Lipid A

We performed a set of experiments to characterize the precision and accuracy of MI for measuring the homogeneous absorption and reduced scattering optical properties. Sixteen turbid phantoms were constructed using a single batch of Liposyn lipid emulsion and water-soluble nigrosin dye stock solutions for the scattering and absorbing properties, respectively. In the first eight phantoms, we varied the absorption coefficient, μ_a, over two orders of magnitude (logarithmically spaced between 0.002 mm⁻¹≤μ_a≤0.12 mm⁻¹), with a constant scattering coefficient constant at ${\mu }_s^{\prime }=0.97{\text{mm}}^{-1}$ . In the second set, we linearly varied ${\mu }_s^{\prime }(0.32{\text{mm}}^{-1}\le {\mu }_s^{\prime }\le 1.8{\text{mm}}^{-1})$ , while holding the absorption coefficient constant at μ_a=0.0046 mm⁻¹. These values were calculated based on infinite-geometry, multifrequency (50 to 500 MHz), multidistance (10 to 25 mm) frequency-domain photon migration measurements15 of one of the Liposyn/nigrosin phantoms.
MI measurements were performed on each sample. Thirty spatial frequencies of illumination were chosen between 0 mm⁻¹ and 0.13 mm⁻¹, corresponding to a total of 90 images per phantom (three spatial phases per frequency). The interfrequency spacing was chosen to accurately capture the MTF curvature of all phantoms, with finer spacing at low frequencies and coarser spacing at high frequencies, accordingly. All measurements were taken at 660 nm with an approximate 75×75 mm illumination area, a 50×50 mm camera field of view, and an integration time of 100 ms. The individual phantoms were measured in a randomized order, and measurements were repeated three times to allow for statistical averaging.
Modulation images of the AC reflectance were obtained at each frequency using Eq. (20). At full CCD resolution, the pixel-by-pixel demodulation approach results in approximately 250,000 separate measurements of reflectance per spatial frequency, highlighting the statistical power of the technique. As the lipid solutions were expected to be highly homogeneous, 20×20 pixel binning was performed on each image to speed computation, resulting in low-resolution, 15×15 pixel modulation images. The resulting 30 images provide a quantitative AC amplitude measurement at each of 100 spatial locations within the field of view. For calibration, a single phantom from the entire set of 16 was chosen as the reference (second-lowest absorption phantom). Using the reference’s known optical properties (determined from infinite-geometry FDPM measurements), we calculate a model-based prediction for the reflectance, R_d,ref,pred(f_x). Then, for each spatial frequency and each spatial location, we use Eq. (23) to calculate R_d(f_x) of the sample. Having retained some low-resolution spatial data, we can calculate a standard deviation of recovered values within an image as an indicator of measurement precision.
The diffusion model of Eq. (10) was used to solve for μ_a and ${\mu }_s^{\prime }$ using both least-squares minimization by a simplex search algorithm (in “fminsearch” MATLAB) and via the two-frequency lookup table approach using the lowest (0 mm⁻¹) and highest (0.13 mm⁻¹) spatial frequencies. For each phantom, each spatial sampling point was separately analyzed, generating images of recovered absorption and scattering values. As these were homogeneous samples, a mean and a standard deviation were calculated to represent each optical property image result, characterizing the accuracy and precision of MI, respectively.