Simple analytical total diffuse reflectance over a reduced-scattering-pathlength scaled dimension of [10-5, 10-1] from a medium with HG scattering anisotropy

Novel needle-probe single-fiber reflectance spectroscopy to quantify sub-surface myoglobin forms in beef psoas major steaks during retail display

Meat discoloration starts at the interface between the bright red oxymyoglobin layer and the interior deoxymyoglobin layer. Currently, limited tools are available to characterize myoglobin forms formed within the sub-surface of meat. The objective was to demonstrate a needle-probe based single-fiber reflectance (SfR) spectroscopy approach for characterizing sub-surface myoglobin forms of beef psoas major muscles during retail storage. A 400-μm fiber was placed in a 17-gauge needle, and the assembly was inserted into the muscle at five depths of 1 mm increment and 1 cm lateral shift. Metmyoglobin content increased at all depths during display and content at 1 mm was greater compared to that of 2 to 5 mm depth. The a* values decreased (P < 0.05) during retail display aligning with the sub-surface formation of metmyoglobin. In summary, the results suggest that needle-probe SfR spectroscopy can determine interior myoglobin forms and characterize meat discoloration.

Diffuse photon remission associated with the center-illuminated-area-detection geometry. II. Approach to the time-domain model

This part proposes a model of time-dependent diffuse photon remission for the center-illuminated-area-detection (CIAD) geometry, by virtue of area integration of the radially resolved time-dependent diffuse photon remission formulated with the master-slave dual-source scheme demonstrated in Part I for steady-state measurements. The time-domain model is assessed against Monte Carlo (MC) simulations limiting to only the Heyney-Greenstein scattering phase function for CIAD of physical scales and medium properties relevant to single-fiber reflectance (SfR) and over a 2 ns duration, in compliance with the timespan of the only experimental report of SfR demonstrated with a 50 µm gradient index fiber. The time-domain model-MC assessments are carried out for an absorption coefficient ranging three orders of magnitude over [0.001,0.01,0.1,1]m m -1 at a fixed scattering, and a reduced scattering coefficient ranging three orders of magnitude over [0.01,0.1,1,10]m m -1 at a fixed absorption, among others. Photons of shorter and longer propagation times, relative to the diameter of the area of collection, respond differently to the scattering and absorption changes. Limited comparisons of MC between CIAD and a top-hat geometry as the idealization of SfR reveal that the time-domain photon remissions of the two geometries differ appreciably in only the early arriving photons.

Diffuse photon remission associated with the center-illuminated-area-detection geometry: Part I, an approach to the steady-state model

Diffuse photon remission associated with the center-illuminated-area-detection (CIAD) geometry has been useful for non-contact sensing and may inform single-fiber reflectance (SfR). This series of work advances model approaches that help enrich the understanding and applicability of the photon remission by CIAD. The general approach is to derive the diffuse photon remission by the area integration of the radially resolved diffuse reflectance while limiting the analysis to a medium exhibiting only the Heyney-Greenstein (HG) scattering phase function. Part I assesses the steady-state photon remission in CIAD over a reduced scattering scaled diameter of μ s ' d _{a r e a} ∈[0.5×10^-3,10³] that covers the range extensively modeled for SfR. The corresponding radially resolved diffuse reflectance is obtained by concatenating an empirical expression for the semi-ballistic region near the point-of-illumination and a formula utilizing a master-slave dual-source scheme over the semi-diffusive to a diffusive regime while being constrained by an extrapolated zero-boundary condition. The terminal algebraic photon remission is examined against Monte Carlo simulations for an absorption coefficient over [0.001,1]m m ^-1, a reduced scattering coefficient over [0.01,1000]m m ^-1, a HG scattering anisotropy factor within [0.5,0.95], and a diameter of the area of collection ranging [50,1000]µm. The algebraic model is also applied to phantom data acquired over a ∼2c m non-contact CIAD configuration and with a 200 µm SfR probe. The model approach will be extended in a subsequent work towards the time-of-flight characteristics of CIAD.

Daily Quantification of Myoglobin Forms on Beef Longissimus Lumborum Steaks Over 7 Days of Display by Near-infrared Diffuse Reflectance Spectroscopy

Near-infrared diffuse reflectance spectroscopy (NIR-DRS) was utilized to develop an algorithm using approximately 18 wavelengths spanning 480 to 650 nm to determine oxymyoglobin (OxyMb), deoxymyoglobin (DeoxyMb), and metmyoglobin (MetMb) contents on beef longissimus lumborum muscles. Daily changes in subsurface myoglobin redox forms were evaluated for 7 d using NIR-DRS and compared with the surface color as assessed by a HunterLab MiniScan spectrophotometer as a reference modality. Both measurements revealed that MetMb increased steadily over the duration of display, showing high correlation (R2 = 0.91) between the 2 methods. Comparatively, whereas NIR-DRS revealed OxyMb to have decreased steadily over the period of display, the HunterLab MiniScan spectrophotometer indicated a much later onset of the apparent decrease of OxyMb, resulting in a moderate correlation (R2 = 0.64) between the 2 methods. No correlation was found between the 2 methods regarding the changes of DeoxyMb over the duration of display. The newly developed NIR-DRS algorithm has potential as an alternative method of color assessment in postrigor skeletal muscle.

Diffuse photon-remission associated with single-fiber geometry may be a simple scaling of that collected over the same area when under centered-illumination

Robust models for single-fiber reflectance (SFR) are relatively complex [Opt. Lett.45, 2078 (2020)OPLEDP0146-959210.1364/OL.385845] due to overlapping of the illumination and collection areas that entails probability weighting of the spatial integration of photon-remission. We demonstrate, via analytical means for limiting cases and Monte Carlo simulation of broader conditions, that diffuse photon-remission collected by single-fiber geometry may be scaled over the center-illuminated photon-remission. We specify for a medium revealing Henyey-Greenstein (HG) scattering anisotropy that the diffuse photon-remission from a sub-diffusive area of a top-hat illumination is ∼84.9% of that collected over the same area when under a centered-illumination. This ratio remains consistent over a reduced-scattering fiber-size product of μs'd_fib=[10^-5,10⁰], for absorption varying 3 orders of magnitude. When applied to hemoglobin oxygenation changes induced in an aqueous phantom using a 200 µm single-fiber probe, the center-illumination-scaled model of SFR produced fitting results agreeing with reference measurements.

Diffuse photon remission from thick opaque media of the high absorption/scattering ratio beyond what is accountable by the Kubelka-Munk function

The Kubelka-Munk (KM) theory of diffuse photon remission from opaque media is widely applied to quality-control processes. Recent works based on radiative transfer revealed that the KM function as the backbone parameter of the method may saturate at strong absorption to cause the KM approach to be unfit to predict the change of diffuse reflectance from the medium at strong absorption. We demonstrate by empirical means based on Monte Carlo results that diffuse photon remission from a strong-absorbing medium depends simply upon the absorption/scattering ratio when evaluated over a large area centered at the point of illumination differing in geometry from those convenient for the KM approach. Our empirical prediction gives ∼11% mean errors of the diffuse photon remission from thick opaque medium having an absorption coefficient ranging 0.001 to up to 1000 times stronger than the reduced-scattering coefficient. A slight modification to the KM function in terms of the absorption weighting and absorption-scattering coupling for use within the KM approach also noticeably improves the prediction of diffuse photon remission from thick opaque medium of strong absorption. Our empirical model and the KM approach using the modified KM function were compared against measurements from a thick opaque medium, of which the absorption coefficient was changed over four orders of magnitude.

Subdiffuse scattering and absorption model for single fiber reflectance spectroscopy

Single fiber reflectance (SFR) spectroscopy is a technique that is sensitive to small-scale changes in tissue. An additional benefit is that SFR measurements can be performed through endoscopes or biopsy needles. In SFR spectroscopy, a single fiber emits and collects light. Tissue optical properties can be extracted from SFR spectra and related to the disease state of tissue. However, the model currently used to extract optical properties was derived for tissues with modified Henyey-Greenstein phase functions only and is inadequate for other tissue phase functions. Here, we will present a model for SFR spectroscopy that provides accurate results for a large range of tissue phase functions, reduced scattering coefficients, and absorption coefficients. Our model predicts the reflectance with a median error of 5.6% compared to 19.3% for the currently used model. For two simulated tissue spectra, our model fit provides accurate results.