2.1.

Instrumentation

SFDI consists of three basic components: a light source, spatial light modulator (SLM), and a CCD camera. A 250-Watt broadband quartz tungsten halogen lamp (Newport Corporation, Irvine, California) is directed onto a DLP Developers Kit (Texas Instruments, Dallas, Texas) consisting of a 1024 × 768 pixel digital micromirror device (DMD). The DMD creates patterns that are projected onto the imaging surface. The patterns on the chip are controlled by customized C# software, and the projection is imaged by a set of lenses onto the surface of the sample at a working distance of 500 mm. Cross polarizers are implemented at the source and detector to eliminate specular reflection and capture diffusely reflected light. A Nuance Multipsectral Imaging System (CRI Inc., Woburn, Massachusetts), which contains a liquid-crystal tunable filter, is used for multispectral data acquisition between 650 and 980 nm with 10-nm resolution. Chromophore fits for oxy-hemoglobin, deoxy-hemoglobin, lipid, and water are generally obtained by taking spectral band data at 34 wavelengths from 650 to 980 nm. Because of the number of spatial frequencies (0 and 0.15 mm⁻¹) and phase offset measurement (0, 120, 240 deg), a total of up to 204 images (2 spatial frequencies × 3 phases × 34 wavelengths) are captured for a single multispectral frame lasting ∼50 s. The image at each wavelength is autoexposed to use the full dynamic range of the camera. Because of the spectral characteristics of the light source and reduced quantum efficiency of the CCD, longer wavelengths have greater exposure times (∼1200 ms at 980 nm) than shorter wavelengths (100 ms at 650 nm). Thus, it takes ∼ 9 s to acquire 34 evenly spaced images across the full wavelength spectrum of the system (650–980 nm). In comparison, a two-wavelength imaging scheme can reduce acquisition time for hemodynamic measurements so that only 12 images are needed (2 spatial frequencies × 3 phases × 2 wavelengths). These wavelengths can be at higher throughput wavelengths, and the temporal resolution is 1.5 s/frame. All image processing was carried out using Matlab software (Mathworks, Natick, Massachusetts).

2.2.

Optical Property Mapping with SFDI

The theory behind tissue optical property characterization and imaging in the spatial frequency domain has been described.^{18, 19, 20} SFDI uses spatially modulated structured illumination patterns projected onto tissue at various frequencies in the following form:

Fig. 1

SFDI data flow. (a) Multiple frequencies (f _x) are projected onto the sample, and remitted intensity I is captured. (b) Each illumination frequency is imaged at three phases, then demodulated and calibrated to yield R _d. (c) The R _d at each pixel is fit for μ_a and μ’_s using a Monte Carlo light-transport model and lookup table to yield optical property maps.

In order to measure intrinsic biological chromophores, such as oxy-hemoglobin, deoxy-hemoglobin, water, and lipid, the scattering corrected optical absorption maps are measured at discrete wavelengths using SFDI. In general, the optical absorption at a single wavelength, λ_i, can be characterized by

Fig. 2

Common tissue chromophores and their basis spectra for typical concentrations and volume fractions.

2.3.

Condition Number Analysis

Corlu have demonstrated a two-step method to determine optimal wavelengths in CW diffuse optical imaging. First, a singular value decomposition of the extinction coefficient matrix gives a measure of the contribution of each chromophore to the overall absorption.¹⁴ The condition number, κ(ɛ), of the extinction coefficient matrix [first term on the right-hand side of Eq. 6] is defined as the ratio of the maximum and minimum singular values (SVD) of the matrix;

2.4.

In Vivo Measurements

In vivo measurements were taken of a human wrist under an approved UC Irvine institutional review board protocol. All SFDI measurements were performed at two spatial frequencies (0 and 0.15 mm⁻¹) and a LUT method was used to calculate the optical properties. Initially, measurements were taken at 34 wavelengths evenly spaced between 650 and 980 nm. The recovered absorption maps at each wavelength were used to extract the chromophore concentrations. The data were then decomposed from 34 wavelengths to a few specific wavelength combinations (670 nm / 850 nm, 730 nm / 850 nm, 710 nm / 980 nm, 670 nm / 850 nm / 980 nm, and 670 nm / 850 nm / 920 nm / 980 nm). The mean cto₂Hb and ctHHb fits for the image were compared to a 34-wavelength fit. In order to demonstrate the improvement in temporal resolution, the optimal wavelength pairs were used to perform a hemodynamic measurement of an arterial occlusion. A patient wrist was measured for 10 min. After 1 min, an arm cuff with 240-mm Hg pressure was applied to the bicep in order to create an arterial occlusion. The occlusion was held in place for 4 min before the pressure was released. Chromophore maps were plotted at all time points, and a region of interest (ROI) was selected to show mean changes in tissue hemodynamic content over time.

3.1.

Simulation of In Vivo Data

Matlab code was generated to plot the condition number of oxy- and deoxy-hemoglobin for all wavelength pairs at 1nm intervals ranging from 650 to 1000 nm. Basis spectra for ctO₂Hb and ctHHb were used from previously published literature.²² The contour plot shows a minimum condition number of 2.21 at wavelength pairs 712 and 980 nm when water and lipid are not included in simulation and fit [Fig. 3]. The graph for condition number is symmetric on the diagonal axis because it shows a metric for the combined fitting stability of ctO₂Hb and ctHHb. It should also be noted that the condition numbers surrounding these wavelength regions are all within 25% of this value. These condition numbers were then compared to simulated absorption spectrum generated from 650 to 1000 nm using typically reconstructed ctO₂Hb and ctHHb concentrations (80 and 30 μM, respectively). Gaussian noise (FWHM 10%) was added randomly to the simulated absorption data in order to replicate a real measurement, and the procedure was repeated 100 times. ctO₂Hb and ctHHb concentrations were reconstructed using wavelength pairs in 1nm intervals. Unlike the condition number analysis, these simulations allow for percent error calculation for each chromophore. The plots are no longer symmetric, as in Fig. 3 as ctO₂Hb (lower right) and ctHHb (upper left) are evaluated seperately. The absolute percent error [Fig. 3] from simulated data maps results in comparable regions of minimized error to the condition number, with an absolute minimum at 710 and 972 nm. This variation from the condition number can be attributed to simulation noise. The coefficient of variation (COV) map [Fig. 3] is a measure of measurement stability and indicates that the same wavelength space produces the most stable results (lowest covariance) in the case of a single measurement. The condition number plot and the simulations are consistent with the consensus opinion in the field that a two wavelength system works best when there is one wavelength above and one wavelength below 800 nm.

Fig. 3

Condition number and simulation of hemodynamics: (a) Condition number (κ) plot for ctO₂Hb and ctHHb. Lower condition number indicates acceptable wavelength combination space. (b) Spectral simulations show average percent error in ctO₂Hb and ctHHb fits for wavelength pairs when water and lipid are not considered in the calculation. (c) COV of the same simulation shows stability of a single measurement for each wavelength pair.

In reality, tissue consists of many contributing chromophores in the NIR: ctO₂Hb, ctHHb, water, and lipid. In order to study the impact of other chromophores, 50% volume fraction of water and 2% volume fraction of lipid were added to typical oxy- and deoxy-hemoglobin concentrations (80 and 30 μM, respectively) to generate absorption spectrum. Water content in skin is shown to vary between 25 and 75% for normal skin; thus 50% was chosen as a central fitting parameter to demonstrate water-independent fitting of hemodynamics.^{24, 25} Lipid values also vary from 0 to 50% based on tissue type, location, and individual.³ In vivo measurements in this study are taken in the wrist, where subcutaneous fat contributions are low. Thus, a representative value of 2% is assumed for simulations. First, fitting was performed for ctO₂Hb and ctHHb in order to determine the effect of confounding chromophores [Fig. 4]. Simulations show that water and lipid content in tissue can lead to large errors (> 10%) for hemodynamic fits. The optimal region in this simulation includes a first wavelength between 670 and 780 nm and second wavelength region between 800 and 850 nm. Second, a two-wavelength fit was performed using assumed fixed values for water (50%) and lipid (2%). Simulations reveal that the error [Fig. 4] can be centered so that the magnitude is much smaller (< 5%). This creates a much larger region of wavelength pairs that produce less than a 5% error on average. A plot of the COV for these simulations reveals the best wavelength regions for stable chromophore fits. The best regions occur when one wavelength is between 620 and 700 nm and the second is between 800 and 900 nm [Fig. 4]. The local minimum for the COV occurs at the wavelength pair 670 and 850 nm. The reason why 730 nm has a larger COV is that water contributes a little more to the overall signal and can further confound the spectra. There is also a distinct ctHHb peak closer to 730 nm in the basis spectrum. Thus, any deviations in the measurement can result in a larger error in the ctHHb fit at 730 versus 670 nm.

Fig. 4

Simulation showing impact of other tissue chromophores (i.e., water and lipid) on hemodynamic fitting. (a) Average percent error for in ctO₂Hb and ctHHb for all wavelength pairs when no assumptions for water and lipid are made limits the acceptable wavelength combination space, with error values of <10%. (b) Making assumptions for water (50%) and lipid (2%) enlarges the acceptable space as shown by the mean percent error. (c) COV for this fit shows the wavelength space with the most stable measurements.

Using the two wavelength pairs that showed the lowest percent error in the second case of simulations, water and lipid distribution was varied 0–100% in the forward spectrum and the impact using a 50% and 2% fixed parameter for fitting for hemodynamics was studied. Analysis of the water variation shows that the two sets of optimal wavelength pairs (670 nm / 850 nm and 730 nm / 850 nm) behave similarly in terms of fits when a fixed assumption (50%) for water and lipid is used [Fig. 5]. The mean percent error at the extremes is under 10% for ctO₂Hb and under 5% for ctHHb when 10% Gaussian noise is added to the simulated signal. Depending on tissue type, water content in skin is shown to vary between 25 and 75%,^{24, 25} which reduces the expected error to 5% for ctO₂Hb and 2.5% for ctHHb. Variation of lipid content has an even smaller impact on fits for both these wavelengths combinations with the expected error always falling below 5% [Fig. 5]. The standard deviation of both simulations and wavelength combinations show a much larger variation for the 730 / 850 nm wavelength pair [Figs. 5 and 5]. The COV for the 670 / 850 pair is ∼0.15 for all values of water. However, the COV is on average 0.22 and 0.35 for ctO₂Hb and ctHHb, respectively, when using the 730 nm/850 nm pair. This indicates that a single measurement will be much more stable when using the 670 nm / 850 nm combina-tion.

Fig. 5

Impact of water and lipid variation on hemodynamic fitting for two ideal wavelength pairs. System variation in (a) water fraction and (b) lipid fraction shows a <10% error in mean hemodynamic fit using two common wavelength pairs (670/850 and 730/850). Both wavelength combinations perform the same in terms of mean, but the 670/850 combination has lower standard deviations, indicating it is much more stable for single point measurements.

3.2.

In Vivo Studies

In vivo data for a human wrist shows the impact of reducing spectral acquisition data. A simple reflectance plot at approximately the isobestic point (805 nm) for hemoglobin shows the vein architecture in the wrist [Fig. 6]. Hemodynamic images are generated using a full 34-wavelength acquisition and fitting procedure [Figs. 6 and 6]. The maps generated when optimized spectral wavelengths are used result in images that have a <10% variation in hemodynamic fits for all pixels in the image. Analysis of tissue ROI with decomposed spectral data show that the 670 nm/850 nm pair with a fixed value of 50% for water performs the best hemodynamic fit compared to the full 34-wavelength fit [Fig. 6]. Flat ROIs were chosen to limit the effect of surface curvature. A 730 nm/850 nm combination results in a slight overestimation in ctHHb as compared to the full fit. A 670 nm/850 nm hemodynamic fit with no water fit results in an overestimation in the mean value of ctO₂Hb (10%). This is even more exaggerated (80%) when considering the 710 nm/980 nm combination that is predicted as optimal by the initial condition number plot. For more accurate fits, water fraction content should be assumed or calculated when calculating hemodynamic parameters in vivo.

Fig. 6

Reduced spectral content maintains integrity of hemodynamic maps. (a) A single snapshot diffuse reflectance map at 800 nm shows high contrast for veins. (b) SFDI chromophore map produced by a 34-wavelength fit produces comparable maps to (c) two-wavelength fit. The mean and standard deviation of a hemodynamic is calculated over a small ROI covering a vein with multiple wavelength combinations. Wavelength combinations include (1) 34 evenly spaced wavelengths between 650 and 980 nm (all), (2) 710 nm/980 nm, (3) 730 nm/850 nm, (4) 670 nm/850 nm, (5) 670 nm/850 nm and (6) 730 nm/850 nm. Combination 1 is fit for four chromophores. Combinations 2–4 are fit for hemodynamic values, with no assumption for water fraction. Underlined combinations 5 and 6 assume a fixed water fraction of 50% to improve fits for hemodynamic parameters. A 670 nm/850 nm pair with assumed water and lipid fractions performs the best.

The main benefit of reduced spectral content is improved temporal resolution. For this SFDI system, a typical 34-wavelength SFDI acquisition takes 50 s to acquire as opposed to 1.5 s for the two-wavelength fit. The imaging time has a nonlinear relationship due to nonuniform power distribution of the source spectrally. In addition, increased imaging time can lead to loss in spatial resolution due to patient motion. In order to demonstrate a time-sensitive measurement, an arterial occlusion was performed on a human patient to measure the tissue hemodynamics. ctO₂Hb and ctHHb values were calculated using the 670 nm / 850 nm wavelength pair. Water and lipid fractions were assumed to be 50% and 2%, respectively. Becuase SFDI is a nonscanning method, the reduced spectral content enables rapid 2-D imaging of the chromophore changes (Fig. 7 and associated video). An ROI can be selected to analyze spatially variant responses of the tissue (i.e., vein versus microvasculature). In this case, the whole image is analyzed to show the response to the arterial occlusion. After blood flow is occluded at t = 1 min, continued tissue oxygen consumption produces an increase in ctHHb at the expense of ctO₂Hb. The release of the occlusion results in rapid tissue reperfusion. As new blood rushes into the region to compensate for the cuff-induced hypoxia, ctO₂Hb and ctHHb increase and decrease, respectively. The values overshoot initially and then return to baseline after recovery as expected. There are still some residual lines in the reconstructed maps at certain time points due to motion artifacts even despite the rapid acquisition.

Fig. 7

Arterial occlusion of the wrist. Reduced spectral content improves temporal resolution for hemodynamic imaging. A human wrist is imaged using SFDI with a bicep arterial occlusion at t = 1 min and release at t = 5 min. SFDI generates maps of hemodynamic changes over time. An ROI from the image is selected, and the mean changes in ctO₂Hb and ctHHb values from baseline are plotted over the course of the occlusion experiment (Video: QuickTime, 416 kB) 1.