Optical property uncertainty estimates for spatial frequency domain imaging

Abstract

Spatial frequency domain imaging (SFDI) is a wide-field diffuse optical imaging modality that has attracted considerable interest in recent years. Typically, diffuse reflectance measurements of spatially modulated light are used to quantify the optical absorption and reduced scattering coefficients of tissue, and with these, chromophore concentrations are extracted. However, uncertainties in estimated absorption and reduced scattering coefficients are rarely reported, and we know of no method capable of providing these when look-up table (LUT) algorithms are used to recover the optical properties. We present a method to generate optical property uncertainty estimates from knowledge of diffuse reflectance measurement errors. By employing the Cramér-Rao bound, we can quickly and efficiently explore theoretical SFDI performance as a function of spatial frequencies and sample optical properties, allowing us to optimize spatial frequency selection for a given application. In practice, we can also obtain useful uncertainty estimates for optical properties recovered with a two-frequency LUT algorithm, as we demonstrate with tissue-simulating phantom and experiments. Finally, we illustrate how absorption coefficient uncertainties can be propagated forward to yield uncertainties for chromophore concentrations, which could significantly impact the interpretation of experimental results.

Diffuse and nonlinear imaging of multiscale vascular parameters for in vivo monitoring of preclinical mammary tumors

“…However, we found a 3× increase in uncertainty in μ a and a 1.4× increase in uncertainty in μ 0 s with 0.05 and 0.1 mm −1 compared with DC and 0.1 mm −1 when considering the tumor optical property range (gray-shaded areas in Figure 5 plots). These results agreed with the SFDI optical property uncertainties predicted using the Cramér-Rao lower bound methodology recently described by Pera et al (3.4× and 1.4×, respectively) [34]. It should be noted that uncertainties in either μ a and μ 0 s for a given sample are dependent on both the μ a and μ 0 s of that sample, as well as on the diffuse reflectance error FIGURE 4 Comparison of depth penetration between SFDI and MPM based on imaging contrast as a function of depth.…”

“…CNR was calculated using μ a at 851 nm for the following f x pairs: (a) 0 and 0.1 mm −1 , and (b) 0.05 and 0.1 mm −1 . The choice of spatial frequencies is based on our prior work which utilized MC simulations to show how SFDI depth sensitivity decreases with increasing f x , and demonstrated how the choice of f x pair affects optical property extraction errors . For MPM, square ROIs were used for CNR analysis.…”

“…The choice of SFDI f x pairs affects both the depth sensitivity of SFDI (as demonstrated in the previous section), as well as the ability to accurately extract optical properties [33,34]. To assess tradeoffs between these two factors, we quantified optical property uncertainties for DC and 0.1 mm −1 , and 0.05 and 0.1 mm −1 given that the former has been identified as a f x pair that minimizes optical property extraction errors [4,34], and the latter was found to provide good agreement in depth sensitivity between SFDI and MPM. We found that there was good agreement in extracting optical properties between the two spatial frequency pairs for a range of optical properties ( Figure 5).…”

Two-layer inverse model for improved longitudinal preclinical tumor imaging in the spatial frequency domain

“…While the MC results can be postprocessed for arbitrary spatial frequencies, the choice to use this frequency pair was made based on our recent work utilizing Cramér-Rao lower bounds to determine optical property uncertainty estimates for SFDI. 26 This analysis revealed DC and 0.1 mm −1 as excellent choices to reduce optical property extraction uncertainty for similar optical property ranges.…”

“…Several prior publications from our group and others have utilized a two-frequency LUT inversion algorithm to extract optical properties from SFDI-derived R d values. 11,24,26,27 At the core of this LUT algorithm is a single conventional MC simulation for a semi-infinite homogeneous medium. The simulation results are postprocessed to provide R d values for arbitrary μ a and μ 0 s combinations using the methods described in Martinelli et al 28 A discrete Hankel transform is then used to transform the spatially resolved R d values to the spatial frequency domain.…”