## Due to intravascular multiple sequential scattering, Diffuse Correlation Spectroscopy of tissue primarily measures relative red blood cell motion within vessels |

Biomedical Optics Express, Vol. 2, Issue 7, pp. 2047-2054 (2011)

http://dx.doi.org/10.1364/BOE.2.002047

Acrobat PDF (685 KB)

### Abstract

We suggest that Diffuse Correlation Spectroscopy (DCS) measurements of tissue blood flow primarily probe relative red blood cell (RBC) motion, due to the occurrence of multiple sequential scattering events within blood vessels. The magnitude of RBC shear-induced diffusion is known to correlate with flow velocity, explaining previous reports of linear scaling of the DCS “blood flow index” with tissue perfusion despite the observed diffusion-like auto-correlation decay. Further, by modeling RBC mean square displacement using a formulation that captures the transition from ballistic to diffusive motion, we improve the fit to experimental data and recover effective diffusion coefficients and velocity de-correlation time scales in the range expected from previous blood rheology studies.

© 2011 OSA

## 1. Introduction

16. H. L. Goldsmith and J. Marlow, “Flow behavior of erythrocytes: II. particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. **71**, 383–407 (1979). [CrossRef]

## 2. Methods

### 2.1. Dynamic light scattering in tissue

*et al.*[15

15. M. Ninck, M. Untenberger, and T. Gisler, “Diffusing-wave spectroscopy with dynamic contrast variation: disentangling the effects of blood flow and extravascular tissue shearing on signals from deep tissue,” Biomed. Opt. Express **1**, 1502–1513 (2010). [CrossRef]

*ex vivo*to track the motion of hemoglobin-depleted ghost RBCs [16

16. H. L. Goldsmith and J. Marlow, “Flow behavior of erythrocytes: II. particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. **71**, 383–407 (1979). [CrossRef]

21. J. M. Higgins, D. T. Eddington, S. N. Bhatia, and L. Mahadevan, “Statistical dynamics of flowing red blood cells by morphological image processing,” PLOS Comput. Biol. **5**, e1000288 (2009). [CrossRef] [PubMed]

*in vivo*in rat venules [22]. It was found that RBCs undergo shear-induced displacements in the bulk flow frame of reference that can be characterized by an effective diffusion coefficient

*D*

_{eff}on the order of 10

^{−5}mm

^{2}/s, much higher than the Brownian diffusion coefficient expected for the RBCs in plasma ~ 5 × 10

^{−8}mm

^{2}/s [22]. Most importantly,

*D*

_{eff}appears to scale linearly with the shear rate. We postulate that this mechanism underlies the measurement of tissue blood flow using Diffuse Correlation Spectroscopy.

*r*

^{2}(

*τ*)〉 = 6

*D*) appears to work well, it assumes that the ballistic to random-walk hydrodynamic transition in the RBC diffusion occurs at time scales shorter than those probed by DCS measurements. Since there is no data to support this assumption, we remove it by using the Langevin formulation for RBC mean squared displacement [1]: where

_{b}τ*D*

_{eff}is the effective diffusion coefficient and

*τ*is the time scale for the randomization of velocity vectors associated with RBC scattering events. By Taylor expanding Eq. (2), it can be shown that this formulation of the displacement term describes ballistic motion at short delay times, and diffusive motion at long delay times. Note that we are referring here to the short time scale ballistic motion contained within any diffusive process (including that of erythrocytes in the bulk flow frame of reference), and not to the bulk ballistic motion of erythrocytes in vasculature as seen in the laboratory frame of reference.

_{c}### 2.2. Experimental approach and data analysis

10. N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO_{2}, CBF index, and rCMRO_{2} in human premature neonates’ brains in the first six weeks of life,” Human Brain Mapp. **31**, 341–352 (2009). [CrossRef]

10. N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO_{2}, CBF index, and rCMRO_{2} in human premature neonates’ brains in the first six weeks of life,” Human Brain Mapp. **31**, 341–352 (2009). [CrossRef]

## 3. Results and discussion

*g*

_{2}(

*τ*) that exemplifies the different fits obtained using displacement formulations corresponding to simplified Brownian diffusion, hydrodynamic diffusion (Eq. (2)) and random flow, respectively. For this data, it is clear that only hydrodynamic diffusion provides a good match to the shape of the auto-correlation decay. The decay predicted by the simplified Brownian diffusion appears too “slow”, while the decay predicted by random flow is too “fast”, leading to incorrect estimation of the

*β*factor as well as of the decay rate. To quantify the quality of the fit, we use the statistical metric “fraction of variance unexplained” (FVU), defined as the ratio of the model mean squared error to the variance of the experimental data. For the data in Fig. 1, the hydrodynamic diffusion model has the lowest residuals (FVU=0.04%), followed by Brownian diffusion (FVU=0.48%), and random flow (FVU=0.76%). The average values of FVU over the entire set of experimental measurements are 0.36% for hydrodynamic diffusion, 0.46% for Brownian diffusion, and 2.32% for random flow, respectively. As seen in previous studies, the simplified Brownian diffusion model is found to have significantly lower fit errors compared to random flow. The same direct comparison cannot be made between the simplified Brownian and full hydrodynamic diffusion models because of their different number of parameters. Instead, we perform a statistical F-test to determine if the improvement in the hydrodynamic model exceeds the reduction in unexplained variance expected from adding an additional fitting parameter (

*τ*) : where

_{c}*SSE*is the sum of the squares of the residuals and

*DoF*is the number of degrees of freedom (number of correlation time bins (137 in our case) minus the number of model parameters (2 for Brownian diffusion (

*D*and

_{b}*β*), 3 for hydrodynamic diffusion (

*D*

_{eff},

*τ*and

_{c}*β*)). For hydrodynamic diffusion to be a better model than Brownian diffusion, the corresponding F-number must exceed a critical F-value, which for

*p*< 0.05 is 3.91 (as calculated using the finv function in Matlab (Mathworks, Natick,MA)). This is true for 80.1% of the individual measurements from our data set, and the whole set F-number is 33.8, corresponding to a highly significant p-value of 4 × 10

^{−8}(calculated using fcdf in Matlab).

*α*and the diffusion coefficient. This quantity has been used as a “blood flow index” in DCS studies, because the value of

*α*generally cannot be estimated independently. Figure 2 shows a scatter plot of the

*αD*

_{eff}vs. the

*αD*values obtained from each of our measurements. We observe an approximate relationship of

_{b}*αD*

_{eff}= 1.07

*αD*+ 2.1 × 10

_{b}^{−7}(mm

^{2}/s).

*α*

*D*

_{eff}has a substantially linear relationship with

*αD*, with a nearly-zero intercept, indicating both parameters can serve as relative blood flow indices, but

_{b}*αD*

_{eff}is expected to provide a more accurate absolute measure. Encouragingly, by assuming

*α*= 0.1 [23

23. A. G. Hudetz, “Blood flow in the cerebral capillary network: a review emphasizing observations with intravital microscopy,” Microcirculation **4**, 233–252 (1997). [CrossRef] [PubMed]

^{−5}– 10

^{−4}mm

^{2}/s) [16

16. H. L. Goldsmith and J. Marlow, “Flow behavior of erythrocytes: II. particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. **71**, 383–407 (1979). [CrossRef]

21. J. M. Higgins, D. T. Eddington, S. N. Bhatia, and L. Mahadevan, “Statistical dynamics of flowing red blood cells by morphological image processing,” PLOS Comput. Biol. **5**, e1000288 (2009). [CrossRef] [PubMed]

*τ*, we observed a range between 0.06 and 7.7

_{c}*μ*s, with an average of 1.3

*μ*s (however values lower than ~ 0.4

*μ*

*s*are not reliable because of the limited time resolution of our correlator). A rough estimation of expected

*τ*values may be obtained from hydrodynamic diffusion theory. For a rigid spherical particle the velocity decorrelation characteristic time is on the order of

_{c}*τ*=

_{v}*ρa*

^{2}

*/*

*η*, where

*a*is the particle size,

*ρ*is the fluid density and

*η*is the fluid viscosity. Assuming a red blood cell diameter of

*a*= 4

*μm*,

*η*= 1.2 cP [22] and the density of water,

*τ*= 13

_{v}*μ*s, within an order of magnitude of our measurements. While the deformable nature of RBCs and the complexity of blood flow make this comparison less meaningful, our results do indicate the ballistic motion time scale (

*τ*<

*τ*) of the RBC hydrodynamic diffusion process is observable in most DCS measurements. Thus the full Eq. (2) should be used to reduce variance in the obtained blood flow velocity estimates and to characterize the diffusive transition time scale. To further characterize

_{c}*τ*we plot in Fig. 3: a)

_{c}*τ*vs. flow velocity, represented by

_{c}*αD*

_{eff}and b)

*τ*vs. inter-RBC distance (expected to be proportional to the inverse cube root of the blood hemoglobin concentration

_{c}*HGB*

^{−1/3}), for all the measurements where

*R*

^{2}of the hydrodynamic fit was greater than 0.999 (giving us confidence in the estimation of

*τ*). We observe a weak but statistically significant decrease in

_{c}*τ*with increased blood flow, as well a weak decrease with increased inter-particle distance that does not reach a p<0.01 significance level. The inverse proportionality between

_{c}*τ*and

_{c}*D*

_{eff}(and hence blood flow) could be explained as an acceleration of the interaction time scale. It is also expected from the short

*τ*Taylor expansion of the mean square displacement expression (Eq. (2)):

*τ*ballistic displacement takes the form 〈Δ

*r*

^{2}(

*τ*)〉 =

*v*

^{2}

*τ*

^{2}, the early ballistic velocity

*v*is proportional to

*v*to be fairly constant (i.e. dependent on blood viscosity and temperature, but not on the speed of the bulk flow), suggesting an inverse-proportional relationship between

*τ*and

_{c}*D*

_{eff}. A similar intuitive explanation is not apparent for the observed decrease in

*τ*with increased inter-particle distance. This trend is likely due to complex blood flow mechanisms. Note though that

_{c}*τ*is known to be affected by particle deformability in colloids [24

_{c}24. S. Roldan-Vargas, M. Pelaez-Fernandez, R. Barnadas-Rodriguez, M. Quesada-Perez, J. Estelrich, and J. Callejas-Fernandez, “Nondiffusive Brownian motion of deformable particles: breakdown of the “long-time tail”,” Phys. Rev. E **80**, 021403 (2009). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | B. J. Berne and R. Pecora, |

2. | D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. |

3. | D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. |

4. | D. A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A |

5. | C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, “In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies,” Phys. Med. Biol. |

6. | T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. |

7. | S. A. Carp, G. P. Dai, D. A. Boas, M. A. Franceschini, and Y. R. Kim, “Validation of diffuse correlation spectroscopy measurements of rodent cerebral blood flow with simultaneous arterial spin labeling MRI; towards MRI-optical continuous cerebral metabolic monitoring,” Biomed. Opt. Express |

8. | G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, “Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI,” Opt. Express |

9. | E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express |

10. | N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO |

11. | M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocritical Care |

12. | C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. |

13. | R. Bonner and R. Nossal, “Model for laser Doppler measurements of blood flow in tissue,” Appl. Opt. |

14. | G. Dietsche, M. Ninck, C. Ortolf, J. Li, F. Jaillon, and T. Gisler, “Fiber-based multispeckle detection for time-resolved diffusing-wave spectroscopy: characterization and application to blood flow detection in deep tissue,” Appl. Opt. |

15. | M. Ninck, M. Untenberger, and T. Gisler, “Diffusing-wave spectroscopy with dynamic contrast variation: disentangling the effects of blood flow and extravascular tissue shearing on signals from deep tissue,” Biomed. Opt. Express |

16. | H. L. Goldsmith and J. Marlow, “Flow behavior of erythrocytes: II. particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. |

17. | T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. |

18. | M. Meinke, G. Muller, J. Helfmann, and M. Friebel, “Empirical model functions to calculate hematocrit-dependent optical properties of human blood,” Appl. Opt. |

19. | C. Desjardins and B. R. Duling, “Microvessel hematocrit–measurement and implications for capillary oxygen-transport,” Am. J. Physiol. |

20. | T. Q. Duong and S. G. Kim, “In vivo MR measurements of regional arterial and venous blood volume fractions in intact rat brain,” Magn. Res. Med. |

21. | J. M. Higgins, D. T. Eddington, S. N. Bhatia, and L. Mahadevan, “Statistical dynamics of flowing red blood cells by morphological image processing,” PLOS Comput. Biol. |

22. | J. J. Bishop, A. S. Popel, M. Intaglietta, and P. C. Johnson, “Effect of aggregation and shear rate on the dispersion of red blood cells flowing in venules,” Am. J. Physiol. Heart Circ. Physiol. |

23. | A. G. Hudetz, “Blood flow in the cerebral capillary network: a review emphasizing observations with intravital microscopy,” Microcirculation |

24. | S. Roldan-Vargas, M. Pelaez-Fernandez, R. Barnadas-Rodriguez, M. Quesada-Perez, J. Estelrich, and J. Callejas-Fernandez, “Nondiffusive Brownian motion of deformable particles: breakdown of the “long-time tail”,” Phys. Rev. E |

**OCIS Codes**

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

(170.1470) Medical optics and biotechnology : Blood or tissue constituent monitoring

(170.3340) Medical optics and biotechnology : Laser Doppler velocimetry

(170.6480) Medical optics and biotechnology : Spectroscopy, speckle

**ToC Category:**

Noninvasive Optical Diagnostics

**History**

Original Manuscript: April 4, 2011

Revised Manuscript: June 13, 2011

Manuscript Accepted: June 17, 2011

Published: June 24, 2011

**Citation**

Stefan A. Carp, Nadàege Roche-Labarbe, Maria-Angela Franceschini, Vivek J. Srinivasan, Sava Sakadžić, and David A. Boas, "Due to intravascular multiple sequential scattering, Diffuse Correlation Spectroscopy of tissue primarily measures relative red blood cell motion within vessels," Biomed. Opt. Express **2**, 2047-2054 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-7-2047

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### References

- B. J. Berne and R. Pecora, Dynamic Light Scattering : with Applications to Chemistry, Biology, and Physics , Dover Ed. (Dover Publications, 2000).
- D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988). [CrossRef] [PubMed]
- D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995). [CrossRef] [PubMed]
- D. A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A 14, 192–215 (1997). [CrossRef]
- C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, “In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies,” Phys. Med. Biol. 46, 2053–2065 (2001). [CrossRef] [PubMed]
- T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15, 037004 (2010). [CrossRef] [PubMed]
- S. A. Carp, G. P. Dai, D. A. Boas, M. A. Franceschini, and Y. R. Kim, “Validation of diffuse correlation spectroscopy measurements of rodent cerebral blood flow with simultaneous arterial spin labeling MRI; towards MRI-optical continuous cerebral metabolic monitoring,” Biomed. Opt. Express 1, 553–565 (2010). [CrossRef]
- G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, “Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI,” Opt. Express 15, 1064–1075 (2007). [CrossRef] [PubMed]
- E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express 17, 12571–12581 (2009). [CrossRef] [PubMed]
- N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates’ brains in the first six weeks of life,” Human Brain Mapp. 31, 341–352 (2009). [CrossRef]
- M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocritical Care 12, 173–180 (2010). [CrossRef]
- C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. 14, 034015 (2009). [CrossRef] [PubMed]
- R. Bonner and R. Nossal, “Model for laser Doppler measurements of blood flow in tissue,” Appl. Opt. 20, 2097–2107 (1981). [CrossRef] [PubMed]
- G. Dietsche, M. Ninck, C. Ortolf, J. Li, F. Jaillon, and T. Gisler, “Fiber-based multispeckle detection for time-resolved diffusing-wave spectroscopy: characterization and application to blood flow detection in deep tissue,” Appl. Opt. 46, 8506–8514 (2007). [CrossRef] [PubMed]
- M. Ninck, M. Untenberger, and T. Gisler, “Diffusing-wave spectroscopy with dynamic contrast variation: disentangling the effects of blood flow and extravascular tissue shearing on signals from deep tissue,” Biomed. Opt. Express 1, 1502–1513 (2010). [CrossRef]
- H. L. Goldsmith and J. Marlow, “Flow behavior of erythrocytes: II. particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. 71, 383–407 (1979). [CrossRef]
- T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010). [CrossRef]
- M. Meinke, G. Muller, J. Helfmann, and M. Friebel, “Empirical model functions to calculate hematocrit-dependent optical properties of human blood,” Appl. Opt. 46, 1742–1753 (2007). [CrossRef] [PubMed]
- C. Desjardins and B. R. Duling, “Microvessel hematocrit–measurement and implications for capillary oxygen-transport,” Am. J. Physiol. 252, H494–H503 (1987).
- T. Q. Duong and S. G. Kim, “In vivo MR measurements of regional arterial and venous blood volume fractions in intact rat brain,” Magn. Res. Med. 43, 393–402 (2000). [CrossRef]
- J. M. Higgins, D. T. Eddington, S. N. Bhatia, and L. Mahadevan, “Statistical dynamics of flowing red blood cells by morphological image processing,” PLOS Comput. Biol. 5, e1000288 (2009). [CrossRef] [PubMed]
- J. J. Bishop, A. S. Popel, M. Intaglietta, and P. C. Johnson, “Effect of aggregation and shear rate on the dispersion of red blood cells flowing in venules,” Am. J. Physiol. Heart Circ. Physiol. 283, H1985–H1996 (2002).
- A. G. Hudetz, “Blood flow in the cerebral capillary network: a review emphasizing observations with intravital microscopy,” Microcirculation 4, 233–252 (1997). [CrossRef] [PubMed]
- S. Roldan-Vargas, M. Pelaez-Fernandez, R. Barnadas-Rodriguez, M. Quesada-Perez, J. Estelrich, and J. Callejas-Fernandez, “Nondiffusive Brownian motion of deformable particles: breakdown of the “long-time tail”,” Phys. Rev. E 80, 021403 (2009). [CrossRef]

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