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J Biomed Opt. Author manuscript; available in PMC 2010 September 1.

Published in final edited form as:

PMCID: PMC2778761

NIHMSID: NIHMS157771

Sheng-Hao Tseng

Sheng-Hao Tseng, National Cheng-Kung University, Department of Electro-Optical Engineering, 1 University Road, Tainan, Taiwan 701;

University of California, Irvine, Beckman Laser Institute, Laser Microbeam and Medical Program, 1002 Health Sciences Road, Irvine, California 92617

Address all correspondence to: Sheng-Hao Tseng, National Cheng-Kung University, Department of Electro-Optical Engineering, 1 University Road, Tainan 701, Taiwan. Tel: 886-6-275-7575; Fax: 886-6-208-4933; Email: moc.liamg@gnest.oahgnehs

The publisher's final edited version of this article is available at J Biomed Opt

See other articles in PMC that cite the published article.

We design a special diffusing probe to investigate the optical properties of human skin *in vivo*. The special geometry of the probe enables a modified two-layer (MTL) diffusion model to precisely describe the photon transport even when the source-detector separation is shorter than 3 mean free paths. We provide a frequency domain comparison between the Monte Carlo model and the diffusion model in both the MTL geometry and conventional semiinfinite geometry. We show that using the Monte Carlo model as a benchmark method, the MTL diffusion theory performs better than the diffusion theory in the semiinfinite geometry. In addition, we carry out Monte Carlo simulations with the goal of investigating the dependence of the interrogation depth of this probe on several parameters including source-detector separation, sample optical properties, and properties of the diffusing high-scattering layer. From the simulations, we find that the optical properties of samples modulate the interrogation volume greatly, and the source-detector separation and the thickness of the diffusing layer are the two dominant probe parameters that impact the interrogation volume. Our simulation results provide design guidelines for a MTL geometry probe.

Near-IR diffuse optical spectroscopy (DOS) is commonly used to determine *in vivo* tissue absorption coefficient *μ _{a}* and reduced scattering coefficient ${\mu}_{s}^{\prime}$, from which tissue functional information, such as hemoglobin concentration, oxygen saturation, water concentration, and averaged scatter size and density can be deduced.

The photon transport model most often utilized for determining optical properties from DOS measurements is the standard diffusion model derived from the radiative transport theory. Because of its simplicity and computational efficiency, the standard diffusion model has been used widely and successfully to recover optical properties of deep tissues.^{12}^{,}^{13} While the standard diffusion model is derived from the radiative transport theory with diffusion approximations, the model cannot be used reliably for recovering the optical properties of typical biological tissues when (*ρ/l _{t}*) is smaller than 10, where

Although methods based on Monte Carlo techniques have, in certain circumstances, been shown to provide the most accurate results among the aforementioned models, the need for intensive computation resources to build a data library in advance limits its applicability. Several researchers have developed the so-called “white Monte Carlo model,” which enables the calculation of optical properties based on a single Monte Carlo simulation to bring the computation time similar to the diffusion theory based models.^{17} However, it is shown that even with the white Monte Carlo method, a data library containing various single scattering phase functions still must be established in advance to properly recover optical properties of superficial tissues, since the single scattering phase function of tissue actively affects the measured reflectance especially when the source-detector separation is^{20} shorter than 1 to 2 mm. By changing the scattering phase function used in the Monte Carlo model, Liu and Ramanujam reported the reflectance generated with different scattering phase functions could have deviation larger than 20% at source-detector separations shorter than 1 mm. This deviation in calculated reflectance resulted in 31.4% error in the recovered absorption coefficient.^{21} In contrast, the diffusion-based models do not require a phase function to recover *μ _{a}* and ${\mu}_{s}^{\prime}$. We demonstrated that using a novel optical probe to facilitate the usage of the diffusion model to recover the optical properties of superficial volume of a tissue phantom $({\mu}_{s}^{\prime}\u2215{\mu}_{a}=25)$ with less than 8% error.

The diffusing probe we proposed employs a slab of highly scattering Spectralon (Labsphere, New Hampshire) (${\mu}_{s}^{\prime}\sim 50\u2215\mathrm{mm}$, *μ _{a}*~10

We successfully applied the diffusing probe to study the optical properties of *in vivo* human skin.^{22} We are planning to use the diffusing probe in many clinical applications. To correctly interpret *in vivo* measurement results obtained from the diffusing probe, it is critical to characterize and understand the effects of parameters of the diffusing probe that may impact the interrogation volume. The primary objective of this paper is to methodically examine the influence of sample optical properties and probe parameters on the depth of interrogation of the diffusing probe.

In this paper, we first demonstrate the accuracy and the advantage of the MTL diffusion model over a standard diffusion approach. The performance of the diffusion model, in either MTL geometry or semiinfinite geometry, was evaluated by a benchmark Monte Carlo model. While the reflectance generated from the Monte Carlo model is sensitive to the choice of the scattering phase function when the source-detector separation is smaller than 1 mm, the Monte Carlo model is usually employed^{23}^{,}^{24} as the gold standard method to calculate diffuse reflectance when the source-detector separation is larger than 1 mm. It was reported that when using different scattering phase functions in the Monte Carlo model, the difference in generated reflectance was less than 10% when the source-detector separation was^{21} larger than 1 mm. Thus, in this study, to use the Monte Carlo model as a benchmark method, we limit the source-detector separations to be larger than 1 mm in all simulations.

We also conducted numerous Monte Carlo simulations with the objective of investigating the dependence of the probing depth of the diffusing probe on the optical properties of samples, scattering, absorption, and thickness of the diffusing layer of the probe, as well as dependence on the source-detector separation. The simulation results presented provide design guidelines for a diffusing probe having specific interrogation depth characteristics.

The superficial diffusing probe employs a source fiber that is coupled to a high-scattering, low-absorption Spectralon slab having known optical properties. Light must pass from the fiber, through the diffusing slab, and into the tissue that is being measured. The detection fiber penetrates the slab and is in contact with the sample, as shown in Fig. 1. In this geometry, the measured reflectance is described using a MTL diffusion model derived from a standard two-layer diffusion model.^{16}^{,}^{25} Previously, we demonstrated^{16}^{,}^{22} that the diffusing probe can be used to accurately determine optical properties of homogeneous tissue phantoms at 660 nm and human skin in the range from 650 to 1000 nm.

To quantitatively evaluate the accuracy of the MTL diffusion model and estimate the effects of various parameters on the interrogation depth of the diffusing probe, we carried out a series of Monte Carlo simulations. The Monte Carlo code used here is an extension of the general multilayer, 3-D, weighted photon Monte Carlo code developed by Wang et al.^{26} Kienle and Patterson^{17} indicated that the asymmetry parameter of tissue is normally greater than 0.8, and an asymmetry parameter between 0.8 and 1 does not significantly influence the reflectance when ${\mu}_{s}^{\prime}$ is constant. Therefore, for all simulations, we employed a Henyey-Greenstein phase function and used an asymmetry parameter of 0.8 for all layers to speed up computation. In the simulations, the optical properties of the diffusing layer (Spectralon) was set at *μ _{a}*=10

In this paper, we will first evaluate the performance of the MTL diffusion model and compare it to the diffusion model in semiinfinite geometry. We utilize the Monte Carlo model, which is in either MTL geometry or semiinfinite geometry, to generate a benchmark frequency domain reflectance that contains phase and amplitude information. Therefore, we can quantitatively calculate the deviation of the frequency domain reflectance generated from the diffusion model, in either geometry, from the benchmark values.

Second, we vary sample optical properties, source-detector separation, and the properties of the diffusing slab in the Monte Carlo model to understand their effect on the interrogation depth of the diffusing probe. We describe the interrogation depth of each Monte Carlo simulation in the following manner. Let ${P}_{i}={W}_{i}\u2215{\sum}_{i=+1}^{n}{W}_{i}$, where *W _{i}* is the final weight of a detected photon packet, and

Moreover, to visualize the distribution of detected photon packets in the superficial diffusing probe geometry, we generate 2-D fluence distribution maps using Monte Carlo simulations. When a photon packet undergoes a collision, a fraction of energy of the photon packet, which is proportional to the weight of the photon packet and the absorption of the medium, is deposited to a local voxel in a 3-D Cartesian coordinate system.^{26} Voxel size is set to be 0.05^{3} mm^{3} or 0.1^{3} mm^{3} when the source-detector separation is 1 or 5 mm, respectively, in our simulations. Local fluence (in joules per square millimeter) is calculated by dividing the deposited energy by the local absorption coefficient. A 3-D photon fluence distribution map is obtained by accumulating the fluence distribution of all photon packets arriving at the detector. The 3-D map is converted to a 2-D *x-z* map by binning along the *y* axis. The maps are normalized by the number of photon packets launched and the volume of a voxel. The photon fluence maps presented here are plotted as logarithm base 10 for greater ease of visualization.

To achieve a relative standard deviation in the predicted reflectance of <5%, a total of 50 million photons were launched in each Monte Carlo simulation for calculating the average interrogation depth unless noted otherwise. Depending on the input parameters, between 10 to 20 h were required to complete a single simulation on an AMD Athlon FX-60-based PC. On the other hand, 50 million photon packets were used in each Monte Carlo simulation for calculating the fluence distribution map, and each required about 60 to 80 h to complete on an AMD Athlon FX-60-based computer. The value of each pixel in the map represents the average fluence of a certain volume.

In this section, we demonstrate the accuracy of reflectance generated from the MTL diffusion model. Results obtained from the Monte Carlo model were used here as a benchmark. In addition, the advantages of using the MTL diffusion model over the conventional diffusion model is discussed.

The Monte Carlo method and the diffusion model were employed to calculate the frequency domain diffuse reflectance in both the MTL geometry and the conventional semiinfinite geometry. In the simulations, the source-detector separation and the thickness of the diffusing layer were 1 and 1.5 mm, respectively. Tissue samples had optical properties of either light skin or dark skin. The optical properties of light skin and dark skin used here were extracted from the *ex vivo* study conducted by Simpson et al.^{24} The optical properties of light skin and dark skin were *μ _{a}*=0.05/mm and ${\mu}_{s}^{\prime}=3\u2215\mathrm{mm}$ and

(a) Amplitude demodulation and (b) phase delay versus source modulation frequency in the MTL geometry with 1-mm source-detector separation. The thickness of the diffusing layer is 1.5 mm. The asymmetry factor *g* is 0.8 for both layers. The sample optical **...**

(a) Amplitude demodulation and (b) phase delay versus source modulation frequency in the semiinfinite geometry with 1-mm source-detector separation. The sample optical properties are designed to simulate light skin (*μ*_{a}=0.05/mm and ${\mu}_{s}^{\prime}$ **...**

The results obtained using the diffusion model in the MTL geometry deviate by a smaller amount from the Monte Carlo model than do the results obtained for the diffusion model in the semi-infinite geometry. In the MTL geometry, the Spectralon layer diffuses the photons emitted from the source fiber, the photons leaving Spectralon and entering tissue sample have a widely varying initial incident angle to the tissue sample surface (this phenomenon can be visually seen in the photon fluence distribution maps that will be shown and discussed shortly). In contrast, in the semiinfinite geometry, all photons from the source fiber have the same incident angle to the sample. Therefore the paths of photons from the source to the detector in these two geometries are much different. From Monte Carlo simulations, we determined that the mean of total path lengths in the sample volume (not including the Spectralon) were 6.1 and 4.3 mm for the MTL geometry and the semiinfinite geometry, respectively, when the source-detector separation was 1 mm and the sample had optical properties of light skin. A longer traveling distance in the sample layer when the MTL geometry is employed means that light propagation in this geometry more closely mimics diffusion. The difference in traveling distance is 1.8 mm, which is equivalent to 5.5 transport mean free paths in a medium that has optical properties of *μ _{a}*=0.05/mm and ${\mu}_{s}^{\prime}=3\u2215\mathrm{mm}$. This explains the reason for the diffusion model performing better in the MTL geometry than in the semiinfinite geometry at a certain source-detector separation.

In addition, from our simulation results (which are shown in Fig. Fig.1010 and and1111 in Sec. 3.5), we found that the interrogation depth of the MTL geometry is 25 to 30% smaller than that of the conventional semiinfinite geometry, at source-detector separations of either 1 or 5 mm. From the Monte Carlo simulations, it was found that most of photons have oblique incidence angles from the diffusing layer to the tissue layer in the MTL geometry. Therefore, photons have shallower interrogation depths in the MTL geometry than in the conventional semiinfinite geometry. This property makes the MTL geometry very suitable for investigating superficial volume of tissues.

Average interrogation depth versus numerical aperture of fibers. The source-detector separations are 1 (lower plot) and 5 mm (upper plot). The optical properties of the slab are *μ*_{a}=10^{−6}/mm and ${\mu}_{s}^{\prime}=50\u2215\mathrm{mm}$. The scattering **...**

Average interrogation depth versus numerical aperture of fibers in the conventional semiinfinite geometry. The source-detector separations are 1 (lower plot) and 5 mm (upper plot). The asymmetry factor *g* is 0.8. The error bars represent standard deviation. **...**

Although the MTL diffusion model results are more accurate than those for the conventional semiinfinite diffusion model results, the conventional semiinfinite diffusion model results deviate from the Monte Carlo results by less than 7%, which is not a large number for computing reflectance. Many researchers have also reported that the standard diffusion model deviates from Monte Carlo simulations by less than 5% even when the ratio of source-detector separation to transport mean free path (*ρ/l _{t}*) is

Because the MTL probe concept originates from a desire to rapidly measure local optical properties close to the source, we limit the analysis of source-detector separation to the 1 to 5-mm range. A detailed analysis of this range follows. We have estimated the attenuation of light from source to detector in this geometry using Monte Carlo simulations of the MTL probe. The attenuation results as a function of source-detector separation are listed in Table 1. In the simulations, the source-detector separation was either 1 or 5 mm, the spectralon thickness was 1.5 or 3 mm, and tissue samples were assigned optical properties corresponding to light skin or dark skin as defined in the Sec. 2. In our previous *in vivo* study, we employed a diffusing probe with 1.5-mm thick Spectralon to successfully recover the optical properties of skin.^{22} Here, we have defined the Spectralon thicknesses to be 1.5 as well as 3 mm to understand the influence of the thickness of the Spectralon on the signal attenuation.

Simulation results shown in Table 1 indicate that when the Spectralon layer is 1.5 mm thick, the attenuations are 22 and 40 dB for light skin at 1 and 5-mm source detector separations, respectively. In a typical frequency domain DOS system such as the one used in our lab, laser diodes deliver about 10 mW of power into the sample. For such a system, with attenuation consistent with that estimated from Monte Carlo simulations, this means that the light intensities will be about −12 and −30 dBm at the detector for source-detector separations of 1 and 5 mm, respectively. If, on the other hand, the sample is similar to dark skin (as described in Sec. 2), the estimated attenuations will be in the range of 24 and 55 dB at 1- and 5-mm source-detector separations respectively. Using our frequency domain DOS system as an example, this will result in a light intensities of −14 and −45 dBm at the detector, respectively.

A typical detector used in the frequency domain DOS measurement is the Hamamatsu APD (model# C5658, Hamamatsu, New Jersey), which has noise level of around −48 dBm. Therefore, a 5-mm source-detector separation is about the largest distance one can use in the frequency domain measurements with this probe design. This is in agreement with our experience in terms of using this probe to measure *in vivo* skin.^{22} Interestingly, at a source-detector separation of 5 mm, the estimated attenuation is reduced when the Spectralon layer thickness is adjusted from 1.5 to 3 mm for measuring dark skin. Because Spectralon essentially doesn’t absorb light (${\mu}_{s}^{\prime}\sim 50\u2215\mathrm{mm}$ and *μ _{a}*~10

Photon fluence distribution maps for a diffusing probe having source-detector separations of (a) 1or (b) 5 mm. The sample optical properties are designed to simulate light color skin (*μ*_{a}=0.05/mm and ${\mu}_{s}^{\prime}=3\u2215\mathrm{mm}$). The thickness **...**

It is known that the optical properties of tissue influence the interrogation depth of DOS techniques.^{6} Because the geometry that we have introduced is somewhat unusual, it is not necessarily obvious how the interrogation depth will be affected by sample optical properties. Hence, Monte Carlo simulations were carried out in an effort to determine the average interrogation depths of the superficial diffusing probe for near-IR optical properties corresponding to those of various biological tissues. The range of sample optical properties used in the simulations was carefully chosen based on a survey of the literature so as to be inclusive of superficial tissues optical properties in the 600 to 1000-nm wavelength range. Hornung et al.^{29} reported that the optical properties of cervical tissues are in the range from 0.015/mm to 0.019/mm for *μ _{a}* and 0.84/mm to 0.90/mm for ${\mu}_{s}^{\prime}$ at the wavelength of 674 nm. Bays et al.

Figures 5(a) and 5(b) (in the next paragraph) illustrate variation in estimated average interrogation depth as a function of sample optical properties for the source-detector separations of 1 and 5 mm, respectively. The circles shown in Fig.4 are the data generated from Monte Carlo simulations. In general, the interrogation depth increases as absorption and reduced scattering coefficients decrease. When the source-detector separation is 5 mm, the average interrogation depth varies from 1766 to 141 *μ*m as the optical properties vary from *μ _{a}*=0.01/mm and ${\mu}_{s}^{\prime}=0.5\u2215\mathrm{mm}$ (low absorption, low scattering) to

$$Z=\frac{{z}_{0}+A01\left({\mu}_{a}\right)+B01\left({\mu}_{s}^{\prime}\right)+B02{\left({\mu}_{s}^{\prime}\right)}^{2}+B03{\left({\mu}_{s}^{\prime}\right)}^{3}}{1+A1\left({\mu}_{a}\right)+A2{\left({\mu}_{a}\right)}^{2}+A3{\left({\mu}_{a}\right)}^{3}+B1\left({\mu}_{s}^{\prime}\right)+B2{\left({\mu}_{s}^{\prime}\right)}^{2}}.$$

(1)

For the data shown in Fig. 4(a) we obtained the following fitting parameter values: *z*_{0}=889.25641, *A*01=13.05555, *B*01=−306.09145, *B*02=75.63521, *B*03=−7.20714, *A*1=14.14781, *A*2=−36.73759, *A*3=39.38632, *B*1=0.04375, and *B*2=−0.01240. For the data shown in Fig. 4(b), we obtained the following fitting parameter values: *z*_{0}=2265.00667, *A*01=−996.31590, *B*01=−887.58451, *B*02=218.58048, *B*03=−20.33626, *A*1=11.22803, *A*2=−35.76202, *A*3=37.73542, *B*1=−0.07432, *B*2=−3.75×10^{−04}. The surfaces demonstrated in Figs. 4(a) and 4(b) are the fitting results based on Eq. (1) and the parameter values listed in the preceding.

Average interrogation depth of the superficial diffusing probe versus sample optical properties. Simulation results are depicted for probes having source-detector separations of (a) 1 and (b) 5 mm. Sample optical properties are in the ranges of 0.01/mm< **...**

Average interrogation depth versus the source-detector separation. Triangles and circles represent the interrogation depth of the diffusing probe applied to dark skin (*μ*_{a}=0.3/mm and ${\mu}_{s}^{\prime}=3\u2215\mathrm{mm}$) and light skin (*μ*_{a} **...**

Figure 5 shows Monte Carlo simulation results that illustrate average interrogation depth versus source-detector separation for samples having optical properties of light and dark skin as described earlier. The average interrogation depth increases linearly with source-detector separation in the range from 1 to 5 mm, despite differences in optical properties of samples. Monte Carlo simulations were used by other groups to aid in probe design.^{30} In practice, Eq. (1) and Fig. 5 can be used to guide the design of the diffusing probe for a particular application. For example, to achieve similar interrogation depth when applying the diffusing probe to study light skin and dark skin, according to Fig. 5, one could use diffusing probes of 1 and 3 mm source-detector separations to study light skin and dark skin, respectively, to obtain an interrogation depth of around 250 *μ*m.

From Fig. 5, it can be clearly seen that the source-detector separation is a dominant factor that can modulate the interrogation depth of the diffusing probe. To visualize the effect of adjusting the source-detector separation on the sampling region, Fig. 6 illustrates Monte Carlo simulated photon fluence distribution maps for a sample having optical properties mimicking light skin (*μ _{a}*=0.05/mm and ${\mu}_{s}^{\prime}=3\u2215\mathrm{mm}$) measured in the MTL geometry, which has a Spectralon thickness of 1.5 mm and a source-detector separation of 1 or 5 mm. Other parameters used in the simulations were consistent with those used to generate Fig. 4. In general, Fig. 6 shows that the interrogation region of a diffusing probe has the shape close to a semioval. The photon fluence distribution in the sample for a 5-mm source-detector separation diffusing probe is wider and deeper than that for a 1-mm source-detector separation diffusing probe. In Figs. 6(a) and 6(b), the magnitude of the photon fluence beneath the detector of the 5-mm source-detector separation probe is weaker than that of the 1-mm source-detector separation probe by a factor of 100. The rapid decline in detected photon fluence as the source-detector separation increases limits the largest source-detector separation that can be employed in real measurements.

In this section we investigate the influence of probe parameters related to the diffusing layer on the interrogation depth of the diffusing probe. Figure 7 shows the simulated dependence of the interrogation depth of the diffusing probe on the diffusing slab thickness and the absorption coefficient at source-detector separations of 1 and 5 mm. The sample optical properties employed here are those of light and dark skin as detailed in the previous subsection.

Average interrogation depth versus absorption coefficient of the diffusing slab when the source-detector separation is (a) 1 or (b) 5 mm. The diffusing slab thicknesses of 1.5 (empty) and 3 mm (solid) are employed in each plot. Simulated tissues have **...**

For the purposes of these simulations, the *μ _{a}* of the diffusing layer was varied from 10

The results presented in Fig. 7 suggest that the interrogation depth of the diffusing probe can be affected by the thickness of the scattering slab. Figure 7(a) shows that when employing a 1-mm source-detector separation diffusing probe to measure light skin and the thickness of the scattering slab is adjusted from 1.5 to 3 mm, the average interrogation depth increases by 25 *μ*m. On the other hand, in Fig. 7(b), the average interrogation depth decreases by 220 *μ*m when a 5-mm source-detector separation diffusing probe is applied to measure light skin and the thickness of scattering slab is adjusted from 1.5 to 3 mm. The range of variation of interrogation depth introduced by adjusting the scattering slab thickness is larger for the 5-mm source-detector separation diffusing probe than that for the 1-mm source-detector separation diffusing probe. In addition, the trends in the variation in the interrogation depths are opposite for these two cases. This is reinforced with two additional photon fluence distribution maps as shown in Fig. 8. Figures 8(a) and 8(b) depict simulated photon fluence distribution maps for probes having a 3-mm-thick scattering slab and with source-detector separations of 1 and 5 mm, respectively. Other parameters are identical to those used to generate Fig. 6. Comparing Fig. 6(a) and Fig. 8(a), it is clear that the interrogation region is widened when the scattering slab thickness of a 1-mm source-detector separation diffusing probe increases from 1.5 to 3 mm. Increasing slab thickness results in greater lateral propagation of light. The positions of the detectors are fixed at 1 mm from the source in both Fig. 6(a) and Fig. 8(a). Thus, in Fig. 8(a), as photons propagate laterally more than 2 mm from the source in the scattering slab, photons have to travel in the sample at a average depth deeper than the average depth determined in the Fig. 6(a) before they arrive at the detector. Therefore, the interrogation depth of a 1-mm source-detector separation diffusing probe increases as the thickness of the scattering slab increases from 1.5 to 3 mm.

In contrast, when the source-detector separation is 5 mm, the magnitude of the photon fluence in the scattering slab at the lateral position of the detector is greater in Fig. 8(b) than that in Fig. 6(b). As the thickness of the scattering slab increases, so does the number of photons that travel through the slab to positions near the detector before entering the sample. Those photons will be more likely to travel superficial trajectories in the sample prior to detection. Accordingly, the interrogation region becomes more concentrated near the top of the sample as the thickness of the scattering slab of a 5-mm source-detector separation diffusing probe is increased from 1.5 to 3 mm.

The detailed dependence of the interrogation depth on the scattering slab thickness for various source-detector separations is shown in Fig. 9. For this set of simulations, the thickness of the scattering slab is varied from 0.75 to 3 mm while the source-detector separation is varied from 1 to 5 mm. The reason for setting the lower bound and upper bound of the Spectralon thickness to 0.75 and 3 mm, respectively, is to understand the effect of varying the Spectralon thickness of the currently working prototype, which has a 1.5-mm Spectralon thickness. The optical properties of the scattering slab and the sample are *μ _{a}*=10

Average interrogation depth versus thickness of the diffusing slab. The source-detector separations employed in the simulations are 1 (square), 3 (circle), and 5 mm (triangle). The optical properties of the slab and the sample are *μ*_{a}=10^{−6} **...**

We also carried out a series of Monte Carlo simulations to study the dependence of the interrogation depths of the diffusing probe on the ${\mu}_{s}^{\prime}$ of the scattering slab. The absorption coefficient of the scattering slab is 10^{−6}/mm while other parameters are the same as those used to generate Fig. 7. When the ${\mu}_{s}^{\prime}$ of the scattering slab is adjusted from 25/mm to 200/mm the interrogation depth varies less than 2%, which is smaller than the standard deviation of simulations, for a particular source-detector separation. Changing the optical properties of the sample or the thickness of the scattering slab used in the simulations does not alter this trend. This means that the ${\mu}_{s}^{\prime}$ of the scattering slab does not play a critical role in modulating the interrogation of the probe. Moreover, our simulation results reveal that the photon detection efficiency would become worse when employing a scattering slab of a certain thickness with a higher scattering coefficient. Therefore, the scattering coefficient of the diffusing layer should be chosen just high enough to make the diffusion approximation valid so that the photon detection efficiency would not be compromised.

To make the diffusion approximation valid in the case where photons transmitting through a slab consist of scatters and absorbers, the slab must have the reduced scattering coefficient much greater than the absorption coefficient and the slab thickness should be larger than 8*l _{r}*, where ${l}_{r}=1\u2215({\mu}_{a}+{\mu}_{s}^{\prime})$ is the transport mean free path.

We also investigated the influence of the numerical aperture (NA) of fibers on the interrogation depth. Simulations were carried out using 1- and 5-mm source-detector separations for a 1.5-mm scattering slab thickness. One hundred million photons were used in the simulations to achieve a standard deviation smaller than 3%. The optical properties of the scattering slab and the sample are *μ _{a}*=10

Finally, since the reduced scattering coefficient can be expressed as ${\mu}_{s}^{\prime}={\mu}_{s}(1-g)$, where *μ _{s}* is the scattering coefficient, and

In addition, we also carried out a series of Monte Carlo simulations to investigate the effect of the asymmetry factor of tissue samples on the interrogation depth of the diffusing probe. In the simulations, we designed the tissue asymmetry factors to be in the range from 0.8 to 0.99. Other parameters were the same as those already mentioned. When the source-detector separation was 1 mm, the interrogation depths were determined to be 274±3 *μ*m. Our simulation results infer that the influence of the tissue asymmetry factor on the interrogation depth of the diffusing probe is weak. Therefore the simulation results shown in this work can also apply to the cases where the asymmetry factor of superficial tissues is higher than 0.8.

We used the results of Monte Carlo simulations to characterize and illustrate the properties of the MTL geometry and contrast this to conventional semiinfinite geometry. We found that the diffusion theory performs better in the MTL geometry than in the conventional semiinfinite geometry at short source-detector separations. In addition, the probing depth of the MTL geometry is smaller than that of the semiinfinite geometry at a same source-detector separation.

We then demonstrated the relationship between the interrogation depth and several parameters of the superficial diffusing probe in MTL geometry, including sample optical properties, source-detector separations, and the properties of the diffusing slab. The results from Monte Carlo simulations illustrate that the optical properties of the samples play a significant role in modulating the interrogation depth of the diffusing probe.

The two dominant probe parameters that influence the interrogatian depth of a diffusing probe are the source-detector separation and the thickness of the scattering layer. The average interrogation depth of the diffusing probe varies linearly with the source-detector separation in the range from 1 to 5 mm. The diffusing probe generally has shallower interrogation depth than a conventional DOS probe at a same source-detector separation. In addition, as shown in Figs. Figs.1010 and and11,11, the dependence of the interrogation depths on the source-detector separation of the diffusing probe is weaker than that of a semiinfinite geometry probe. Although the thickness of the scattering layer has an effect on the interrogation depth, we illustrated that the magnitude of this effect depends on the source-detector separation. To choose a proper scattering layer thickness for a diffusing probe, both the validity of the diffusion approximation and the probe reliability should be taken into consideration.

On the other hand, the dependence of the interrogation depths on the NA of detection fiber is much weaker than that of a semiinfinite geometry probe. Thus, the NA of the detection fiber is not an efficient parameter that can be used to control the interrogation depth. While the optical properties, including absorption coefficient, reduced scattering coefficient, and asymmetry factor, of the diffusing slab have a negligible influence on the interrogation depth, they can greatly affect the photon detection efficiency. Our simulation results provide guidelines for designing a diffusing probe with a specific average interrogation depth for various clinical applications, including skin hydration measurements, monitoring of the oral cavity, and optical characterization of skin cancer and precancer.

Dr. Tseng would like to acknowledge the support provided by the National Science Council of Taiwan under Grant No. NSC-98-2218-E-006-013. Dr. Durkin is supported by the National Institutes of Health/National Center for Research Resources (NCRR) under Grant No. P41-RR01192 (Laser Microbeam and Medical Program: LAMMP).

1. Cubeddu R, Pifferi A, Taroni P, Torricelli A, Valentini G. Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast. Appl. Phys. Lett. 1999;74:874–876.

2. Bevilacqua F, Berger AJ, Cerussi AE, Jakubowski D, Tromberg BJ. Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods. Appl. Opt. 2000;39:6498–6507. [PubMed]

3. Mourant JR, Freyer JP, Hielscher AH, Eick AA, Shen D, Johnson TM. Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics. Appl. Opt. 1998;37:3586–3593. [PubMed]

4. Cerussi A, Shah N, Hsiang D, Durkin A, Butler J, Tromberg BJ. In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy. J. Biomed. Opt. 2006;11:044005. [PubMed]

5. Bevilacqua F, Depeursinge C. Monte Carlo study of diffuse reflectance at source-detector separations close to one transport mean free path. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 1999;16:2935–2945.

6. Bevilacqua F, You JS, Hayakawa CK, Venugopalan V. Sampling tissue volumes using frequency-domain photon migration. Phys. Rev. E. 2004;69:051908. [PubMed]

7. Tromberg BJ, Shah N, Lanning R, Cerussi A, Espinoza J, Pham T, Svaasand L, Butler J. Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy. Neo-plasia. 2000;2:26–40. [PMC free article] [PubMed]

8. Hebden JC, Gibson A, Austin T, Yusof RM, Everdell N, Delpy DT, Arridge SR, Meek JH, Wyatt JS. Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography. Phys. Med. Biol. 2004;49:1117–1130. [PubMed]

9. Bevilacqua F, Piguet D, Marquet P, Gross JD, Tromberg BJ, Depeursinge C. In vivo local determination of tissue optical properties: applications to human brain. Appl. Opt. 1999;38:4939–4950. [PubMed]

10. Bays R, Wagnieres G, Robert D, Braichotte D, Savary JF, Monnier P, van den Bergh H. Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry. Appl. Opt. 1996;35:1756–1766. [PubMed]

11. Amelink A, Sterenborg HJCM, Bard MPL, Burgers SA. In vivo measurement of the local optical properties of tissue by use of differential path-length spectroscopy. Opt. Lett. 2004;29:1087–1089. [PubMed]

12. Ishimaru A. Wave Propagation and Scattering in Random Media. Academic Press; New York: 1978.

13. Kienle A, Patterson MS. Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 1997;14:246–254. [PubMed]

14. Yoo KM, Liu F, Alfano RR. When does the diffusion-approximation fail to describe photon transport in random-media. Phys. Rev. Lett. 1990;64:2647–2650. [PubMed]

15. Martelli F, Bassani M, Alianelli L, Zangheri L, Zaccanti G. Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation. Phys. Med. Biol. 2000;45:1359–1373. [PubMed]

16. Tseng SH, Hayakawa C, Tromberg BJ, Spanier J, Durkin AJ. Quantitative spectroscopy of superficial turbid media. Opt. Lett. 2005;30:3165–3167. [PubMed]

17. Kienle A, Patterson MS. Determination of the optical properties of turbid media from a single Monte Carlo simulation. Phys. Med. Biol. 1996;41:2221–2227. [PubMed]

18. Carp SA, Prahl SA, Venugopalan V. Radiative transport in the delta-P-1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media. J. Biomed. Opt. 2004;9:632–647. [PubMed]

19. Hull EL, Foster TH. Steady-state reflectance spectroscopy in the P-3 approximation. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 2001;18:584–599.

20. Thueler P, Charvet I, Bevilacqua F, St Ghislain M, Ory G, Marquet P, Meda P, Vermeulen B, Depeursinge C. In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties. J. Biomed. Opt. 2003;8:495–503. [PubMed]

21. Liu Q, Ramanujam N. Scaling method for fast Monte Carlo simulation of diffuse reflectance spectra from multilayered turbid media. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 2007;24:1011–1025. [PubMed]

22. Tseng SH, Grant A, Durkin AJ. In vivo determination of skin near-infrared optical properties using diffuse optical spectroscopy. J. Biomed. Opt. 2008;13:014016. [PMC free article] [PubMed]

23. Palmer GM, Zhu C, Breslin TM, Xu F, Gilchrist KW, Ramanujam N. Monte Carlo-based inverse model for calculating tissue optical properties. Part II: application to breast cancer diagnosis. Appl. Opt. 2006;45:1072–1078. [PubMed]

24. Simpson CR, Kohl M, Essenpreis M, Cope M. Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique. Phys. Med. Biol. 1998;43:2465–2478. [PubMed]

25. Kienle A, Patterson MS, Dognitz N, Bays R, Wagnieres G, van den Bergh H. Noninvasive determination of the optical properties of two-layered turbid media. Appl. Opt. 1998;37:779–791. [PubMed]

26. Wang LH, Jacques SL, Zheng LQ. Mcml—Monte-Carlo modeling of light transport in multilayered tissues. Comput. Methods Programs Biomed. 1995;47:131–146. [PubMed]

27. Tseng SH, Hayakawa CK, Spanier J, Durkin AJ. Determination of optical properties of superficial volumes of layered tissue phantoms. IEEE Trans. Biomed. Eng. 2008;55:335–339. [PMC free article] [PubMed]

28. Pham TH, Coquoz O, Fishkin JB, Anderson E, Tromberg BJ. Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy. Rev. Sci. Instrum. 2000;71:2500–2513.

29. Hornung R, Pham TH, Keefe KA, Berns MW, Tadir Y, Tromberg BJ. Quantitative near-infrared spectroscopy of cervical dysplasia in vivo. Hum. Reprod. 1999;14:2908–2916. [PubMed]

30. Liu Q, Ramanujam N. Sequential estimation of optical properties of a two-layered epithelial tissue model from depth-resolved ultraviolet-visible diffuse reflectance spectra. Appl. Opt. 2006;45:4776–4790. [PubMed]

31. Elaloufi R, Carminati R, Greffet JJ. Diffusive-to-ballistic transition in dynamic light transmission through thin scattering slabs: a radiative transfer approach. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 2004;21:1430–1437. [PubMed]

32. Wang AM, Bender JE, Pfefer J, Utzinger U, Drezek RA. Depth-sensitive reflectance measurements using obliquely oriented fiber probes. J. Biomed. Opt. 2005;10:44017. [PubMed]

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