## Effect of dependent scattering on the optical properties of Intralipid tissue phantoms |

Biomedical Optics Express, Vol. 2, Issue 8, pp. 2265-2278 (2011)

http://dx.doi.org/10.1364/BOE.2.002265

Acrobat PDF (1210 KB)

### Abstract

The calibration of optical tissue-simulating phantoms remains an open question in spite of the many techniques proposed for accurate measurements of optical properties. As a consequence, a reference phantom with well known optical properties is still missing. As a first step towards a reference phantom we have recently proposed to use dilutions of Intralipid 20%. In this paper we discuss a matter that is commonly ignored when dilutions are prepared, i.e., the possibility of deviations from the simple linear relationships between the optical properties of the dilution and the Intralipid concentration due to the effects of dependent scattering. The results of an experimental investigation showed that dependent scattering does not affect absorption. As for the reduced scattering coefficient the effect can be described adding a term proportional to the square of the concentration. However, for concentrations of interest for tissue optics deviations from linearity remain within about 2%. The experimental investigation also showed that the microphysical properties of Intralipid are not affected by dilution. These results show the possibility to easily obtain a liquid diffusive phantom whose optical properties are known with error smaller than about 1%. Due to the intrinsic limitations of the different techniques proposed for measuring the optical properties it seems difficult to obtain a similar accuracy for solid phantoms.

© 2011 OSA

## 1. Introduction

1. S. Madsen, B. Wilson, M. Patterson, Y. Park, S. Jacques, and Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. **31**, 3509–3517 (1992). [CrossRef] [PubMed]

3. E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express **16**, 10440–10454 (2008). [CrossRef]

4. S. Fantini, M. Franceschini, and E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B **11**, 2128–2138 (1994). [CrossRef]

5. H. Xu and M. Patterson, “Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference,” Opt. Express **14**, 6485–6501 (2006). [CrossRef]

6. P. Marquet, F. P. Bevilacqua, C. D. Depeursinge, and E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement, part I: comparison between experiments and simulations,” Opt. Eng. **34**, 2055–2063 (1995). [CrossRef]

9. N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. **13**, 050501 (2008). [CrossRef]

10. A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Mller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. **44**, 2104–2114 (2005). [CrossRef]

11. J. Bouchard, I. Veilleux, R. Jedidi, I. Noiseux, M. Fortin, and O. Mermut, “Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method,” Opt. Express **18**, 11495–11507 (2010). [CrossRef]

10. A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Mller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. **44**, 2104–2114 (2005). [CrossRef]

*μ′*) and 30% for the absorption coefficient (

_{s}*μ*). In Ref. [11

_{a}11. J. Bouchard, I. Veilleux, R. Jedidi, I. Noiseux, M. Fortin, and O. Mermut, “Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method,” Opt. Express **18**, 11495–11507 (2010). [CrossRef]

12. F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express **15**, 486–500 (2007). [CrossRef]

*λ*= 751 nm has been discussed making use of experimental results obtained at concentrations significantly higher than concentrations of interest for tissue simulating phantoms, and at a shorter wavelength (

*λ*= 632.8 nm) [20

20. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high density media,” Appl. Opt. **42**, 4023–4030 (2003). [CrossRef]

*μ′*of practical interest for tissue phantoms (

_{s}*μ′*< 2 mm

_{s}^{−1}) deviations remain within about 2%.

## 2. Materials and Methods

### 2.1. Monitoring the Microphysical Properties of Diluted Intralipid

*ɛ*can therefore be used to monitor any change in the microphysical properties of fat droplets due to the dilution of Intralipid 20% in water or to the addition of absorbers: If dilution or addition of absorbers affects the size distribution or the refractive index of fat droplets we expect to obtain different values of

_{eil}*ɛ*from measurements carried out on dilutions prepared in different ways.

_{eil}*μ*< 0.05 mm

_{e}^{−1}). Intralipid was diluted inside a scattering cell and the transmitted power

*P*(

*ρ*) has been measured for different concentrations. Inverting the Lambert-Beer law the value of the extinction coefficient has been obtained for each concentration as where

_{il}*L*is the thickness of the cell, and

*ɛ*has been determined from the slope of the straight line that best fits

_{eil}*μ*(

_{e}*ρ*) as a function of

_{il}*ρ*.

_{il}### 2.2. Dependent Scattering

19. A. Ishimaru and Y. Kuga , “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. **72**1317–20 (1982). [CrossRef]

20. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high density media,” Appl. Opt. **42**, 4023–4030 (2003). [CrossRef]

*μ′*of interest for tissue phantoms can be larger than 0.01 (as an example, the volume concentration of Intralipid 20% necessary to obtain

_{s}*μ′*= 2 mm

_{s}^{−1}at

*λ*= 751 nm is

*ρ*≅ 0.1, that corresponds to a volume concentration of fat droplets of ≅ 0.022), to obtain phantoms with well calibrated optical properties it is therefore necessary to check if the dependent scattering leads to significant deviations from the linearity.

_{il}*μ*has been obtained from multidistance measurements of fluence rate

_{eff}*ϕ*(

*r*) carried out in an infinite medium illuminated by an isotropic CW source [20

20. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high density media,” Appl. Opt. **42**, 4023–4030 (2003). [CrossRef]

*r*from a point source emitting a unitary power: we obtain and

*μ*is obtained from the slope of the straight line that best fits ln[

_{eff}*rϕ*(

*r*)] as a function of the source-receiver distance

*r*. The overall procedure can be summarized in 6 steps.

*ρ*. Denoting with

_{ink}*μ′*(

_{sil}*ρ*) and

_{il}*μ*(

_{ail}*ρ*) the reduced scattering and the absorption coefficient of the diluted Intralipid and with

_{il}*ɛ*the absorption coefficient of non diluted ink,

_{aink}*ɛ*is obtained as where

_{aink}*S*is the slope of the straight line that best fits

_{ink}*ρ*. We point out that if the effect of dependent scattering is significant Eq. (8) is approximated and the error on

_{ink}*μ′*(

_{s}*ρ*) affects the value of

_{il}*ɛ*.

_{aink}**42**, 4023–4030 (2003). [CrossRef]

*ρ*the method consists in measuring

_{il}*μ*after the addition of small quantities of the calibrated ink that changes the absorption coefficient of the dilution of known quantities Δ

_{eff}*μ*(

_{a}*ρ*) =

_{ink}*ɛ*. Using Eq. (11),

_{aink}ρ_{ink}*μ′*(

_{s}*ρ*) and

_{il}*μ*(

_{a}*ρ*) are obtained as where

_{il}*S*

_{1ink}and

*I*

_{1ink}are respectively the slope and the intercept of the straight line that best fits

*ρ*.

_{ink}*μ′*(

_{s}*ρ*) and

_{il}*μ*(

_{a}*ρ*) measured at step 3 are plotted as a function of

_{il}*ρ*. Since, as it will be shown in Sect. 3.1, the microphysical properties of fat droplets are not affected by the dilution of Intralipid in water and by the addition of India ink, deviations from linearity can be ascribed to dependent scattering. As it will be shown by experimental results of Sect. 3.2, for concentrations of Intralipid 20% of practical interest for tissue phantoms deviations from the linearity of

_{il}*μ′*as a function of

_{s}*ρ*are well described by with

_{il}*ɛ′*

_{s2il}significantly smaller than

*ɛ′*

_{s1il}, while for

*μ*(

_{a}*ρ*) no appreciable deviation from the linear behavior (Eq. (7)) has been observed. The coefficients

_{il}*ɛ′*

_{s1il}and

*ɛ′*

_{s2il}are obtained again with a linear fit from the intercept

*I*

_{1il}and the slope

*S*

_{1il}of the straight line that best fits

*μ′*(

_{s}*ρ*)/

_{il}*ρ*as a function of

_{il}*ρ*. In particular the ratio

_{il}*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}can be obtained as: We point out that the ratio

*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}is not affected by the error on

*ɛ*. In fact, the error on

_{aink}*ɛ*causes a systematic overestimation or underestimation of

_{aink}*μ′*(

_{s}*ρ*) by a constant factor that does not affect the ratio

_{il}*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}.

*I*

_{2}

*and the slope*

_{il}*S*

_{2}

*of the straight line that best fits*

_{il}*μ*(

_{a}*ρ*) as a function of

_{il}*ρ*, according to Eq. (7) we obtain:

_{il}*ɛ*

_{aH2O}=

*I*

_{2il}and

*ɛ*=

_{ail}*S*

_{2il}+

*I*

_{2il}. We notice that these values are affected by the error on the absorption coefficient of India ink calibrated at step 2.

*μ′*(

_{s}*ρ*) the expression that includes the effect of dependent scattering, i.e., using Eq. (15) instead of Eq. (6). Equation (8) changes to:

_{il}*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*(see Sect. 3.2) it is possible to show that the contribution of the term proportional to

_{ail}*ρ*at which measurements with the method of absorption of water have been carried out. This term can be therefore neglected in Eq. (17) and a new linear relationship between

_{il}*ρ*is obtained, but with different coefficients with respect to Eq. (8). Using this new relationship, from the slope and the intercept of the line that best fits

_{il}*ρ*we obtain Comparison of Eqs. (18) and (19) with Eqs. (9) and (10) shows that the value of

_{il}*ɛ′*obtained using the method of water absorption with the assumption of independent scattering, actually represents the term

_{sil}*ɛ′*

_{s1il}of Eq. (18), and that the correct value of

*ɛ*can be obtained using for the ratio

_{ail}*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}in Eq. (19) the value obtained at step 4.

*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*.

_{ail}*ɛ′*

_{s1il}is obtained from Eq. (18),

*ɛ*from Eq. (19) using for

_{ail}*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}the value obtained with the method of adding absorption, and

*ɛ′*

_{s2il}from the values of

*ɛ′*

_{s1il}and of

*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}. Of the results obtained with the method of adding absorption we therefore use only the ratio

*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}that, as previously pointed out, is independent of the error on the calibration of India ink.

### 2.3. Experimental Setup

**42**, 4023–4030 (2003). [CrossRef]

*μ′*and

_{s}*μ*at which measurements have been carried out this volume was sufficiently large to act as an infinite medium. The volume concentration

_{a}*ρ*has been obtained from the weight of Intralipid and water using the value 0.988 for the relative density of Intralipid 20% with respect to water [21

_{il}21. R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express **16**, 5907–5925 (2008). [CrossRef]

^{−1}), it would be difficult to weigh with good accuracy the very small quantities of ink necessary to obtain the concentrations of interest for our measurements. For more detailed information on the use of India ink we refer to Ref. [23

23. P. Di Ninni, F. Martelli, and G. Zaccanti, “The use of India ink in tissue-simulating phantoms,” Opt. Express **18**, 26854–26865 (2010). [CrossRef]

## 3. Experimental Results

17. P. Di Ninni, F. Martelli, and G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. **56**, N21–N28 (2011). [CrossRef]

### 3.1. Monitoring the Microphysical Properties of Diluted Intralipid

*λ*= 751 nm and 833 nm carrying out measurements on dilutions with similar concentrations but prepared in different ways. Examples of results are reported in Fig. 1. Panels a)–c) pertain to

*λ*= 751 nm, panels d)–f) to 833 nm. The error bars are not shown since smaller than the marks. Panels a) and d) show the results for a dilution prepared taking a sample directly from the bag of Intralipid 20%. To obtain accurate values for the concentrations the sample has been prediluted (1.185 g of Intralipid in 98.348 g of water).

*λ*= 751 nm (267.0 g of Intralipid 20% in 2478 g of water).

*λ*= 751 nm for step 2 (80.11 g of Intralipid 20% and 2.49 g of prediluted ink in 2458 g of water). The contribution to the extinction coefficient due to the small quantity of prediluted ink was negligible (smaller than 0.1%). The value expected for

*ɛ*from these measurements is therefore the same obtained from measurements on other samples provided the added ink does not change the microphysical properties of Intralipid. The results we have obtained for

_{eil}*ɛ*from measurements at 751 nm (panels a)–c)) were 66.3±0.3, 66.3±0.3, and 66.2±0.3 mm

_{eil}^{−1}respectively, and at 833 nm (panels d)–f)) 50.9±0.3, 51.1±0.3, and 50.8±0.3 mm

^{−1}respectively. Within the standard deviation the results are indistinguishable both at 751 nm and at 833 nm, showing that the microphysical properties of diluted Intralipid do not depend on the way the dilution has been prepared. In particular, they are not affected by the addition of the India ink used for measurements at steps 2 and 3.

21. R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express **16**, 5907–5925 (2008). [CrossRef]

### 3.2. Dependent Scattering

*λ*= 751 nm and 833 nm are summarized in Figs. 2 and 3 respectively. Different panels show the results pertaining to the different steps of the measuring procedure together with the straight lines that best fit the results.

*ɛ′*and

_{sil}*ɛ*with the method of water absorption (Eqs. (9) and (10), step 1). For the absorption coefficient of water, since published data show an appreciable spread of values and often the information on the standard error is not provided (see Ref. [12

_{ail}12. F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express **15**, 486–500 (2007). [CrossRef]

12. F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express **15**, 486–500 (2007). [CrossRef]

*ɛ*

_{aH2O}= (2.77±0.02)×10

^{−3}mm

^{−1}and (3.55±0.02)×10

^{−3}mm

^{−1}at 751 and 833 nm respectively.

*ɛ*(step 2) are plotted in panel b). The concentration of Intralipid 20% was

_{aink}*ρ*= 0.0289 at 751 nm and 0.0306 at 833 nm, and was not appreciably changed by the addition of the prediluted ink (

_{il}*ρ*changed less than 0.1%).

_{il}*μ′*(

_{s}*ρ*) and

_{il}*μ*(

_{a}*ρ*) (step 3). Panel c) reports measurements for the smallest value of

_{il}*ρ*we considered (

_{il}*ρ*= 0.0204 at 751 nm and 0.0214 at 833 nm) and panel d) for the largest value (

_{il}*ρ*= 0.1408 at 751 nm and 0.1082 at 833 nm). The values of

_{il}*μ′*(

_{s}*ρ*) and

_{il}*μ*(

_{a}*ρ*) measured at step 3 are displayed in panels e) and f) respectively. These data are used to evaluate the effect of dependent scattering (step 4). To highlight the small deviations from the linearity observed for

_{il}*μ′*in panel e) we displayed the ratio

_{s}*μ′*(

_{s}*ρ*)/

_{il}*ρ*. The ratio would be independent of

_{il}*ρ*if the microphysical properties of Intralipid are not affected by the dilution or by the addition of India ink and the assumption of independent scattering (Eq. (6)) is fulfilled. Since it has been shown in Sect. 3.1 that dilution does not affect the microphysical properties, variations of the ratio

_{il}*μ′*(

_{s}*ρ*)/

_{il}*ρ*are therefore ascribed to the effect of dependent scattering. The experimental results show that

_{il}*μ′*(

_{s}*ρ*)/

_{il}*ρ*slightly decreases as

_{il}*ρ*increases, i.e., the dependent scattering slightly decreases the reduced scattering efficiency. As anticipated in Sect. 2.2 the results are fitted reasonably well by a straight line, and the ratio

_{il}*S*

_{1il}/

*I*

_{1il}is used to obtain

*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}(Eq. (15)). Panel f) shows

*μ*(

_{a}*ρ*) as a function of

_{il}*ρ*. Also these results are fitted reasonably well by a straight line. This indicates that the dependent scattering does not appreciably affect absorption and also that absorption of Intralipid is smaller than absorption of water. From the slope and the intercept of the straight line the values of

_{il}*ɛ*and

_{ail}*ɛ*

_{aH2O}are obtained using Eq. (7).

*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*are obtained (step 5). Finally, using for

_{ail}*μ′*(

_{s}*ρ*) the value evaluated with the results obtained at step 5), a more accurate value for

_{il}*ɛ*is obtained from the data of panel b) (step 6).

_{aink}*ɛ*both the results obtained at steps 4 and 5. The two values are consistent, however since the value obtained at step 4 is affected by the error on the calibration of India ink, the value obtained at step 5 is more reliable. We also note that the value of

_{ail}*ɛ*

_{aH2O}obtained at step 4 is consistent with that obtained from direct attenuation measurements in pure water (section 3.2 and Ref. [12

**15**, 486–500 (2007). [CrossRef]

## 4. Discussion and Conclusions

17. P. Di Ninni, F. Martelli, and G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. **56**, N21–N28 (2011). [CrossRef]

*ρ*< 0.1 to obtain

_{il}*μ′*< 2 mm

_{s}^{−1}) deviations remain within about 2%.

19. A. Ishimaru and Y. Kuga , “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. **72**1317–20 (1982). [CrossRef]

**42**, 4023–4030 (2003). [CrossRef]

24. B. L. Drolen and C. L. Tien, “Independent and dependent scattering in packed-sphere systems,” J. Thermophys. **1**, 63–68 (1987). [CrossRef]

26. J. Kalkman, A. Bykov, D. Faber, and T. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express **18**, 3883–3892 (2010). [CrossRef]

*μ*and

_{a}*μ′*have been reported only in [20

_{s}**42**, 4023–4030 (2003). [CrossRef]

**42**, 4023–4030 (2003). [CrossRef]

*λ*= 632.8 nm and were focussed on high concentrations of Intralipid 20% (up to

*ρ*= 1). The results reported in this paper are in agreement with those of Ref. [20

_{il}**42**, 4023–4030 (2003). [CrossRef]

*μ*and

_{a}*μ′*: absorption is not affected by dependent scattering while the efficiency of reduced scattering decreases as

_{s}*ρ*increases. From measurements at 751 and 833 nm for moderate concentrations (

_{il}*ρ*< 0.15) we obtained for the ratio

_{il}*ɛ′*

_{s2il}/

*ɛ′*

_{s1il}the values −0.27±0.04 and −0.29±0.05 respectively. The value obtained from Ref. [20

**42**, 4023–4030 (2003). [CrossRef]

*λ*= 632.8 nm and high concentrations was −0.37.

*ɛ*,

_{eil}*ɛ*, and

_{ail}*ɛ′*are in excellent agreement with the results we reported in Ref. [23

_{sil}23. P. Di Ninni, F. Martelli, and G. Zaccanti, “The use of India ink in tissue-simulating phantoms,” Opt. Express **18**, 26854–26865 (2010). [CrossRef]

17. P. Di Ninni, F. Martelli, and G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. **56**, N21–N28 (2011). [CrossRef]

*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*have been determined. The accuracy is ultimately limited by random and systematic errors on the parameters

_{ail}*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*and on the concentration

_{ail}*ρ*. With our setup the parameters

_{il}*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*have been determined with a random error of 0.2%, 15%, and 10%, respectively. As for systematic errors, from the discussion in Ref. [12

_{ail}**15**, 486–500 (2007). [CrossRef]

*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*are of about 0.5%. In positioning the source and the receiving fibers we estimated an uncertainty of 0.1 mm. The corresponding systematic errors are of 1%, 1%, and 5% for

_{ail}*ɛ′*

_{s1il},

*ɛ′*

_{s2il}, and

*ɛ*respectively, when measurements of fluence are carried at interfibre distances between 10 and 35 mm, as is the case for the results reported in section 3. However, this error can be easily reduced if measurements are carried out for larger interfibre distances. As an example, with an uncertainty of 0.1 mm the errors are reduced to 0.2%, 0.2%, and 1%, i.e., smaller than random errors, if measurements are carried out between 20 and 45 mm. The disadvantage in carrying out measurements at larger interfibre distances is the larger volume of diffusive medium necessary to mimic the infinite medium.

_{ail}*ρ*. Since the density of Intralipid 20% is close to the density of water, it is possible with negligible error to obtain the optical properties referred to the weight concentration

_{il}*ρ*taking into account that for concentrations of practical interest is

_{wil}*ρ*≅

_{il}*ρ*/0.988.

_{wil}*μ′*, and that at the NIR wavelengths we investigated for dilutions of practical interest the absorption coefficient is practically equal to the absorption of pure water. Furthermore, using the calibrated Intralipid it is possible to measure the absorption coefficient of India ink with the same accuracy we have on the reduced scattering coefficient of Intralipid. Mixing calibrated Intralipid as a scattering medium and calibrated India ink as an absorbing medium it is therefore possible to obtain liquid phantoms with the desired scattering and absorption properties with errors smaller than 1%.

_{sil}11. J. Bouchard, I. Veilleux, R. Jedidi, I. Noiseux, M. Fortin, and O. Mermut, “Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method,” Opt. Express **18**, 11495–11507 (2010). [CrossRef]

27. S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express **12**, 2102–2111 (2004). [CrossRef]

28. G. Zaccanti, L. Alianelli, C. Blumetti, and S. Carraresi, “Method for measuring the mean time of flight spent by photons inside a volume element of a highly diffusing medium,” Opt. Lett. **24**, 1290–1292 (1999). [CrossRef]

## Acknowledgments

## References and links

1. | S. Madsen, B. Wilson, M. Patterson, Y. Park, S. Jacques, and Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. |

2. | R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, and G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. |

3. | E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express |

4. | S. Fantini, M. Franceschini, and E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B |

5. | H. Xu and M. Patterson, “Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference,” Opt. Express |

6. | P. Marquet, F. P. Bevilacqua, C. D. Depeursinge, and E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement, part I: comparison between experiments and simulations,” Opt. Eng. |

7. | R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers,” Opt. Lett. |

8. | C. Chen, J. Q. Lu, H. Ding, K. Jacobs, Y. Du, and X. H. Hu, “A primary method for determination of optical parameters of turbid samples and application to intralipid between 550 and 1630nm,” Opt. Express |

9. | N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. |

10. | A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Mller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. |

11. | J. Bouchard, I. Veilleux, R. Jedidi, I. Noiseux, M. Fortin, and O. Mermut, “Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method,” Opt. Express |

12. | F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express |

13. | L. Spinelli, F. Martelli, A. Farina, A. Pifferi, A. Torricelli, R. Cubeddu, and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method,” Opt. Express |

14. | B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. |

15. | M. Zude (Ed.), |

16. | J. Johansson, S. Folestad, M. Josefson, A. Sparn, C. Abrahamsson, S. Anderson-Engels, and S. Svanberg, “Time-resolved NIR/Vis spectroscopy for analysis of solids: Pharmaceutical tablets,” Appl. Spectrosc. |

17. | P. Di Ninni, F. Martelli, and G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. |

18. | M. I. Mishchenko, L. D. Travis, and A. A. Lacis, |

19. | A. Ishimaru and Y. Kuga , “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. |

20. | G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high density media,” Appl. Opt. |

21. | R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express |

22. | C. F. Bohren and D. R. Huffman, |

23. | P. Di Ninni, F. Martelli, and G. Zaccanti, “The use of India ink in tissue-simulating phantoms,” Opt. Express |

24. | B. L. Drolen and C. L. Tien, “Independent and dependent scattering in packed-sphere systems,” J. Thermophys. |

25. | G. Göbel, J. Kuhn, and J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves in Random Media |

26. | J. Kalkman, A. Bykov, D. Faber, and T. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express |

27. | S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express |

28. | G. Zaccanti, L. Alianelli, C. Blumetti, and S. Carraresi, “Method for measuring the mean time of flight spent by photons inside a volume element of a highly diffusing medium,” Opt. Lett. |

**OCIS Codes**

(160.4760) Materials : Optical properties

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

(170.7050) Medical optics and biotechnology : Turbid media

**ToC Category:**

Calibration, Validation and Phantom Studies

**History**

Original Manuscript: June 8, 2011

Revised Manuscript: June 29, 2011

Manuscript Accepted: July 6, 2011

Published: July 14, 2011

**Citation**

Paola Di Ninni, Fabrizio Martelli, and Giovanni Zaccanti, "Effect of dependent scattering on the optical properties of Intralipid tissue phantoms," Biomed. Opt. Express **2**, 2265-2278 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-8-2265

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### References

- S. Madsen, B. Wilson, M. Patterson, Y. Park, S. Jacques, and Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992). [CrossRef] [PubMed]
- R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, and G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994). [CrossRef]
- E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 16, 10440–10454 (2008). [CrossRef]
- S. Fantini, M. Franceschini, and E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994). [CrossRef]
- H. Xu and M. Patterson, “Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference,” Opt. Express 14, 6485–6501 (2006). [CrossRef]
- P. Marquet, F. P. Bevilacqua, C. D. Depeursinge, and E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement, part I: comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995). [CrossRef]
- R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers,” Opt. Lett. 27, 246–248 (2002). [CrossRef]
- C. Chen, J. Q. Lu, H. Ding, K. Jacobs, Y. Du, and X. H. Hu, “A primary method for determination of optical parameters of turbid samples and application to intralipid between 550 and 1630nm,” Opt. Express 14, 7420–7435 (2006). [CrossRef]
- N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008). [CrossRef]
- A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Mller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. 44, 2104–2114 (2005). [CrossRef]
- J. Bouchard, I. Veilleux, R. Jedidi, I. Noiseux, M. Fortin, and O. Mermut, “Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method,” Opt. Express 18, 11495–11507 (2010). [CrossRef]
- F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express 15, 486–500 (2007). [CrossRef]
- L. Spinelli, F. Martelli, A. Farina, A. Pifferi, A. Torricelli, R. Cubeddu, and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method,” Opt. Express 15, 6589–6604 (2007). [CrossRef]
- B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006). [CrossRef]
- M. Zude (Ed.), Optical Monitoring of Fresh and Processed Agricultural Crops , (Contemporary Food Engineering Series), (CRC Press, Boca Raton, Florida, 2009).
- J. Johansson, S. Folestad, M. Josefson, A. Sparn, C. Abrahamsson, S. Anderson-Engels, and S. Svanberg, “Time-resolved NIR/Vis spectroscopy for analysis of solids: Pharmaceutical tablets,” Appl. Spectrosc. 56, 725–731 (2002). [CrossRef]
- P. Di Ninni, F. Martelli, and G. Zaccanti, “Intralipid: towards a diffusive reference standard for optical tissue phantoms,” Phys. Med. Biol. 56, N21–N28 (2011). [CrossRef]
- M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles , (Cambridge University Press, Cambridge, UK, 2002).
- A. Ishimaru and Y. Kuga , “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 721317–20 (1982). [CrossRef]
- G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high density media,” Appl. Opt. 42, 4023–4030 (2003). [CrossRef]
- R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16, 5907–5925 (2008). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles , (John Wiley and Sons, New York, 1983).
- P. Di Ninni, F. Martelli, and G. Zaccanti, “The use of India ink in tissue-simulating phantoms,” Opt. Express 18, 26854–26865 (2010). [CrossRef]
- B. L. Drolen and C. L. Tien, “Independent and dependent scattering in packed-sphere systems,” J. Thermophys. 1, 63–68 (1987). [CrossRef]
- G. Göbel, J. Kuhn, and J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves in Random Media 5, 413–426 (1995). [CrossRef]
- J. Kalkman, A. Bykov, D. Faber, and T. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express 18, 3883–3892 (2010). [CrossRef]
- S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004). [CrossRef]
- G. Zaccanti, L. Alianelli, C. Blumetti, and S. Carraresi, “Method for measuring the mean time of flight spent by photons inside a volume element of a highly diffusing medium,” Opt. Lett. 24, 1290–1292 (1999). [CrossRef]

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