Optical efficiency
The simulated photon distribution in the skin matrix for each optical configuration is shown in Fig. 1. There are relatively higher fluence rate in the central area of the profile for transmission and transfection configurations in Fig. 1 (a) and (b). In the experimental system, the diameter of illumination light, which was modulated and went out of FTIR, was around 50 mm. To put this light into 3 mm diameter optical fiber, focusing lens was used. This lens optics was included in the simulation, and caused higher fluence rate in the central area near the illuminated skin surface.
The optical efficiency is defined as the number of detected photons divided by the number of illuminated photons. The optical efficiency is also measured by taking the ratio of the illuminated and the detected light power in the experiments. The simulation result shows ranges of the optical efficiency. This comes from the fact that the optical coefficients of skin vary with the wavelength. In the experiment, the optical power was measured with a band pass filter of 400 nm bandwidth. Thus, the experimental result of the optical efficiency is a representative value. Table 1 compares the simulation with the experimental results of the optical efficiency for each configuration and wavelength range, where the comparison shows a good accordance between the results. Several orders of magnitude difference in optical efficiency is apparent depending on the measurement configurations. In the first overtone wavelength range, the optical efficiency is ten to hundred times larger than the combination wavelength range.
Table 1
Optical efficiency comparison between simulation and experiment for each optical configuration.
Optical efficiency | Transmission | Transflection | Reflection |
Simulation | 10− 1 ~ 3×10− 1 (O), 1×10− 3 ~ 5×10− 2 (C) | 10− 3 ~ 3×10− 2 (O), 10− 4 ~ 3×10− 3 (C) | 10− 4 ~ 2×10− 4 (O), 3×10− 6 ~ 5×10− 6 (C) |
Experiment | N/A | 10− 3 (O), 10− 4 (C) | 10− 4 (O), 10− 6 (C) |
Photon travel length
Photon travel length is defined as the trajectory length of a photon from the incident point to the exit point of a skin matrix. Due to random multiple scattering process, there are various trajectories of photons traveling in the skin matrix. During the simulation, each photon has record of its traveling path. After selecting photons that arrived at the detector, the travel length of each photon can be calculated with its record.
Simulated distributions of the photon travel length at various wavelengths for each optical configuration are compared using histogram plots in Fig. 4. Wavelength dependency of the photon travel length distribution results from difference in values of absorption, scattering and anisotropy coefficient for each wavelength. Generally, more photons in the first overtone range survive and arrive at the detector due to low absorptivity compared to photons in the combination range. Relatively narrow distribution of the photon travel length for transmission mode in Fig. 4(a) shows that forward scattering is dominant in skin media. As shown in Fig. 4(b), the transflection mode exhibits the broadest distribution of travel length, which matches well with its conical shaped geometry where various path lengths exist between the illuminating and the detecting waveguides.
Average values of the photon travel length for various wavelengths are shown in Fig. 5. The transmission configuration shows relatively leveled photon travel length along the wavelength change. In contrast, wide ranges of average photon travel length exist in the transflection and the reflection configurations. The wavelength profiles of these two configurations are similar to that of anisotropy coefficient. For these two configurations, the photons need to be scattered and change its direction to arrive at the detector, where higher anisotropy coefficient results in smaller change in photon direction and results in longer trajectory between the source and the detector.
Absorbance spectra
The simulated skin absorbance spectra for each optical configuration are compared with the measured skin spectra and the water absorption coefficient in Fig. 6. The simulated skin spectrum for the transmission configuration shows larger absorbance than the water absorption spectrum in Fig. 6 (a). Although the separation between the source and the detector is set to be 1 mm, a number of photons travel longer than 1 mm path due to the scattering in skin. The photons experience more absorption and as a result, the absorbance is larger than the absorbance of water in 1mm thick cuvette.
In the transflection configuration, the absorbance is lower than that of 1 mm thick water. Due to the 90-degree angle configuration between the source and the detection waveguide, small amount of the illuminated photons can be detected in air, while more photons in skin can reach the detection waveguide owing to the scattering characteristics of the skin. The output light intensity for the air reference is smaller than that of the skin. Thus, the absorbance of skin in the first overtone range can take negative values.
For the case of the reflection configuration, the measured skin spectrum shows larger absorbance than water, while the simulated skin spectrum is far lower than the water absorbance curve and has negative value at some wavelength range. Diffuse reflection at the rough surface of the actual Spectralon was not taken into account in this simulation. The surface of the Spectralon was set to be flat and mirror-like in the simulation. The majority of the photons were reflected back at the surface around the position of the illumination waveguide, and could not reach the detection waveguide which is separated from the illumination waveguide with a 0.2 mm gap. On the other hand, the actual surface of the Spectralon is rougher, so more diffusely reflected photons could have chances to arrive at the detection waveguide. The simulated model for the Spectralon has smaller reflected photons than the experimental result, which leads to constant offset difference between the simulated and the measured skin absorbance spectra. This offset, however, doesn’t have any negative influence on the calculation of the optical efficiency or the effective water path length.
While the simulated skin spectra by using water absorption coefficient only has smooth line shapes, the measured skin spectra have a few small peaks especially in the combination wavelength range owing to the absorption from other skin components such as protein and fat. The overall shape of the simulated skin spectra, however, is similar to the measured spectra as the major absorption component of the skin is water.
Effective water path length
To quantify the concentration of target molecules dissolved in skin fluid by Beer’s law, the effective water path length needs to be calculated first from the measured spectra3. The effective water path length can be linearly regressed from the skin spectrum based on multiple scattering correction (MSC) method where the skin components’ absorptivities, constant and slope terms are used3,43 as the following equation:
$${\text{A}}_{skin}={\text{c}}_{water}{\text{A}}_{water}+{\text{c}}_{collagen}{\text{A}}_{collagen}+{\text{c}}_{keratin}{\text{A}}_{keratin}$$
$$+{\text{c}}_{fat}{\text{A}}_{fat}+{\text{c}}_{offset}{\text{A}}_{offset}+{\text{c}}_{slope}{\text{A}}_{slope}+{\epsilon }$$
1
where \({\text{A}}_{skin}\) represents the measured skin spectrum,\({\text{A}}_{water}\), \({\text{A}}_{collagen}\), \({\text{A}}_{keratin}\) and \({\text{A}}_{fat}\) represent pure component absorption of water, collagen, keratin, and fat, respectively, \({\text{A}}_{offset}\) and \({\text{A}}_{slope}\) correspond to the offset and slope terms, respectively, \({\text{c}}_{water}\), \({\text{c}}_{collagen}\), \({\text{c}}_{keratin}\), \({\text{c}}_{fat}\), \({\text{c}}_{offset}\) and \({\text{c}}_{slope}\) represent regression coefficients from fitting the corresponding standard absorbance spectrum, and ε is residual spectrum. The regression coefficient of water (\({\text{c}}_{water}\)) from this spectral fits indicates the amount of water within the optical path. This effective water path length is related to the relative difference of detected photon numbers between center and outer wavelengths of the overtone or the combination region. Water absorption is strongest near outer parts of each wavelength region (1500, 1800, 2000 and 2500 nm), thus the amount of detected photons is lowest near these wavelengths. Meanwhile, water absorption is weakest near the center wavelengths (1650 and 2250 nm) and the amount of detected photons is highest near these wavelength regions. Table II summarizes the regressed effective water path length from the simulated and the measured skin spectra in each optical configuration shown in Fig. 6.
The regressed effective water path length for transmission mode is 1.33 mm for the first overtone range and 1.28 mm for the combination range. These values are somewhat larger than the average photon travel length which is in the range of 1.21 ~ 1.25 mm for overtone and 1.17 ~ 1.19 mm for combination region. This difference seems to result from the distribution shape of photon travel length in Fig. 4, where the distribution shows a longer tail from the average value toward larger travel length numbers.
Comparison between the simulated and the measured water path length of the transflection and the reflection modes shows good consistency except for the first overtone range of transflection mode, where the simulated value (1.25 mm) is 31% smaller than the measured value (1.8 mm). The nature of wide photon travel length distribution of the transflection configuration in the first overtone region seems to influence this result. Unlike the other configurations, a large portion of photons travel longer than 2 mm in the first overtone wavelength region in the transflection configuration as shown in Fig. 4(b). When the photons travel longer distance in skin, there exists more uncertainty in optical parameters used in simulation due to the skin inhomogeneity. The photons with wavelength near 1500 or 1800 nm experienced more extinction than simulated, which led to the discrepancy in absorbance between the simulation and the measurement. In the future, simulation exploiting multi layered skin model can be used to investigate further improvement of the estimation accuracy. For the other three cases, the simulated water path length matches well to the measured value with the error less than 6.7%.
Table 2
Effective water path length comparison between simulation and experiment for each optical configuration.
Effective water path length | Transmission | Transflection | Reflection |
Simulation | 1.33 mm (O), 1.28 mm (C) | 1.25 mm (O), 0.82 mm (C) | 1.12 mm (O), 0.97 mm (C) |
Experiment | NA | 1.80 mm (O), 0.85 mm (C) | 1.20 mm (O), 0.93 mm (C) |
Selection of optimal skin probe design
Overall, the transmission configuration shows the largest optical efficiency and the smallest photon travel length variation along the wavelength range in use, which can provide the best performance from the spectroscopic point of view. However, the locations for in vivo measurement are limited to the earlobes or other folded skin for this configuration.
While the transflection configuration has intermediate optical performance and can be applied to measurement of general skin surfaces, pulling up the skin surface and maintaining the configuration shape may require complex mechanical parts such as vacuum pumping.
Probing principle of the reflection measurement is more convenient to use in obtaining spectra compared with the transmission or transflection measurements. The reflectance measurement can be applied to most of the skin surface. However, the reflectance configuration has extremely low light throughput compared to the other configurations. Thus, multi-optical fibers based skin probe providing large optical throughput or high power light sources such as super luminescent diodes (SLD) or tunable lasers may be better choices to acquire enough optical SNR.
Once the measurement site on skin is given, an optimal configuration could be determined. Then, precise performance estimation and optimization of the detailed skin probe design can be carried out using the simulation methodology in this study.