2.1.

Phantoms

Two types of phantoms were used in this study: (1) a liquid phantom consisting of blood and intralipid having oxygen saturation that could be systematically varied by adding yeast and (2) two-layered silicone-based solid phantoms.

2.1.2.

Two-layered phantoms

Solid two-layered phantoms were created to mimic the layered structure of skin tissue. Two bottom layer phantoms were employed to mimic the dermal properties of skin at two distinct concentrations of hemoglobin. Nine top layer phantoms were fabricated to mimic epidermal properties having three distinct fractions of melanin (using coffee as a surrogate) at three thicknesses. All of these phantoms were fabricated at the Beckman Laser Institute, University of California, Irvine, and used polydimethylsiloxate (PDMS) (Kit P-4, Eager Plastics, Chicago) as the base medium, following the general methods previously published by these authors elsewhere.^8,9 These methods were slightly modified to suit the needs of this particular investigation and are articulated below.

To mimic the spectral properties of melanin, freeze-dried coffee has been shown to be a reasonable surrogate.⁹ Concentrations of 0, 2, and 4 g of coffee dissolved in acetone (per 100 ml PDMS) were used to fabricate three batches of epidermal phantoms that mimic various fractions of melanin in the skin, approximately covering a range of skin types I to IV according to the Fitzpatrick scale.¹⁰ In this instance, 10 g of freeze-dried coffee was added to 20 ml of acetone in a disposable beaker. As the coffee crystals were dissolved by the acetone, it formed a thick liquid mass that settled to the bottom of the beaker. Extracting this coffee concentrate from the beaker using an irrigation syringe, the coffee was added directly to the raw PDMS by mass and mixed prior to the addition of the curing agent. These three concentrations of coffee are from now on referred to as “no coffee,” “low coffee,” and “high coffee” epidermis phantoms. Titanium oxide [titanium(IV) oxide, anatase, Sigma Aldrich, Saint Louis] (0.17 g per 100 ml PDMS) was used to provide scattering properties in all batches. The vigorous mixing required to homogeneously distribute the absorbing and scattering agents will also introduce air bubbles in the viscous PDMS medium. To that end, the mixture is placed in a Nalgene vacuum chamber for $\sim 15$ to 20 min in order to remove the air bubbles.^8,9 For each batch, three thicknesses, simulating the epidermis, were fabricated. Rather than using rectangular molds of varying thickness, as proposed previously, we used 100- and 60-mm-diameter petri dishes. Here, a discrete volume of the mixed and degassed PDMS liquid was extracted using a 3-ml irrigation syringe and placed into the center of the petri dish. Each dish was placed on a spin coater (SCK-200 Digital Spin Coater Kit, Intras Scientific, New Jersey) at low RPM ($<120$) until the PDMS was evenly distributed along the bottom of the dish. The volume of PDMS used in each case correlates with the desired thickness of the cured phantom, based on the diameter of the dish used. For this study, target thicknesses were 100, 200 and $300\mu \mathrm{m}$, which translates to 0.79 ml (100 mm dish), 1.57 ml (100 mm dish), and 0.85 ml (60 mm dish), respectively. Since cured PDMS is electrostatic, additional amounts of the mixed PDMS was added to the edges of the dish to provide additional structure and support for the purpose of increasing mechanical integrity in these noncritical areas to enable handling.

Because PDMS is hydrophobic, it is exceptionally challenging to incorporate hemoglobin or find a suitable proxy that mimics its characteristic spectral absorption features across visible and near-infrared domains.¹¹ We have developed a method to utilize freeze-dried bovine hemoglobin (Sigma Aldrich) in these PDMS phantoms. First, the freeze-dried hemoglobin is vigorously mixed with a common surfactant (triton X-100, Sigma-Aldrich) to dissolve/soften the larger flakes. It is then sonicated (Bransonic M1800, Branson Ultrasonics) for 90 to 120 min (repeated over the course of 3 days) to further reduce the size of these freeze-dried hemoglobin particles. This process breaks down the hemoglobin flakes into submicron-sized particles (verified using microscopy). Acting more like a pigment (particle) rather than a dye (solution), the hemoglobin remains fixed in its chemical structure, yet only minimally contributes to the scattering properties of the resulting phantom, as verified by integrating sphere measurements described in Sec. 2.2 and illustrated in the scattering spectra shown in Fig. 7(a). It is worth noting that this form of hemoglobin is not an ideal proxy, as the freeze-drying process results in additional contributions of hemoglobin breakdown products such as methemoglobin to the mixture (as shown in the resulting absorption properties in Fig. 6). For the two dermal phantoms, 4 and 8 ml of this hemoglobin slurry ($\sim 1$ and 2 g of hemoglobin, respectively) was added to 350-ml PDMS. These two dermis phantoms are from now on referred to as the “low” and “high” hemoglobin concentration dermis phantoms. 0.6 g of titanium oxide was added to each, to approximate the same scattering properties of the epidermal layers. Molded in $100\times 100\mathrm{mm}$ plastic cases, these phantoms were 35 mm thick. As the actual concentrations of hemoglobin are not precisely controlled in this particular protocol, three thin samples were poured from each batch, so their respective optical properties could be determined via an integrating sphere-based inverse adding-doubling method described in Sec. 2.2.

Measurements were performed on a total of 20 combinations of those epidermal and dermal phantoms. Either the dermis phantom with low or with high hemoglobin concentration was used in all combinations. On top of the dermal phantom either no epidermal phantom was used (2 cases), or an epidermal layer with any of the three coffee concentrations with any of the three thicknesses was used (18 cases). A metal rod was rolled over the thin phantom in order to reduce air bubbles so as to improve index of refraction matching between layers. The EPOS probe (see Sec. 2.3) was held in place by hand using a gentle pressure (Fig. 1). For each of the 20 phantom combinations, four separate measurements were performed positioning the probe halfway between the center and periphery of the epidermal layer on the two-layered phantoms and moved clockwise between the measurements.

Fig. 1

Measurement on a two-layered PDMS phantom. The thin epidermis-mimicking coffee phantom is placed on top of the thick dermis phantom, and the measurement probe is held in place by the fingers. Small air-bubbles and/or surface inhomogeneities can be observed in the two-layered phantom.

2.2.

Measurement of Phantom Optical Properties

In order to independently verify the respective optical properties of the two-layered phantoms, diffuse reflectance and transmittance spectra were measured for all thin samples (including thin samples concurrently fabricated from the two hemoglobin phantoms used in this investigation). These spectra were collected via a custom-built, validated single integrating sphere system specifically designed for broadband illumination and detection at the Beckman Laser Institute, a system that is thoroughly described in references.^9,12,13 Each phantom set was measured at every thickness and at five spatial locations per sample to ensure homogeneity and consistency within each phantom set. Using the inverse adding-doubling code developed by Prahl,^14,15 the absorption and reduced scattering coefficient spectra were calculated from the respective reflectance and transmittance measurements over a 450 to 1000 nm range at $\sim 1\mathrm{nm}$ resolution.

2.3.

Measurement System

The microcirculation (phantom) parameters that were evaluated were measured using a PeriFlux 6000 EPOS system, integrating DRS and LDF in a fiber-optic probe.⁵ The system consisted of a PF6010 laser Doppler unit, a PF6060 spectroscopy unit, a broadband white light source (Avalight-HAL-S, Avantes BV, The Netherlands), and a fiber-optic thermostatic heating probe. The PF6060 unit had two spectrometers (AvaSpec-ULS2048L, Avantes BV) with optical notch filters mounted behind the $100\text{-}\mu \mathrm{m}$ slit in order to suppress wavelengths $790\pm 20\mathrm{nm}$ to ensure minimal influence from the PF6010 laser light on the DRS spectra. The fiber-optic probe consisted of two central emitting fibers and three detecting fibers. The fibers for the LDF laser light source and the detecting fiber at a distance of 0.8 mm had a diameter of $125\mu \mathrm{m}$. Two detecting fibers were placed at a distance of 0.4 and 1.2 mm from the white light source fiber and were each connected to separate spectrometers. Those fibers had a diameter of $200\mu \mathrm{m}$ and all fibers had a numerical aperture of 0.37 and were made of fused silica. The probe was designed for measurements in reflection mode where in principle all detected light is scattered multiple times within the measured object. The data from the LDF unit were not used in this study.

An inverse Monte Carlo method is applied in the EPOS system in order to determine the parameters of a multilayered skin model. RBC oxygen saturation and tissue fraction as well as speed resolved perfusion are extracted from the skin model when the model is adapted to measured data. In this study, only DRS spectral data from the two spectrometers were used to determine the model parameters, hence no perfusion information was extracted. The inverse Monte Carlo method is thoroughly described elsewhere.^2,5 In short, the forward problem of calculating DRS spectra at two source–detector separations for a given skin model is solved by applying Beer–Lamberts law on presimulated path-length distributions from each layer. The path-length distributions are presimulated for various epidermis thicknesses and scattering coefficients. The Beer–Lambert modified distributions from each layer are then merged together to give the detected intensity for a certain wavelength and source–detector separation. The inverse problem is a nonlinear optimization problem of fitting forward calculated spectra to the measured spectra while updating the model parameters in an iterative manner. The nonlinear optimization problem is solved using a trust region reflective algorithm with a tailor-made error function that for example emphasizes the spectral shape in the 500- to 600-nm hemoglobin absorption bands.

The model contained the 10 variable parameters $t_{\mathrm{epi}}$, $\alpha$, $\beta$, $\gamma$, $c_{\mathrm{heme},1}$, $c_{\mathrm{heme},2}$, $S_{{\mathrm{O}}_2}$, $D$, $f_{\mathrm{mel}}$, and ${\gamma }_{\mathrm{mel}}$. These are used to express the epidermis layer thickness and wavelength-dependent reduced scattering and absorption coefficients for all three layers according to: epidermis layer thickness ($t_{\mathrm{epi}}$); wavelength- ($\lambda$) dependent reduced scattering coefficient (same for all layers) expressed as

For the solid two-layered phantoms, $c_{\mathrm{heme},1}=c_{\mathrm{heme},2}$ and the vessel diameter $D$ was set to zero, whereas $c_{\mathrm{heme},1}$ and $c_{\mathrm{heme},2}$ were allowed to differ and $D$ was allowed to take any value for the liquid phantoms. The mean cell hemoglobin concentration was assumed to be $31\mathrm{g}/\mathrm{dl}$ RBC for the bovine blood used in the liquid phantoms, thus giving the following relation between $f_{\mathrm{RBC}}$ and $c_{\mathrm{heme}}$

For the intralipid/blood-based liquid phantoms, ${\mu }_{\mathrm{a},\mathrm{Hb},\text{liquid}}$ was based on data from Ref. 16 and ${\mu }_{{\mathrm{a},\mathrm{HbO}}_2,\text{liquid}}$ was based on data from Ref. 17. The reduced absorption spectrum (${\mu }_{\mathrm{a},\mathrm{Hb},\mathrm{liquid}}$) was taken from Ref. 16, since it agrees better to data from other Refs. 1819.–20, whereas oxygenized absorption spectrum (${\mu }_{{\mathrm{a},\mathrm{HbO}}_2,\text{liquid}}$) was taken from Prahl, since it agrees better with data from the same references. In our experience, the spectral model generally fit in vivo measurements better (no systematic residual) when using those spectra than when choosing both spectra from either Refs. 16 or 17 (unpublished data), an observation that holds also for this study. For the solid two-layered phantoms, ${\mu }_{\mathrm{a},\mathrm{Hb},\text{solid}}$ was set to the measured absorption spectrum of any of the dermis phantoms, i.e., with low or high hemoglobin concentration, whereas the artificial saturated dermis phantom absorption spectrum ${\mu }_{{\mathrm{a},\mathrm{HbO}}_2,\text{solid}}$ was set to

Fig. 2

Comparison of the absorption spectra of hemoglobin with concentration relevant for normal blood and phantoms {high concentration hemoglobin phantom and its artificial “saturated” counterpart [Eq. (8)]}. The latter two have been rescaled in order to be more easily seen.

2.4.

Sampling Volume

In order to interpret the results obtained from measurements of the two-layered phantoms in a relevant manner, it is necessary to account for the fraction of the sampling volume that is included in each layer. The sampling volume for a specific model was defined as the average sampling volume over included wavelengths and over both source–detector separations. For each wavelength and source–detector separation, the sampling volume was estimated as previously described in Ref. 5. When considering, for example, the expected reduced scattering coefficient from the two-layered phantoms, the reduced scattering from the two layers was weighted according to the fraction of the sampling volume contained in each layer.

2.5.

Data Exclusion

The analysis method in the EPOS system relies on the spectral shape of the diffuse reflectance spectra for determining the model parameters. For a robust determination of those parameters, distinct spectral characteristics, especially in the wavelength interval 500 to 600 nm (Fig. 2), where both reduced and oxygenated hemoglobin have characteristic absorption peaks, are a necessity. Therefore, data were excluded when the abovementioned wavelength interval contained too little characteristic hemoglobin-related spectral shape. This was done using an approach similar to what has previously been presented by Jonasson et al.^21,22 for in vivo measurements. The exclusion criterion that was determined in those studies, and which is applied here, is that the magnitude of the area bounded by the measured spectrum and a line between the intensities at 506 and 614 nm had to be greater than 1.5 in order to be included in the study. The spectrum from the long source–detector separation (1.2 mm) was used when determining this exclusion criterion. Two examples of this area are shown in Fig. 3; one measurement with almost minimal acceptable heme-area [Figs. 3(a)–3(b); low coffee $75\text{-}\mu \mathrm{m}$ epidermal layer on low hemoglobin dermal phantom, Table 1], and one with a higher heme-area [Figs. 3(c)–3(d); no coffee $90\text{-}\mu \mathrm{m}$ epidermal layer on high hemoglobin dermal phantom, Table 1]. Note that the Hb optical signature is not visible in the short distance DRS spectrum in Fig. 3(a), whereas it is visible in Fig. 3(c). Based on the heme-area criterion, measurements from a total 11 of the 20 solid phantoms were included (see Table 1). All measurements from the liquid phantoms were included. As an example, measurements on forearm skin normally display a heme-area well above 1.5. The heme-area is normally lower than 1.5 for very low RBC tissue fractions ($<0.1\%$).

Fig. 3

Example of DRS spectra at source–detector distance of (a and c) 0.4 mm and (b and d) 1.2 mm, with heme-areas marked in gray in (b) and (d). The spectra in (a) and (b) originate from one of the four measurements on the phantom with low hemoglobin dermis and thin epidermis with low coffee concentration, with a heme-area of 1.6. The spectra in (c) and (d) originate from one measurement on the phantom with high hemoglobin dermis and thin epidermis with no coffee phantom, with a heme-area of 4.0.

Table 1

List of solid phantoms with epidermis thickness and average heme-areas for the four measurements of each phantom. Phantoms with average heme-area <1.5 were excluded.

3.1.

Liquid Phantoms

Examples of the spectral fit at two points in time (10 and 60 min) in the first liquid phantom with $f_{\mathrm{RBC}}=1.6\%$ are shown in Fig. 4.

Fig. 4

Examples of measured spectra and calculated spectra from best fit model at (a and b) 10 and 60 min in the first phantom, for source–detector separation (a and c) 0.4 mm and (b and d) 1.2 mm. At 10 min, the estimated $S_{{\mathrm{O}}_2}=96\%$ compared to expected 99%, and estimated $f_{\mathrm{RBC}}=1.49\%$ compared to expected 1.60%. Corresponding numbers at 60 min were 47%/58% and 1.46%/1.60% for $S_{{\mathrm{O}}_2}$ and $f_{\mathrm{RBC}}$, respectively.

The liquid phantom temperature was between 37.2°C and 37.7°C for the two experiments. The first experiment took 75 min to complete. A first low dose of yeast was added during the first 10 min. This caused a very small decrease in $S_{{\mathrm{O}}_2}$. Higher doses of yeast (see Sec. 2.1) were added causing visible changes in $S_{{\mathrm{O}}_2}$ at time points 38, 60, and 72 min [see Fig. 5(a)]. For the second experiment, taking 20 min, yeast was added in intermediate doses more frequently. In this experiment, the time points when adding the yeast were not observable.

Fig. 5

Estimated oxygen saturation from the EPOS system compared to calculated values based on measured ${\mathrm{pO}}_2$ for the two liquid phantoms with $f_{\mathrm{RBC}}$ of (a) 1.60% and (b) 0.80%.

Estimated oxygen saturation [$S_{{\mathrm{O}}_2}$, Eq. (6)] over time for the two liquid phantoms is shown in Fig. 5 and compared with calculated $S_{{\mathrm{O}}_2}$ values based on the measured $p{\mathrm{O}}_2$ [Eq. (1)]. The root-mean-square (RMS) deviation from values calculated from the $p{\mathrm{O}}_2$ readings was 5.2% units for the first measurement and 2.9% units for the second.

The estimated $f_{\mathrm{RBC}}$ was $1.49\pm 0.03\%$ ($\text{mean}\pm \text{standard}\text{deviation}$) compared to expected $f_{\mathrm{RBC}}=1.60\%$ for the first liquid phantom, with an RMS deviation for all samples of 11%. For the second phantom, corresponing numbers were $0.85\pm 0.02\%$, expected 0.80%, RMS deviation 5.3%. The estimated average vessel diameter $D$ was $1\pm 1$ and $2\pm 2\mu \mathrm{m}$, respectively, in the measurements of the two phantoms. For these homogeneous phantoms without blood vessels, the expected vessel diameter is $0\mu \mathrm{m}$.

3.2.

Two-Layered Phantoms

Absorption spectra for the two hemoglobin phantoms as well as for the three concentrations of coffee in the epidermis phantoms are found in Fig. 6. The reduced scattering coefficients, ${\mu }_{\mathrm{s}}^{\prime }$, of the phantoms are included in Fig. 7.

Fig. 6

Absorption spectra of (a) the two hemoglobin phantoms and (b) the three epidermis phantoms, measured as described in Sec. 2.2.

Fig. 7

(a) Measured ${\mu }_{\mathrm{s}}^{\prime }$ for the five types of phantoms (solid, thick) and estimated ${\mu }_{\mathrm{s}}^{\prime }$ from the 44 included measurements on two one-layered and nine two-layered phantoms (dotted). (b) Estimated ${\mu }_{\mathrm{s}}^{\prime }$-deviation from sampling volume weighted measured values as function of wavelength for the 44 included measurements. Average (solid) $\pm \text{standard deviation}$ (dotted).

The optical and geometrical properties of the phantoms were used to create models representing the phantoms. From those models, the fraction of the sampling volume that was located in the hemoglobin layer was estimated. At least 75% of the sampling volume was located in the dermis layer—the fraction was the lowest for the hemoglobin phantom with higher absorption, higher for thinner epidermis layers, and higher for the epidermis phantoms with higher absorption.

The RMS deviation from zero in the estimated $S_{{\mathrm{O}}_2}$ was 2.9%, where the maximum deviation in the 44 included measurements was 5.1%.

The estimated concentration of hemoglobin absorbers, $c_{\mathrm{heme}}$, in the sampling volume was generally overestimated. The relative RMS deviation for $c_{\mathrm{heme}}$ for the 44 included measurements (heme-area $>1.5$; four measurements on each of the 11 included phantoms) was 25%, whereas the relative RMS deviation for the four phantoms (16 measurements, all from the high hemoglobin phantom) with the most pronounced hemoglobin signature (heme-area $>3.5$) was 11%.

The RMS deviation of the estimated epidermis thickness was $137\mu \mathrm{m}$ for the 44 included measurements. The results for the estimated epidermis layer absorption showed a general high overestimation.

The relative RMS deviation of the estimated reduced scattering coefficient from the measured reduced scattering coefficient taking the sampling volume into account was 15% for the included wavelengths (475 to 850 nm). The spectral shape of the scattering was generally well estimated, as can be seen in Fig. 7(a). The average deviation in estimated ${\mu }_{\mathrm{s}}^{\prime }$ was $-4.6\%$, $-6.0\%$ for wavelengths $<500\mathrm{nm}$ and $-1.9\%$ for wavelengths $>800\mathrm{nm}$.