## A fiberoptic reflectance probe with multiple source-collector separations to increase the dynamic range of derived tissue optical absorption and scattering coefficients

Optics Express, Vol. 18, Issue 6, pp. 5580-5594 (2010)

http://dx.doi.org/10.1364/OE.18.005580

Acrobat PDF (416 KB)

### Abstract

Measurement of tissue optical absorption and (transport) reduced scattering coefficients (μ* _{a}* and μ

*', respectively) is fundamental to many applications of light in medicine and biology. We report a handheld fiberoptic probe to determine these coefficients by measuring the diffuse reflectance at multiple source-collector distances, which allows for a larger dynamic range than a single source-collector separation. Diffusion theory and*

_{s}*a priori*knowledge of the spectral shape of μ

*and μ*

_{a}*' are used in a forward model of the diffuse reflectance. The dynamic range and accuracy of this method were evaluated using Monte Carlo simulations, phantom experiments and tissues*

_{s}*in vivo*.

© 2010 OSA

## 1. Introduction

*) and transport (reduced) elastic scattering (μ*

_{a}*') coefficient and their spectral dependence, is central to many diagnostic and therapeutic optical techniques. For example, the outcome of treatments such as photodynamic therapy [1*

_{s}1. R. A. Weersink, A. Bogaards, M. Gertner, S. R. Davidson, K. Zhang, G. Netchev, J. Trachtenberg, and B. C. Wilson, “Techniques for delivery and monitoring of TOOKAD (WST09)-mediated photodynamic therapy of the prostate: clinical experience and practicalities,” J. Photochem. Photobiol. B **79**(3), 211–222 (2005). [CrossRef] [PubMed]

2. L. C. Chin, W. M. Whelan, and I. A. Vitkin, “Models and measurements of light intensity changes during laser interstitial thermal therapy: implications for optical monitoring of the coagulation boundary location,” Phys. Med. Biol. **48**(4), 543–559 (2003). [CrossRef] [PubMed]

3. B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive *in vivo* characterization of breast tumors using photon migration spectroscopy,” Neoplasia **2**(1/2), 26–40 (2000). [CrossRef] [PubMed]

5. A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H. J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues *in vitro* in the visible and near infrared spectral range,” Phys. Med. Biol. **47**(12), 2059–2073 (2002). [CrossRef] [PubMed]

*ex vivo*tissue samples, adding uncertainty due to distorting factors such as deoxygenation, loss of blood and the effects of tissue handling (

*e.g.*cryofreezing) [6

6. E. Chan, T. Menovsky, and A. J. Welch, “Effects of cryogenic grinding on soft-tissue optical properties,” Appl. Opt. **35**(22), 4526–4532 (1996). [CrossRef] [PubMed]

*in vivo*, especially for clinical applications. These are generally based on either fiberoptics in contact with, or a non-contact detector in close proximity to, the tissue. Frequency-domain [3

3. B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive *in vivo* characterization of breast tumors using photon migration spectroscopy,” Neoplasia **2**(1/2), 26–40 (2000). [CrossRef] [PubMed]

7. M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, and J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. **30**(31), 4474–4476 (1991). [CrossRef] [PubMed]

8. T. Svensson, J. Swartling, P. Taroni, A. Torricelli, P. Lindblom, C. Ingvar, and S. Andersson-Engels, “Characterization of normal breast tissue heterogeneity using time-resolved near-infrared spectroscopy,” Phys. Med. Biol. **50**(11), 2559–2571 (2005). [CrossRef] [PubMed]

*in vivo*methods, where the dynamic migration of photons through tissue is measured. Steady-state fluence rate [1

1. R. A. Weersink, A. Bogaards, M. Gertner, S. R. Davidson, K. Zhang, G. Netchev, J. Trachtenberg, and B. C. Wilson, “Techniques for delivery and monitoring of TOOKAD (WST09)-mediated photodynamic therapy of the prostate: clinical experience and practicalities,” J. Photochem. Photobiol. B **79**(3), 211–222 (2005). [CrossRef] [PubMed]

2. L. C. Chin, W. M. Whelan, and I. A. Vitkin, “Models and measurements of light intensity changes during laser interstitial thermal therapy: implications for optical monitoring of the coagulation boundary location,” Phys. Med. Biol. **48**(4), 543–559 (2003). [CrossRef] [PubMed]

9. L. C. Chin, A. E. Worthington, W. M. Whelan, and I. A. Vitkin, “Determination of the optical properties of turbid media using relative interstitial radiance measurements: Monte Carlo study, experimental validation, and sensitivity analysis,” J. Biomed. Opt. **12**(6), 064027 (2007). [CrossRef]

10. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of *in vivo* human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. **44**(4), 967–981 (1999). [CrossRef] [PubMed]

11. T. J. Farrell, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. **19**(4), 879–888 (1992). [CrossRef] [PubMed]

12. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. **30**(11), 1354–1356 (2005). [CrossRef] [PubMed]

8. T. Svensson, J. Swartling, P. Taroni, A. Torricelli, P. Lindblom, C. Ingvar, and S. Andersson-Engels, “Characterization of normal breast tissue heterogeneity using time-resolved near-infrared spectroscopy,” Phys. Med. Biol. **50**(11), 2559–2571 (2005). [CrossRef] [PubMed]

3. B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive *in vivo* characterization of breast tumors using photon migration spectroscopy,” Neoplasia **2**(1/2), 26–40 (2000). [CrossRef] [PubMed]

*et al*. takes images with sinusoidal frequencies of up to 0.63 mm

^{−1}projected on the tissue, thus integrating over tissue surface areas ~1 cm

^{2}[12

12. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. **30**(11), 1354–1356 (2005). [CrossRef] [PubMed]

11. T. J. Farrell, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. **19**(4), 879–888 (1992). [CrossRef] [PubMed]

13. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. **35**(13), 2304–2314 (1996). [CrossRef] [PubMed]

*r*. Since there is only one reflectance measurement per wavelength,

*λ*, solving for μ

*and μ*

_{a}*' relies upon spectral constraints,*

_{s}*i.e.*applying

*a priori*knowledge of the shapes of μ

*(*

_{a}*λ*) and μ

*'(λ) in a forward model, which can then be used to solve for the absolute coefficient values. Recent efforts using this approach have explored the use of very small source-collector distances, <1 mm [14*

_{s}14. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. **46**(29), 7317–7328 (2007). [CrossRef] [PubMed]

^{3}and fast acquisition times (<1 sec to ~seconds).

*and μ*

_{a}*' that can be measured with a single source-collector distance. Here, three source-collector distances (260, 520 and 780 μm) were used. Since each distance spans a unique range over which μ*

_{s}*and μ*

_{a}*' can be measured, overlap of the reflectance measurements at the three distances extends the dynamic range beyond that of each distance separately. This approach is distinct from the aforementioned spatially-resolved diffuse reflectance techniques in that the multiple source-collector distances are used to expand the dynamic range of optical properties measurement, not to constrain the solution. We believe that this approach has distinct advantages over other reported methods, in particular the extended range of optical properties over which it is valid and the ability to make rapid, highly localized measurements of these properties which is advantageous in many applications.*

_{s}## 2. Theory

### 2.1 Using diffusion theory and spectral constraints to extract optical properties

10. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of *in vivo* human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. **44**(4), 967–981 (1999). [CrossRef] [PubMed]

15. P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. **10**(3), 034018 (2005). [CrossRef] [PubMed]

*(*

_{a}^{oxyHb}*λ*) and µ

*(*

_{a}^{deoxyHb}*λ*) are the wavelength-dependent absorption coefficients of oxygenated hemoglobin and deoxygenated hemoglobin, respectively, in units of [cm

^{−1}·L/g].

*f*is the total hemoglobin concentration [g/L] and

_{Hb}*StO*

_{2}is the oxygenation fraction. Only the significant chromophores should be included in order to have an accurate absorption model. In this work, optical properties in the visible light range are measured, with hemoglobin being dominant. Other absorbers, such as beta carotene in breast tissue [16], should be included if their concentration is significant. Water absorption is neglected here, since the diffuse reflectance is measured in the range 450-850 nm where water is optically clear relative to hemoglobin.

10. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of *in vivo* human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. **44**(4), 967–981 (1999). [CrossRef] [PubMed]

14. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. **46**(29), 7317–7328 (2007). [CrossRef] [PubMed]

15. P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. **10**(3), 034018 (2005). [CrossRef] [PubMed]

*A*and

*k*are constants.

*A priori*knowledge of the shapes of these spectra can be combined with a forward model of the diffuse reflectance. Non-linear fitting can then be applied to extract the free parameters,

*f*,

_{Hb}*StO*

_{2},

*A*and

*k*, from which μ

*(*

_{a}*λ*) and μ

*'(*

_{s}*λ*) can be computed using Eqs. (1) and (2). Our approach was to use the well-known diffusion theory equation for steady-state diffuse reflectance,

*R*, as the forward model, with the assumption of homogeneous optical properties in the volume of light interrogation [11

_{DT}11. T. J. Farrell, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. **19**(4), 879–888 (1992). [CrossRef] [PubMed]

*r*is then fixed and μ

*(*

_{a}*λ*) and μ

*'(*

_{s}*λ*) are wavelength-dependent:, where

*z*

_{0}= 1/µ

*'*

_{s}_{,}and

*r*

_{1}

^{2}=

*z*

_{0}

^{2}+

*r*

^{2}and

*r*

_{2}

^{2}= (

*z*

_{0}+ 2

*z*)

_{b}^{2}+

*r*

^{2}. The parameters

*z*

_{0},

*r*

_{1},

*r*

_{2},

*z*and µ

_{b}*are then all wavelength-dependent.*

_{eff}*z*depends on µ

_{b}*, µ*

_{a}*' and the internal reflection parameter к = (1 +*

_{s}*r*)/(1-

_{id}*r*) due to index mismatch between tissue and the external medium. The extrapolated boundary distance is given by

_{id}*z*= 2κ

_{b}*D*, where

*D*is the diffusion constant given by

*D*= (3µ

*')*

_{s}^{−1}. To quantify the index mismatch at the boundary,

*r*has been empirically determined as

_{id}*r*= −1.44

_{id}*n*

_{rel}^{−2}+ 0.71

*n*

_{rel}^{−1}+ 0.67 + 0.0636

*n*[17

_{rel}17. R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. **22**(16), 2456–2462 (1983). [CrossRef] [PubMed]

*= (3µ*

_{eff}*µ*

_{a}*')*

_{s}^{1/2}, and μ

*(*

_{a}*λ*) and μ

*'(*

_{s}*λ*) are given by Eqs. (1) and (2).

*D,*has been variously cited as (3μ

*')*

_{s}^{−1}or [3(μ

*' + μ*

_{s}*)]*

_{a}^{−1}[11

**19**(4), 879–888 (1992). [CrossRef] [PubMed]

13. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. **35**(13), 2304–2314 (1996). [CrossRef] [PubMed]

18. J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A **22**(3), 546–551 (2005). [CrossRef]

*et al*. [11

**19**(4), 879–888 (1992). [CrossRef] [PubMed]

*a*' = µ

*'/(µ*

_{s}*' + µ*

_{s}*). If it is modeled as an exponentially decaying line source extending into the tissue, then Eq. (3) includes the*

_{a}*a*' term. This will be discussed further below, where we empirically show that

*D*= (3µ

*')*

_{s}^{−1}and the exponential line source model is most suitable for this fiberoptic geometry. Note that for μ

*= 0 this issue does not matter, since then*

_{a}*D*= (3μ

*')*

_{s}^{−1}and

*a*' = 1 in all cases.

### 2.2 Upper and lower bounds of validity of the diffusion theory model

*r*value, there is a range of μ

*and μ*

_{a}*' values over which Eq. (3) can be accurately applied to solve the inverse problem to derive the optical properties. Hence, in order to increase the overall range, we have used three source-collector distances (*

_{s}*r*= 260, 520 and 780 μm). For a fixed

*r*, the diffuse reflectance does not monotonically increase with increasing μ

*',*

_{s}*i*.

*e*. there is a peak reflectance (Fig. 2 ). Hence, to avoid ambiguity correlating μ

*' to reflectance, the range of μ*

_{s}*' must be restricted to either the monotonically increasing or monotonically decreasing part of the curve. The absorption coefficient does not have this problem, since increasing μ*

_{s}*always reduces the reflectance signal. Here, we have used the monotonically increasing part since the reflectance is far more sensitive to changes in μ*

_{a}*' over this region, as evidenced by the steeper slope in Fig. 2. The peak reflectance then represents an upper bound for estimating μ*

_{s}*'. As shown in Table 1 , this upper bound decreases with μ*

_{s}*, so it should be taken as the largest expected μ*

_{a}*value (here, 10 cm*

_{a}^{−1}). In practice, this was set as the value of μ

*' at 90% peak reflectance, to provide an additional safety margin. From Table 1, the upper bounds for*

_{s}*r*= 260, 520 and 780 μm were then μ

*' = 52.9, 26.1 and 17.1 cm*

_{s}^{−1}, respectively. Note that the existence of the upper bound has nothing to do with diffusion model accuracy in the monotonically decreasing part of the reflectance-μ

*' curve; rather, the upper bound is placed to ensure that only the monotonically increasing part of the curve is used (for the reasons stated above) to solve the inverse problem to extract μ*

_{s}*and μ*

_{a}*', as detailed later on in Section 3.3.*

_{s}*', single scattering dominates, invalidating the Similarity Principle defining μ*

_{s}*' = μ*

_{s}*(1-*

_{s}*g*), where

*g*is the scattering anisotropy, and thus also invalidating the diffusion approximation. This condition was investigated using Monte Carlo modeling for a pencil light beam incident on an optically semi-infinite turbid medium, using the on-line C-code implementation developed by S. Jacques and colleagues [19

19. S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol. **67**(1), 23–32 (1998). [CrossRef] [PubMed]

*r*value and for µ

*' = 2-20 cm*

_{s}^{−1}, µ

*= 0-1 cm*

_{a}^{−1}and

*g*= 0.6-0.95. This range of

*g*is typical for tissues as determined

*ex vivo*in the breast [20

20. V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. **35**(9), 1317–1334 (1990). [CrossRef] [PubMed]

5. A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H. J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues *in vitro* in the visible and near infrared spectral range,” Phys. Med. Biol. **47**(12), 2059–2073 (2002). [CrossRef] [PubMed]

21. M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, “Measurement of the optical properties of the skull in the wavelength range 650-950 nm,” Phys. Med. Biol. **38**(4), 503–510 (1993). [CrossRef] [PubMed]

22. S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. **12**(5), 510–519 (1992). [CrossRef] [PubMed]

*', µ*

_{s}*and*

_{a}*g*dimensions. Examples of the resulting Monte Carlo reflectance

*versus*µ

*' curves are shown in Fig. 3a , together with the diffusion theory model graphs. The root-mean-square (RMS) error,*

_{s}*ε*, of the Monte Carlo data compared to the diffusion theory model was used as a measure of the goodness of fit, as illustrated in Fig. 3b. We applied an

_{RMS}*ε*cut-off of 10% to determine the ranges of validity of the diffusion theory model. As would be expected, as

_{RMS}*r*decreased the corresponding µ

*' value at*

_{s}*ε*increased, since single scattering effects are amplified with smaller inter-fiber distances. An interesting artifact is evident in Fig. 3b, where the

_{RMS}*ε*increases slightly with increasing µ

_{RMS}*' after reaching a minimum. This is likely due to loss of photons outside the finite (2 cm dia.) tissue volume used in the Monte Carlo simulations to reduce the computation time.*

_{s}*' values at the 10%*

_{s}*ε*crossover points, for the three

_{RMS}*r*distances and for µ

*= 0.1, 0.5 and 1 cm*

_{a}^{−1}. Based on the above, Eq. (3) is valid in the ranges µ

*' >16.4, 10.1 and 5.8 cm*

_{s}^{−1}for

*r*= 260, 520 and 780 µm, respectively. Figure 4 then displays the corresponding ranges of validity of the diffusion theory model. Recall that the motivation for using three source-collector distances was to provide overlapping regions of validity to increase the overall dynamic range of the optical coefficient measurements. The resulting dynamic range then has µ

*' ranges of 5.8-52.9 cm*

_{s}^{−1}for a µ

*range of 0-10 cm*

_{a}^{−1}. Note that if the cut-off is >10%, then the lower limit of µ

*' for all fiber distances will be decreased.*

_{s}*r*= 1 and 2 mm to further demonstrate how increasingly larger fiberoptic separations have a desirable decrease in the lower limit, but also an undesirable corresponding decrease in the overall range. This trade-off between the lower limit and overall range is important to inform the design of fiberoptic reflectance probes using this technique.

## 3. Materials and methods

### 3.1 Instrumentation

*r*. The total time for each measurement was approximately 3 sec.

*r*distances) having a standard deviation of only 0.37 cm

^{−2}, or 3.6%.

### 3.2 Calibration

*and μ*

_{a}*'. Fortuitously, the diffuse reflectance curve with respect to μ*

_{s}*' has a characteristic peaked shape (Fig. 2) that may be exploited. The approach was to measure the reflectance in a scattering fluid that was diluted over a range such that the reflectance*

_{s}*versus*μ

*' curve (of all dilutions) captures the peak reflectance over all wavelengths. The aliquot fraction of scattering fluid was a 3% concentration of Intralipid-20% (Fresenius Kabi, Uppsala, Sweden) in distilled water. The dilutions were then 3, 6, 9, ..., 48%. Figure 6a displays the uncalibrated reflectance at 600 nm, with both the*

_{s}*x*- and

*y*-axis needing calibration.

*versus*μ

*' curve was then used to fit the reflectance measurements to the diffusion theory model with the appropriate*

_{s}*x*- and

*y*-axis scaling. The

*y*-axis scale at each wavelength and source-collector distance is calculated as, where

*V*is the subset of μ

*' for which the diffusion theory model is valid (see Fig. 6b for properly scaled, calibrated data). This scale factor (Eq. (4)) was used to scale the (relative) reflectance measurements with the probe in order to yield the reflectance in absolute units (*

_{s}*i.e.*cm

^{−2}) so that the inverse problem may be solved to extract µ

*and µ*

_{a}*'.*

_{s}### 3.3 Inverse algorithm to recover optical properties

*r*(260, 520 and 780 μm). To recover μ

*(*

_{a}*λ*) and μ

*'(*

_{s}*λ*), a Levenberg-Marquardt non-linear least squares algorithm was applied to Eqs. (1)-(3) over the spectral range

*λ*= 450-850 nm. This minimized the variance between the diffusion theory reflectance equation,

*R*(

_{DT}*λ*), and the reflectance measurement,

*R*(

_{meas}*λ*), with

*f*,

_{Hb}*StO*

_{2},

*A*and

*k*as the free parameters. The optical properties spectra, μ

*(*

_{a}*λ*) and μ

*'(*

_{s}*λ*), can then be derived. Only one reflectance spectrum is required to estimate μ

*(*

_{a}*λ*) and μ

*'(*

_{s}*λ*). The selection of this reflectance spectrum is based on the optical properties range for each

*r*, as shown in Fig. 4. The following inversion algorithm was found to be suitable, with values for the μ

*' boundaries taken from Fig. 4.*

_{s}- i) Perform inversion with
*r*= 260 μm. If μ'>16.4 cm_{s}^{−1}for >50% of the spectral range (*i.e.*450-850 nm), output μ(_{a}*λ*) and μ'(_{s}*λ*) and end; else go to ii). - ii) Perform inversion with
*r*= 520 μm. If μ' > 10.1 cm_{s}^{−1}for > 50% of the spectral range, output μ(_{a}*λ*) and μ'(_{s}*λ*) and end; else go to iii). - iii) Perform inversion with
*r*= 780 μm. Output μ(_{a}*λ*) and μ'(_{s}*λ*).

### 3.4 Phantom measurements for diffusion theory model validation

**19**(4), 879–888 (1992). [CrossRef] [PubMed]

18. J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A **22**(3), 546–551 (2005). [CrossRef]

*i.e.*<1 mm) relative to these previous studies, necessitating confirmation of the model. As mentioned in the Theory section, there are different expressions for the diffusion coefficient,

*D*. The general form is

*D*= [3(µ

*' + αµ*

_{s}*)]*

_{a}^{−1}, with α variously cited as 0, 1 or some function of the optical properties [11

**19**(4), 879–888 (1992). [CrossRef] [PubMed]

18. J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A **22**(3), 546–551 (2005). [CrossRef]

*D*and light source model for our probe geometry.

*= 1, 5 or 10 cm*

_{a}^{−1}and μ

*' = 7, 14 or 21, prepared in all combinations. Since there are three*

_{s}*r*distances, this results in 27 total data points. This range of μ

*and μ*

_{a}*' spans the majority of tabulated*

_{s}*in vivo*optical properties in the review by Kim and Wilson for

*λ*= 450-850 nm [4]. Note that this phantom experiment does not include cases where μ

*is close to zero, since both forms of*

_{a}*D*and both forms of the light source model converge to the same model at μ

*= 0.*

_{a}*of Intralipid alone is assumed to be negligible for*

_{a}*λ*= 450-850 nm.

### 3.5 Phantom measurements to determine probe accuracy

23. M. Roy and B. C. Wilson, “An accurate homogenized tissue phantom for broad spectrum autofluorescence studies: a tool for optimizing quantum dot-based contrast agents,” Proc. SPIE **6870**, 68700E (2008). [CrossRef]

*T*(λ), and diffuse reflectance,

_{d}*R*(λ), spectra were measured with a 15 cm diameter integrating sphere (SphereOptics: Contoocook, NH, USA) coupled to a spectrometer (S2000, Ocean Optics). A Monte Carlo simulation was used to calculate the expected

_{d}*R*and

_{d}*T*for µ

_{d}*and µ*

_{a}*' values ranging from 0 to 100 cm*

_{s}^{−1}and 0-100 cm

^{−1}, respectively. The tissue optical properties were then calculated from

*T*(λ) and

_{d}*R*(λ) using an inverse interpolation algorithm. For this set of measurements, the phantoms were formulated first with μ

_{d}*= 21.7 and μ*

_{a}*' = 24.7cm*

_{s}^{−1}(at 715 nm) and then diluted into serial fractions of 95 to 5%, such that μ

*and μ*

_{a}*' scale linearly with concentration. Each of the 20 phantoms was measured by both the probe and the integrating sphere.*

_{s}*3.6* In vivo *measurements to demonstrate utility*

*in vivo*, as well as to obtain brain optical properties for separate studies on optical diagnostics during brain resection surgery, female Lewis rats (Charles River, QC, Canada) were used, under institutional ethics approval (University Health Network, Toronto). The animals were brought under general anesthesia with 4% isofluorane (oxygen flow at 2 L/min) and sustained by an injection of ketamine/xylazine (80/13 mg/kg, i.p.), and the eyes lubricated with tear gel. The scalp was reflected and a 1 cm dia. craniotomy was performed using a 1 mm drill bit, exposing both hemispheres. The dura was cut with microscissors, exposing the cortical surface. The fiberoptic probe was placed in gentle contact with the brain tissue and measurements taken. As well, measurements were obtained from exposed facial muscle adjacent to the craniotomy site. After measurements were taken, 120 mg/kg bodyweight of Euthanyl under heavy anesthesia (2.5% isofluorane with 1 L/min oxygen) was used for euthanasia. In this article, representative data from these measurements are presented to demonstrate the utility of the probe in an

*in vivo*application, although 5 animals were used in total. All studies were carried out under institutional animal-care approval (University Health Network, Toronto, Canada).

## 4. Results

### 4.1 Phantom measurements for diffusion theory model validation

*r*, μ

*and μ*

_{a}*' (with the exception of the data with μ*

_{s}*' values lower than the lower bounds on the diffusion theory model, as defined previously). The fit to the variations in the diffusion theory model was quantified using the coefficient of determination (*

_{s}*R*

^{2}) and the normalized root-mean-square error (NRMSE). This was done for all combinations of the two diffusion constant variations, and the two light source models (buried point source and exponential line source). The statistics for these four cases are shown in Table 3 . Based on this analysis, the exponential line source model and a diffusion constant of

*D*= (3µ

*')*

_{s}^{−1}were found to be optimal for the probe geometry. The measured reflectance values (from the probe) were then plotted against the modeled reflectance values (based on μ

*and μ*

_{a}*' measurements from the integrating sphere), again with the proviso that, for a given μ*

_{s}*', the values were within the range of validity as discussed in the Theory section (Fig. 7 ).*

_{s}### 4.2 Phantom measurements to determine probe accuracy

*and μ*

_{a}*', respectively. Figure 8a shows corresponding optical spectra for one measurement from this data set, demonstrating good correlation between the probe and integrating sphere measurements. Figure 8b then also shows good agreement between the diffuse reflectance measurement and the fit to the diffusion theory model.*

_{s}*4.3* In vivo *measurements to demonstrate feasibility*

*in vivo*optical properties data measured at the rat brain cortical surface and facial muscle are shown in Figs. 9a and 9c. The estimated free parameters from the brain measurement are

*f*= 4.89 g/L,

_{Hb}*StO*

_{2}= 40.5%,

*A*= 125.46 and

*k*= 0.2576. From the muscle data set, the values are

*f*= 2.66 g/L,

_{Hb}*StO*

_{2}= 68.5%,

*A*= 12.49 and

*k*= 0.0934. The diffusion theory model of reflectance fits very well to both data sets, with

*R*

^{2}= 0.963 and 0.971 for brain and muscle, respectively (Fig. 9b and 9d).

*in vivo*probe data and the

*in vitro*integrating sphere technique; however, this was not technically feasible due to significant distortions moving from the

*in vivo*to the

*in vitro*situation. For example, we took probe measurements in cortical brain tissue

*in vivo*and also after the brain was extracted post-sacrifice. We found on average that μ

*dropped by 44% at 500 nm from the*

_{a}*in vivo*to the

*ex vivo*situation due to loss of blood perfusion upon death and/or brain extraction (

*n*= 5 animals). Since tissue needs to be further prepared by slicing for integrating sphere measurements (and possibly frozen to preserve the tissue prior to these measurements) this is highly likely to introduce further handling artifacts, as demonstrated by Chan

*et al*. [6

6. E. Chan, T. Menovsky, and A. J. Welch, “Effects of cryogenic grinding on soft-tissue optical properties,” Appl. Opt. **35**(22), 4526–4532 (1996). [CrossRef] [PubMed]

*in vivo*as well as to demonstrate algorithm convergence in tissue—estimates of the inter-animal variation on the derived optical properties in larger sets of animals are planned and will be reported in future work, with the focus of this current article on instrument/algorithm development and validation.

## 5. Discussion

*and μ*

_{a}*' values that can be determined from the reflectance measurements for any given source-collector distance,*

_{s}*r*. Using multiple inter-fiber distances to overlap these ranges increases the overall dynamic range of optical properties that can be accurately measured. The lower limit of μ

*' is the major issue in utilizing the technique described here. One potential improvement is to add reflectance measurements at*

_{s}*r*> 780 µm to reach μ

*'<5.8 cm*

_{s}^{−1}. There is a tradeoff, however: with increasing

*r*, the signal-to-noise decreases significantly and the probe head necessarily has to be larger (limiting the versatility of the technique). As well, the overall μ

*' range decreases with increasing*

_{s}*r*, as shown in Fig. 4. Restricting

*r*to small values also limits the effective tissue sampling depth of the measurements, which is advantageous for highly localized measurements and for application in small tissue structures. Figure 10 shows Monte Carlo modeling using the current probe geometry to determine the effective sampling depth (90% of the detected photons) for the different μ

*' and μ*

_{s}*values, with the deepest penetration occurring at low μ*

_{a}*' and low μ*

_{s}*.*

_{a}*et al.*implemented a probe with

*r*= 250 µm, and used Monte Carlo simulations of the reflectance signal to determine the effect of varying

*g*while holding μ

*' constant [14*

_{s}14. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. **46**(29), 7317–7328 (2007). [CrossRef] [PubMed]

*g*= 0.75-0.95 and μ

*' = 5, 10 and 20 cm*

_{s}^{−1}. We report very similar findings extrapolated from our Monte Carlo data, with the reflectance at

*r*= 260 μm reflectance having a variation <15% for μ

*' > 5.1 cm*

_{s}^{−1}for

*g*= 0.6-0.95. A similar diffusion theory analysis to that used here was performed by Sun

*et al.*[24

24. J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. **45**(31), 8152–8162 (2006). [CrossRef] [PubMed]

*r*: for μ

*= 2.5 cm*

_{a}^{−1}, μ

*' = 6.4 cm*

_{s}^{−1}and

*g*= 0.84, the diffusion theory errors were <20% for

*r*> 500 μm. Our results are comparable, with the

*r*= 520 μm fiber giving an error <10% for μ

*' > 9.3 cm*

_{s}^{−1}(μ

*= 1 cm*

_{a}^{−1},

*g*= 0.6-0.95) (see Fig. 3b).

*D*= (3µ

*')*

_{s}^{−1}as the diffusion constant, so that

*z*

_{0}= (µ

*')*

_{s}^{−1}and µ

*= (3µ*

_{eff}*µ*

_{a}*')*

_{s}^{1/2}. In practice, this simpler form of

*D*is not only more accurate, it also makes the inversion of Eq. (3) more robust than the alternative with

*D*= [3(µ

*+ µ*

_{a}*')]*

_{s}^{−1}(and, thereby,

*z*

_{0}= (µ

*+ µ*

_{a}*')*

_{s}^{−1}and µ

*= [3µ*

_{eff}*(µ*

_{a}*+ µ*

_{a}*')]*

_{s}^{1/2}): it was found that the nonlinear least squares algorithm used for inversion often did not converge in this alternative formulation. We note also that the exponential line source model is more accurate than the buried point source model under these experimental conditions, possibly because of the close source-collector separations used.

*' spectrum may cause difficulties with this technique, as outlined in Tseng*

_{s}*et al*. [25

25. S.-H. Tseng, P. Bargo, A. Durkin, and N. Kollias, “Chromophore concentrations, absorption and scattering properties of human skin in-vivo,” Opt. Express **17**(17), 14599–14617 (2009). [CrossRef] [PubMed]

*', making it difficult to spectrally constrain the solution. As well, it has been shown in skin that a piece-wise power law function fits better to μ*

_{s}*', rather than a single power law function as used in this work. For these reasons, the technique presented in this work is likely not well-suited to skin in its present form, although it may be extended or modified to include skin. It is not obvious*

_{s}*a priori*that an algorithm based on homogeneous tissue will translate to layered turbid media such as skin.

*' and low*

_{s}*r*is that scattering phase function information is encoded in the reflectance signal. The Monte Carlo results in Fig. 3 suggest that, for μ

*' < 16.4 cm*

_{s}^{−1}at low absorption (μ

*= 0.1 cm*

_{a}^{−1}), the reflectance at

*r*= 260 µm will be sensitive to both μ

*' and*

_{s}*g*, whereas at

*r*= 780 µm it is sensitive only to μ

*'. The idea that anisotropy is encoded into the reflectance signal at very small*

_{s}*r*separations may be useful in some applications. Since the scattering phase function depends only on the ‘morphology’ of the scattering structures, while μ

*' depends on both morphology and abundance, a measure of both may provide additional biological information.*

_{s}*and μ*

_{a}*' and then applying a*

_{s}*post hoc*spectral constraint to determine the optical properties. The main advantage of using the diffusion theory approach is that it allows use of a simple, closed-form analytic equation that integrates the spectral constraint with the reflectance model, allowing the inverse problem to be solved in a straightforward manner using a Levenberg-Marquardt algorithm. At this time, it is not obvious which approach (diffusion theory or Monte Carlo) is better for this probe geometry and under what conditions. Relevant factors include the overall accuracy, ease of implementation, computational speed and robustness against, for example, tissue inhomogeneity, out-of-range μ

*and μ*

_{a}*' values and measurement noise. This would be an interesting subject for future studies.*

_{s}*') travelled by the detected photons is relatively small; Monte Carlo simulations show that this is in the range of roughly 2-5 transport mean free paths for μ*

_{s}*' between 5 and 25 cm*

_{s}^{−1}. We speculate that this may be partially due to the fact that we are applying a spectral constraint to the model, which differs from the more typical situation for when diffusion theory is applied at single wavelengths, which might require a larger number of transport mean free paths to be robust. It may also be that the exponential line source model is more accurate than the point source model for close fiber separations.

## 6. Conclusions

*and μ*

_{a}*' values, beyond that of any single source-collector separation. The dynamic range is µ*

_{s}*' = 5.8-52.9 cm*

_{s}^{−1}for µ

*= 0-10 cm*

_{a}^{−1}for this geometry. Optical phantoms experiments demonstrated that the derived μ

*and μ*

_{a}*' values are accurate to 5.4% and 4.3%, respectively, when compared against integrating sphere estimates.*

_{s}## References and links

1. | R. A. Weersink, A. Bogaards, M. Gertner, S. R. Davidson, K. Zhang, G. Netchev, J. Trachtenberg, and B. C. Wilson, “Techniques for delivery and monitoring of TOOKAD (WST09)-mediated photodynamic therapy of the prostate: clinical experience and practicalities,” J. Photochem. Photobiol. B |

2. | L. C. Chin, W. M. Whelan, and I. A. Vitkin, “Models and measurements of light intensity changes during laser interstitial thermal therapy: implications for optical monitoring of the coagulation boundary location,” Phys. Med. Biol. |

3. | B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive |

4. | A. Kim, and B. C. Wilson, “Measurement of |

5. | A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H. J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues |

6. | E. Chan, T. Menovsky, and A. J. Welch, “Effects of cryogenic grinding on soft-tissue optical properties,” Appl. Opt. |

7. | M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, and J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. |

8. | T. Svensson, J. Swartling, P. Taroni, A. Torricelli, P. Lindblom, C. Ingvar, and S. Andersson-Engels, “Characterization of normal breast tissue heterogeneity using time-resolved near-infrared spectroscopy,” Phys. Med. Biol. |

9. | L. C. Chin, A. E. Worthington, W. M. Whelan, and I. A. Vitkin, “Determination of the optical properties of turbid media using relative interstitial radiance measurements: Monte Carlo study, experimental validation, and sensitivity analysis,” J. Biomed. Opt. |

10. | R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of |

11. | T. J. Farrell, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. |

12. | D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. |

13. | A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. |

14. | R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. |

15. | P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. |

16. | A. Kim, U. Kasthuri, B. C. Wilson, A. White, and A. L. Martel, “Preliminary clinical results for the |

17. | R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. |

18. | J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A |

19. | S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol. |

20. | V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. |

21. | M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, “Measurement of the optical properties of the skull in the wavelength range 650-950 nm,” Phys. Med. Biol. |

22. | S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. |

23. | M. Roy and B. C. Wilson, “An accurate homogenized tissue phantom for broad spectrum autofluorescence studies: a tool for optimizing quantum dot-based contrast agents,” Proc. SPIE |

24. | J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. |

25. | S.-H. Tseng, P. Bargo, A. Durkin, and N. Kollias, “Chromophore concentrations, absorption and scattering properties of human skin in-vivo,” Opt. Express |

**OCIS Codes**

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.3890) Medical optics and biotechnology : Medical optics instrumentation

(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics

(170.7050) Medical optics and biotechnology : Turbid media

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: January 19, 2010

Revised Manuscript: February 18, 2010

Manuscript Accepted: February 19, 2010

Published: March 3, 2010

**Virtual Issues**

Vol. 5, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Anthony Kim, Mathieu Roy, Farhan Dadani, and Brian C. Wilson, "A fiberoptic reflectance probe with multiple source-collector separations to increase the dynamic range of derived tissue optical absorption and scattering coefficients," Opt. Express **18**, 5580-5594 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-6-5580

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### References

- R. A. Weersink, A. Bogaards, M. Gertner, S. R. Davidson, K. Zhang, G. Netchev, J. Trachtenberg, and B. C. Wilson, “Techniques for delivery and monitoring of TOOKAD (WST09)-mediated photodynamic therapy of the prostate: clinical experience and practicalities,” J. Photochem. Photobiol. B 79(3), 211–222 (2005). [CrossRef] [PubMed]
- L. C. Chin, W. M. Whelan, and I. A. Vitkin, “Models and measurements of light intensity changes during laser interstitial thermal therapy: implications for optical monitoring of the coagulation boundary location,” Phys. Med. Biol. 48(4), 543–559 (2003). [CrossRef] [PubMed]
- B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2(1/2), 26–40 (2000). [CrossRef] [PubMed]
- A. Kim, and B. C. Wilson, “Measurement of ex vivo and in vivo tissue optical properties: Methods and theories,” in Optical-Thermal Response of Laser-Irradiated Tissue, A.J. Welch and M.J.C. van Gemert eds., (Springer SBM, in press 2010), Chap. 8.
- A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H. J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Phys. Med. Biol. 47(12), 2059–2073 (2002). [CrossRef] [PubMed]
- E. Chan, T. Menovsky, and A. J. Welch, “Effects of cryogenic grinding on soft-tissue optical properties,” Appl. Opt. 35(22), 4526–4532 (1996). [CrossRef] [PubMed]
- M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, and J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30(31), 4474–4476 (1991). [CrossRef] [PubMed]
- T. Svensson, J. Swartling, P. Taroni, A. Torricelli, P. Lindblom, C. Ingvar, and S. Andersson-Engels, “Characterization of normal breast tissue heterogeneity using time-resolved near-infrared spectroscopy,” Phys. Med. Biol. 50(11), 2559–2571 (2005). [CrossRef] [PubMed]
- L. C. Chin, A. E. Worthington, W. M. Whelan, and I. A. Vitkin, “Determination of the optical properties of turbid media using relative interstitial radiance measurements: Monte Carlo study, experimental validation, and sensitivity analysis,” J. Biomed. Opt. 12(6), 064027 (2007). [CrossRef]
- R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]
- T. J. Farrell, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19(4), 879–888 (1992). [CrossRef] [PubMed]
- D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30(11), 1354–1356 (2005). [CrossRef] [PubMed]
- A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35(13), 2304–2314 (1996). [CrossRef] [PubMed]
- R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46(29), 7317–7328 (2007). [CrossRef] [PubMed]
- P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10(3), 034018 (2005). [CrossRef] [PubMed]
- A. Kim, U. Kasthuri, B. C. Wilson, A. White, and A. L. Martel, “Preliminary clinical results for the in vivo detection of breast cancer using interstitial diffuse optical spectroscopy,” in Proc. MICCAI-Biophotonics, 75–82 (2006).
- R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. 22(16), 2456–2462 (1983). [CrossRef] [PubMed]
- J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A 22(3), 546–551 (2005). [CrossRef]
- S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol. 67(1), 23–32 (1998). [CrossRef] [PubMed]
- V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35(9), 1317–1334 (1990). [CrossRef] [PubMed]
- M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, “Measurement of the optical properties of the skull in the wavelength range 650-950 nm,” Phys. Med. Biol. 38(4), 503–510 (1993). [CrossRef] [PubMed]
- S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12(5), 510–519 (1992). [CrossRef] [PubMed]
- M. Roy and B. C. Wilson, “An accurate homogenized tissue phantom for broad spectrum autofluorescence studies: a tool for optimizing quantum dot-based contrast agents,” Proc. SPIE 6870, 68700E (2008). [CrossRef]
- J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. 45(31), 8152–8162 (2006). [CrossRef] [PubMed]
- S.-H. Tseng, P. Bargo, A. Durkin, and N. Kollias, “Chromophore concentrations, absorption and scattering properties of human skin in-vivo,” Opt. Express 17(17), 14599–14617 (2009). [CrossRef] [PubMed]

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