2.1.

Wavelength and Source-Detector Separation Selection for Simulation

Figure 1 shows representative absorption spectra of endogenous chromophores in tissue to provide a visual comparison of the NIR and SWIR wavelength bands. Absorption spectra were computed using published extinction spectra.^17–19 Tissue concentrations of water, oxy-hemoglobin (${\mathrm{HbO}}_2$), and deoxy-hemoglobin (HHb) are average values reported for healthy breast tissue, with lipid estimated at 40% by volume.²⁰ As seen in this figure, water absorption overtakes that of hemoglobin past $\sim 900\mathrm{nm}$, whereas lipid exceeds hemoglobin absorption past $\sim 1100\mathrm{nm}$ for this tissue type. Water absorption becomes very high past 1400 nm, limiting imaging penetration depth and signal levels. A SWIR window of 980 to 1300 nm (shaded region) in Fig. 1) was chosen for the probe illumination based on these considerations. Discrete wavelengths at 980, 1200, and 1300 nm were then chosen based on LED availability. Water absorption is relatively high at all three of these wavelengths, whereas lipid absorption has a peak near 1200 nm. For the NIR, 900, 930, and 970 nm were chosen based on spectral features commonly exploited and LED availability. Four source-detector (S-D) separations (7, 10, 13, and 16 mm) were included in the simulations. In total, this resulted in 12 unique wavelength/separation pairs for the SWIR and NIR.

Fig. 1

Absorption of endogenous chromophores in healthy breast tissue from 600 to 1700 nm (for water and lipid) and 600 to 1300 nm (for ${\mathrm{HbO}}_2$ and HHb). Tissue concentrations for this example are as follows: water = 51.5%, lipid = 40%, ${\mathrm{HbO}}_2=11.3\mu \mathrm{M}$, $\mathrm{HHb}=5.3\mu \mathrm{M}$. The shaded region (980 to 1300 nm) refers to desired SWIR wavelength region for our probe design.

2.2.

Simulation Workflow

Simulations were performed using both Matlab and Python, and the workflow is described here and summarized in Fig. 2(a). For a single simulation, water, lipid, and scattering properties were randomized for the simulated “sample.” For each simulation performed, water and lipid concentrations were randomly selected from uniform distributions between 0% and 100% and always summed to 100% (entire simulated sample comprised of just water and lipid). The percentage refers to percent by volume. A power law [Eq. (1)] described the scattering relationship with wavelength, with scattering amplitude ($A$) and slope ($b$) as the randomized properties

Fig. 2

(a) Simulation flowchart for the comparison of SWIR and NIR wavelengths. (b) A table of architecture and training parameters for the DNNs used in this study. (c) Loss (MSE) as a function of epoch during training for both the SWIR and NIR DNNs. (d) All 25,000 recovered water values plotted versus ground truth for SWIR and NIR wavelengths. (e) Same as (d), but for lipid. (f) Bar plots of the mean and standard deviation of differences between recovered and ground truth values for both SWIR and NIR.

Possible amplitude values were defined as a uniform distribution from 0.2 to $10{\mathrm{mm}}^{-1}$ (referenced to 980 nm). Scattering slope values were defined as a normal distribution with $\mu =1.29$, $\sigma =0.52$, which are typical slope values for soft tissue.²¹ Next, the absorption coefficient (${\mu }_a$) and reduced scattering coefficient (${\mu }_s^{\prime }$) were computed for each of the three SWIR and NIR wavelengths. Beer’s Law was used to compute ${\mu }_a$ (using the same extinction spectra from Sec. 2.1), and Eq. (1) was used to compute ${\mu }_s^{\prime }$. A pre-generated look-up table (LUT) of Monte Carlo-derived diffuse reflectance ($R_d$) values then mapped optical property pairs to $R_d$ values for each of the 12 unique wavelength/separation pairs, for both the SWIR and NIR groups (Monte Carlo simulations described in more detail in the following section). Zero-mean Gaussian noise was then added to the $R_d$ values, with $\sigma =5\%$. These noise-added $R_d$ values were then input to an inverse model to recover water and lipid estimates. A fully connected DNN was used as the inverse model. This process was repeated 25,000 times, resulting in 25,000 sets of recovered water and lipid values for both the SWIR and NIR groups. These recovered values were compared to the ground truth values to compute the mean and standard deviation of extraction errors.

2.3.

Forward and Inverse Models: Monte Carlo and DNN

White Monte Carlo simulations were run and the results were used to map optical property pairs to surface diffuse reflectance. Simulations were run in Matlab using Monte Carlo eXtreme.²² The sample geometry was defined as a slab with dimensions of $6\mathrm{cm}\times 6\mathrm{cm}\times 10\mathrm{cm}$, approximating a semi-infinite medium. Optical properties were homogenous, with ${\mu }_a=0{\mathrm{mm}}^{-1}$ and ${\mu }_s^{\prime }$ ranging from 0.2 to $10{\mathrm{mm}}^{-1}$. Detectors were placed 7, 10, 13, and 16 mm from the source, and a steady-state illumination source fiber was used. Collected photons for each ${\mu }_s^{\prime }$ value were then scaled for a range of absorption values using the Beer-Lambert law, with ${\mu }_a$ ranging from 0.001 to $0.2{\mathrm{mm}}^{-1}$. Anisotropy factor $g$ and index of refraction $n$ were set to 0.7 and 1.435, respectively, which are values for lipid-water emulsions adapted from Flock et al.²³ and Aernouts et al.²⁴ After the Monte Carlo simulations were completed, the ${\mu }_a$, ${\mu }_s^{\prime }$, and resultant $R_d$ values at each S-D separation were saved in a LUT.

The DNN was implemented in Python using the Keras library. The architecture and training parameters are summarized in Fig. 2(b) and are briefly described here. The DNN consists of an input layer with 12 nodes ($R_d$ for each wavelength/separation pair), 3 hidden layers, each with 20 nodes, and an output layer with 2 nodes (recovered water and lipid). The rectified linear unit was selected as the activation function for hidden layer nodes, and a linear function was the activation function for the output layer. The Adam optimizer was the training algorithm with a learning rate = 0.001. The loss function (or error function) was the mean squared error (MSE) of water and lipid. A trial-and-error approach was used to select the number of hidden layers and nodes/layer, initially exploring 1 to 6 hidden layers and 10 to 100 nodes/layer. It was found that adding more layers beyond 3 had diminishing returns in error minimization, and likewise beyond 20 nodes/layer. However, this optimization was coarse, and other functional architectures exist. The chosen activation function, training algorithm, learning rate, and loss function are all commonly used for fully connected DNNs. For training data, 75,000 sets of water, lipid, and $R_d$ values (generated using the same Monte Carlo LUTs described previously) were constructed in Matlab and imported into Python, using the same randomization process and parameters described for the 25,000 test datasets in Sec. 2.2. These parameters are also reported in Table S1 in the Supplementary Material. The $R_d$ inputs were log-normalized prior to training. The spectral constraints described in Sec. 2.2, namely (1) absorption limited to a linear sum of water and lipid contributions and (2) the wavelength dependence of scattering defined by a power law, provided important constraints during training, which helped to reduce the solution space. Two DNNs were trained, one for SWIR and one for NIR. Initially, automatic stopping was implemented during training, stopping when the mean loss over the previous 200 epochs was no longer decreasing. This occurred after $\sim 2000$ epochs for both SWIR and NIR. To be cautious, the final DNNs used for comparison were trained with 3000 epochs. All subsequent DNNs in this study (after the SWIR versus NIR comparison), however, were trained with 2000 epochs.

2.4.

Simulation Results

Figure 2(c) illustrates the first indication that SWIR outperforms NIR in water and lipid recovery by showing the MSE during training of the two DNNs. The NIR MSE plateaued at around ${10}^{-4}$, whereas the SWIR MSE dropped below ${10}^{-5}$, indicating that, even prior to noise addition, the SWIR wavelengths were able to achieve a lower error in water and lipid extractions. Figures 2(d) and 2(e) show plots of recovered water and recovered lipid versus their ground truths, respectively, for the 25,000 noise-added test sets described in Sec. 2.2. It is evident that for both water and lipid, the spread of recovered values more closely approaches the identity line for the SWIR wavelengths. This is especially true for high water/low lipid samples, with more comparable errors for near-100% lipid samples. Figure 2(f) quantifies this error, showing the mean and standard deviation of the difference between recovered and true values for all 25,000 sets of water and lipid values. For SWIR wavelengths, the errors for water and lipid recovery were $-0.1\%\pm 1.3\%$ and $0.2\%\pm 1.3\%$, respectively. The NIR error was higher, with values for water and lipid of $0.3\%\pm 5.8\%$ and $-0.3\%\pm 5.8\%$, respectively. These results suggest that the chosen SWIR wavelengths outperform NIR wavelengths in water and lipid recovery.

3.1.

Printed Circuit Board and Probe Housing

The system consists of two components: a probe and a microcontroller (FRDM-K64F). The probe has one InGaAs PIN photodiode (G12180-30, Hamamatsu), four 980 nm LEDs (MTE9730CP), four 1200 nm LEDs (MTSM0012-843-IR), and four 1300 nm LEDs (MTSM0013-199-IR). All LEDs were purchased from Marktech. The photodiode has an active area of $\sim 7{\mathrm{mm}}^2$ and is sensitive to the 900 to 1700 nm wavelength range. The quantum efficiency at the illumination wavelengths is as follows: $\sim 63\%$ at 980 nm, $\sim 83\%$ at 1200 nm, $\sim 86\%$ at 1300 nm. LEDs were positioned at four different distances from the photodiode: 7, 10, 13, and 16 mm. These were the minimal distances achievable given the size of the optical elements. A transimpedance amplifier (OPA3S32), with three integrated switchable gain levels (0.5, 1, and 10 MΩ), was used to amplify and convert the photodiode current into voltage. This output voltage is read by a 16-bit analog to digital converter embedded on the microcontroller. The intensity of the twelve LEDs is controlled with the 12-bit digital to analog converter (DAC) embedded on the microcontroller. The DAC output voltage is translated into current with an operational amplifier (TLV272IS-13) and NPN bipolar junction transistor (TTC1949-GR,LF). The microcontroller communicates with the probe through a high-definition multimedia interface (HDMI) connection, and the user can interact with the system with a Python GUI (graphical user interface). The sampling rate of the system was set to 1 Hz.

The SWIR probe is shown in Fig. 3(a) and the probe with control hardware is shown in Fig. 3(b). Figure 3(c) shows the probe adhered to a forearm with Velcro. The probe was encased in a custom 3D-printed plastic housing with overall dimensions of $7.1\mathrm{cm}\times 3.1\mathrm{cm}\times 1.4\mathrm{cm}$. Black silicone was used to isolate the optical elements. The silicone (Ecoflex-030, Smooth-On Inc.) and black dye (Silc-Pig, Smooth-On Inc.) are skin-safe and were mixed together with a curing agent, de-gassed in a vacuum chamber for 15 min, and poured directly onto the exposed PCB (printed circuit board) surface.

Fig. 3

(a) Sample-facing and side views of the encased SWIR probe, with optical elements labeled. (b) The probe attached to its external control hardware (the microcontroller) via HDMI. (c) An example of how the probe might be worn on the forearm of a human subject with a Velcro strap.

3.2.

Performance Characterization

Signal-to-noise ratio (SNR) and system drift were measured on a liquid optical phantom containing 1% Intralipid solution in water. Both the water and lipid absorb light at SWIR wavelengths, and the lipid micelles are highly scattering, creating a diffusive medium. The optical properties of 1% Intralipid across the SWIR probe wavelengths, calculated using Beer’s Law and Mie theory, range from 0.04 to $0.13{\mathrm{mm}}^{-1}$ for ${\mu }_a$ and 0.49 to $0.78{\mathrm{mm}}^{-1}$ for ${\mu }_s^{\prime }$. The probe was wrapped tightly in clear plastic wrap and fixed in a slightly submerged position within the liquid phantom during measurement acquisition.

For the SNR measurement, the signal for each S-D pair was recorded for 1 min at the fixed rate of 1 Hz. An initial background measurement was recorded with all of the LEDs off prior to the acquisition. SNR was then computed as

Table 1

Performance characteristics of SWIR probe. SNR and drift values are shown for just the shortest and longest S-D separations (7 and 16 mm).

For the drift measurement, the signal for each S-D pair was recorded for 1 h. The voltage and time data were then fit to a linear function to quantify the slope, which was normalized to the initial voltage and multiplied by 100 to get units of % V/h. Drift values for S-D separations $\le 10\mathrm{mm}$ were $<1.1\%$ V/h (Table 1).

4.1.

Water-in-Oil Emulsion Phantoms

Five water-in-oil emulsion phantoms were fabricated using soybean oil, water, and Triton X-100 as the emulsifier as described in Merritt et al.⁷ Lipid concentrations were 65% to 85%, in steps of 5%. High ($\ge 65\%$) lipid concentrations were used to minimize scattering differences across phantoms, which occurs as a result of dependent scattering.²⁴ The SWIR probe was wrapped in clear plastic wrap and submerged in the emulsion phantoms. The probe optical elements were at least 1.5 cm from the phantom edge. Ten seconds of data were acquired at 1 Hz for each phantom measurement.

The processing pipeline is depicted in Fig. 4. Measured sample and dark voltage measurements were first gain-corrected, and all sample voltage measurements were dark subtracted. Next, a forward model (Monte Carlo LUT) was used to map the known optical properties (${\mu }_a$ and ${\mu }_s^{\prime }$) of the calibration phantom to a theoretical $R_d$ value. As the photodiode operates linearly with incident light power, the $R_d$ value was divided by the calibration measurement voltage to get a linear scaling factor, specific to each S-D pair. The corrected sample voltage was then multiplied by this scaling factor to compute ${\mathrm{R}}_d$ for that S-D pair.

Fig. 4

Data processing flowchart for in vitro validation experiments.

The 85% lipid phantom was used as the calibration phantom. Beer’s Law was used to compute ${\mu }_a$, and the empirical formula given by Aernouts et al.²⁴ was used to compute ${\mu }_s^{\prime }$. This formula defines ${\mu }_s^{\prime }$ as a function of wavelength and lipid concentration for emulsions up to 20% lipid concentration. However, the dependency on concentration nearly flattens at this upper limit due to dependent scattering. Therefore, we approximated the scattering values for 85% lipid as being equal to those of 20% lipid. These optical properties ranged from 0.04 to $0.13{\mathrm{mm}}^{-1}$ for ${\mu }_a$ and 4.8 to $8.9{\mathrm{mm}}^{-1}$ for ${\mu }_s^{\prime }$ for the three measurement wavelengths. The DNN architecture was nearly identical to the DNN described in Sec. 2, except the 16 mm S-D separation measurements were removed due to low signal, resulting in 9 $R_d$ inputs to the DNN. The DNN was trained with 75,000 sets of 9 $R_d$ values. Additional information related to the training data is given in Table S1 in the Supplementary Material.

Figures 5(a) and 5(b) show $R_d$ versus lipid concentration for the 7 and 10 mm separations. $R_d$ increased as lipid concentration increased and water concentration decreased. This is expected at 980 and 1300 nm as water has high absorption compared to lipid. While lipid’s extinction coefficient at 1200 nm is slightly higher than water’s, it is very close to an isosbestic point for the two chromophores, and the LED illumination is broad ($\sim 80\mathrm{nm}$ full-width at half maximum). This likely explains why the 1200 nm data appears to behave similarly to the other wavelengths. Also, $R_d$ at 1200 nm is below that of both 980 and 1300 nm, which is consistent with the fact that both water and lipid have relatively high absorption here. Figures 5(c) and 5(d) show the correlations between recovered water and lipid, respectively, and their ground truth values. Both the water and lipid estimates follow the identity line closely. Removing the calibration phantom from the sample set, the mean ± standard deviation of the error (defined as error = estimated – true) was $2.1\%\pm 1.1\%$ for water recovery and $-1.2\%\pm 1.5\%$ for lipid recovery. These results indicate that the SWIR probe is sensitive to variation in water and lipid content, and that, given certain a priori information, it can accurately quantify water and lipid content in vitro.

Fig. 5

a) $R_d$ versus lipid concentration for S-D separation = 7 mm. (b) Same as (a), but for S-D separation = 10 mm. (c) Recovered water versus true water. The inset zooms in on the 25% water data point, showing the length of the error bars. These error bars refer to the standard deviation across the 10 consecutive time points that were acquired for each phantom. All four subfigures have these error bars, but they are barely visible when zoomed out. (d) Same as (c), but for lipid recovery.

4.2.

Dilution of Oil-in-Water Emulsion with ${\mathrm{D}}_2\mathrm{O}$

To further validate the SWIR probe’s sensitivity to water concentrations over a wide range, measurements were taken on a solution of 1% Intralipid in pure water (${\mathrm{H}}_2\mathrm{O}$), which was serially diluted with 1% Intralipid in deuterium oxide (${\mathrm{D}}_2\mathrm{O}$). ${\mathrm{D}}_2\mathrm{O}$ molecules consist of two ${\mathrm{H}}^2$ isotopes instead of ${\mathrm{H}}^1$, and their absorption is greatly reduced in the SWIR compared to ${\mathrm{H}}_2\mathrm{O}$ molecules.²⁵ The initial 1% Intralipid solution was measured in a well embedded in a diffusive solid silicone phantom. The well had a volume of 150 ml and was 2.5 cm deep. The SWIR probe was wrapped in clear plastic wrap and fixed at the surface of the solution, slightly submerged. Data acquisition was started and measurements were taken for 10 s at 1 Hz. Ten phantoms were measured, with ${\mathrm{H}}_2\mathrm{O}$ concentrations ranging from 99% to 9% in steps of 10%. The concentration of scattering lipid particles was preserved across all phantoms.

The 1% Intralipid in ${\mathrm{H}}_2\mathrm{O}$ solution was used as the calibration phantom for this experiment, using the same known optical properties listed in Sec. 3.2. The Monte Carlo LUTs used to produce the DNN training data were generated with the index of refraction set to 1.33 to reflect the low lipid concentration. The combinations of ${\mathrm{H}}_2\mathrm{O}$ and lipid were not constrained to sum to 100%, as the decreasing ${\mathrm{H}}_2\mathrm{O}$ concentration was replaced by ${\mathrm{D}}_2\mathrm{O}$, not lipid. Furthermore, we assumed that ${\mathrm{D}}_2\mathrm{O}$ absorption was collinear with ${\mathrm{H}}_2\mathrm{O}$ absorption but with 1/10th the magnitude, an estimate based on the extinction spectra reported in Wang et al.²⁵ This ${\mathrm{D}}_2\mathrm{O}$ ${\mu }_a$ contribution was taken into account when generating the training data. Finally, the scattering was fixed to be equal to that of 1% Intralipid. All 12 S-D pairs, spanning all four S-D separations, were input to this experiment’s DNN. The DNN training data details are listed in Table S1 in the Supplementary Material.

Figures 6(a) and 6(b) show $R_d$ as a function of ${\mathrm{H}}_2\mathrm{O}$ concentration for the 7 and 10 mm S-D separations respectively. The slope of $R_d$ is steepest for 1300 nm, explained by the relatively high absorption from ${\mathrm{H}}_2\mathrm{O}$ at this wavelength compared to the other two. We can assume that these trends in $R_d$ are strictly absorption-dependent since the scattering lipid particle concentration was held constant. Figure 6(c) shows the recovered ${\mathrm{H}}_2\mathrm{O}$ concentration compared to the ground truth concentration. The estimates are within 4% of the ground truth from 49% to 99% ${\mathrm{H}}_2\mathrm{O}$ and are within 10% for all data points. Over the full range of concentrations, the mean ± standard deviation of the error was $3.1\%\pm 3.7\%$. This suggests that the SWIR probe has sensitivity to water at all concentrations, although the accuracy of water estimation appears to degrade at very low concentrations.

Fig. 6

(a) $R_d$ versus H2O concentration for S-D separation = 7 mm. (b) Same as (a), but for S-D separation = 10 mm. (c) Recovered ${\mathrm{H}}_2\mathrm{O}$ versus ground truth compared to the identity line. For all subfigures, error bars are presented as the standard deviation across the 10 consecutive time points for each phantom measurement. Error bars are present but barely visible.