1.

Introduction

Spatial frequency domain imaging (SFDI) is a reflectance-based technique that can measure and map absorption (${\mu }_{\mathrm{a}}$) and scattering (${\mu }_{\mathrm{s}}^{\prime }$) coefficients in tissue on a pixel-by-pixel basis. SFDI works by structuring light into sinusoidal patterns and projecting them onto the tissue surface. The tissue acts as a spatial filter and blurs the structured patterns. By projecting patterns of differing spatial frequencies, the modulation transfer function of the tissue can be found from which a unique pair of optical absorption and scattering coefficients is determined. Further filtering of the remitted light with either a series of bandpass filters or with a liquid-crystal tunable filter allows unique spectra of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\text{'}}$ to be found in different tissue types.^1,2

Recent applications of SFDI to skin imaging include in vivo monitoring of burn wounds,^3,4 determining flap perfusion during surgical procedures,^5,6 and assessing cutaneous vascular abnormalities.⁷ SFDI has also been used for characterizing brain in small animal models of stroke,⁸ glioblastoma,⁹ and Alzheimer’s disease.¹⁰ In each example, multispectral maps of tissue scattering are separately constructed from tissue absorption. This allows formation of chromophore images such as oxy-hemoglobin (${\mathrm{HbO}}_2$), deoxy-hemoglobin (Hb), lipid, and water using the Beer–Lambert law. The inverse relationship between spatial frequency and average photon pathlength¹¹ also facilitates SFDI depth sectioning and tomography of absorbing and fluorescent inhomogeneities.^12–14

In this work, we present a low cost, three-wavelength SFDI system that operates in the visible spectral regime using three light-emitting diodes (LEDs) (460, 530, and 632 nm). The cost savings of a consumer electronics-based SFDI system can be appreciated by comparing the price of a commercial LED microprojector (e.g., $\sim \$250$ for an AAXA M2 microprojector) with that of a scientific-grade digital light projector (e.g., $\sim \$8000$ for a Texas Instrument DLP Discovery 4100 Kit). We sought to quantify this consumer-grade SFDI system’s performance in the more challenging visible regime where ${\mu }_{\mathrm{a}}\sim {\mu }_{\mathrm{s}}^{\prime }$ and small amounts of noise in measured light levels can introduce large inaccuracies in separating absorption from scattering.² SFDI instrumentation is described and validated in tissue-simulating Intralipid phantoms, and optical property maps of a mouse brain are measured in order to demonstrate overall sensitivity and performance. In addition, we examine the impact of saline windows commonly used in rodent model neuroimaging in order to assess how this preparation may influence tissue absorption and scattering values. Implementation of our system offers great potential for measuring optical properties of superficial tissues such as skin epidermis and rodent brain cortex.

2.

Methods

2.1.

Flexible LED and Modulation Element (FLaME) Instrumentation

We modified a LED-based microprojector (M2, AAXA Technologies, Inc., Tustin, California) to project a field of view of $40\times 30{\mathrm{mm}}^2$ by extending the focusing tube lens slightly beyond the manufactured limit. All other settings and components of the projector were used as received, including the three individual blue, green, and red LEDs centered at 460, 523, and 625 nm, respectively [Fig. 1(b)]. These wavelengths are sufficient for differentiating oxy- and deoxy-hemoglobin concentration: 523 nm is near an isosbestic point for oxy- and deoxy-hemoglobin, oxy-hemoglobin is about twice as absorbing as deoxy-hemoglobin at 460 nm, and deoxy-hemoglobin is about four times as absorbing as oxy-hemoglobin at 625 nm [Fig. 3(a)]. The projector was used as a second monitor and images were created in Matlab (Mathworks) and displayed as figures in the second monitor. The refresh rate of the liquid crystal on silicon chip in the AAXA projector was 70 Hz or about $14.286\mathrm{ms}/\text{frame}$. Thus, we used multiples of 14.286 ms as the exposure time to achieve consistent light levels.

Fig. 1

(a) Diagram of FLaME experimental imaging setup. All components were controlled using LabVIEW software on a personal computer. (b) Expanded view of the AAXA M2 microprojector.

As shown in the block diagram in Fig. 1(a), multispectral reflectance images were separated spectrally with dichroic mirrors (475DCLP, 560DCLP, Omega Optical, Inc., Brattleboro, Vermont) and bandpass filters (FB460-10, FB530-10, FL632.8-10, Thorlabs, Inc., Newton, New Jersey). Filtered images were detected using three 12-bit charge-coupled device cameras (Flea2G, Point Grey, Richmond, BC, Canada). Images from the three cameras were co-registered with one another using a fiducial marker (reflective sticker, 1-mm diameter) on a solid tissue-simulating phantom.¹⁵ A crossed linear polarizer (Edmund Optics, Barrington, New Jersey) was also placed before the cameras to reduce the effect of specular reflectance from the sample. The input–output curve (gamma function) of the projector was determined empirically by sequentially projecting 256 grayscale level images on spectralon (Labsphere) and recording the average pixel intensity from the camera, normalized to the brightest projection (Fig. 2). We found that the nonlinear gamma function of the projector distorts a sine wave image input from the computer to appear as a square wave. We adjusted the computer image input levels, based on the gamma function, such that the actual projected image was sinusoidal when detected (Fig. 2). The projector and cameras were connected to a personal computer and controlled by custom LabVIEW software (National Instruments, Austin, Texas).

Fig. 2

The nonlinear input–output intensity curve (gamma function) of the projector (middle) distorts a sine wave image input from the computer (top left) to appear as a square wave (top right). Using the projector response function as a look-up-table, the computer image input was adjusted such that the actual projected image (bottom left) is sinusoidal when detected on spectralon (Labsphere) (bottom right). Cross-section intensity profiles of the images are shown in red under the images to better illustrate the projection transformation.

2.3.

Phantom Validations

Hemoglobin is approximately an order of magnitude more absorbing in the blue–green wavelengths (e.g., 460 and 530 nm) versus 632 nm and above¹⁷ [Fig. 3(a)]. While SFDI has been validated in the near-infrared (NIR)² where ${\mu }_{\mathrm{a}}\ll {\mu }_{\mathrm{s}}^{\prime }$, we needed to establish that FLaME could be used to separate absorption from scattering when ${\mu }_{\mathrm{a}}\sim {\mu }_{\mathrm{s}}^{\prime }$. To determine the relevant range of ${\mu }_{\mathrm{a}}$ values, we used the Beer–Lambert law to predict ${\mu }_{\mathrm{a}}$ at the three wavelengths when total hemoglobin (THb) ranged from 50 to 150 μM with 60% oxygen saturation (${\mu }_{\mathrm{a}}=0.03$ to $1.3{\mathrm{mm}}^{-1}$). Our previous work in mice showed a THb around 150 μM¹⁰ while others have used concentrations of around 100 μM.¹⁸ Then, keeping ${\mu }_{\mathrm{s}}^{\text{'}}$ constant at $1{\mathrm{mm}}^{-1}$, we used a scaled Monte Carlo model² to predict reflectance as a function of spatial frequency when we varied ${\mu }_{\mathrm{a}}$ from 0.01 to $0.1{\mathrm{mm}}^{-1}$ [Fig. 3(b)] and from 0.1 to $1{\mathrm{mm}}^{-1}$ [Fig. 3(c)]. The reflectance changes much more with respect to spatial frequency ($\delta R_{\mathrm{d}}/\delta fx$) in the lowest absorbing sample ($\delta R_{\mathrm{d}}/\delta fx=2.6\mathrm{mm}$) versus the highest absorbing sample ($\delta R_{\mathrm{d}}/\delta fx=0.038\mathrm{mm}$), showing low signal-to-noise may be a source of error when inverting the model and fitting for ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\text{'}}$ at high values of ${\mu }_{\mathrm{a}}$.

Fig. 3

(a) Absorption spectra of oxy-hemoglobin (${\mathrm{HbO}}_2$) and deoxy-hemoglobin (Hb). Vertical lines highlight 460, 530, and 632 nm absorption features. (b) Scaled Monte Carlo predictions of diffuse reflectance as a function of spatial frequency with ${\mu }_{\mathrm{s}}^{\prime }$ constant at $1{\mathrm{mm}}^{-1}$ and ${\mu }_{\mathrm{a}}$ increasing by increments of $0.03{\mathrm{mm}}^{-1}$ from 0.01 to $0.1{\mathrm{mm}}^{-1}$. (c) Scaled Monte Carlo predictions of diffuse reflectance as a function of spatial frequency with ${\mu }_{\mathrm{s}}^{\prime }$ constant at $1{\mathrm{mm}}^{-1}$ and ${\mu }_{\mathrm{a}}$ increasing by increments of $0.3{\mathrm{mm}}^{-1}$ from 0.1 to $1{\mathrm{mm}}^{-1}$.

To validate the performance of the system, we conducted a series of controlled experiments in tissue-simulating phantoms. First, 19 mL solutions of 0.25, 0.5, and $1\mathrm{g}/\mathrm{L}$ napthol green B solution (Sigma, St. Louis, Missouri) were made in double-distilled water and measured in transmission mode with a VIS–NIR spectrophotometer (UV-3600, Shimadzu, Inc., Kyoto, Japan) from 450 to 1000 nm. Similarly, a sample of fresh pig blood was acquired (protocol No. 2007-2743), stored in a vial with heparin anticoagulant, and diluted to a $1:100$ ratio in phosphate-buffered saline before being measured in the spectrophotometer. The ${\mu }_{\mathrm{a}}$ absorption spectra were calculated by taking the negative logarithm of the percent transmission and dividing by the pathlength traveled (10 mm for the dye solutions, 5 mm for the pig blood solution). After measurement with the spectrophotometer, 1 mL of 20% Intralipid (Fresenius Kabi, Bad Homburg, Germany) was then added to 19 mL of the solutions to mimic scattering in tissue¹⁹ and each solution was measured with the FLaME system.

3.

Data Analysis

In post-processing, the 10 repetitions of raw images acquired were averaged before being demodulated, calibrated, and fitted for ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$. Values for ${\mu }_{\mathrm{a}}$, ${\mu }_{\mathrm{s}}^{\prime }$, and hemoglobin were calculated for each pixel in the image. THb was calculated as the sum of oxy-hemoglobin (${\mathrm{HbO}}_2$) and deoxy-hemoglobin (Hb). Oxygen saturation (${\mathrm{O}}_2$ sat) was calculated as $({\mathrm{HbO}}_2/\mathrm{THb})\times 100$. ROI were selected and an average value with standard deviation was calculated for each ROI. For phantom comparisons with the spectrophotometer, FLaME-derived ${\mu }_{\mathrm{a}}$ was multiplied by 1.05 to account for dilution with 1 mL Intralipid in 19 mL solution. All analyses were done in matlab.

4.

Results and Discussion

The strategy to use multiple spatial frequencies in fitting for ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ was integral in minimizing fitting error, as the impact of uncertainties in diffuse reflectance measurements at one spatial frequency is reduced and data fits are better constrained by multifrequency content [Fig. 4(a)]. The fitted absorption coefficients in the napthol green B titrations were on average $-0.064\pm 0.095{\mathrm{mm}}^{-1}$ different from spectrophotometer ${\mu }_{\mathrm{a}}$’s, or $-16\%\pm 11\%$ off [Fig. 4(b)]. If the data are plotted as FLaME ${\mu }_{\mathrm{a}}$ versus spectrophotometer ${\mu }_{\mathrm{a}}$ [Fig. 4(d)], it is more apparent at ${\mu }_{\mathrm{a}}=1.5{\mathrm{mm}}^{-1}$ that the FLaME fit is an outlier. Without this highest point, the FLaME ${\mu }_{\mathrm{a}}$’s were on average $-0.035\pm 0.034{\mathrm{mm}}^{-1}$ different from spectrophotometer ${\mu }_{\mathrm{a}}$’s, or $-11\%\pm 13\%$ off. While there is a natural variation in Intralipid batches,²⁰ we show in Fig. 4(c) that FLaME-fitted scattering values are within the range of the Mie theory-predicted scattering for 1% Intralipid,²¹ with a mean error of $3\%\pm 0.3\%$.

Fig. 4

(a) Example plot of $R_{\mathrm{d}}$ at 0, 0.05, 0.1, 0.2, and $0.4{\mathrm{mm}}^{-1}$ spatial frequencies for three concentrations of napthol green B at 460 nm. Lines are the least-squares fits of the Monte Carlo forward model of $R_{\mathrm{d}}$ as a function of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$. Standard deviation bars of the data $<0.006$ and are not shown for clarity. (b) Plot of ${\mu }_a$ spectra of three concentrations of napthol green B. Lines are from the spectrophotometer and points are from FLaME measurements. Standard deviation bars of the FLaME data $<0.03$ and are not shown for clarity. (c) Plot of ${\mu }_{\mathrm{s}}^{\text{'}}$ spectra of three concentrations of napthol green B in 1% Intralipid solution. Line is the expected scattering of 1% Intralipid from Mie theory. Standard deviation bars of the FLaME data $<0.07$ and are not shown for clarity. (d) Plot of data from (b) showing an outlier in FLaME data when the expected ${\mu }_{\mathrm{a}}=1.5{\mathrm{mm}}^{-1}$.

Interestingly, the $-0.035{\mathrm{mm}}^{-1}$ offset in the FLaME-fitted ${\mu }_{\mathrm{a}}$’s compared to the spectrophotometer artificially causes a higher percentage of error at the lower ${\mu }_{\mathrm{a}}$’s ($\sim 30\%$) compared to the higher ${\mu }_{\mathrm{a}}$’s ($\sim 5\%$). Better calibration of the silicone reference phantom at visible wavelengths is needed to correct for this offset.

In Fig. 5, we see FLaME ${\mu }_{\mathrm{a}}$ values within 7% of spectrophotometer values for 460 and 530 nm, but the much lower absorption of blood at 632 nm results in a 78% error ($0.011{\mathrm{mm}}^{-1}$ versus $0.051{\mathrm{mm}}^{-1}$). Absorption measurements at the three wavelengths were fit to hemoglobin concentrations using the Beer–Lambert law and compared to hemoglobin fits from the spectrophotometer (Table 1). For the spectrophotometer measurement, scattering of the red blood cells was modeled to follow a wavelength-dependent power law, ${\mu }_{\mathrm{s}}^{\prime }=A{\lambda }^{-b}$,²² where $A$ is the scattering amplitude and $b$ is the scattering power. Previously, Mourant et al. showed microspheres with diameters of 0.1 to 2 μm in solution have $b$ value magnitudes ranging from 4 to 0.37, respectively.²² The diameter of red blood cells in pig blood is 6 μm,²³ so we assumed $b$ to be 0.37 and scattering amplitude, $A$, was fit for as the third chromophore in the Beer–Lambert law and found to be $1.4\times {10}^6$. FLaME comparisons with the spectrophotometer hemoglobin fits were within 3% for ${\mathrm{HbO}}_2$, 20% for Hb, 4% for Total Hb, and ${\mathrm{O}}_2$ saturation was 96.7% (spectrophotometer) versus 96.2% (FLaME) (Table 1). The fitted ${\mu }_{\mathrm{s}}^{\prime }$ values from FLaME (Table 2) were slightly higher than the napthol green B measurements, probably from the additional scattering from the red blood cells.

Fig. 5

Blood phantom spectra acquired using a conventional transmission spectrophotometer (thick green line), FLaME (red dots), and the best fit of the spectrophotometer data to hemoglobin (dashed black line). Standard deviations for FLaME data are ${\sigma }_{460\mathrm{nm}}=0.05{\mathrm{mm}}^{-1}$, ${\sigma }_{530\mathrm{nm}}=0.04{\mathrm{mm}}^{-1}$, and ${\sigma }_{632\mathrm{nm}}=0.002{\mathrm{mm}}^{-1}$. They are not shown for clarity.

Table 1

Table of oxy-hemoglobin (HbO2) and deoxy-hemoglobin (Hb) fits determined from the spectrophotometer spectrum (450 to 1000 nm) and from the FLaME absorption data at 460, 530, and 632 nm.

Table 2

Absorption and reduced scattering coefficients acquired from FLaME imaging of the blood/Intralipid phantom are shown with standard deviation of the 150,880 pixels in the regions of interest.

A potential application of the FLaME system is to characterize rodent brain absorption and scattering properties in disease models, assess physiologic changes, and monitor therapeutic interventions. We show below in Fig. 6, the mouse brain with skull intact being imaged with 530 nm light. As expected, vessels are clearly seen in the raw and diffuse reflectance images from THb absorption as well as in the ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ maps.

Fig. 6

A summary of the SFDI process in a mouse brain at 530 nm: (Top row) Raw camera snapshots of mouse brain with projected spatial frequencies. (Middle row) Cropped and calibrated diffuse reflectance images of the mouse brain as a function of spatial frequency. (Bottom row) Pixel-by-pixel fitted ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ maps of the mouse brain at 530 nm. The midsagittal vein, a prominent vessel on the midline surface of the brain, can be seen on the ${\mu }_{\mathrm{a}}$ map. The sagittal skull suture is marked by increased scattering on the ${\mu }_{\mathrm{s}}^{\prime }$ map.

While we used saline to reduce specular reflections from a dry skull, it is unknown how this might affect the detected optical properties. In Fig. 7, we show the FLaME system is sensitive to a reduction in ${\mu }_{\mathrm{s}}^{\prime }$ when saline is added to the skull [Fig. 7(f)]. As expected, the scatter-corrected absorption [Fig. 7(e)] and hemoglobin concentrations (Table 3) do not differ significantly. Visible wavelengths only penetrate 250 to 500 μm into tissue,²⁴ and optical properties of overlying rodent skull can significantly contribute to optical properties measured by SFDI. The ability to measure intrinsic tissue scattering and the impact of saline well or similar preparations can improve measurement accuracy and allow more quantitative comparisons between different subjects.

Fig. 7

Adding a saline well over the skull, as commonly done in optical intrinsic signal imaging causes a significant ($p<0.05$) decrease in the detected scattering when compared to imaging a dry skull. (a and b) Images of the dry and saline-soaked regions of interest (ROI). Plots of diffuse reflectance as a function of spatial frequency for the dry skull (c) and the wet skull (d). (e) A comparison of fitted ${\mu }_{\mathrm{a}}$ values for a dry skull (squares) versus a wet skull (circles). (f) A comparison of fitted ${\mu }_{\mathrm{s}}^{\prime }$ values for a dry skull (squares) versus a wet skull (circles). All error bars are standard deviation of the ROI pixels.

Table 3

Fitted hemoglobin concentrations and oxygen saturation for FLaME imaging of a brain with an overlying dry skull versus saline-soaked skull.

5.

Conclusion

We have described a low-cost multispectral imaging platform that uses a commercially available LED-based digital light projector and a scaled Monte Carlo light propagation model to acquire tissue absorption and reduced scattering properties in visible (blue, green, and red) spectral regions using SFDI. No modifications to the microprojector hardware is required, however, computer-synthesized projection patterns must be corrected for nonuniformities in projector output using a calibration procedure. The accuracy of the FLaME system was 11% and 3%, respectively, for determining ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ in tissue-simulating liquid phantoms over a $\sim 20$-fold range of realistic tissue absorption values. FLaME measurements of oxy-, deoxy-hemoglobin, and THb were within 3% to 20% of true values as determined by a spectrophotometer. Optical absorption and scattering maps of a mouse brain were measured in vivo with visible light for the first time, showing this easily accessible platform may have applications in multispectral neuroimaging and similar settings that require quantitative assessment of tissue hemodynamics and composition.