Use of Noncontact Diffuse Reflectance Spectroscopy and Optical Coherence Tomography Techniques to Characterize Both Spectral Reflectance and Internal Backscattering of Beef Psoas Major and Longissimus Lumborum Muscles

Daqing Piao; Scott Mattison; Ardalan Farazmand; Nafiseh Farahzadi; Anuj Sharma; Ranjith Ramanathan; Daqing Piao; Scott Mattison; Ardalan Farazmand; Nafiseh Farahzadi; Anuj Sharma; Ranjith Ramanathan

doi:10.22175/mmb.20195

The rate at which meat discolors varies by muscle type. However, currently, there are no noncontact methods available to characterize inter- and within-muscle differences in color stability. The objective of this study was to assess whether combining reflectance and scattering-based properties helps differentiate intermuscle differences in color stabilities better than using reflectance. This study assessed both the surface myoglobin forms using noncontact diffuse reflectance spectroscopy (DRS) and internal backscattering characteristics using optical coherence tomography (OCT) to understand intermuscle differences affecting the color stability between beef psoas major (PM) and longissimus lumborum (LL) muscles. Surface color measured using a contact HunterLab MiniScan colorimeter and noncontact DRS, and depth- resolved backscattering imaged by OCT, was conducted on PM and LL Choice steaks from day 0 to day 4 of retail display. The colorimetric measurement indicated that [Met]% in PM (LL) increased from 22.8 ± 10.1% (20.7 ± 13.2%) on day 0 to 49.2 ± 14.8% (27.1 ± 13.1%) on day 4 (P < 0.0001). The noncontact DRS assessed that [Met]% of the PM (LL) increased from 6.6 ± 21.1% (6.9 ± 25.1%) on day 0 to 47.8 ± 28.8% (14.5 ± 28.8%) on day 4 (P < 0.0001). The OCT revealed that there was a muscle type × storage time interaction in the rate of signal decay (4.3 ± 1.2dB/mm for PM versus 6.9 ± 1.2dB/mm for LL, P < 0.0001) as well as a muscle type main effect difference in the depth of penetration between PM and LL (P < 0.0001). The depth-resolved backscattering properties accessible by OCT provided imaging evidence of morphological differences in PM and LL muscles, supporting different rates of [Met]% progression in retail display. The current study indicates that the use of DRS (reflectance) and OCT (scattering) will provide information about meat color changes and morphological features of meat.

Keywords: meat color, myoglobin, non-contact diffuse reflectance spectroscopyomography, scattering, non-contact diffuse reflectance spectroscopy, optical coherence tomography

How to Cite: Piao, D. , Mattison, S. , Farazmand, A. , Farahzadi, N. , Sharma, A. & Ramanathan, R. (2025) “Use of Noncontact Diffuse Reflectance Spectroscopy and Optical Coherence Tomography Techniques to Characterize Both Spectral Reflectance and Internal Backscattering of Beef Psoas Major and Longissimus Lumborum Muscles”, Meat and Muscle Biology. 9(1). doi: https://doi.org/10.22175/mmb.20195

Introduction

The global demand for meat is projected to increase by 15% by 2031, compared to 2021 (Miller et al., 2022). In the United States, beef is the largest contributor among agricultural commodities to annual cash receipts (USDA-ERS, 2022). For fresh meat, color is the most important quality attribute affecting the purchase decisions of consumers (Feuz et al., 2020; Mancini et al., 2022; Thies et al., 2025). Surface discoloration, which is perceived as quality deterioration, causes approximately 2.5% of fresh beef to be wasted at retail stores in the US (Ramanathan et al., 2022). This leads to an estimated 428 million pounds of nutritious beef being discarded, which corresponds to 780,000 animals being wasted and a concomitant annual revenue loss of $3.7 billion (Ramanathan et al., 2022). Hence, there is a critical need to develop novel technologies to better understand and assess meat discoloration to minimize losses from wasting discolored beef.

Meat color attributes vary between and within muscles (McKenna et al., 2005; Seggern et al., 2005). For example, beef longissimus lumborum (LL) is a color-stable muscle, whereas psoas major (PM) is a color-labile muscle (Hunt and Hedrick, 1977; Ledward, 1985; O’Keeffe and Hood, 1982). Furthermore, color stability differences are observed even within the longissimus muscles (Canto et al., 2015). Traditional spectrophotometric studies using a commercial handheld colorimeter or sarcoplasmic extracts have characterized the color stability of muscles with storage (Harr et al., 2024; Kasthuri Dias et al., 2024). We recently developed noncontact diffuse reflectance spectroscopy (DRS) (Piao et al., 2024) to characterize the color of beef. Trends in the progression of myoglobin form changes during retail display, as measured by noncontact DRS from the superficial part of muscle, were closely matched to those measured by contact DRS using an applicator probe of 3-mm source-detector separation, rendering a sampling depth of ∼1 mm (enables color measurement without touching the meat or its packaging [Piao et al., 2022b]). Traditional color measurements of assessing the surface muscle and our previous contact DRS approach, assessing no more than 1 mm thick subsurface muscle, require touching the meat samples to record spectral characteristics. In contrast, noncontact spectrophotometry enables color measurement without touching the meat or its packaging, which is advantageous in retail settings. However, this method has limited capability to visualize interior features that inform color stability, such as changes in chromatic heme pigments like the formation of metmyoglobin in deeper muscle layers, which often precedes surface discoloration (Denzer et al., 2024). Interior features also include structural or morphological characteristics of constituents of muscle, such as shape, size, and orientation of muscle fiber, which remain unchanged but play a critical role in the phases of discoloration (Hughes et al., 2020).

To date, there is no noncontact method of measurement that can access both spectral characteristics and structural details from the interior of muscle to help assess and predict the color stability. Optical coherence tomography (OCT) is a noncontact-viable optical modality that forms 2-dimensional morphological images of the interior of an object (Huang et al., 1991), over a few millimeters of depth. OCT excels at resolving layered tissue structures by detecting backscattered light from microstructural features along the ballistic path of light. The depth-resolved information is encoded through interferometry, allowing OCT to reconstruct cross-sectional tomographic images with micron-scale spatial resolution. This capability enables clear visualization of distinct tissue layers, such as epithelium, connective tissue, and muscle fibers, making OCT a valuable tool for assessing subsurface structural organization and changes. Previously, OCT has been used in assessing the fine structure of skeletal muscles (Klyen et al., 2014), intramuscular fat content (Thampi et al., 2021), and tenderness (Thampi et al., 2019). However, there has been no study on the depth-resolved muscle-specific morphology relevant to color stability.

We hypothesized that the depth-resolved backscattering properties accessible via OCT could provide imaging evidence of intermuscle structural differences between PM and LL muscles, which were expected to show different rates of [Met]% progression during retail display as measured by DRS. Because structural details shall remain unchanged during discoloration, in contrast to the progression of myoglobin forms during retail display, any intermuscle difference of structural details between muscles measured at any time point may provide new information on the consistency of the changes of color or myoglobin during retail display. Combining DRS and OCT to assess both spectral reflectance and backscattering information could help characterize meat color changes with storage better than using DRS alone. Therefore, the objective of the study was to apply both noncontact DRS and noncontact OCT on color-labile PM muscle and color-stable LL muscle, to examine whether OCT reveals any intermuscle difference that is inaccessible to DRS’s quantification of myoglobin forms but is predictive of discoloration.

Materials and Methods

Processing of muscles

Eight United States Department of Agriculture Choice Porterhouse steak sections (containing beef PM and LL muscles from different animals) were purchased from a commercial beef purveyor. The steak sections were approximately 21 days postmortem. Muscle pH was measured using a pH probe (Handheld HI 99163; probe FC232; Hanna Instruments) on the day of retail display. All sections were within a normal pH range of 5.5–5.6 (standard error = 0.1; PM = 5.6 ± 0.1; LL = 5.5 ± 0.1). Steaks of 2.54-cm thick were packaged in black Styrofoam^™ trays overwrapped with polystyrene polyvinyl chloride film (15,500–16,275 cm³, O²/m²/24 h at 23°C, E-Z Wrap Crystal Clear Polyvinyl Chloride Wrapping Film, Koch Supplies, Kansas City, MO, USA). All steaks were placed in a coffin-style retail display case at 2 ± 1°C for 4 d. There was continuous LED lighting at 1,100 ± 20 lux (Philips LED lamps, 12 watts, 48 in., color temperature = 3,500 K, 54 Philips, China) throughout the retail display. All packages were rotated daily to minimize the effects of variation in light intensity or temperature due to location.

Raw color analysis using colorimeter

Surface color was measured every 24 h for 4 d using a HunterLab MiniScan handheld colorimeter with muscles in contact with the instrument and using noncontact DRS. In addition, samples were measured with a wavenumber swept source (Insight Photonics, 1260–1310 nm) OCT device to measure depth sectioned backscattering of light.

The surface of each steak was read at 3 randomly selected positions using a HunterLab 4500L MiniScan EZ Spectrophotometer (2.5-cm aperture, illuminant A, and 10° standard observer angle; HunterLab, Reston, VA, USA) (Piao et al., 2022) on both the PM and LL muscles. The surface color was characterized by the Commission Internationale de l´Eclairage (CIE) L*, a*, and b* values and reflectance from 400 nm to 700 nm. In addition, a* and b* values were used to calculate chroma $(a *) 2 + (b *) 2$ and hue $tan − 1 (b * / a *)$ , which represent respectively the red intensity of the perceivable color and the color perceivable (King et al., 2023).

Dual-modality noncontact DRS and OCT for assessing muscles

The dual-modality noncontact DRS&OCT system for assessing the muscles is schematically illustrated in Figure 1. The dual-modal DRS&OCT system was composed of a DRS system and an OCT system controlled separately by 2 computers. The panel (A) of Figure 1 depicts the noncontact DRS configured in a center-illuminated-area-detection (CIAD) geometry (Piao et al., 2024). The panel (B) of Figure 1 depicts the OCT system developed around a swept laser source (Mattison et al., 2015). The instrument details of the DRS and OCT systems are given in Appendices A and B, respectively. The panel (C) of Figure 1 illustrates how the free-space optical channels of DRS and the probing head of the OCT were arranged over laboratory-controlled samples for noncontact dual-modality assessment of the same sample. The DRS source channel was aligned to project vertically onto the sample. The optical axis of the DRS collection channel was oriented at an angle of approximately 30 degrees with respect to the optical axis of the source channel. The 2 channels of the DRS were aligned to have their optical axes coincide at the same spot of a reference level of the surface to position the sample. The OCT probing head had a scanning mechanism to scan a collimated beam transversely over a few millimeters on the sample surface.

Figure 1.

Schematic diagram of the configuration combining noncontact diffuse reflectance spectroscopy (DRS) & optical coherence tomography (OCT) to assess the surface of the same sample. The dashed-line framed panel (A) corresponds to the DRS unit, and the solid-line framed panel (B) corresponds to the OCT unit. The DRS and OCT units were housed on 2 separate carts, but the sample probing optics of the OCT were placed on a platform mounted on the cart of DRS to allow the 2 modalities to assess the same medium. The bottom panel (C), including a photograph, shows the 1”-cage configurations of the source and detection channels of the DRS unit and the sample probing optics of the OCT unit above an aqueous phantom. The white spot of light seen on the surface of the ink-desolved aqueous sample marked the illumination by the DRS. The illumination of the OCT channel was invisible as it was infrared.

Sequences of the instrument measurements on steaks

To minimize the effect of ambient lighting on DRS, the sample platform and the illumination and collection channels of DRS were shielded using black clothes. As shown in Figure 1(C), the OCT scanning head could be placed within the light-shielded space and fiber-optically connected to the main OCT unit on a separate cart. Such a configuration was necessary for testing on controlled laboratory samples, including aqueous phantoms that had the optical properties varied dynamically over a large range (Piao et al., 2024) as specified in Appendix C. However, such a configuration for sample measurement to be controlled by optical systems and computers housed on 2 carts became logistically challenging in the space of the research retail display facility. As a result, the OCT scanning head was detached from the DRS unit to measure the steaks. With such changes to the dual-modality setup, it became imperative to implement the following sequences for the daily repeated measurements of the 8 steaks by 3 types of instruments, including a handheld contact-mode MiniScan colorimeter, a noncontact DRS, and OCT.

The sequence of measuring signals from both the PM muscle and LL muscle of each steak to make the gross area of measurements on a muscle to be consistent among the 3 types of instrument sampling is conceptually shown in Figure 2. Each steak was subjected to repeated measurements on both the PM and LL muscles, in the following sequences by manually switching a steak among 3 instruments and positioning a muscle at the same spot-of-measurement or field-of-view of each instrument: (1) measuring by the colorimeter in 3 random positions on the PM side and then on the LL side (represented by round white circles), (2) measuring by the noncontact DRS in 5 random positions on the PM side and then on the LL side (represented by rainbow-colored arbitrary shapes), and (3) measuring by the OCT in 5 or more (as needed) random positions on the PM side first then on the LL side (represented by yellow stars). The measurements were conducted at room temperature, and a complete round of measurements on all samples using all technologies on each day took approximately 2 h of continuous operation.

Figure 2.

Schematic representation of the locations on the beef psoas major (PM) and longissimus lumborum (LL) muscles where colorimeter (3 measurements), DRS (5 measurements), and OCT (5 measurements) readings were taken.

Deducing myoglobin forms using colorimeter rendered spectral reflectivity

The raw spectral reflectivity profile acquired by HunterLab MiniScan, covering wavelengths from 400 nm to 700 nm at a 10-nm spectral interval, was transferred to a computer for offline processing to deduce the percentage numbers of myoglobin forms in addition to the instrument reading of L*, a*, and b*, from which chroma and hue were deduced. The deducing of the myoglobin forms using the colorimeter’s feed of spectral diffuse reflectivity from the muscles followed the modified Krzywicki’s equations (Piao et al., 2025). Details are included in Appendix D.

Deducing myoglobin forms using noncontact DRS

The spectral diffuse reflectance profile acquired by the noncontact DRS from 400 nm to 700 nm at a spectral resolution of 2 nm was transferred to a computer for offline processing to deduce the percentage numbers of myoglobin forms. The spectral diffuse reflectance values were first converted to spectral absorption coefficients (Piao et al., 2025), assuming a spectrally flat reduced scattering coefficient. Then, the spectral absorption coefficients were implemented in a linear inversion algorithm (Piao et al., 2024) to resolve the 3 forms of myoglobin. The details of the algorithms are referred to Appendix E.

Deducing depth of penetration and rate of signal decay in OCT

The OCT image was in a 2-dimensional B-scan form consisting of many one-dimensional A-lines that were profiled with respect to the depth of a few millimeters into the muscle, and staggered along the lateral dimension scanned along the surface of the muscle. Each A-line profile represented the logarithmically scaled intensity of backscattering that grossly reduced as a function of depth into the muscle. The depth from the surface of the muscle down to a position at which the signal dropped to 2 times the baseline noise level was calculated as the depth of penetration in units of mm. Each A-line was also fitted by a linear pattern over the depth range to which the depth of penetration was relevant. The magnitude of the slope of the linear fit to the A-line profile was calculated as the rate of signal decay in a unit of dB/mm. The calculations were averaged over the entire number of useful A-lines of a B-scan image to arrive at one value of the depth of penetration and one value of the rate of signal decay for the image. More details of the principles applying to the OCT images are referred to Appendix F.

Statistical analysis

The experimental design was a randomized complete block. The muscles from each animal served as a block (random term). The fixed effects to be assessed included muscle type, storage time, and interactions between muscle type and storage time. The variables included the following: colorimeter readings of L*, a*, and b*, chroma and hue derived using the colorimeter; [Oxy]%, [Deoxy]%, [Met]% deduced from the colorimeter; [Oxy]%, [Deoxy]%, [Met]% deduced from the noncontact DRS; and depth of penetration and rate of signal decay deduced from OCT. Each repeated measurement was processed to the respective terminal step of processing before calculating the mean and standard deviation (STD) of each variable over all measurements acquired on each day and for each type of muscle.

This study was conducted on 8 paired PM and LL muscles. On each PM or LL muscle, repeated measurements (on the same steaks) were acquired every 24 h by colorimeter (3 positions), noncontact DRS (5 positions), and OCT (5 or more positions), respectively. On each day of the retail display from day 0 to day 4, the total measurements (number of positions per muscle × number of muscles) for each instrument were averaged to obtain a mean and a STD. One outcome of this study was assessing if the change of individual variables, such as colorimeter or DRS-deduced [Oxy]%, [Deoxy]%, or [Met]%, over the retail display differed between paired PM and LL. For such intermuscle comparison of individual variables between the paired PM and LL muscles, the data groups had the same data structures and sample sizes. The intermuscle difference of any of these variables between paired PM and LL muscles on each day of retail display was subjected to a 2-tailed unpaired t-test per day. The effect of muscle type between PM and LL, the storage time from day 0 to day 4, and the interaction between muscle type and storage time were assessed by means of 2-way analysis of variance (ANOVA). Due to the variances of OCT’s alignments that changed over the day, the number of useful data varied over the retail display, causing the PM and LL data sets of OCT to have different total sizes even though they had the same data structures. These OCT data groups were then subjected to a 2-way ANOVA. For the t-test, the data groups were a priori calculated from the mean value and STD in MATLAB for loading into GraphPad Prism (Ver 6.0, La Jolla, CA, USA). For 2-way ANOVA, the grouped data were loaded into GraphPad Prism to calculate the row factor (storage time), the column factor (muscle type), and the interaction between the row and column factors. P value of <0.05 was considered statistically significant.

Results

Instrumental colors and colorimeter-deduced myoglobin forms of the PM and LL muscles over the retail display

The instrument colors, including L*, a*, b*, chroma, and hue of the PM and LL muscles over the retail display of day 0 to day 4 are tabulated in Tables 1 through 5, respectively. Out of the 5 instrument color parameters, 4 parameters, including L*, a*, b*, and chroma, exhibited similar statistical patterns, showing muscle type (P < 0.0001) and storage time (P < 0.0001) effects. In comparison, hue, presented in Table 5, demonstrated muscle type (P < 0.0001) and storage time (P < 0.05) interaction (P < 0.001). Figure 3 plots the hue of the PM and LL muscles over the retail display to visualize the differences in the changes.

Table 1.

Instrument color L* of PM and LL muscles (averaged for 3 repeated measurements per muscle and 8 muscles per day) from day 0 to day 4.

	Day 0	Day 1	Day 2	Day 3	Day 4
L* (PM)	44.2 ± 2.1	42.5 ± 2.2	41.9 ± 2.7	41.6 ± 3.4	40.9 ± 3.1
L* (LL)	47.6 ± 2.7	45.7 ± 2.6	45.5 ± 3.2	45.1 ± 3.0	44.8 ± 2.7

There was a main effect of muscle type (P < 0.0001). There was a main effect of storage time (P < 0.0001). But there was no interaction between muscle type and storage time.

Table 2.

Instrument color a* of PM and LL muscles (averaged for 3 repeated measurements per muscle and 8 muscles per day) from day 0 to day 4.

	Day 0	Day 1	Day 2	Day 3	Day 4
a* (PM)	25.1 ± 3.4	23.8 ± 3.3	22.2 ± 3.5	21.0 ± 4.9	18.2 ± 3.6
a* (LL)	26.2 ± 3.0	26.4 ± 3.9	25.5 ± 2.7	23.6 ± 4.0	23.6 ± 3.6

There was a main effect of muscle type (P < 0.0001). There was a main effect of storage time (P < 0.0001). But there was no interaction between muscle type and storage time.

Table 3.

Instrument color b* of PM and LL muscles (averaged for 3 repeated measurements per muscle and 8 muscles per day) from day 0 to day 4.

	Day 0	Day 1	Day 2	Day 3	Day 4
b* (PM)	20.8 ± 1.8	20.0 ± 1.7	19.5 ± 1.7	19.2 ± 2.3	18.0 ± 1.5
b* (LL)	22.9 ± 1.3	22.3 ± 2.2	22.1 ± 1.9	20.9 ± 2.2	20.7 ± 2.7

There was a main effect of muscle type (P < 0.0001). There was a main effect of storage time (P < 0.0001). But there was no interaction between muscle type and storage time.

Table 4.

Instrument chroma of PM and LL muscles (averaged for 3 repeated measurements per muscle and 8 muscles per day) from day 0 to day 4.

	Day 0	Day 1	Day 2	Day 3	Day 4
chroma (PM)	32.6 ± 3.6	31.1 ± 3.5	29.6 ± 3.6	28.6 ± 5.0	25.6 ± 3.3
chroma (LL)	34.9 ± 2.8	34.6 ± 4.2	33.8 ± 2.9	31.6 ± 4.2	31.4 ± 4.3

There was a main effect of muscle type (P < 0.0001). There was a main effect of storage time (P < 0.0001). But there was no interaction between muscle type and storage time.

Table 5.

Instrument hue of PM and LL muscles (averaged for 3 repeated measurements per muscle and 8 muscles per day) from day 0 to day 4.

	Day 0	Day 1	Day 2	Day 3	Day 4
hue (PM)	39.9 ± 2.1	40.3 ± 2.3	41.6 ± 3.0	43.0 ± 4.3	45.2 ± 4.6
hue (LL)	41.3 ± 2.8	40.5 ± 2.7	41.1 ± 2.5	41.7 ± 2.9	41.4 ± 2.8

There was a main effect of muscle type (P < 0.0001). There was a main effect of storage time (P < 0.05), and there was an interaction between muscle type and storage time (P > 0.001).

Figure 3.

The hue values (mean and standard deviation) of the PM muscle and LL muscle over the retail display from day 0 to day 4, derived from the MiniScan handheld colorimeter. The P values annotated at the right give the respective statistical significance of the effect of muscle type, treatment time, and the interaction between muscle type and treatment time. The stars atop a pair of bars denote that the difference between the pair of measurements was statistically significant (P < 0.05) by an unpaired t-test. Four stars correspond to P < 0.0001.

The analysis of instrumental colors may be summarized as follows: there were significant main effects of muscle type and storage time for all instrument colors, including L*, a*, b*, chroma, and hue. As expected, LL muscles exhibited greater redness, indicated by higher a* and chroma values (P < 0.05), compared to PM muscles. In addition, LL steaks were lighter in color (greater L* values; P < 0.05) than PM steaks, while PM steaks showed greater yellowness (P < 0.05) than LL steaks throughout the retail display. As shown in Figure 3, hue demonstrated a significant interaction (P < 0.001) between muscle type and storage time. On day 4, PM steaks exhibited significantly greater discoloration (P < 0.0001) than LL steaks.

The 3 forms of myoglobin calculated using reflectance spectra from the HunterLab MiniScan spectrophotometer (contact measurement) are presented in Figure 4. Among the 3 forms of myoglobin, a significant interaction (P < 0.05) between muscle type and storage time was observed for both oxymyoglobin and metmyoglobin levels. LL steaks had lower metmyoglobin (P < 0.05) than PM steaks on days 2, 3, and 4. However, there were no differences in metmyoglobin or deoxymyoglobin between days 0 and 1 in LL or PM steaks. Oxymyoglobin levels were greater (P < 0.05) in LL steaks than in PM steaks on each day of the retail display.

Figure 4.

The percentage (mean overlapped with standard deviation) of the oxymyoglobin (A), deoxymyoglobin (B), and metmyoglobin (C) over the retail display from day 0 to day 4, deduced using the spectral diffuse reflectance acquired by the MiniScan handheld colorimeter. The [Deoxy]% shown in (B) and [Met]% shown in (C) were calculated independently. The [Oxy]% shown in (A) was calculated as the difference between the combined [Deoxy]% and [Met]% from 100%. The P values annotated at the upper part of each figure give the respective statistical significance of the effect of muscle type, treatment time, and the interaction between muscle type and treatment time. The stars at the top of a pair of bars indicate that the difference between the pair measurements was statistically significant based on an unpaired t-test. One star corresponds to P < 0.05, 2 stars correspond to P < 0.01, 3 stars correspond to P < 0.001, and 4 stars correspond to P < 0.0001.

Noncontact DRS assessment of the myoglobin forms of the PM and LL muscles during the retail display

The 3 forms of myoglobin calculated using reflectance spectra from the noncontact DRS using methods specified in Appendix E are presented in Figure 5. The values of [Oxy]%, [Deoxy]%, and [Met]% on each day of the retail display are tabulated in Table 1a for PM and 1b for LL of Supplemental Materials.

Figure 5.

The percentage numbers (mean overlapped with standard deviation) of the oxymyoglobin (A), deoxymyoglobin (B), and metmyoglobin (C) over the retail display from day 0 to day 4, deduced using the spectral diffuse reflectance acquired by noncontact DRS. All 3 forms were calculated independently. The P values annotated at the upper part of each figure give the respective statistical significance of the effect of muscle type, treatment time, and the interaction between muscle type and treatment time. The stars atop a pair of bars denote that the difference between the pair of measurements was statistically significant by the unpaired t-test. One star corresponds to P < 0.05, 2 stars correspond to P < 0.01, 3 stars correspond to P < 0.001, and 4 stars correspond to P < 0.0001.

The [Oxy]% of PM muscles changed from 72.7% ± 21.0% on day 0 to 38.8% ± 28.7% on day 4. In comparison, the [Oxy]% of LL muscles changed from 70.3% ± 32.5% on day 0 to 69.9% ± 31.9% on day 4. There were effects of both muscle type and storage time on the change of [Oxy]%. And there was an interaction (P < 0.01) between muscle type and storage time on the change of [Oxy]%.

The [Deoxy]% of PM muscles varied from 20.7% ± 9.6% on day 0 to 23.4% ± 15.1% on day 4. In comparison, the [Deoxy]% of LL muscles varied from 22.8% ± 16.1% on day 0 to 15.6% ± 8.6% on day 4. There was no effect of muscle type or storage time on the change of [Deoxy]%. There was no interaction (P < 0.01) between muscle type and storage time on the change of [Deoxy]%.

The [Met]% of PM muscles increased from 6.6% ±21.1% on day 0 to 37.8% ± 28.8% on day 4. In comparison, the [Met]% of LL muscles increased from 6.9% ± 25.5% on day 0 to 14.5% ± 28.8% on day 4. There were effects of both muscle type and storage time on the change of [Met]%. And there was an interaction (P < 0.01) between muscle type and storage time on the change of [Oxy]%.

Gross features of noncontact DRS and OCT of the PM and LL muscles

Figure 6 contains 2 column panels with 4 rows of subfigures in each column panel. The left panel corresponds to the PM muscle, and the right panel corresponds to the LL muscle. Both panels have an identical figure (A) to depict the spectral absorbance of oxymyoglobin, deoxymyoglobin, and metmyoglobin, over the spectral range of 480 nm to 650 nm (Piao et al., 2022b). The absorbance of oxymyoglobin exhibits a distinctive double-peak feature near 540 nm and 580 nm. The absorbance of deoxymyoglobin has a broadened peak near 560 nm, which is close in magnitude to the double-peak of oxymyoglobin and has smoothly tapered shoulders. Comparatively, the absorbance of metmyoglobin is spectrally much less varying than that of both oxymyoglobin and deoxymyoglobin over the visible spectral range, but it does have a locally more prominent peak near 500nm and a less apparent peak local to 630 nm.

Figure 6.

Gross patterns of the measurements acquired from the PM muscle (left column) and LL muscle (right column). The top row containing 2 identical plots illustrates the spectral absorbance of the 3 forms of myoglobin, including oxymyoglobin (red), deoxymyoglobin (blue), and metmyoglobin (black). The second row from the top displays the spectral diffuse reflectance (at a wavelength resolution of 10nm) measured over day 0 to day 4 of the retail display, by the MiniScan handheld colorimeter in contact with the surfaces of the steak. The third row from the top displays the spectral diffuse reflectance at a wavelength resolution of 2nm, over day 0 to day 4 of the retail display, measured by the noncontact DRS device from the surfaces of the steak. The bottom row displays representative cross-sectional images and illustrative depth-resolved signal profiles of the OCT measured off-contact from the surfaces of the steak.

Figure 6(B) displays the raw spectral diffuse reflectivity profiles acquired by the colorimeter. The spectral reflectivity was displayed from day 0 to day 4 and over the same spectral range of 480 nm to 650 nm as the top figure. The displayed traces look sparse because of the coarse 10 nm spectral resolution of the colorimeter. There was a double-valley feature over the 540 nm–580 nm range that strongly correlated with the double-peak of oxymyoglobin. This double-valley feature became less distinctive over the retail display, suggesting a reduction of the oxymyoglobin forms. In comparison, the spectral reflectance near 640 nm appeared to reduce gradually over the retail display, which correlated with a less apparent yet discernible peak of absorbance of metmyoglobin near 640 nm. This reduction in spectral reflectivity around 640 nm suggested an increase in metmyoglobin forms over the retail display. The profile for LL at the right panel was analogous to that for the PM muscle at the left panel, except for a slightly smaller reduction of the spectral reflectivity around 640 nm, suggesting a lesser amount of the increase of metmyoglobin forms in LL muscle than in PM muscle over the retail display.

Figure 6(C) displays the raw profiles of the spectral diffuse reflectance acquired by noncontact DRS. The displayed mesh of the traces appears much smoother spectrally than that of the colorimeter, due to the much finer spectral resolution of the spectrometer than that of the colorimeter. The finer details of the spectral dimensions than that of the colorimeter acquisition revealed features resembling those observed with the colorimeter above: there was a double-valley feature over the 540 nm–580 nm range, strongly correlating with the double-peak of oxymyoglobin. This double-valley feature became less distinctive over the course of retail display. During the same period, the spectral reflectance near 640 nm appeared to decrease gradually. The feature near 640 nm correlated with a less apparent yet discernible peak of the absorbance of metmyoglobin near 640 nm. The profile for LL at the right panel was very close in shape to that for the PM muscle at the left panel, except for a slightly smaller reduction of the spectral reflectivity around 640 nm, which suggested that the increase of metmyoglobin forms in LL muscle was less than that in PM muscle. Overall, there was a subtle difference between PM and LL on the spectral reflectivity when assessed grossly, regardless of using the contact or noncontact mode of measurements.

Figure 6(D) displays the OCT of PM on the left and the OCT of LL on the right panel. The 2-dimensional pseudo-colored B-scan image represented a cross-sectional view into the muscle with a field-of-view of 3mm × 4mm. The top-down dimension of 3mm represented a depth direction into the muscle, and the left-right dimension of 4mm represented a transverse direction of scanning along the surface of the muscle. A clear margin indicating the interfacing between the 2 regions was observable at the top quarter of each image, which was formed by the strong reflection at the muscle surface. And the continuous mass inferior to the margin was the appearance of the muscle parenchyma. In the image on the left, a thin, faint line can be observed stretching from approximately the middle section towards the right edge, forming a sharp angle with respect to the margin indicating the muscle surface. That faint line corresponded to the polystyrene polyvinyl chloride film wrapping the tray. On each of the B-scan images, a dashed vertical line crossing the margin representing the muscle surface was depicted. The signal along the vertical direction of the dashed vertical line would present as a one-dimensional A-line profile, like the one sketched to the right of the B-scan image.

OCT assessment of the light penetration of the PM and LL muscles during the retail display

The results of near-infrared OCT imaging (1260–1310 nm) of the PM and LL muscles are displayed in Figure 7. The 2 B-scan images displayed in (A) and (B) are the same as those in the bottom row of Figure 6. The 2 B-scan images are used as the reference to illustrate how the 2 parameters of OCT indicating backscattering were assessed. The 2 parameters derived from the OCT images were depth of penetration and rate of signal decay as specified in Appendix F. Due to the degradation of the optical alignment in the OCT system, OCT images acquired from day 0 to day 4 had various numbers of repeated measurements per day, between 10 and 51 combined, on PM or LL muscles, respectively. To account for structural variation of the muscles, the A-lines of each useful image were averaged to obtain one A-line per image, and then further averaged over all images obtained for the type of muscle on that day to obtain the mean and STD of the depth and decay rate of the signal of the A-line of that day for a muscle type. The depth of penetration and the rate of signal decay over the retail display from day 0 to day 4 are given in Table 2a for PM and 2b for LL of Supplemental Materials.

Figure 7.

A representative pseudo-color B-scan image of a PM muscle (A) and an LL muscle (B). The one-dimensional plot in (A) or (B) depicts the A-line profile expected from a view into the muscle along the dashed line marked on the respective B-scan image. The A-line profile displays the signal (dB) as a function of depth (mm) into the muscle. The dark strip parallel to the axis of depth marks the range of the signal-to-noise ratio below 2. The depth from the muscle surface to the depth at which the SNR drops to 2 was the depth of penetration. The linearly fitted rate of signal reduction with depth of penetration was the rate of signal decay. The rate of signal decay of the PM and LL muscle over the retail display of day 0 to day 4 is compared in (C). The P values annotated to the left give the respective statistical significance of the effect of muscle type, treatment time, and the interaction between muscle type and treatment time. The stars atop a pair of bars denote that the difference between the pair of measurements was statistically significant by the unpaired t-test. * P < 0.05, ** P < 0.01, *** P < 0.001, and **** P < 0.0001.

The depth of penetration of the PM (LL) muscles varied from 2.26 ± 0.41 mm (1.50 ± 0.20 mm) on day 0 to 2.05 ± 0.24 mm (1.20 ± 021 mm) on day 4. There was no interaction between muscle type (P < 0.0001) and storage time (P < 0.01) on the depth of penetration of the OCT signal. The rate of signal decay of the PM (LL) muscles varied from 4.61 ± 1.32 dB/mm (7.46 ± 1.17 dB/mm) on day 0 to 4.45 ± 0.96 dB/mm (7.51 ± 1.60 dB/mm) on day 4. There was interaction (P < 0.01) between muscle type (P < 0.0001) and storage time (P < 0.0001) on the rate of signal decay of the OCT signal. The intermuscle difference in the rate of signal decay between PM and LL is also displayed in Figure 7(C). The daily intermuscle difference was statistically significant on every day of day 0 to day 4. If averaged over the retail display, the rate of signal decay was 4.3 ± 1.2 dB/mm for PM and 6.9 ± 1.2 dB/mm for LL muscle.

Discussion

Muscle-specific differences in color stability in fresh beef have been characterized by studying protein, metabolites, and lipid oxidation (Ke et al., 2017; Ramanathan et al., 2021; Zhai et al., 2020). The intermuscle difference of color stability between PM and LL has been associated with intermuscle differences in the abundance of sarcoplasmic proteome (including antioxidant proteins, chaperones, and glycolytic enzymes), metabolites, and mitochondrial properties (Joseph et al., 2012; Nair et al., 2018; Ramanathan et al., 2021). Although wet-laboratory techniques are powerful and accurate, rapid determination of color stability without time-consuming analysis and without destroying or contacting the sample will be very valuable for the industry.

The most convenient and routine nondestructive, but not noncontact, assessment of beef to inform the color stability of meat is the measurement of instrumental color by using handheld colorimeters such as HunterLab MiniScan (Holman et al., 2015) or Minolta colorimeter (Henriott et al., 2020). These colorimetry devices acquire spectral diffuse reflectance of the visible light (450 to 700 nm) from muscle surfaces to calculate the instrumented colors, including L* (light vs. dark), a* (red vs. green), and b* (yellow vs. blue), and chroma and hue values that are different combinations of a* and b*. These instrument-derived parameters are accepted measures of the perceived color, but they indirectly represent the myoglobin forms, including oxymyoglobin, deoxymyoglobin, and metmyoglobin, that together determine the true perceived color of the meat. Among the myoglobin forms, the percentage of the brownish-red metmyoglobin [Met]% may be the dominating pigment form to be measured to assess color stability. However, the instrumental color is not the sole indicator or specific predictor of the color degradation (Denzer et al., 2025) due to postmortem changes of proteome components.

Other than the myoglobin forms, muscle fiber has been recognized as a major contributing factor to the beef color instability via the differences in mitochondrial content and biochemistry (Ramanathan et al., 2021). Beef PM has greater mitochondrial content than the LL counterparts, primarily owing to differences in muscle fiber type (Hunt and Hedrick, 1977). Since muscle fibers that influence discoloration of the muscle are also strong light scatterers, assessing both myoglobin content and muscle fiber structure may provide information that would be missed by assessing either factor alone. It is important to note that assessing pigments by using light, whether in contact or noncontact mode, relies upon the interplay between pigments and the microscopic structures of muscle, including fibers. This is because the spectrally significant absorption of myoglobin molecules within the muscle parenchyma cannot be accessed by light in a reflection geometry of the contact-colorimeter or noncontact DRS, unless the scattering of muscle structures makes the light diffusely propagate in the muscle parenchyma to interact with the absorbing myoglobin molecules.

This study has used the popular handheld contact-mode colorimeter, a novel noncontact DRS, and OCT on paired PM and LL muscles over a retail display. At each round of the daily measurements, the same steak was sampled on both the PM and the LL section, within a short time gap of no more than a minute for each method of measurement. Such a configuration using paired PM and LL muscles ensured that the variations in environment and operator that could affect the consistency of the measurement conditions were minimized. With the minimization of the variances that could bias intermuscle comparison, the resulting instrument-derived differences between the PM and LL muscles could then be associated with definitive biological and morphological differences existing between the PM and LL muscles.

Past studies suggested that instrument measurement of the color is an effective parameter for quantifying the discoloration and predicting the shelf life of meat. However, questions remain about whether different muscles, such as the PM and LL muscles, can be distinguished based solely on instrument color measurement. In this work, we used noncontact DRS to assess the expected intermuscle differences in the change of myoglobin forms between PM and LL muscles. From the same muscles assessed by noncontact DRS, we have also used noncontact OCT to assess if there were any intermuscle differences in backscattering properties between PM and LL muscles. The information rendered by DRS originated from the differences of spectral absorption among the 3 forms of myoglobin in muscle, expected to change over the retail display. In comparison, the information rendered by OCT originated from microscopic heterogeneities of the muscle’s physical structures causing backscattering, which was to remain stable over the retail display. The information of DRS and the information of OCT were thus complementary to each other, as the former assessed absorption by muscle pigments like myoglobin and the latter probed scattering by the muscle’s microstructures.

What is the potential advantage of combining DRS and OCT for the long-term objective to differentiate and predict color stability in beef muscles? The intensity of an OCT signal represents how strong the back-reflection or backscattering is of the muscle parenchyma at some depth, convolved with the integrated spectral absorption properties of the sample up to that depth (Andrews et al., 2008). A greater depth of penetration could be associated with stronger scattering, leading to a stronger entrance intensity of the signal that could bear a faster rate of signal decay (Li et al., 2020) to reach the depth of the SNR threshold. A greater depth of penetration could also be associated with a weaker scattering that may produce a lower entrance intensity but decay at a slower rate to reach a longer depth (Kodach et al., 2010) to reach the SNR threshold. In addition, a lower depth of penetration could instead imply stronger optical absorption (Chen et al., 2025) of the OCT imaging spectrum, causing signal intensity to decay at a faster rate. Deeper penetration combined with a smaller rate of signal decay, however, relates to more light penetrating deeper into the issue as a result of both scattering and absorption properties of the media. Our OCT system operated in the second NIR window (1250–1350 nm), where optical absorption properties are reduced (Shi et al., 2016) compared to the visible window, at which the pigment forms have been assessed. Therefore, the difference in the OCT image was expected to be minimally affected by the difference in the spectral absorption between 2 muscles of differing colors. The use of the same narrow optical spectrum on imaging PM and LL allows the scattering properties to be attributed as the primary driver of OCT signal parameters to differentiate between PM and LL muscle types. Muscle fibers scatter light with a bias to the forward direction (Haskell and Carlson, 1981), and the degree of the forward scattering, which determines how much light is backscattered, is strongly related to the size of the fiber.

PM has more type-I, smaller fibers than LL, has a greater volume density of muscle fibers, and higher myoglobin content than LL (Zou et al., 2023; Salim et al., 2024). A slower rate of signal decay, combined with a greater penetration of light of OCT in PM than in LL, was consistent with the PM muscle having more type-I fibers of smaller sizes than the LL muscle to give rise to more isotropic scattering for the backscattering to decay more slowly and be acquired deeper into the muscle. A previous study determining the biochemical basis for discoloration within longissimus noted that predominant glycolytic fibers in LL delay discoloration (Salim et al., 2019) compared with PM having more type-I fibers. Conversely, lipid and marbling of the muscles may drive signal decay due to variances in absorption and refractive index mismatches between muscle fibers and fat. In either case, the use of OCT will help to differentiate muscles of different backscattering characteristics, informing differences in the fiber factors of the color stability. In the current research, 21-d postmortem samples were used. Studies have shown that aging decreases color stability (King et al., 2021). Future studies using comparison of OCT signals from the first NIR window (800–900 nm), where myoglobin is strongly absorbing, or 1000–1100 nm, where lipids are strongly absorbing, may provide insight into the ability of OCT to differentiate and identify muscle types. In addition, early postmortem muscles will help to understand the usefulness of DRS and OCT in differentiating muscles of varying color stability or even within-muscle differences in the color stability.

Conclusion

A noncontact dual-modality system applying both DRS and OCT was employed to assess discoloration in the beef PM and LL muscles. Noncontact DRS detected changes in myoglobin forms with storage time that were consistent with estimates obtained from a HunterLab MiniScan spectrophotometer. OCT analysis revealed that the PM muscle exhibited deeper signal penetration and a slower rate of signal attenuation, indicative of more isotropic light scattering—potentially due to smaller muscle fiber dimensions. This study highlights OCT’s unique capability to provide depth-resolved, scattering-related morphological information that is not accessible through DRS alone. Advancing such novel imaging tools could improve understanding of meat discoloration to help reduce economic losses from discolored beef.

Conflict of Interest

The authors declare no conflicts of interest regarding the content of this manuscript.

Author Contributions

Daqing Piao conceived the study, developed instrument, conducted the study, collected data, analyzed data, and wrote the draft manuscript; Scott Mattison developed instrument, conducted the study, collected data, analyzed data, and edited the manuscript; Ardalan Farazmand developed instrument, collected data, and reviewed the manuscript; Nafiseh Farahzadi collected data, and reviewed the manuscript; Anuj Sharma conducted the study, collected data, and reviewed the manuscript; Ranjith Ramanathan secured funding, edited the manuscript, and provided supervision.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Appendices

A. Non-contact diffuse reflectance spectroscopy system

The light from a broadband visible spectrum source (FOSTEC LR92240 Fiber Optic Light Source for microscopy, 400-750nm) was fiber-optically coupled (200μm) to the source channel of the DRS via a customized 1”-cage fiber-launching module built with a 20× microscope objective lens [RMS20X, Thorlabs, Trenton, NJ, USA]. The source channel mounted at an upright position for downward projection contained a 4× microscope objective lens (RMS4X, Thorlabs, Trenton, NJ) to project light onto the medium over a spot of ∼2mm in diameter. The diffusely reflected light from the medium was acquired by a detection channel with its optical axis aligned at an approximate 30 degrees with respect to the optical axis of the source channel or the illumination path. The collection channel used a 4× microscope objective lens for coupling light to a fiber patch cord (400μm) connected to a compact spectrometer (FLAME-T-UV-VIS-ES, Ocean Optics, Orlando, FL). The optics of the detection channel collected light over an area of ∼4mm in diameter centered on the spot of illumination, making this non-contact DRS respond to the superficial-layer pigments of ∼1mm in total depth corresponding to the ∼2mm radius of the area of light correction. The exposure time of the spectrometer varied between 5ms and 100ms, depending upon the sample (steak or controlled phantom), but were kept as consistent as possible. The raw spectral profile acquired using the vendor-provided interface of the compact spectrometer was saved to TXT format and off-line processed by using MATLAB (R2022a, MathWorks, Natick, MA) for resolving myoglobin forms.

B. Optical coherence tomography system

The non-contact OCT for cross-sectional, B-scan imaging into the sample was designed around an akinetic swept source laser (Insight Photonics, Broomfield, CO) with balanced detection for an operating wavelength of 1250 – 1310 nm. The spectral span of this laser to source OCT imaging could theoretically render an axial or depth resolution of ∼12 μm in air, equivalent to ∼9 μm in water or soft tissue. Fiber-coupled light from the OCT laser passed through a circulator then was split by a 50:50 fiber-coupler into reference and sample arms. Light in the reference arm was collimated, passed through an adjustable mechanical slit to control power, a dispersion compensator, and then back reflected into the fiber optics. Light in the sample arm was collimated and then focused through a low NA objective (LSM03, Thorlabs, Trenton, NJ) for a lateral or transverse resolution of 20 μm at the focal spot. Interference signal formed between the reference beam reflected by the mirror of the reference arm and the sample beam backscattered by the sample over a depth of focus of a few millimeters was collected on a 400 MHz balanced photodiode (Insight Photonics, Broomfield, CO). The signal was low-pass filtered at 200 MHz to prevent aliasing and digitized using a clock synchronized 12-bit digitizer at 400 MHz (AlazarTech, Pointe-Claire, QC, Canada). At the 100 kHz sweep rate and 82.5% duty cycle of the laser of the OCT, the sampling and digitization corresponded to a Nyquist imaging depth of ∼2.7 cm, which was approximately one order of magnitude greater than the depth of light penetration in muscle and the optical depth of focusing giving rise to useful signal-to-noise ratio.

C. Sample configuration used for calibrating the dual-modality responses of DRS and OCT

The dual-modality configuration of the DRS/OCT system as shown in Figure 1(C) was used for laboratory testing on controlled samples for calibration purposes. For example, the sample photographed was an aqueous medium of 1000ml water housed in a container atop a magnetic stirrer (VWR 12621-054 Digital High Volume Magnetic Stirrer). The magnetic stirrer was also used as a base platform for placing different samples to align the height of the surface of the sample exposed to the measurements. The aqueous sample shown was prepared by dissolving various amounts of TiO2 powder (Sigma-Aldrich, 248576, St. Louis, MO) and Indian ink (Handy Art, Black Velvet, Hobby Lobby, Oklahoma City, OK) in water, homogenized by agitating using a 2.75” magnetic bar at a speed of 180 RPM, to control the scattering and absorption properties for calibrating the responses of the DRS and OCT to the same sample with the optical properties varying over large ranges. The large range of the scattering of the aqueous medium was developed by dissolving TiO2 powder with the cumulative weight spanning more than 4 orders of magnitude. The large range of the absorption of the aqueous medium was developed by dissolving Indian ink with the cumulative volume spanning more than 4 orders of magnitude. These large ranges of scattering and absorption of the aqueous medium were used to set the analytical forward model of DRS conforming to the CIAD geometry (see Supplemental Materials), which predicted monotonic responses to the increasing of scattering or absorption. Linear inversion of the analytical forward model facilitated spectral inversion and unmixing to resolve the myoglobin forms. Over the same large ranges of the scattering of the aqueous medium, the responses of OCT were bi-phasic. The bi-phasic responses of the OCT help remove an ambiguity in the spectral inversion of DRS concerning the scattering properties of the medium.

D. Algorithms to deduce myoglobin forms using colorimeter

The spectral reflectivity values, denoted by $R ∞ (λ)$ , were first converted to spectral absorption coefficient of $μ a (λ)$ (having a unit of $m m − 1)$ [Piao et al, MMb 2025] scaled over an assumed spectrally flat reduced scattering coefficient of the muscle of $μ s ′ (λ) = μ s 0 ′$ by the equation of the following:

μ a (λ) / μ s 0 ′ = 0.25 {1 [2 π R ∞ (λ)] 2 + 0.16} 1 2.2 − 0.11875

(A1)

The spectrally flat reduced scattering $μ s 0 ′$ would be cancelled out in any operation that takes the ratio between two values of $μ a (λ) / μ s 0 ′$ . Therefore, the descriptions that follow and concern the ratio between two values of $μ a (λ)$ would not be affected by the value chosen for $μ s 0 ′$ (it can use the same value of assumption needed for the algorithms of non-contact DRS). The resulting spectral absorption coefficient $μ a (λ)$ at 470 nm, 480 nm, 520nm, 530nm, 570nm, and 580nm were then linearly weighted to interpolate the absorption coefficients at three isosbestic wavelengths of respectively 474 nm, 525 nm, and 572 nm. The spectral absorption coefficients estimated for these three isosbestic wavelengths were used to calculate [Deoxy]% and [Met]% according to Krzywicki’s equations without considering a baseline value of 730nm [Piao et al, 2025, MMB] as follows:

[D e o x y] % = α D e o x y {β D e o x y − γ D e o x y μ a (λ 1) μ a (λ 2)} × 100

(A2)

[M e t] % = α M e t {β M e t − γ M e t μ a (λ 3) μ a (λ 2)} × 100

(A3)

Where $α D e o x y = 2.375$ , $α M e t = 1.0$ , $β D e o x y = 1.0$ , $β M e t = 1.395$ , $γ D e o x y = γ M e t = 1.0$ , $λ 1 = 474 n m$ , $λ 2 = 525 n m$ , and $λ 3 = 572 n m$ . The [Oxy]% was then calculated by subtracting [Deoxy]% and [Met]% from 100.

E. Algorithms to deduce myoglobin forms using non-contact DRS

A precious study [Piao et al, 2024] has modeled the spectral diffuse reflectance of the unique geometric configuration of the non-contact DRS. Testing on an aqueous sample with the scattering and absorption properties varied respectively over more than 4 orders of magnitude has led to the following forward model of the spectral reflectance $I D R S (λ)$ of the non-contact DRS associated with an area of a radius of 2mm for the light collection:

I D R S [μ s ′ (λ), μ a (λ)] = 0.03 0.04 [1 + 3.96 (μ s ′ (λ) · 2) 1.4] + [μ a (λ) μ s ′ (λ)] 1.15

(A4)

The spectral diffuse reflectance values $I D R S [μ s ′ (λ), μ a (λ)]$ were first converted to spectral absorption coefficient of $μ a (λ)$ [Piao et al, 2024], assuming that the reduced scattering coefficient of muscle to be spectrally flat as $μ s ′ (λ) = 3 m m − 1$ , as follows:

μ a (λ) = μ s ′ (λ) * {0.03 I [μ a (λ), μ s ′ (λ)] − 0.04 [1 + 3.96 · (μ s ′ (λ) · ρ) − 1.4]} 1 / 1.15

(A5)

The resulting spectral absorption coefficient $μ a (λ)$ at 480nm to 650nm at an interval of 10nm were then fed into a linear inversion algorithm [Piao et al, 2024] to arrive at the three myoglobin forms.

F. Estimation of the depth of penetration and the rate of signal decay of OCT

The amplitude of OCT signal corresponding to a depth of z and being proportional to the refelectivity of the sample at that depth can be modeled as follows [10]:

I OCT (z) = β 0 (N A, g) · (μ s ′ · Δ z) · exp [− 2 (μ e f f · z)]

(A6)

Where $β 0 (N A, g)$ is a coefficient detemined by the numerical aperture of the collection optics and the aniostropy factor of the scattering, $Δ z$ is the coherence length or axial resolution, and $μ eff (λ)$ is effective attenuation coefficient. Testing the OCT system of this study on aqueous phantoms with the scattering and absorption varied more than four orders of magnitude as aforementioned suggested that the signal of OCT for this study needed to be modeled as the following:

I OCT (z) = β 1 · (μ s ′ (λ) · Δ z) β 2 · exp [− 2 (μ eff (λ) z · β 3) β 4]

(A7)

Equation (A6) is simply a special case of Eq. (A7). By converting the OCT signal to dB value as would be routine for visualization, either of Eq. (A6) or Eq. (A7) leads to the following form:

20 ln [I OCT (z)] = − K OCT · z + A OCT

(A8)

Where $K OCT$ represents a rate of the decay of the signal in a unit of dB/mm, and $A OCT$ is a lumped saturation-level signal corresponding to the air-muscle interface.

	Day 0	Day 1	Day 2	Day 3	Day 4
[Oxy]%	72.7 ± 21.0	64.3 ± 20.8	59.9 ± 31.7	50.9 ± 27.9	38.8 ± 28.7
[Deoxy]%	20.7 ± 9.6	21.5 ± 11.8	21.1 ± 13.0	20.2 ± 10.8	23.4 ± 15.1
[Met]%	6.6 ± 21.1	14.2 ± 19.6	19.0 ± 30.2	28.9 ± 30.2	37.8 ± 28.8

	Day 0	Day 1	Day 2	Day 3	Day 4
[Oxy]%	70.3 ± 32.5	68.8 ± 44.8	76.8 ± 25.4	73.1 ± 27.6	69.9 ± 31.9
[Deoxy]%	22.8 ± 16.1	19.4 ± 15.3	18.4 ± 13.1	18.4 ± 13.9	15.6 ± 8.6
[Met]%	6.9 ± 25.1	11.8 ± 36.1	4.8 ± 22.4	8.5 ± 24.6	14.5 ± 28.8