SNR up to 10 times.

© 2003 Optical Society of America

## 1. Introduction

1. A. Villringer, J. Planck, C. Hock, L. Schleinkofer, and U. Dirnagl, “Near infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activ ation of brain function in human adults,” Neurosci. Lett. **154**, 101–104 (1993). [CrossRef] [PubMed]

2. R.M. Danen, Y. Wang, X.D. Li, W.S Thayer, and A.G. Yodh, “Regional imager for low-resolution functional imaging of the brain with diffusing near-infrared light,” Photochem Photobiol. **67**, 33–40 (1998). [CrossRef] [PubMed]

6. G. Alexandrakis, T.J. Farrell, and M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. **37**,7401–7409(1998). [CrossRef]

6. G. Alexandrakis, T.J. Farrell, and M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. **37**,7401–7409(1998). [CrossRef]

*AC*/

*DC*, of the photon density wave. We present the results of two studies: one performed experimentally using a sub-nanosecond pulsed light source and a spherical absorbing inhomogeneity immersed in a highly scattering solution, and the other performed numerically using Monte Carlo simulations of light transport in the MRI-based digital phantom of the adult human head [9

9. C. Yu, C. Mu, X. Intes, and B. Chance, “Signal-to-noise analysis for detection sensitivity of small absorbing heterogeneity in turbid media with single-source and dual-interfering-source,” Opt. Express **9**, 212–224 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-4-212. [CrossRef]

## 2. The noise model and its validation

*AC*decreases with the frequency, the phase noise increases.

*AC*/

*DC*This means that the MD noise decreases with the frequency, so that the SNR may not decrease with frequency as rapidly as the phase SNR.

4. V. Toronov, A. Webb, J. H. Choi, M. Wolf, L. Safonova, U. Wolf, and E. Gratton. “Study of Local Cerebral Hemodynamic Fluctuations by Simultaneous Frequency-Domain near-infrared spectroscopy and fMRI,” Optics Express **9**, 417–427 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-8-417. [CrossRef] [PubMed]

*in vivo*frequency-domain measurements.

## 3. Experimental study of changes in frequency-domain parameters caused by an absorptive inhomogeneity immersed in a semi-infinite medium

*µ*′

_{s}≈11 cm

^{-1},

*µ*′

_{a}≈0.1 cm

^{-1}). The half-maximum width of the pulse at the fiber output was roughly 0.5 ns. The scattered light was collected at the surface of the medium at a variable distance from the source by means of a 3 mm fiber bundle and then sent to the PMT detector (Hammamatsu R5600P). The acquisition system was based on the SPC-830 single photon counting board which measured the detected photon arrival times and produced a time histogram representing the averaged received pulse.

*µ*′

_{s}≈11 cm

^{-1},

*µ*

_{a}≈0.2 cm

^{-1}) was placed at 15 mm depth between the source and detector as shown in Fig. 3.

## 4. Monte Carlo simulations of changes in phase and modulation depth caused by cerebral activation

10. D.A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express **10**, 159–170 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159. [CrossRef] [PubMed]

8. I.G. Zubal, C.R. Harrell, E.O. Smith, Z. Rattner, G. Gindi, and P.B. Hoffer, “Computerized 3-Dimensional Segmented Human Anatomy,” Med. Phys. **21**, 299–302 (1994), http://noodle.med.yale.edu/zubal/. [CrossRef] [PubMed]

^{-1}, 0.01 cm

^{-1}, 0.1 cm

^{-1}, and 0.13–0.26 cm

^{-1}(since no absolute values for the optical properties of the activated brain tissue have yet been published, in our simulations we used various values of µa in the range 0.13–0.26 cm

^{-1}.), respectively. The reduced scattering coefficients were 10 cm

^{-1}, 1.0 cm

^{-1}, 10 cm

^{-1}, and 10 cm

^{-1}, respectively. The values of absorption and reduced scattering coefficients for the outer layer and the brain correspond approximately to those we obtained in our experimental study [11]. The values of the optical properties for the low-scattering and low-absorbing CSF layer (µ

_{a}=0.01 cm

^{-1}and µ′

_{s}=1 cm

^{-1}) were taken from the literature [10

10. D.A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express **10**, 159–170 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159. [CrossRef] [PubMed]

^{8}rays were propagated. These data were used to calculate the phase and the MD of the detected photon-density waves with and without activation, and the SNR for the changes in these parameters caused by activation (see [10

10. D.A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express **10**, 159–170 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159. [CrossRef] [PubMed]

## 5. Discussion

7. D. A. Boas, M. A. OLeary, B. Chance, and A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. **36**, 75–92 (1997) [CrossRef] [PubMed]

*in vivo*corresponds to the quantum shot noise model, for which the dependence of the phase and MD noise on the frequency can be obtained analytically.

7. D. A. Boas, M. A. OLeary, B. Chance, and A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. **36**, 75–92 (1997) [CrossRef] [PubMed]

12. M. Firbank, E. Okada, and D.T. Delpy, “A theoretical study of the signal contribution of regions of the adult head to near infrared spectroscopy studies of visual evoked responses,” Neuroimage **8**, 69–78 (1998). [CrossRef] [PubMed]

12. M. Firbank, E. Okada, and D.T. Delpy, “A theoretical study of the signal contribution of regions of the adult head to near infrared spectroscopy studies of visual evoked responses,” Neuroimage **8**, 69–78 (1998). [CrossRef] [PubMed]

2. R.M. Danen, Y. Wang, X.D. Li, W.S Thayer, and A.G. Yodh, “Regional imager for low-resolution functional imaging of the brain with diffusing near-infrared light,” Photochem Photobiol. **67**, 33–40 (1998). [CrossRef] [PubMed]

6. G. Alexandrakis, T.J. Farrell, and M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. **37**,7401–7409(1998). [CrossRef]

5. V. Toronov, A. Webb, S. Walker, R. Gupta, J. H. Choi, E. Gratton, and D. Hueber, “The Roles of Changes in Deoxyhemoglobin Concentration and Blood Volume in the fMRI BOLD Signal,” Neuroimage **19**, 1521–1531 (2003). [CrossRef] [PubMed]

**37**,7401–7409(1998). [CrossRef]

## 6. Conclusion

*in vivo*corresponds to the quantum shot noise model. We have shown that the SNR for these changes can be very significantly improved compared to its value at 100 MHz by increasing the modulation frequency to 400–500 MHz. The source-detector distance which optimizes the SNR for both phase and modulation depth signals is about 20–25 mm.

## Appendix

*a*,

*b*,

*ω*and

*ϕ*are the modulation amplitude, the intensity, the modulation frequency, and the phase of the photon density wave, respectively The detector anode current is proportional to the number of photo-electrons

*N*

_{pe}induced by light per unit of time:

*q*is the electron charge,

*Δf*is the bandwidth, and

*g(t)*is the gain. Alternatively,

*i(t)*can be represented as a sum of the average value and the fluctuation

*ξ*(

*t*) is a non-stationary random process with the zero average. The ensemble average value 〈

*i*(

*t*)〉 at each moment of time can be obtained by averaging the right hand side of Eq. (2), which is proportional to 〈

*N*

_{pe}〉 (assuming that the gain noise is small compared to the variation in the number of photoelectrons). Since

*η*and

*S*are the quantum efficiency and the detecting area of the detector, and

*ν*is the frequency of light, 〈

*i*(

*t*)〉 can be written as

*ω*′=

*ω*+Ω, where the cross-correlation frequency

*Ω*is very small compared to

*ω*:

*g*(

*t*)=

*g*

_{0}(1+

*m*cos(

*ω*′

*t*+

*ϕ*)),

*m*≤1. Therefore, Eq. (5) can be rewritten as

*A*and

*B*are the constants proportional to

*a*and

*b*, respectively.The cross-correlation waveforms of the detector signal (i.e., waveforms of period T=2π/Ω) are then Fourier transformed to obtain the complex value

*X*:

*AC*and phase are then obtained as

*A*and

*ϕ*, respectively. The variances in the corresponding errors are

*DC*〉=4

*B*, and

*ζ*is the random DC error equal to

*ξ*(

*t*). We assume that the gain noise is small, and the light intensity is high enough to neglect the thermal noise and other sources of electronic noise. Then, the only source of noise in

*i(t)*is the fluctuation of the number of photoelectrons, i.e., the shot noise, and the cross-correlation function for

*ξ*(

*t*) is

*t*') is the variance. Assuming that the mean squared fluctuation in the number of photoelectrons is equal to 〈

*N*

_{pe}〉, from Eq. (2) one can derive

*Ω*, and the integrals in Eqs. (7), (10), and (11) are approximated by finite fast Fourier transforms. However, one can show that Eqs. (14)–(18) are valid both for both discrete and continuous Fourier transforms. It is important to note that, as follows from Eqs. (17) and (18),

*σ*

_{AC}does not depend on the modulation frequency

*ω*, and

*σ*

_{Φ}depends on

*ω*through 〈

*AC*〉 in the denominator.

*AC*〉/〈

*DC*〉 one can show that the corresponding standard deviation is

*AC*〉/〈

*DC*〉.

## Acknowledgment

## References and links

1. | A. Villringer, J. Planck, C. Hock, L. Schleinkofer, and U. Dirnagl, “Near infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activ ation of brain function in human adults,” Neurosci. Lett. |

2. | R.M. Danen, Y. Wang, X.D. Li, W.S Thayer, and A.G. Yodh, “Regional imager for low-resolution functional imaging of the brain with diffusing near-infrared light,” Photochem Photobiol. |

3. | C.D. Kurth and W.S. Thayer, “A multiwavelength frequency-domain near-infrared cerebral oximeters,” Phys. Med. Biol. |

4. | V. Toronov, A. Webb, J. H. Choi, M. Wolf, L. Safonova, U. Wolf, and E. Gratton. “Study of Local Cerebral Hemodynamic Fluctuations by Simultaneous Frequency-Domain near-infrared spectroscopy and fMRI,” Optics Express |

5. | V. Toronov, A. Webb, S. Walker, R. Gupta, J. H. Choi, E. Gratton, and D. Hueber, “The Roles of Changes in Deoxyhemoglobin Concentration and Blood Volume in the fMRI BOLD Signal,” Neuroimage |

6. | G. Alexandrakis, T.J. Farrell, and M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. |

7. | D. A. Boas, M. A. OLeary, B. Chance, and A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. |

8. | I.G. Zubal, C.R. Harrell, E.O. Smith, Z. Rattner, G. Gindi, and P.B. Hoffer, “Computerized 3-Dimensional Segmented Human Anatomy,” Med. Phys. |

9. | C. Yu, C. Mu, X. Intes, and B. Chance, “Signal-to-noise analysis for detection sensitivity of small absorbing heterogeneity in turbid media with single-source and dual-interfering-source,” Opt. Express |

10. | D.A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express |

11. | J. H. Choi, M. Wolf, V. Toronov, U. Wolf, C. Polzonetti, D. Hueber, L. Safonova, R. Gupta, A. Michalos, W. Mantulin, and E. Gratton, “Noninvasive determination of absolute optical properties of adult human brain: near infrared spectroscopy approach,” J. Biomed. Opt. (in press) |

12. | M. Firbank, E. Okada, and D.T. Delpy, “A theoretical study of the signal contribution of regions of the adult head to near infrared spectroscopy studies of visual evoked responses,” Neuroimage |

**OCIS Codes**

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(170.5270) Medical optics and biotechnology : Photon density waves

(170.5280) Medical optics and biotechnology : Photon migration

**ToC Category:**

Research Papers

**History**

Original Manuscript: July 31, 2003

Revised Manuscript: October 9, 2003

Published: October 20, 2003

**Citation**

Vlad Toronov, Enrico D'Amico, Dennis Hueber, Enrico Gratton, Beniamino Barbieri, and Andrew Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain," Opt. Express **11**, 2717-2729 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-21-2717

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### References

- A. Villringer, J. Planck, C. Hock, L. Schleinkofer, U. Dirnagl, "Near infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activation of brain function in human adults,�?? Neurosci. Lett. 154, 101-104 (1993). [CrossRef] [PubMed]
- R.M. Danen, Y.Wang, X.D. Li, W.S.Thayer, A.G. Yodh, �??Regional imager for low-resolution functional imaging of the brain with diffusing near-infrared light,�?? Photochem Photobiol. 67, 33-40 (1998). [CrossRef] [PubMed]
- C.D. Kurth and W.S. Thayer, �??A multiwavelength frequency-domain near-infrared cerebral oximeters,�?? Phys. Med. Biol. 44, 727-740 (1999). [CrossRef] [PubMed]
- V. Toronov, A. Webb, J. H. Choi, M. Wolf, L. Safonova, U. Wolf, E. Gratton. �??Study of Local Cerebral Hemodynamic Fluctuations by Simultaneous Frequency-Domain near-infrared spectroscopy and fMRI,�?? Optics Express 9, 417-427 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-8-417">.http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-8-417</a> [CrossRef] [PubMed]
- V. Toronov , A. Webb, S. Walker, R. Gupta, J. H. Choi, E. Gratton, D. Hueber, �??The Roles of Changes in Deoxyhemoglobin Concentration and Blood Volume in the fMRI BOLD Signal,�?? Neuroimage 19, 1521-31 (2003). [CrossRef] [PubMed]
- G. Alexandrakis, T.J. Farrell, and M. S. Patterson, �??Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,�?? Appl. Opt. 37, 7401-7409 (1998). [CrossRef]
- D. A. Boas, M. A. OLeary, B. Chance, A. G. Yodh, �??Detection and characterization of optical in homogeneities with diffuse photon density waves: a signal-to-noise analysis,�?? Appl. Opt. 36, 75-92 (1997). [CrossRef] [PubMed]
- I.G. Zubal, C.R. Harrell, E.O. Smith, Z. Rattner, G. Gindi, P.B.Hoffer, �??Computerized 3-Dimensional Segmented Human Anatomy," Med. Phys. 21, 299-302 (1994), <a href="http://noodle.med.yale.edu/zubal/">http://noodle.med.yale.edu/zubal/</a>. [CrossRef] [PubMed]
- Y. Chen, C. Mu, X. Intes, B. Chance, �?? Signal-to-noise analysis for detection sensitivity of small absorbing heterogeneity in turbid media with single-source and dual-interfering-source,�?? Opt. Express 9, 212 �??224 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-4-212">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-4-212</a>. [CrossRef]
- D.A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, �??Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,�?? Opt. Express 10, 159-170 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159</a>. [CrossRef] [PubMed]
- J. H. Choi, M. Wolf, V. Toronov, U. Wolf, C. Polzonetti, D. Hueber, L. Safonova, R. Gupta, A. Michalos, W. Mantulin, E. Gratton, �??Noninvasive determination of absolute optical properties of adult human brain: near infrared spectroscopy approach,�?? J. Biomed. Opt. (in press)
- M. Firbank, E. Okada, D.T. Delpy, �??A theoretical study of the signal contribution of regions of the adult head to near infrared spectroscopy studies of visual evoked responses,�?? Neuroimage 8, 69-78 (1998). [CrossRef] [PubMed]

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