Influence of tissue absorption and scattering on the depth dependent sensitivity of Raman fiber probes investigated by Monte Carlo simulations.

We present a Monte Carlo model, which we use to calculate the depth dependent sensitivity or sampling volume of different single fiber and multi-fiber Raman probes. A two-layer skin model is employed to investigate the dependency of the sampling volume on the absorption and reduced scattering coefficients in the near infrared wavelength range (NIR). The shape of the sampling volume is mainly determined by the scattering coefficient and the wavelength dependency of absorption and scattering has only a small effect on the sampling volume of a typical fingerprint spectrum. An increase in the sampling depth in nonmelanoma skin cancer, compared to normal skin, is obtained.

1. Introduction

Raman spectroscopy is a powerful analytical tool due to its ability to provide molecular information without the need for exogenous labels. Applications of this technique in biomedical research are rapidly increasing, including the diagnosis of breast [1,2], skin [3-5] and cervical cancer [6,7], among others. In order to use Raman spectroscopy as a tool for real-time medical diagnostics, the spectra from a suspicious lesion need to be obtained in clinically feasible measurement times (few seconds and less) while using low laser powers. This motivates the use of measurement geometries that optimize the light throughput of the detection system, which is typically limited by the spectrograph, leading to measurement volumes larger than achievable by confocal Raman microscopy. For many in vivo applications, Raman fiber probes provide the required flexibility to access the tissue sites. Most Raman fiber probes are so called high-volume probes, which interrogate a relatively large tissue volume (≈1 mm3). While single fiber measurements with a 200 µm fiber have been reported in the high wavenumber region [5], many fingerprint Raman probes consist of a central illumination fiber surrounded by several detection fibers with integrated filters [8-13]. Some probes increase the overlap of excitation and detection area by beam-steering [8] or use lenses on the distal end of the probe to efficiently collect the backscattered light [10,13], while others utilize adjacent excitation and detection spots [9]. Another approach is to increase the spatial offsets of excitation and detection spots (spatially offset Raman spectroscopy, SORS) to enhance the fraction of subsurface signal [14-18]. To improve the signal contribution of a specific thin tissue layer, e.g. for the detection of epithelial cancer, confocal probes [19,20] can be employed to reduce the signal contribution from other tissue layers.

This variety of probe geometries leads to respective differences in the portion(s) of tissue interrogated by each probe. Thus, when selecting the most suitable Raman probe for a specific application, it is important to predict the tissue volume which contributes to the signal, often called measurement volume, interrogation volume or sampling volume, to accurately ascribe sources of the collected Raman signal. In addition to the measurement geometry, the sampling volume depends on the absorption and scattering properties of the sample itself. Therefore, accurate biochemical interpretation of Raman measurements requires accounting for both the optical geometry of the Raman probe as well as the tissue architecture-specific optical properties, to assess respective Raman signal contributions from various tissue strata.

Here we use the Monte Carlo (MC) method to calculate the spatial distribution of Raman sensitivity depending on the measurement geometry and the optical properties of the sample. Similar calculations have been performed previously for fluorescence measurements [21,22]. MC models for Raman scattering have been previously developed by Enejder et al. [23] for predicting the effect of measurement geometry on the detected Raman signal of blood. A MC model for SORS measurements of layered turbid media was developed by Matousek et al. [24]. Shih et al. used a MC model to validate their method to correct Raman spectra for the influence of scattering and absorption [25]. The MC calculation of spatial resolution and sensitivity with focus on non-absorbing samples was shown by Everall et al. [26]. Recently, Keller et al. adapted a fluorescence code for the prediction of SORS measurements [27], where the sensitivity for detected Raman photons originating from a certain depth was calculated. Further, Mo et al. [13] developed a MC code to simulate the sampling volume of a ball-lens fiber probe depending on diameter and refractive index of the ball lens and probe-tissue distance. However, previous simulations of sampling volumes use fixed optical parameters and the influence of absorption and scattering on the sampling volume has not yet been investigated systematically.

In this study, we applied our MC method to calculate the sampling volume of a 0.2 mm and 2 mm single fiber probe as well as a SORS configuration and a widely used 7-around-1 multi fiber probe [9,10]. We show how the sampling volume of these probes varies depending on the absorption coefficient µa and the reduced scattering coefficient µs´ typical for skin in the near infrared wavelength range (NIR), the results of which can be generalized to other epithelial tissues. For the 7-around-1 probe, the sampling volume variation over the fingerprint range (785-910 nm) for a typical skin spectrum was investigated. Further, we compared the sampling volume in nonmelanoma skin cancer to the sampling volume in normal skin and investigated the effect on the sampling volume if µa and µs´ of both skin layers vary independently in the range of the literature values. Finally, we investigated the influence of the probe-tissue interface on the sampling volume.

2. Materials and methods

2.1 Model for Raman scattering in turbid media and determination of spatial distribution of sensitivity

Here we give a detailed motivation for our Monte Carlo method. As the number of Raman processes is very small compared to elastic scattering and absorption, we have not introduced an explicit Raman process in our method as this would be statistically inefficient.

In this article, we use the following definitions:

Position vector: r, unit vector defining propagation direction: s

Radiance: L(r,s) in units of photons/(s mm2 sr)

Phase function for elastic scattering: p(s,s’)

Total radiance: in units of photons/(s mm2)

Detector signal: S corresponding to an excitation power of 1 photon / s

Raman-scattering coefficient: in units of mm−1

Scattering coefficient: µ in units of mm−1

Reduced scattering coefficient: µ (1-g) with g = 0.8 in units of mm−1

Total attenuation coefficient: µ in units of mm−1

Raman-scattering cross section: σRaman in units of mm2

Number density of the Raman active molecule: cRaman in units of mm−3

With µRaman<<µa, µs´ we neglect multiple Raman scattering of photons. In this case we can define a radiance LExc(r,s) which describes the light distribution of excitation at wavelength λExc and a radiance LRaman(r,s) for Raman scattered light with the Stokes shifted wavelength. Both quantities are given by the well known radiative transport equation [28] with optical parameters corresponding to the excitation or Stokes shifted wavelength:

Here p(s,s’) is the phase function for elastic scattering and Q is a volume source term. Further, s and denote directions of propagation and Ω is a solid angle. For the excitation radiance Q(r,s) = 0 in most cases, as the illumination of the probe is taken into account by boundary conditions of the radiation transport equation. Under the assumption of single Raman scattering, it can be shown that the source term for the Raman scattered radiance is

The right hand side in the above equation follows by assuming that Raman scattering is isotropic. Integrating QRaman over all directions, we get the number density nRaman of Raman scattering processes:

Here we used the second line of Eq. (1), so the approximation in Eq. (2) is not necessary.

As there are no boundary sources for LRaman it follows from Eq. (1) that LRaman is a linear function of QRaman and can therefore be written using a Green’s function:

G(r,s,r´,s´) is the radiance resulting from a point source at r´ radiating in direction s´. Any Raman detector signal SRaman is a linear functional of LRaman. It follows from Eqs. (2), (3) and (4) with the assumption that Raman scattering is isotropic that the Raman signal can be written as

In Eq. (5), f(r) is the detected Raman signal for an isotropic point source of radiation located at r with the Stokes shifted wavelength.

We define a function w(r) which can be considered as the spatial sensitivity distribution of the measurement, which is the quantity of interest here:In the following, the range of r values where w(r) is large is considered as the sampling volume of the Raman measurement.

The total radiance is related to the number density of absorption or scattering processes and the corresponding coefficients for excitation radiation:

Thus, in the Monte Carlo method Φexc can be represented by an ensemble of absorption or scattering processes with number density nexcabs(r) or nexcscatter(r) gained from an ensemble of excitation photons. With Eq. (5) we have

In our Monte Carlo method, f(r) is calculated with an ensemble of photon trajectories with NPhoton members starting at position r with an isotropic distribution of initial directions and counting the number of photons which reach the detector:

Correspondingly, SRaman is calculated in the following way: calculating the trajectories of NPhoton excitation photons results in an ensemble of Nabs absorption positions rabs of excitation photons. Each position is used as the starting position for a Raman scattered photon. Again the number of photons which reach the detector are counted. As the quantity rabs is a random variable with probability density nexcabs(r) one can show that SRaman in Eq. (6) is given by

Here the factor 1/NPhoton is due to the normalization of SRaman to an excitation power of one photon per second.

For µs>µa, it is statistically more efficient to use the elastic scattering processes to represent Φexc.

For a stratified medium where all quantities depend on the depth coordinate z only we define a depth sensitivity function wz(z) which is the integral of w(r) over lateral coordinates leading to

For a homogeneous medium it follows that

is the Raman signal Sraman normalized by the molecule specific µRaman, previously named RamT /µRaman in units of mm [29].

is the fraction of the detected Raman signal originating from a z-interval with thickness ∆z.

With the exception of the results in Fig. 2a below, we neglect the Stokes shift of the Raman photon energy for the sake of simplicity.

Fig. 2

Dependency of wz(z) / ∫wz(z) dz on optical properties of skin (in mm−1) for the 7-around-1 fiber probe. a) Optical properties corresponding to the case of maximal Stokes shift and zero Stokes shift are used. In addition, the maximal Stokes shift case is compared to the case when mean optical parameters of excitation and maximal Stokes shift photons are used. b) Optical properties of normal skin, nodular basal cell carcinoma (BCC) as well as squamous cell carcinoma (SCC) are used.

2.2. Fiber probe geometries

Single fiber measurements were simulated by defining an overlapping excitation and detection spot of identical diameter d with d = 0.2 mm or d = 2 mm as well as intermediate and smaller diameters. The illumination and acceptance angle was set according to the fiber numerical aperture (NA) of 0.22. These models of measurements geometries apply also to non-contact measurements, where the images of excitation and detection fibers coincide on the sample surface.

For the SORS probe, a spatial offset r = 0.4 mm was set between an excitation and detection fiber with d = 0.2 mm and NA = 0.22. The 7-around-1 probe consists of a central excitation fiber with 400 µm diameter surrounded by 7 detection fibers with 300 µm diameter, each with NA = 0.22 as per [8]. The distance between the centers of source and detection fibers was set to 385 µm, which accounts for the thicknesses of the respective claddings. The filters on the distal end of the probe were neglected and we assumed a closed silica shield to be in contact with the skin. For all probe geometries the refractive index n of the probe was set to 1.45. For comparison with an air-skin interface, n was set to 1.

2.3. Skin model

As a skin model, we used a two-layer geometry consisting of an epidermis with a thickness of 100 µm and a semi-infinite dermis. The optical properties of skin in the wavelength range of 785-910 nm were chosen based on the literature, which we briefly review here in order to give an impression of the large range of reported values. Many reported values of µa and µs´ were obtained by in vivo diffuse reflectance measurements and therefore correspond to a weighted average of epidermal and dermal optical properties [31-34], while only a few characterized both layers separately [35,36]. The wavelength dependent change of optical properties is comparable or lower than the sample-to-sample variation and the variation among different references. According to the model of Jacques [35], which is based on measurements of rat skin, the absorption coefficient of the epidermis µa_epi ranges from 0.15 mm−1 to 0.91 mm−1 at 785 nm and from 0.09 mm−1 to 0.58 mm−1 at 910 nm, depending on the melanosome concentration. The values of Salomatina et al. range from 0.19 +/−0.07 mm−1 at 785 nm to 0.08 +/− 0.04 mm−1 at 910 nm [36], where the error is the sample-to-sample variation.

The absorption coefficient of the dermis, µa_derm, according to Jacques ranges from 0.025 mm−1to 0.049 mm−1 (with negligible wavelength dependency) for blood volume fractions of 0-5% while the values of Salomatina range from 0.15 +/−0.03 mm−1 at 785 nm to 0.08 +/− 0.02 mm−1 at 910 nm. The scattering of epidermis and dermis is considered to be similar by Jacques (µs´ = 1.8 mm−1 at 785 nm to 1.2 at 910 nm) while Salomatina et al. report 3.6 +/− 0.3 mm−1 at 785 nm and 3.2 +/− 0.3 mm−1 at 910 nm for the epidermis and 2.2 +/−0.2 mm−1 at 785 nm and 2.0 +/−0.2 mm−1at 910 nm for the dermis. Literature values with mixed contributions of both layers range from µa = 0.01 mm−1 [31] to 0.25 mm−1 [30] (and references therein) and µs´ = 0.6 mm−1 [31] to 5 mm−1 [36]. The refractive index of skin was selected as 1.43+/−0.1 for the epidermis (including stratum corneum) and 1.38+/−0.2 for the dermis in the wavelength range of interest, as measured by Ding et al. [37]. The g factor, which describes the anisotropy of the Henyey-Greenstein phase function for elastic scattering, was set to 0.8 for both layers as this is a typical value for tissue.

3. Results and discussion

3.1. Influence of absorption and scattering on sampling volume of different fiber probe geometries

In order to focus on the geometry dependent effects in this section, we used here a skin model with matched absorption and scattering coefficients of epidermis and dermis using parameters as typically reported for in vivo diffuse reflectance measurements in the NIR, see section 2.3. The normalized depth dependent sensitivity wz(z) / ∫wz(z) dz or sampling volume of four different fiber probe geometries is shown in Fig. 1a-d .

Fig. 1

Dependency of wz(z) / ∫wz(z) dz on µa and µs´ in mm−1 for a) single fiber measurement with d = 0.2 mm b) single fiber measurement with d = 2 mm c) SORS measurement with d = 0.2 mm and r = 0.4 mm d) 7-around-1 probe with dex = 0.4 mm, ddet = 0.3 mm and r = 0.385 mm e) Dependency of Фexc on µa and µs´ in mm−1 for 7-around-1 probe e) Dependency of wz(z) on µa and µs´ in mm−1 for 7-around-1 probe. Error bars are not shown to maintain clarity, but deviation from a smooth curve shape is due to statistical errors.

As expected from previous simulations for fluorescence probes and Raman measurement geometries [21,24,27], the sampling depth increases with fiber diameter and spatial offset. Further, we show here that in the investigated parameter range, the shape of the sampling volume depends mainly on µs´, independent of the specific fiber probe geometry. For the single fiber measurement with d = 0.2 mm, variations of µa by one order of magnitude have only a negligible effect on the shape of the sampling volume, see Fig. 1a. In contrast, a ten times increase in µs´ shifts the sensitivity towards shallower depths. For the single fiber measurement with d = 2 mm, a ten times increase of µa shifts the sensitivity towards shallower depths, but in a lower magnitude as the effect of a ten times increase in µs´, see Fig. 1b. In the SORS geometry, with the same fiber diameters as in the first case but a spatial offset of 0.4 mm, a ten times increase in µa also shifts the sensitivity towards shallower depths, see Fig. 1c. The effect of a ten times increase in µs´ is again larger as it is demonstrated by a large shift of the sensitivity maximum. Interestingly, in this configuration the depth of maximal sensitivity seems to depend only on µs´. In the case of the 7-around-1 fiber probe, the results are similar as for the SORS probe, which might be due to the fact that the chosen spatial offset is similar to the center-to-center distance of excitation and detection fibers in the 7-around-1 probe, see Fig. 1d.

In Fig. 1e, we show how the total radiance Фexc of excitation photons depends on z for the same parameters as used for Fig. 1d. It can be seen that the slope of the depth dependent decrease is much smaller than for the normalized sensitivity. The corresponding wz(z) is presented in Fig. 1f. Integration of wz(z) over z leads to the detected Raman signal intensity SRaman/µRaman as defined by Eq. (7). As previously described for the detected Raman signal intensity, wz(z) increases with decreasing µa as well with increasing µs´ [25,29]. Further analysis of the influence of scattering and absorption on the intensity of the detected Raman signal is not within the scope of this article.

To detect changes in the Raman signal of the dermal layers it is useful to reduce the signal contribution of tissue below the dermis, because this will enhance the signal contrast between different states of the dermal layers. Moreover, variations in the contribution of deeper tissue may affect the analysis of the measurement adversely (e.g. chemometric analysis). The same argument holds if changes in the Raman signal of the epidermis are to be analyzed.

The total fraction of Raman signal originating from a certain tissue depth can be obtained by integrating the normalized wz(z) over the z range of interest. In our 2-layer tissue model, the dermis is semi-infinite, with z>0.1 mm. For a quantitative comparison of the different fiber probe geometries we compared the signal fractions originating from depths z<0.1mm (epidermis), z<0.7 mm or z<1 mm, see Table 1 . We chose the optical parameters µa = 0.01 mm−1 and µs´ = 1 mm−1, which are rather low values for skin, and therefore the resulting sampling depth is an upper limit for skin. In addition to the fiber probe geometries used above, sensitivity distributions have been calculated for single fibers with d = 0.4 mm, d = 0.1 mm, d = 0.05 mm and d = 0.01 mm. It is obvious that a fiber diameter d = 0.2 mm is required to ensure that contributions of tissue at z>1 mm are below 5%. Aiming at measuring ≈95% of the signal from the 100µm thick epithelium requires even d<0.01mm (at NA = 0.22).

Table 1

Signal contribution from z<0.1 mm, z<0.7 mm and z<1.0 mm for the 7-around-1 fiber probe, the SORS geometry and single fibers with different diameters

µa = 0.01 mm−1, µs´ = 1mm−1	7-around-1	d = 0.2 mm, r = 0.4 mm	d = 2 mm	d = 0.4 mm	d = 0.2 mm	d = 0.1 mm	d = 0.05 mm	d = 0.01 mm
Signal from z<0.1mm	4%	4%	7%	20%	31%	45%	61%	93%
Signal from z<0.7mm	54%	51%	55%	86%	94%	97%	99%	100%
Signal from z<1.0mm	70%	68%	64%	90%	96%	98%	99%	100%

Choosing an optimal probe design based on these results is however not trivial. It depends on whether the analysis is limited by non systematic variance of the spectra, which is mainly due to the variance of normal surrounding tissue, or rather limited by detector noise. In the latter case, it is preferable to maximize the systematic signal of interest and admit higher contributions of deeper tissue, which is achievable by larger fiber diameters and/or higher NA of the probe. Increasing the NA was found to cause a slight shift of the sampling volume towards lower z values (data not shown).

In order to link the values in Table 1 directly to measurement data, one has to keep in mind that we have assumed a homogeneous Raman scatterer distribution and normalized the data with respect to µRaman. For inhomogeneous Raman scatterer distributions the integral in Eq. (7) must be calculated. But if a homogeneously distributed bioconstituent produces a distinct Raman peak, then the signal fractions in Table 1 can be directly interpreted as fraction of the Raman peak size.

3.2. Influence of skin optical properties on sampling volume of a typical 7-around-1 Raman fiber probe

Using the 7-around-1 probe geometry as an example, we investigated the wavelength dependent variation of the sampling volume that can occur when a typical fingerprint spectrum (785 nm-910 nm) is measured. The wavelength dependency of absorption and scattering plays a role since each Raman band in the spectrum is determined by the propagation of the photons according to the optical parameters at the excitation wavelength (µa_ex, µs´_ex), and after the Raman scattering, by the propagation according to the optical parameters at the Stokes shifted wavelength (µa_st, µs´_st).

The effect on the sampling volume is shown in Fig. 2a, where we compared the case of zero Stokes shift to the case where the Raman photon propagates with optical properties corresponding to a maximal Stokes shift of ≈1800 cm−1 at 910 nm, using the optical parameters measured by Salomatina et al. [36]. The resulting difference in sampling volume, which is an upper limit for the sampling volume variation over the whole NIR skin spectrum, is fairly small. The corresponding signal fractions originating from z<0.7 mm (1.0 mm) are 81% (91) % for the zero Stokes shift case and 84% (93) % for the maximal Stokes shift case, see Table 2 . We further define the 70% (90%)-sampling depth as the depth where 70% (90%) signal contribution is obtained from the tissue above. For the 70% (90%)-sampling depth we obtain 0.43 mm (0.90 mm) for the zero Stokes shift case and 0.46 mm (0.83 mm) for the maximal Stokes shift case. Thus, this dispersion effect on the sampling volume seems negligible for the chosen spectral range and tissue type. Consequently, individual Raman bands in a NIR skin spectrum originate from a similar sampling volume. However, the effect may be stronger in the visible or mid-infrared spectral range.

Table 2

Signal contribution from z<0.1 mm, z<0.7 mm and z<1.0 mm for the 7-around 1 fiber probe for the optical properties specified in Fig. 2

	Zero Stokes shift	Max. Stokes shift	Mean/normal	Nodular BCC	SCC
Signal from z<0.1 mm	12%	14%	14%	6%	6%
Signal from  z<0.7 mm	81%	84%	84%	66%	66%
Signal from z<1.0 mm	91%	93%	93%	80%	82%

In the same graph, we show that comparable results can be obtained for the sampling volume using the mean optical properties of excitation and Stokes shifted wavelength in the simulation while neglecting the Stokes shift. Next, we investigated how diagnostically relevant changes of µa and µs´ can affect the sampling volume. In the spectral range of interest here, Salomatina et al. [36] reported a decrease of both µs´ and µa for nodular basal cell carcinoma (BCC) and squamous cell carcinoma (SCC) compared to normal tissue. Since the thickness of the cancerous tissue samples in [35] were between 0.17 and 0.85 mm, we set the optical properties of both epidermis and dermis to the values reported for nodular BCC and SCC, respectively. In Fig. 2b we show that the variation in optical properties found in the cancerous tissue shifts the sampling volume to higher z values, corresponding to signal contributions for z<1.0 mm of 80% (82) % for nodular BCC (SCC) versus 93% in case of normal skin, see Table 2. For the 70% (90%)-sampling depth we obtained 0.44 mm (0.84 mm) for the normal tissue, 0.70 mm (1.34 mm) for the nodular BCC and 0.70 mm (1.44 mm) for SCC. However, these results are not valid for early stages of skin cancer, which typically originates in the epidermis, because we assumed that the cancer tissue is semi-infinite.

Finally, we investigated the variation of the sampling volume when the optical parameters of each skin layer are varied independently. We chose the parameters such that the complete range of literature values described in section 2.3 was covered, only µs´<1 mm−1 was omitted for clarity and because we found only one reference that reported such low values.

As in section 3.1, the µs´ determines the depth of the sensitivity peak while large variations of µa cause only moderate changes in the shape of the sampling volume.

In Fig. 3a , the µs´ of both layers is matched while the µa varied independently. The influence of µa _epi on the normalized sensitivity is very small, which indicates a minor influence of skin pigmentation on the sampling volume.

Fig. 3

Dependency of wz(z)/∫wz(z)dz on typical optical properties of skin for the 7-around-1 fiber probe. a) µa_epi and µa_derm (in mm−1) are varied independently. b) µs´_epi is varied independently

The influence of µs´_epi is however larger, as demonstrated per Fig. 3b, where µs´_epi is varied and µa of both layers is matched. An increase of µs´_epi from 1 to 5 mm−1 even leads to the same depth of maximal sensitivity as for a µs´ = 5 mm−1 in both layers, but the overall sensitivity distribution is still significantly different compared to the case of matched µs´. This indicates that variations of µs´_epi of external or natural origin are a major source of sampling volume variation. The signal contributions originating from certain tissues regions for some representative data of Fig. 3 are given in Table 3 .

Table 3

Signal contribution from z<0.1 mm, z<0.7 mm and z<1.0 mm for the 7-around 1 fiber probe for representative parameter combinations of the data in Fig. 4

µa_epi [mm−1], µs´_epi [mm−1]	0.01, 1	0.01, 5	0.1, 1	0.1, 3	0.1, 5	0.1, 5	1.0, 1	1.0, 5	1.0, 1	1.0, 5
µa_derm [mm−1], µs´_derm [mm−1]	0.01, 1	0.01, 5	0.1, 1	0.1, 1	0.1, 1	0.1, 5	0.1, 1	0.1, 5	0.2, 1	0.2, 5
Signal from z<0.1 mm	4%	15%	5%	10%	15%	19%	5%	17%	6%	20%
Signal from z<0.7 mm	54%	81%	65%	74%	78%	92%	65%	92%	70%	95%
Signal from z<1.0 mm	70%	90%	82%	86%	88%	97%	82%	97%	86%	99%

3.3. Influence of tissue-probe interface on sampling volume

In order to investigate the influence of the probe-skin interface, we compared calculations for a silica-skin interface and an air-skin interface for the 7-around-1 probe, a situation which could be obtained by imaging the fiber probe onto the tissue surface or by an air-gap between probe and tissue. Figure 4 shows the results for different µa and µs´, which are matched for both layers. The normalized sensitivity is similar for high z values but shifts towards superficial tissue in the range of lower z values. This means that if the coupling of the probe to the skin is interrupted by an air gap, the normalized sensitivity changes mainly in a depth z below ≈1mm. This can be explained by the fact that total reflection at the skin-air interface reduces the photon escape probability and thus leads to longer average pathlengths through the Raman scattering medium. In case of the silica-skin interface, there is no total reflection since the refractive index of silica is slightly higher than the refractive index of the epidermis. This influence of the probe-tissue interface was negligible for the d = 0.2 mm single fiber geometry (data not shown).

Fig. 4

Dependency of wz(z)/∫wz(z)dz on the refractive index of the medium which is in contact with the skin for the 7-around-1 probe. The µa and µs´ (in mm−1) of both layers is matched.

4. Conclusion

The depth dependent sensitivity of a given measurement geometry is of fundamental importance for the interpretation of Raman spectral measurements.

Our results show that independent of the investigated fiber probe geometry, an increase in tissue scattering as well as an increase in absorption shifts the sampling volume to shallower depths. However, in the investigated range of optical parameters and probe geometries, differences in tissue absorption have a smaller influence on the shape of the sampling volume than variations in scattering.

As Raman spectroscopy is increasingly applied for the discrimination of cancerous versus normal tissue, the change of optical properties in cancerous tissue should be accounted for in the interpretation of the Raman measurement. In the case of the 7-around-1 probe geometry, our results show that the variation of optical properties increases the 70% (90%)-sampling depth by 0.26 mm (0.50 mm) or 0.26 mm (0.60 mm), when nodular BCC or SCC is compared to normal skin. This previously unaccounted disparity in sampling volume may inherently cause variations in the respective tissue spectra, potentially creating artifactual band assignments in the correlation of spectra with pathologic biochemistry. In order to accurately link the MC results to real measurement values of a layered tissue, the distribution of Raman scatterers as well as potentially different Raman cross sections of constituents contributing to the same band need to be taken into account.

For a typical NIR fingerprint spectrum of skin, the dispersion of absorption and scattering has only a small effect on the sampling volume, which means that individual Raman bands in a spectrum originate from a similar sampling volume. However, the effect may be larger in the visible or mid-infrared spectral range as well as for other tissues.

In addition to the variations in depth dependent sensitivity or sampling volume, it must be kept in mind that variations in absorption and scattering also change the intensity of the detected Raman signal. Even in a homogeneous system, where sampling volume variations are not relevant, the intensity of the Raman band is modulated by variations of absorption and scattering. This is important if Raman band intensities of different samples are compared quantitatively or if ratios of Raman bands at different wavelengths are analyzed. In case of the examples shown in Fig. 2, the Raman band intensity at maximum Stokes shift relative to the intensity at zero Stokes shift is 93% and the mean Raman intensity of BCC (SCC) relative to the intensity of normal tissue is 114% (92%). Further analysis of the effect of varying scattering and absorption on the detected Raman signal intensity and possible correction methods are described elsewhere [25,29,38,39].

For Raman spectral diagnosis of diseased versus normal tissue, identifying and/or isolating contributions from epithelial layers may provide increased discriminant abilities.

Assuming that the analysis of the subtle spectral changes accompanying precancerous tissue (including chemometric techniques) is limited by the non systematic variance of the spectra, which is mainly due to the variance of normal surrounding tissue, minimization of signal contributions from surrounding tissue is important. For the detection of epithelial cancer, our results suggest that single fiber geometries of unpractically small diameters would be required to minimize dermal contributions. As single fiber Raman measurements are only suited for high wavenumber measurements, more sophisticated probe designs have been suggested for that purpose [13,19,20].

If the analysis of the Raman measurement is not limited by unsystematic contributions but by detector noise, it will be better to maximize the systematic signal of interest and admit higher contributions of deeper tissue. In this case the optimal probe design might shift to larger fiber diameters and/or higher NA of the probe, depending on instrumental parameters such as available spectrometer étendue and excitation power.

In the future, it might be useful to compare the performances of such confocal and other probe designs in terms of sampling volume and detection efficiency.

Using MC simulations to investigate the sampling volumes of specific probe or measurement geometries can both improve the interpretation of the collected Raman signals as well as guide the design of probes with increased discriminant ability for biomedical diagnostics.