2.1.

Absorption Features of Water and Lipid in the 900- to 1000-nm Wavelength Region

Figure 1 shows the absorption spectra of various chromophores as well as tissue types in the 600- to 1300-nm wavelength range.^22–26 The quantitative mapping of tissue water and lipid content with structured light was initially demonstrated by SWIR-MPI that utilized the 900- to 1300-nm wavelength region.¹⁷ Specifically, SWIR-MPI primarily utilized the water absorption feature at 970 nm and the lipid absorption feature at 1210 nm. While the commonly used silicon-based cameras have access to the 970-nm wavelength, the 1210-nm wavelength is beyond their detection range, and requires specialized detectors such as InGaAs or germanium-based cameras. In other words, the lack of sensitivity to the lipid absorption feature near 1210-nm wavelength excludes the use of silicon-based detectors in SWIR-MPI. On the other hand, as shown in Fig. 1(a), although much smaller than the 1210-nm peak, there is another lipid absorption peak around 930 nm, which is within the sensitivity range of silicon-based detectors.^23,24,27 In fact, fiber-based techniques such as diffuse optical spectroscopic imaging (DOSI) have been utilizing the 930- and 970-nm wavelengths to quantify tissue water and lipid content.²⁸ Therefore, in this work, we explore the 900- to 1000-nm wavelength region and develop a hyperspectral SFDI system for the quantification of tissue water and lipid content. In addition, we note that SWIR-MPI is essentially SFDI operating in the SWIR wavelength region. They both use structured illumination to probe tissue optical properties (i.e., absorption and reduced scattering). The major difference is that SWIR-MPI operates in the SWIR region, whereas SFDI typically operates in the visible and near-infrared region. Consequently, in terms of detection hardware, SWIR-MPI requires InGaAs or germanium-based cameras, while typical SFDI systems use silicon-based cameras.

Fig. 1

(a) Absorption spectra of oxyhemoglobin ($9.5\mu \mathrm{M}$), deoxyhemoglobin ($0.08\mu \mathrm{M}$), water (26.1%), and lipid (22.5%) contents of human skin in the 600- to 1300-nm wavelengths. (b) Absorption spectra in the 600- to 1300-nm wavelength range for various tissue types.

2.2.

Spatial Frequency Domain Imaging

The details of SFDI image acquisition and processing have been described in detail elsewhere.²⁹ Briefly, during image acquisition, SFDI projects spatially modulated light patterns onto the sample, and the reflectance images are collected by a camera. Typically, the spatial frequencies of the projected patterns (e.g., sinusoidal patterns projected along one-dimension) are carefully selected to ensure measurement accuracy.³⁰ In data processing, the collected images are demodulated with Eq. (1), where $I_1$, $I_2$, and $I_3$ represent raw images acquired at each phase of the projected patterns.³¹ The diffuse reflectance image of spatial frequency $f_x$ is obtained by calibrating the demodulated images, as shown in Eq. (2), where $R_d(f_x)$, $R_{d,\mathrm{ref}}(f_x)$, $I(f_x)$, and $I_{\mathrm{ref}}(f_x)$ represent diffuse reflectance of the sample, diffuse reflectance of the reference phantom, demodulated image of the sample, and demodulated image of the reference phantom, respectively. The $R_d$ maps are then fed into a pre-computed Monte Carlo look-up-table (LUT) to extract optical absorption (${\mu }_a$) and reduced scattering (${\mu }_{s^{\prime }}$) coefficients in a pixel-by-pixel manner for each measurement wavelength. The chromophore concentrations, such as oxyhemoglobin, deoxyhemoglobin, water and lipid concentrations, can be extracted by fitting the measured absorption spectra using Beer’s law^32,33

2.3.

Selection of Measurement Wavelengths and Spatial Frequencies

To identify optimal spatial frequencies for the measurement of water and lipid content with the 900- to 1000-nm wavelength region, we used the established Cramér–Rao bound (CRB) to explore SFDI measurement uncertainties as a function of wavelength under different spatial-frequency combinations.³⁰ The noise parameters were obtained for our SFDI instrument following the procedures described in Pera et al.³⁰ Specifically, the noise parameters were obtained with a set of 12 phantoms covering a wide range of optical properties in the 900- to 1000-nm wavelength range (i.e., 0.0067 to $0.082{\mathrm{mm}}^{-1}$ for absorption and 0.67 to $4.2{\mathrm{mm}}^{-1}$ for reduced scattering). The phantoms were homogeneous liquid phantoms with nigrosin and intralipid added water to control ${\mu }_a$ and ${\mu }_{s^{\prime }}$, respectively. Their optical properties spanned a range of values representative of the applications in our study, e.g., intralipid phantoms, porcine tissue, and small animal (mouse) imaging. In addition, a series of spatial frequency combinations were explored, including [0, 0.05], [0, 0.1], [0, 0.2], and $[0,0.4]{\mathrm{mm}}^{-1}$. It is worthy to note that the zero spatial frequency is constant in the pair because it helps accurate extraction of optical properties. As demonstrated in Pera et al.,³⁰ using only a pair of higher spatial frequencies would yield inaccurate optical property estimations.

In addition, the choice of wavelengths is also critical for the measurement of water and lipid content in tissue. With the wavelength range of 900 to 1000 nm, one could conduct SFDI measurements with 1-nm increment, but it would take a long time for data acquisition and potentially cause motion artifacts for in-vivo measurements. Alternatively, one could also measure with 10 nm increments, but the small number of wavelengths might lead to large measurement errors. To investigate the tradeoff between the number of measurement wavelengths and the measurement accuracy for water and lipid content, we further conducted simulations for the concentration extraction with reference to physiological values in literature.^34–36 Specifically, instead of choosing fixed increments, the concentrations of water and lipid were set to 15% to 90% and 20% to 80%, respectively, with reference to physiological values in literature.^34–36 A total of 100,000 concentration combinations were randomly selected (using the rand function in MATLAB) from the above ranges, and corresponding absorption spectra were generated. In addition, zero-mean Gaussian noise was added to the absorption values of each wavelength increment, where the standard deviation was determined by the CRB measurement uncertainty.³⁰ The water and lipid concentrations were then calculated using Beer’s law with the absorption spectra, which ranged from 900 to 1000 nm with increments of 1, 2, 5, and 10 nm, respectively. For each wavelength increment, the average and standard deviation of percent error were calculated by comparing the percent difference between the extracted concentrations from the generated absorption spectra and the known ground truth values. Since the generated absorption spectra have zero-mean Gaussian noise, the average percent errors of each wavelength increment would be close to zero, and the standard deviation of the percent errors would indicate the goodness of the concentration extraction. In addition, oxyhemoglobin and deoxyhemoglobin were not included for the wavelength selection because (1) the simulation study was intended to identify wavelengths for accurate water and lipid content estimation and (2) the estimation of oxyhemoglobin and deoxyhemoglobin has been extensively studied by Mazhar et al.³² and requires a wavelength region below 900 nm for accurate extraction.

2.4.

Optical Instrumentation

The SFDI system built for experimental validation of this study is shown in Fig. 2(a). The light source is composed of a tungsten halogen lamp with a wavelength range of 300 to 2500 nm (HL1000, NBeT, Beijing, China) and a monochromator (HGISW151, HGOAN, Beijing, China). The spectral resolution (i.e., FWHM) of the monochromator (with fully opened slits to maximize light throughput) is $\sim 1$ to 2 nm according to the manufacturer. The output from the light source is collimated and sent to a digital micromirror device (DMD, V-650L, ViALUX, Saxony, Germany) for spatial modulation. A series of spatially modulated light patterns (shifted 120 deg sequentially in phase) are then projected onto the sample, and the reflectance images are collected by a silicon-based camera (BFS-U3-04S2M-CS, FLIR, Oregon). In addition, five projection patterns were used for each wavelength. Specifically, a “white” and a “black” pattern were used for the $0{\mathrm{mm}}^{-1}$ spatial frequency, and three sinusoidal patterns (shifted 120-deg sequentially in phase) were used for the $0.2\text{-}{\mathrm{mm}}^{-1}$ spatial frequency. The camera exposure time in our study was 50 to 130 ms. Correspondingly, the measurements took 1.71 to 2.35 s per wavelength. An achromatic lens with 75-mm focal length and 50.8-mm diameter (GLH-31, Heng Yang Guang Xue, Shenzhen, China) was used as the projection lens. Orthogonal linear polarizers (#12-474, Edmund Optics, New Jersey) are used to reduce specular reflection from the sample surface. The image acquisition of the camera, spatial modulation of the DMD, and the output wavelength of the light source are synchronized and controlled by a custom software on the personal computer (PC). The synchronization sequence of the system components is shown in Fig. 2(b). The light source is first set to the desired wavelength by the control software through serial communication (i.e., RS-232). Then, the DMD is triggered with a $10\text{-}\mu \mathrm{s}$ transistor-transistor logic (TTL) signal to project illumination patterns with specific spatial frequency and phase. The camera subsequently captures the reflectance images upon another TTL signal that starts $20\mu \mathrm{s}$ after the TTL for DMD. The camera exposure time is 50 to 130 ms in this study depending on different measurement samples. After exposure, the control program waits 70 ms for the acquired image to be transferred to the host computer and saved on hard drive. Subsequently, another $10\text{-}\mu \mathrm{s}$ TTL signal is sent to the DMD to trigger the next projection pattern. The duration of one pattern projection is therefore $\sim 70\mathrm{ms}$ plus camera exposure time. The acquisition process is repeated for each measurement wavelength. The time between wavelengths is 1.71 to 2.35 s depending on different camera exposure times. The TTL signals are generated by an Arduino board controlled by the custom software, which is publicly available for download.³⁷ In addition, the system is mounted on a $65\times 40\mathrm{cm}$ aluminum plate, and the physical size of the entire system is approximately within $80\times 40\times 40\mathrm{cm}$. The imaging field-of-view of the system is $3.2\times 2.1\mathrm{cm}$. Furthermore, a drift test was conducted over 2 h to demonstrate measurement robustness (Note S1 in the Supplementary Material). For data processing, the computation was conducted using a desktop computer with Intel i9-9900K CPU and 64 GB RAM. The inversion from raw data to optical properties took 0.98 s per wavelength, and the extraction of chromophore maps from optical property maps took 0.76 s.

Fig. 2

(a) SFDI system diagram. (b) Synchronization sequence of the system components.

2.5.

Experimental Validations

For experimental validations, we first conducted a phantom study to validate the quantification of water and lipid content with the proposed method. We then conducted lipid content mapping with ex-vivo porcine tissue, as well as in-vivo longitudinal water content monitoring with small animals.

Liquid phantoms with specific proportions of water and lipid were made by varying ratios of water and intralipid (Fresenius Kabi SSPC, Jiangsu, China). A total of five phantoms were made for each concentration. The SFDI measurements were conducted on liquid phantoms ranging from 5% to 20% lipid with 900 to 1000 nm wavelengths of 5-nm increments and $[0,0.2]{\mathrm{mm}}^{-1}$ spatial frequencies. With reference to Tabassum et al.,¹² a small 10% intralipid phantom was placed in the field-of-view for measurement correction. The water and lipid concentrations were estimated by fitting the measured absorption spectra using Beer’s law and then compared with known values. For each concentration, the average and standard deviation of error was calculated by comparing the difference between the extracted concentrations and the known values. The extracted water and lipid concentrations of a single phantom were calculated over an $\sim 1\times 0.5\mathrm{cm}$ region-of-interest at the center of the $2\times 1\mathrm{cm}$ phantom surface. In addition, the calibration phantom used in this study was 10% intralipid whose optical properties have been characterized in the literature.^23,24 Specifically, to compute the extracted concentration values and errors, for a given water-lipid recipe, spatially averaged water and lipid concentrations were computed for each phantom, and then the average and standard deviation of those spatially averaged concentrations across the five phantoms for a given recipe were computed and listed under “extracted concentrations” in Table 1 (and Table S2 in the Supplementary Material). In addition, for every pixel in every phantom, the difference between the pixel value and the known concentration was computed. Then, the computed differences for each phantom were spatially averaged. For a given water-lipid recipe, the average and standard deviation of those spatially averaged differences were computed across the five phantoms, and those values were listed under errors in Table 1 (and Table S2 in the Supplementary Material).

Table 1

Extracted water and lipid concentrations. Five phantoms were measured per water-lipid recipe.

In addition, while lipid content has been an important parameter in the evaluation of meat product,^38,39 we demonstrated the proposed method on lipid content mapping for an ex vivo porcine tissue purchased from a local supermarket. The measurement was conducted using $[0,0.2]{\mathrm{mm}}^{-1}$ spatial frequencies and 900- to 1000-nm wavelengths with 5-nm increments. Additionally, oxyhemoglobin and deoxyhemoglobin were not extracted for the ex vivo porcine tissue with reference to recent literature.⁴⁰ Specifically, Lam et al. utilized narrowband hyperspectral diffuse reflectance in the 900- to 1000-nm range to get point estimations on tissue water and lipid content, in which oxyhemoglobin and deoxyhemoglobin were not extracted potentially due to the absence of blood content in the ex vivo tissues.

The accumulation of tissue water content in the extravascular interstitial space (i.e., edema) is closely associated with many physiological processes, such as tissue healing, inflammation, and sports injury.⁴¹ Therefore, we further demonstrated the proposed method for the monitoring of the presence, extent, and time course of in-vivo tissue water content. Specifically, tissue edema was simulated using subcutaneous injections of phosphate-buffered saline (PBS; no injection, 0.1 ml, or 0.2 ml) in the flank of BALB/c mice. A total of four mice were included for each injection group. With regard to “no injection,” we note that it would also be good to still insert the needle but not inject anything to control for the effect of inserting the needle for the actual PBS injections. The measurements were conducted using $[0,0.2]{\mathrm{mm}}^{-1}$ spatial frequencies and 650- to 1000-nm wavelengths with 5-nm increments. The measurements were repeated every 5 min for a total of 20 time points. With reference to our prior work, a silicone phantom was placed in the field of view for the correction of measurements over time.¹² Chromophore concentrations were extracted for water, lipid, oxyhemoglobin, and deoxyhemoglobin using Beer’s law. The water content of each mouse was calculated by spatially averaging the water content map with a 0.5-cm diameter around the injection site. The averages and standard deviations were then computed from the four water content values of each group. In addition, oxyhemoglobin and deoxyhemoglobin were included in the chromophore fitting since they are also major absorbers (in addition to water and lipid) for in-vivo tissues in the 900- to 1000-nm wavelength range. The 650- to 1000-nm wavelength range was used with reference to prior DOSI literature for the extraction of oxyhemoglobin, deoxyhemoglobin, water, and lipid.^34–36 Additionally, the PBS injection was conducted immediately after three repeated baseline measurements, after which 17 measurements were made with a time interval of 5 min between measurements. The animals were under anesthesia during the procedure with $\sim 2\%$ isoflurane anesthesia. All animal procedures were reviewed and approved by the Beihang University Biological and Medical Ethics Committee.

3.1.

Selection of Measurement Wavelengths and Spatial Frequencies

The measurement uncertainties in optical absorption and reduced scattering are shown in Fig. 3 for wavelengths ranging from 900 to 1000 nm with 5-nm increments. The results show that the spatial frequency combination of $[0,0.05]{\mathrm{mm}}^{-1}$ have the largest measurement uncertainties among the four combinations. In contrast, the $[0,0.2]{\mathrm{mm}}^{-1}$ and $[0,0.4]{\mathrm{mm}}^{-1}$ both have relatively low uncertainties. With reference to Cuccia et al.,³¹ we further calculated the effective penetration depth of the 0.2 and $0.4{\mathrm{mm}}^{-1}$ spatial frequencies using optical properties of tissue-mimicking 10% intralipid phantom. The average effective penetration depth of $0.2{\mathrm{mm}}^{-1}$ and $0.4{\mathrm{mm}}^{-1}$ over the 900- to 1000-nm wavelengths were 2 and 1.6 mm, respectively. With reference to Hayakawa et al.,⁴² we also calculated the optical sampling depth (i.e., photon 90th percentile depth penetration) of the 0.2 and $0.4{\mathrm{mm}}^{-1}$ spatial frequencies using optical properties of tissue-mimicking 10% intralipid phantom. The average photon 90th percentile depth penetration over the 900 to 1000 nm wavelengths was 0.93 mm for $0.2{\mathrm{mm}}^{-1}$ and 0.55 mm for $0.4{\mathrm{mm}}^{-1}$, respectively. To give more information, the optical sampling depth and effective depth penetration were plotted and shown in Fig. S2 in the Supplementary Material for 900- to 1300-nm wavelength range and $[0,0.05,0.1,0.2,0.4]{\mathrm{mm}}^{-1}$ spatial frequencies. Furthermore, it is noted that the 0 and $0.2{\mathrm{mm}}^{-1}$ spatial frequencies each probes a different depth of the tissue, which is known as the partial volume effect and represents a limitation of SFDI (and other diffuse optical imaging methods). The partial volume effect could potentially be minimized by using other spatial frequency pairs that are close to each other, such as $[0.05,0.1]{\mathrm{mm}}^{-1}$. However, this would lead to larger measurement uncertainties, which has been demonstrated in Pera et al.³⁰ In addition, we have also calculated optical property measurement uncertainties using spatial frequency combinations such as [0.05, 0.1], [0.05, 0.2], [0.1, 0.2], and $[0.05,0.4]{\mathrm{mm}}^{-1}$ (Fig. S3 in the Supplementary Material). It shows that in comparison to the $[0,0.2]{\mathrm{mm}}^{-1}$ pair, other spatial frequency pairs without $0{\mathrm{mm}}^{-1}$ consistently have larger measurement uncertainties. Given the relatively lower measurement uncertainty as well as larger effective penetration depth and optical sampling depth, the spatial frequency combination of $[0,0.2]{\mathrm{mm}}^{-1}$ was selected for this study.

Fig. 3

Measurement uncertainties of (a) absorption and (b) reduced scattering for different spatial frequency combinations in the 900- to 1000-nm wavelength region.

The average and standard deviation of percent errors of the extracted water and lipid concentrations are shown in Fig. 4 for each wavelength increment. It is worthy to note that since the magnitude of average percent errors were close to zero (all below 0.02% for both water and lipid) for different wavelength increments under zero-mean Gaussian noise, the standard deviations were used to assess the goodness of concentration extraction. As expected, the 10-nm increment (i.e., a total of 11 measurement wavelengths in the range of 900 to 1000 nm) led to the largest errors out of the four assessed wavelength increments. The smallest errors were achieved with 1-nm increment (i.e., a total of 101 measurement wavelengths). Overall, the measurement errors decrease with decreasing increment of wavelength, but the required data volume and time cost increase accordingly. Therefore, the 5-nm increment was selected in this study as a tradeoff between accuracy and increment of measurement wavelength.

Fig. 4

Average and standard deviation of percent errors of extracted concentrations for (a) water and (b) lipid. It is worthy to note that since the magnitude of average percent errors were close to zero (all below 0.02% for both water and lipid) for different wavelength increments under zero-mean Gaussian noise, the standard deviations were used to assess the goodness of concentration extraction.

3.2.

Phantom Study for the Validation of Water and Lipid Content Quantification

A series of homogeneous phantoms with varying water and lipid content was measured with the proposed method to validate the accuracy of chromophore extraction. The average error for water content estimation calculated over all phantoms was $0.9\pm 1.2\%$, and the average error for lipid was $-0.4\pm 0.7\%$ over a wide physiological range (5% to 20% for lipid, 80% to 95% for water).^22,36,38,43 In addition, for each concentration combination, the average and standard deviation of extracted water and lipid content are given in Table 1 and compared with the known concentrations (with one significant digit after the decimal). For comparison, given intralipid phantoms of the same water and lipid concentrations in the SWIR-MPI work,¹⁷ the average error for water content estimation was $-0.2\pm 2.5\%$, and the average error for lipid was $0.3\pm 1.6\%$. While the amplitudes of the average errors for water and lipid were larger with the presented method, the standard deviations were smaller than those of the SWIR-MPI, suggesting comparable accuracies between the two methods. These results demonstrate that the proposed method can extract water and lipid concentrations with high accuracy. In addition, representative water and lipid concentration maps for each water-lipid recipe are shown in Fig. S4 in the Supplementary Material.

3.3.

Lipid Content Mapping on Ex-Vivo Porcine Tissue

Lipid content has been an important parameter in meat product grading and evaluation.^38,39 We demonstrate lipid content mapping of an ex vivo porcine tissue purchased from a local supermarket. The white-light image of the tissue is shown in Fig. 5(a), where the lipid-rich area is visually apparent. The absorption and reduced scattering maps at 930 nm are shown in Figs. 5(b) and 5(c), respectively. The lipid content map is shown in Fig. 5(d), where the lipid concentration is quantified and spatially mapped. The results demonstrate that the proposed method can potentially be applied to widefield quantitative evaluation of meat products such as porcine tissues.

Fig. 5

(a) White-light image of the porcine tissue. (b) Absorption map at 930 nm. (c) Reduced scattering map at 930 nm. (d) Extracted lipid content map of the porcine tissue. No pixels in the maps are not a number (NaNs).

3.4.

In-Vivo Water Content Monitoring on Small Animals

Tissue edema is closely associated with many physiological processes such as tissue healing, inflammation, and sports injury.⁴¹ The tissue edema was simulated by no injection as control group, and subcutaneous injections of 0.1 or 0.2 ml PBS, respectively on three groups of mice ($n=4$). Figure 6(a) shows the spatial distribution and magnitude of water content changes immediately after injection, where a dose-dependent effect is clearly demonstrated. Figure 6(b) shows the time series of the changes in average water content. The average water content was calculated by spatially averaging the water content map with a 0.5-cm diameter circular region-of-interest centered at the injection site [shown as magenta dashed circles in Figs. 6(a) and 6(c)]. The injections were conducted immediately after three repeated baseline measurements. Figure 6(c) shows the temporal dynamics of the water content changes on a representative mouse with 0.2-ml PBS injection. These results demonstrate that the proposed method can longitudinally track water content for in-vivo applications.

Fig. 6

Longitudinal monitoring of in-vivo water content. (a) Representative mice are shown for the changes of water content immediately after subcutaneous injection of PBS ($n=4$ per group). The magenta dashed circle is centered at the injection site and represents the 0.5-cm diameter region-of-interest used for calculating the average water content. (b) Time series of average water content changes for each group (error bars indicate standard deviations). (c) Temporal dynamics of water content on a representative mouse in the 0.2-ml group.