3.1.

Frequency-Domain Setup

Frequency-domain measurements were performed using a setup similar to that described by Madsen et al.;³³ A schematic drawing of the device is shown in Fig. 1. As light sources, three laser diodes were used [SDL 7432-H1 (λ=678 nm), SDL 2352-H1 (λ=808 nm), and SDL 5432-H1 (λ=835 nm), all from Spectra Diode Labs, San Jose, California]. The laser diodes were selectively bias-modulated in the frequency range between 300 kHz and 200 MHz by a vector network analyzer (HP 8712C, Hewlett Packard, Palo Alto, California) in combination with a high-frequency multiplexer (7016, Keithley, Cleveland, Ohio) and three bias tees (5580, Picosecond Labs, Boulder, Colorado). The modulated laser light was delivered to the sample via quartz/quartz optical fibers with a core diameter of 600 μm and a numerical aperture of 0.2. An identical fiber was used to collect the remitted photons at several source-detector separations ρ (between 3 and 9 mm). A high-speed avalenche-photodiode receiver (APD S90302C, EG&G Electrooptics, Boudreuil, Canada) with a spectral bandwidth of 800 MHz was used as optical detector. All measurements were performed with a frequency resolution of 4 MHz (51 data points) and a spectral bandwidth of 3.7 kHz. Phase and intensity data were averaged 16 times. The multiplexer and the network analyzer were controlled by a personal computer that was also used to record the measured data. The acquisition time for a single frequency sweep was approximately 400 ms.

Figure 1

Experimental setup of the frequency-domain spectrometer: LDD1–LDD3, laser diode drivers; LD1–LD3, laser diodes; S1–S3, shutters; FC1–FC3, fiber couplers; APD, avalanche photodiode; MPX, multiplexer.

3.2.

Scattering and Absorbing Phantoms

Tissue phantoms were designed to perform an evaluation of the new technique. Several recipes have been published to manufacture solid phantoms with defined scattering and absorption properties.³⁴ We embedded TiO ₂ particles (TiPure 960, DuPont, Mechelen, Belgium) into clear polyester resin (Norpol 340-500, Reichhold, Hamburg, Germany) as described in Ref. 35. A stock solution of 800 mg TiO ₂ in 20 ml ethanol was used. The effective diameter of the TiO ₂ particles was 350 nm. In order to determine the volume filling fraction of the scatterers (f _sca ), we performed integrating-sphere measurements²¹ for a series of thin phantoms with various amounts of TiO ₂ particles. We found that a volume filling fraction of f _sca =3 of the stock solution resulting in reduced scattering coefficients of 1.03 mm⁻¹ at 678 nm, 0.71 mm⁻¹ at 808 nm, and 0.71 mm⁻¹ at 835 nm, respectively (see Table 1), was best suited to mimic the scattering properties of neonatal skin (∼1 mm⁻¹ in the NIR-wavelength range²⁴).

Table 1

The absorption properties of the phantoms were adjusted with regard to the absorption coefficients of human skin at the wavelengths of interest. The respective data have been calculated using Eq. (8) (see below) from the known extinction spectra of Hb and HbO ₂ (Ref. 3) for a total hemoglobin content of 190 g/l, which is typical for fetal blood.³⁶ The volume fraction occupied by blood vessels was assumed to be 5.³⁷ The resulting absorption coefficients at the wavelengths of interest are shown in Fig. 2. They were found to be between 0.01 and 0.1 mm⁻¹. A series of nonscattering phantoms that consisted of various amounts of an absorbing stock solution (1 mg of an infrared dye, ProJet 900 NP by Zeneca Colors, Manchester, England, solved in 10 ml ethanol) in resin was manufactured. The relative absorptivity Δμ_a/Δf _abs (i.e., the absorption coefficient per unit volume of absorber) of these phantoms was then determined with a conventional absorption spectrometer (Lambda 19, Perkin Elmer, Shelton, Connecticut). It was found that volume filling fractions of the absorber between 0.0 and 3.1 simulated best the various oxygenation states of fetal skin. According to these results, six solid scattering and absorbing phantoms (dimensions: diameter 50 mm, thickness 30 mm) with volume filling fractions of 3 scatterer and 0.0 to 3.1 absorber were manufactured and were used for further investigations.

Figure 2

Calculated absorption coefficients of fetal skin containing 5 of blood as a function of the oxygen saturation.

As can be seen from Eq. (4), the refractive index has to be known in order to deduce the absorption coefficient of the sample. Because more than 93 of the phantom volume is filled with resin, it was assumed that the latter determines the refractive index of the samples. To characterize the phantoms completely, we determined the refractive index of the resin by goniometric reflection measurements. Therefore, a clear resin sample was irradiated using p-polarized light in the wavelength range from 400 to 860 nm. The angle of incidence パ of the collimated beam was varied between 15 and 75 deg in steps of 2.5 deg. The refractive index n was obtained by fitting the experimental data to the Fresnel function for p-polarized light R_p(パ):

3.3.

Interaction Volume

Prior to the in vivo testing, the interaction volume of the detected photons in the skin was determined using Monte-Carlo simulations as described previously.³⁸ This volume is of great importance because the measured absorption coefficient represents an average value over the probed sample volume.³⁹

Human skin consists of three layers^{25 40 41} with different optical properties. The uppermost layer (epidermis) is typically 60 μm thick and does not contain blood vessels. The second layer (dermis) is typically 2 mm thick and contains a fine capillary network of arteries and veins. Underneath the dermis, there is a layer of subcutaneous fat with a thickness of several millimeters, depending on the exact location at the body surface. The optical properties of the epidermis, the dermis, and the subcutaneous fat have been well characterized by several authors.^{24 25 26 27 28 29 30} In the epidermis, the dominant absorbing chromophore is melanin. The fraction of melanin present in the epidermis f _mel depends on the skin type and is reported to vary between 1.3 to 6.3 for lightly pigmented skin and 18 to 43 for heavily pigmented skin.²⁶ Thus, the absorption coefficient of the epidermis can be calculated from the melanin content (f _mel ) and the background absorption of unpigmented skin [μ_a ^unpigm (λ)] ²⁵:

In our simulations, we modeled the skin as a medium consisting of the three layers mentioned above. The thickness of the layers was set to 60 μm for the epidermis and to 2 mm for the dermis. A typical value for the depth of the subcutaneous fat layer is 8 mm. The influence of the underlying tissue layers can be neglected, provided that the detected photons do not penetrate more than 1 cm into the tissue for the considered source-detector separations. Thus, the thickness of the subcutaneous fat layer can be set to infinity in the Monte-Carlo model.

The absorption coefficients of the epidermis and dermis were calculated from Eq. (7) and Eq. (8). A volume filling fraction of blood of 5 according to a THC of 116 μmol/l and an oxygen saturation of 90 was assumed for the dermis. Four series of simulations were performed where the melanin content of the epidermis was varied (f _mel =5, 10, 15 and 20). The reduced scattering coefficients of the dermis and epidermis were calculated as described in Ref. 25. The absorption coefficient and the reduced scattering coefficient of subcutaneous fat were obtained from Ref. 28. The scattering coefficients of the skin layers were calculated from the reduced scattering coefficients assuming the anisotropy factor of 0.9 (Ref. 30). For refractive indices of the various skin layers, a value of n=1.4 was used.⁴² The resulting optical properties for a wavelength of 808 nm are shown in Table 2.

Table 2

In the calculations, photons were launched into the multi-layered semi-infinite medium. The illuminated area and the angular distribution of the launched and detected photons were chosen according to the diameter (600 μm) and numerical aperture (0.2) of the employed source and detector fiber. The propagation of the photons in the medium was calculated using a variable step size Monte-Carlo algorithm that was described in Ref. 38. When a photon crossed the boundary between two layers, the new position of the photon was calculated according to the optical properties of the new layer.³⁹ In addition, the Fresnel reflections at the surface of the skin were taken into account.

On the surface of the medium, nine detector fibers were defined at distances between 2 and 10 mm from the source fiber in steps of 1 mm. For those photons that were diffusely reflected, the positions and the angles at which the photons left the surface were calculated. From these data the probability for launched photons to be detected by one of the detector fibers could be determined. The simulation was terminated when a total number of 1000 photons was detected at the largest distance (10 mm) from the source fiber. Consequently, much larger numbers of photons were registered for the smaller distances (>30,000 for the smallest distance of 2 mm).

For further data processing, the trajectories of those photons that reached one of the detector fibers were stored in the computer. Therefore, a Cartesian coordinate system was defined such that the surface of the medium was located in the x-y plane and the z-axis is perpendicular to the surface. The (x,y,z) coordinates of the source and detector fiber were (0,0,0) and (ρ,0,0), respectively. For those photons that entered the detector fiber located at x=ρ, a grid of cubic voxels was defined where the basic length was set to Δl _ρ=ρ/100. In this discrete space, the position of a single voxel could be characterized by three integer numbers i, j and k, where the coordinates of the voxel were (x_i,y_j,z_k)=(i^*Δl _ρ,j^*Δl _ρ,k^*Δl _ρ). As a measure of the interaction volume, we defined the interaction density of the detected photons S_ρ(x_i,y_j,z_k) as the number of scattering events of the detected photons in the voxel located at the position (x_i,y_j,z_k). A two-dimensional projection S_ρ(x_i,z_k) of the interaction volume can be obtained by adding the values of the interaction density at fixed x_i and z_k positions for all y_j positions:

3.4.

In vivo Measurements

In contrast to the existing “large-volume” methods for the measurement of the oxygen saturation and total hemoglobin content in vivo,^{10 11 12} the small-volume approach measures the average absorption properties of the epidermis and dermis weighted by the interaction density of the two layers. To interpret the measured in vivo data, we consider a turbid medium that consists of two layers A and B with different scattering coefficients (μ_s ^A and μ_s ^B) and absorption coefficients (μ_a ^A and μ_a ^B) as shown in Fig. 3. The photons that are scattered into the detector fiber travel different paths in the medium. In Fig. 3, the trajectory of a single photon between the source and the detector fiber is shown. The length of the trajectory in layers A and B is referred to as d^A and d^B, respectively. For a large number of photons that are scattered into the detector fiber, the average pathlengths of the photons in layers A and B are denoted 〈d^A〉 and 〈d^B〉. When the multi-layered medium in Fig. 3 is examined using the MBL [Eq. (4)], the average absorption coefficient μ_a of the two layers A and B will be obtained whereby the average is weighted with the average pathlengths of the photons in the medium:

Figure 3

Schematic drawing of the trajectory of a single photon between a source and a detector fiber in a turbid medium, which consists of two layers A and B with different optical properties (scattering coefficients μ_s ^A and μ_s ^B , absorption coefficients μ_a ^A and μ_a ^B ) . The pathlengths of the photon in layers A and B are d ^A and d ^B , respectively. When a large number of photons with different trajectories between source and detector fibers is considered, the mean pathlengths 〈d ^A 〉 and 〈d ^B 〉 are relevant.

In order to demonstrate the feasibility of the new technique to determine S[O ₂] and THC in vivo, a homemade applicator consisting of two source and two detector fibers was positioned on the forearm of the volunteer at rest (blood pressure at rest was 115/80 mm Hg). The arrangement of the fibers is presented in Fig. 4. The dimensions of the applicator head are 10×8×10 mm³ (length×width×height). A homemade fiber switch consisting of a magnetic shutter and a 2-in-1 fiber coupler allowed consecutive recording of the signal obtained by the two detector fibers. For the in vivo measurements, two wavelengths (λ₁=678 nm, λ₂=808 nm) were chosen. At 678 nm, the difference of the absorption coefficients of oxy-and deoxyhemoglobin is maximal while at 808 nm there is an isosbestic point of the two absorbers (see Fig. 2).³ Thus, the sensitivity to detect small changes in S[O ₂] can be expected to be largest for the available wavelengths. For both wavelengths, the refractive index of n=1.4 was assumed.⁴²

Figure 4

In vivo experiment to determine the oxygen saturation and the total hemoglobin content at the forearm of a volunteer using a blood pressure cuff to occlude the arm vessels. The inset shows the arrangement of the source and detector fibers [wavelengths: λ₁=678 nm, λ₂=808 nm; source-detector separations for λ₁: ρ₁=5 mm, ρ₂=7 mm; source-detector separations for λ₂ in analogy (not depicted)].

At the beginning of the in vivo measurements, baseline data were acquired over 5 minutes. Thereafter, a pneumatic blood pressure cuff was inflated to a pressure of 150 to 160 mm Hg for 4.5 minutes inducing vascular occlusion. After release of the cuff, measurements of the absorption coefficients were continued for another 5 minutes. The acquisition time for a single data set was approximately 15 seconds. During the experiment, the data sets were collected in intervals of 30 seconds. The personal computer used to control the experimental setup was also employed to calculate S[O ₂] and THC from the measured quantities. The sequence of the steps that were performed for the calculation of the oxygen saturation and the total hemoglobin content from the frequency-domain data is outlined in Fig. 5.

Figure 5

Sequence of the determination of the oxygen saturation S[O ₂] and the total hemoglobin content THC from the frequency-domain data.

4.1.

Phantom Measurements

4.1.1.

Refractive index

The refractive index of the phantoms was determined from the goniometric reflection measurements using Eq. (6) as described above. The result of these measurements is shown in Fig. 6. From the measured values of the refractive index, the following two-parameter Sellmeier formula was obtained:

Eq. (14)

$$n^2(\lambda )=1+\frac{1.3025{\left\{\lambda \right\}}^2}{{\left\{\lambda \right\}}^2-{(0.1375)}^2}(\{\lambda \}\text{in}\mu \text{m}).$$

The refractive index of the phantoms was calculated at the wavelengths of interest using Eq. (14).

Figure 6

Refractive index of resin: experimental values (symbols, mean and standard error) and Sellmeier fit according to Eq. (14) (solid line).

4.1.2.

Absorption properties

Frequency-domain measurements were then performed for the six phantoms containing different amounts of absorber to determine the time-integrated intensity I _DC and the mean time of flight 〈t〉 of the detected photons. Figure 7 shows the time-integrated intensity I _DC as a function of the mean time of flight 〈t〉 at various source-detector separations between 3 and 9 mm for the wavelength of λ=678 nm. The mean time of flight varied between 150 and 550 ps corresponding to a mean pathlength of the photons 〈L〉=c_n〈t〉 between 29 and 107 mm. Thus, it exceeded the source-detector separation by a factor of up to 12. As predicted by the modified MBL, the logarithm of the DC intensity decreased linearly with increasing time of flight. The correlation coefficients for all wavelengths were greater than 0.98. According to Eq. (4), the absorption coefficient of the sample can be obtained from the slope of the ln{I _DC } vs. 〈t〉 plots. The resulting absorption coefficients are presented in Fig. 8 for all employed wavelengths. A linear dependence of μ_a from the volume filling fraction of the absorbers was obtained (correlation coefficient R=0.993 for λ=678 nm, 0.992 for λ=808 nm, and 0.989 for λ=835 nm). The relative absorptivities Δμ_a/Δf _abs obtained from the slopes of Fig. 8 were compared to the relative absorptivities of the non-scattering phantom samples determined using the conventional absorption spectrometer. As can be seen in Fig. 9, the frequency-domain technique data agreed very well with the results obtained from the conventional spectrophotometer. The resulting optical properties of the phantoms used in this study are summarized in Table 1.

Figure 7

Logarithm of the time-integrated intensity as a function of the mean time of flight for the various phantoms at a wavelength of λ=678 nm (symbols, mean and standard error; dotted line, linear regression). All correlation coefficients are >0.98.

Figure 8

Absorption coefficient of the phantoms as a function of the volume filling fraction of the absorber (symbols, mean and standard error; dotted line, linear regression). The regression coefficients are R=0.9929 (λ=678 nm), R=0.9917 (λ=808 nm), and R=0.9885 (λ=835 nm).

Figure 9

Comparison of the relative absorptivities measured using the frequency-domain spectrometer (symbols, mean and standard error) with the mean relative absorptivity determined with a conventional absorption spectrometer for a series of non-scattering phantoms (solid line).

4.2.

Monte-Carlo Simulations

Figure 10 shows a typical result for the interaction density as a function of the depth in the turbid medium at a distance of ρ=5 mm from the source fiber. The optical properties correspond to the wavelength of 808 nm and the melanin content in the dermis of 5 (Table 2). The banana-like shape of the probed sample volume is clearly visible. The mean penetration depth 〈z〉 is shown in Fig. 11 as a function of ρ for the wavelength of 808 nm. As can be seen in this figure, 〈z〉 increases linearly with ρ from 1.2 mm at ρ=2 mm to approximately 5 mm at ρ=10 mm. No significant dependence of the mean penetration depth on the melanin content of the epidermis was found in the Monte-Carlo simulations between ρ=2 and 9 mm.

Figure 10

Interaction density S_ρ(x_i,z_k) of the detected photons for a three-layer semi-infinite model of human skin (epidermis, dermis, and subcutis) determined with a Monte-Carlo simulation for a source-detector separation of ρ=5 mm (logarithmic grayscale, arbitrary units). The layer boundaries are at z=0.06 mm and z=2.06 mm. The optical properties of the layers correspond to the epidermis, dermis, and subcutaneous fat at the wavelength of 808 nm and the melanin content of 5 in the epidermis. Source and detector fiber are located at x=0 mm and x=5 mm, respectively.

Figure 11

Penetration depths of the detected photons as a function of the source-detector separation determined with a Monte-Carlo simulation in a three-layer semi-infinite medium for different melanin contents f _mel in the epidermis (mean±standard error). The optical properties correspond to the wavelength of 808 nm. For the small source-detector separations, a larger number of photons was detected. Thus, a better statistical accuracy was achieved.

Furthermore, the ratio of the pathlength of the photons in the epidermis to the total pathlength f ^epidermis was calculated for the different values of f _mel . The dependence of f ^epidermis on the source-detector separation is shown in Fig. 12 for the wavelength of 808 nm. For the source-detector separation of 2 mm and the melanin content of f _mel =5, about 2.7 of the interaction events occurred within the first layer of the medium. The fraction decreases to approximately 1.1 at ρ=5 mm and 0.8 at ρ=7 mm. At the wavelength of 678 nm and the melanin content of 5, the value of 0.9 at ρ=5 and 0.7 at ρ=7 mm was obtained for f ^epidermis . With regard to these findings, a mean value of f ^epidermis =0.9 was used for the processing of the in vivo data.

Figure 12

Fractional contribution f ^epidermis of the epidermal layer (thickness 60 μm²⁶) to the photon pathlength in human skin determined from Monte-Carlo simulations at the wavelength of 808 nm for different source-detector separations and different melanin contents f _mel (mean±standard error).

4.3.

In vivo Measurements

Figure 13 shows the absorption coefficients at 678 and 808 nm and the calculated concentrations of Hb and HbO ₂ in the probed region before, during, and after occlusion of the blood vessels. Using Eqs. (12) and (13), the total hemoglobin content and the oxygen saturation have been calculated from the measured data assuming a fractional melanin content of f _mel =5 and an average fractional pathlength in the epidermis of f ^epidermis =0.9. The result of these calculations is shown in Fig. 14. During occlusion, the calculated THC rapidly decreased from approximately 220 to 250 μmol/l to values between 150 and 190 μmol/l and the calculated S[O ₂] dropped from approximately 94 to 95 to 82 to 86. After release of the blood pressure cuff, THC and S[O ₂] increased rapidly and returned to the values measured before occlusion of the blood vessels.

Figure 13

Absorption coefficient and concentration of hemoglobin and oxyhemoglobin determined in the in vivo experiment. The error bars represent the uncertainties due to experimental errors. The shaded area indicates the period of cuff occlusion.

Figure 14

Result of the in vivo determination of the oxygen saturation and the total hemoglobin content. The error bars represent the uncertainties due to experimental errors. The shaded area indicates the period of cuff occlusion.