## 2. Results

A total of 9 participants were recruited for this study (5 female, 27 ± 6 years). One participant only completed a single arterial occlusion due to time constraints; three arterial occlusions from another participant were discarded because the slope of the difference between oxy- and deoxyhemoglobin (HbD) increased during occlusion; DCS data from another participant was discarded due to technical difficulties with the laser during acquisition; and NIRS data from a single epoch of one participant was also discarded due to issues with writing data to file. The remaining datasets were all included for analysis.

Table 1 outlines the mean ± standard deviation (SD) NIRS-measured resting-state optical properties, hemoglobin concentrations, and oxygen saturation for each participant. Cohort averaged resting-state total hemoglobin concentration (HbT

_{0}) was 48.1 ± 18.2 μM and oxygen saturation (StO

_{20}) was 55.5 ± 9.9%. Similarly,

Table 2 reports the mean ± SD NIRS-measured VO

_{2AO}, VO

_{2VO}, and BF along with DCS-measured BFI and NIRS + DCS-measured VO

_{2i} for each participant along with group averages. VO

_{2i} averaged prior to the venous occlusion was not statistically significantly different from VO

_{2i} averaged prior to the arterial occlusion; therefore, only mean ± standard deviation of VO

_{2i} prior to arterial occlusion was reported. Although BF, VO

_{2AO}, and VO

_{2VO} were measured at 4 source-detector separations, data is reported from 3.5 cm, which was consistently higher than the other separations (all

p < 0.05). There were no statistically significant differences in any of the parameters reported in

Table 1 and

Table 2 between sexes. Excellent intra-participant repeatability was observed for VO

_{2AO}, VO

_{2VO}, VO

_{2i}, BF, HbT

_{0}, and StO

_{20} as indicated by ICC > 0.75; BFI repeatability was rated good (ICC = 0.62,

Table 3). Coefficient of variation (CV) was <0.27 for all measured parameters, with HbT

_{0} and StO

_{20} demonstrating the least amount of variation (mean CV = 0.06 and 0.03, respectively). ICC values for VO

_{2AO}, VO

_{2VO}, and BF were highest and CV values were lowest at the 3.5 cm source-detector separation; however, regardless of separation, all parameters had ICC > 0.49 and CV < 0.27 (

Supplementary Table S2).

Results from the linear mixed effect model (LMM) where DCS-measured BFI averaged 15 s prior to venous occlusion was regressed on NIRS-measured BF (

Figure 1) demonstrated a significant positive linear association between BF and BFI (slope = 5.8 × 10

^{−7};

p = 0.06) with a correlation, adjusted for repeated measures, of 0.70. Significant variation in the subject-specific slope estimates were not observed (

p = 0.37).

Results from the LMM where VO

_{2VO} was regressed on VO

_{2AO} (

Figure 2A) revealed that VO

_{2AO} and VO

_{2VO} were significantly and positively associated (slope = 0.96,

p = 0.01) with a correlation, adjusted for repeated measures, of 0.51, even after accounting for significant between-subject variation in the estimated subject-specific slope (

p = 0.041). Notably, as indicated in the Bland–Altman plot (

Figure 2B), VO

_{2AO} was generally higher than VO

_{2VO}, and the bias tended to increase as mean VO

_{2} increased, resulting in a poor agreement between the two methods (CCC = 0.40).

Results from the LMM where VO

_{2i} averaged 15 s prior to arterial occlusion was regressed on VO

_{2AO} (

Figure 3A) demonstrated significant between-subject variation in the estimated subject-specific slope (

p = 0.06). After accounting for this random variation, we failed to detect a significant association between VO

_{2AO} and VO

_{2i} (slope = 0.93 × 10

^{−6},

p = 0.16) with a repeated measures adjusted correlation of 0.62. Similarly, results from the LMM where VO

_{2i} averaged 15 s prior to venous occlusion was regressed on VO

_{2VO} (

Figure 3B) demonstrated a significant between-subject variation in the estimated subject-specific slope parameter (

p = 0.09). After accounting for this random variation, we failed to detect a significant association between VO

_{2AO} and VO

_{2i} (slope = 0.25 × 10

^{−6};

p = 0.55; repeated measures adjusted correlation of 0.41).

## 3. Discussion

In this work we quantified resting oxygen metabolism in the medial gastrocnemius (MG) muscle using 3 different non-invasive, optical methods; two NIRS-only measures taken during a venous and arterial occlusion (VO

_{2VO} and VO

_{2AO}, respectively), and a combination NIRS + DCS measure averaged 15 s prior to the venous or arterial occlusion (VO

_{2i}). Using the NIRS-only arterial occlusion method, oxygen metabolism was highest at the 3.5 cm separation, likely because the contribution from adipose tissue, which has lower metabolism than muscle, is smallest at this separation [

21]. Mean oxygen metabolism in the calf at 3.5 cm was 0.031 mLO

_{2}/min/100 g, with a range of values extending from 0.011 to 0.052 mLO

_{2}/min/100 g (

Table 2). These values, which were obtained while sitting with leg extended, are similar to previous work performed while supine [

15,

24], suggesting that resting-state metabolic rate may be independent of posture. Note, previous work did not account for the factor of ½ when calculating VO

_{2AO} (Equation (4)), thus our VO

_{2AO} values were half those previously reported. All measures of metabolism achieved excellent repeatability, as determined by the intraclass correlation coefficient >0.75, and average coefficients of variation were <0.27 (

Table 3). ICCs were highest and CVs were lowest for the NIRS-only measures at 3.5 cm, presumably because the variable response of adipose tissue to occlusion is minimized [

21]. Because the sensor was repositioned in between each epoch, this result suggests that sensor pressure and positioning have minimal influence on our resultant estimation, and this high repeatability agrees well with other publications [

15,

18,

21,

22,

24].

To our knowledge, this work is the first to investigate the relationship between NIRS + DCS-measured VO

_{2i} and the NIRS-measured VO

_{2VO} and VO

_{2AO} in the muscle. Despite the lack of previous validation, VO

_{2i} is often employed as a measure of oxygen metabolism in the muscle. Typically VO

_{2i} is first calibrated into physiological units using VO

_{2AO} (or, in theory, VO

_{2VO}) [

15,

16]. However, we found no significant correlation between VO

_{2i} and VO

_{2AO} (

p = 0.15,

Figure 3A), nor between VO

_{2i} and VO

_{2VO}, (

p = 0.55,

Figure 3B). Reasons for the lack of correlation may include inter-participant variations in the assumed fraction of venous blood volume in the interrogated tissue (γ, Equation (3)), blood hemoglobin concentration (Hgb, Equation (3)), and/or differences in depth sensitivity between VO

_{2i} and VO

_{2AO}/VO

_{2VO} estimations. VO

_{2i} scales proportionally with Hgb and inversely with γ (Equation (6)); significant inter-participant variations in either Hgb or γ would lead to errors in VO

_{2i} and could, in turn, weaken correlations with VO

_{2AO}/VO

_{2VO}. Alternatively, VO

_{2i} and VO

_{2AO}/VO

_{2VO} may sample different depths in the tissue. While depth sensitivity of all diffuse optical modalities scales roughly with source-detector separation, the exact depth sensitivity of each measure depends on tissue geometry, optical properties, and the optical modality (i.e., NIRS, DCS). Given that oxygen metabolism of adipose tissue is significantly less than muscle [

21], and that the thickness of the adipose tissue layer in the MG can be appreciable and can vary widely between participants (ranging from roughly 0.1–2 cm [

34]), differences in depth sensitivity between VO

_{2i} and VO

_{2AO}/VO

_{2VO} could lead to different fractions of signal that arises from adipose tissue versus muscle. Regardless of the reason, the correlation between VO

_{2i} and VO

_{2AO}/VO

_{2VO} shows that the variability in the calibration coefficient between VO

_{2i} and VO

_{2AO}/VO

_{2VO} is substantial across participants. Thus, it is preferrable to calibrate VO

_{2i} prior to every monitoring session. Important future work is needed to compare VO

_{2i}/VO

_{2AO}/VO

_{2VO} against other gold standard modalities like PET or MRI.

Of note, we also investigated the relationship between VO

_{2AO} and VO

_{2VO}. We found VO

_{2VO} was significantly correlated with VO

_{2AO} (

p = 0.01,

Figure 2A), as has been observed in the forearm [

19,

22]. However, the agreement between the two methods was poor (CCC = 0.40), with a significant positive bias. This lack of agreement may be due to the fact that the venous occlusion was always performed prior to the arterial occlusion within each epoch. Because participants were permitted to readjust their legs between epochs, it is possible that 2 min was not enough time to return to a resting level of oxygen metabolism before the venous occlusion. Alternatively, because participants often reported the desire to move their legs to restore circulation at the end of each epoch, it is possible that metabolism dropped over the course of the epoch in response to restricted perfusion. Previous work found a similar reduction in VO

_{2VO} with successive venous occlusions [

22]. To avoid any potential effect of occlusion order, future work should randomize the order of venous and arterial occlusions. Nevertheless, given the moderate correlation between VO

_{2AO} and VO

_{2VO}, these results suggest that venous and arterial occlusion measurements in the MG at these source-detector separations may not be interchangeable.

Finally, we also quantified and compared NIRS- and DCS-measured blood flow (BF and BFI, respectively). Our NIRS-measured blood flow ranged from 0.179 to 1.049 mL/min/100 g, which is lower than previously reported in the MG while supine (0.46 to 1.36 mL/min/100 g) [

15]. This discrepancy is consistent with the known postural dependence of muscle perfusion [

35]. While VO

_{2i} did not correlate with VO

_{2AO} or VO

_{2VO}, DCS-measured BFI was indeed correlated with NIRS-measured BF (

p = 0.06,

Figure 1). Previous work found a similar correlation between BFI averaged during the venous occlusion and BF in the forearm [

33]. In the MG, we found BFI averaged both prior to and during the venous occlusion were correlated with BF, suggesting that blood flow quantified during a venous occlusion reflects the value of blood flow in a non-occluded state. Additionally, BFI had good repeatability (ICC = 0.62, mean CV = 0.25), which further supports the notion that BFI could potentially be used as a surrogate for BF to circumvent the need for venous occlusions to estimate blood flow.

## 4. Materials and Methods

Nine healthy, ambulatory participants >18 years were recruited. Subjects were excluded for participation if they had a history of lower extremity joint pain, contractures, major sensory deficits, evidence of orthopedic, muscular, or physical disability, evidence of vestibular, auditory, or proprioceptive impairment, orthostatic hypotension, and/or any neurological insult. All experiments were approved by the Emory University Institutional Review Board. All participants gave informed written consent before participating.

The experimental protocol is outlined in

Figure 4. A pressure occlusion tourniquet (Zimmer ATS 2000 Tourniquet System) was affixed to the thigh of the dominant leg just above the knee. Participants were seated with their dominant leg and foot weight supported, and they were instructed to relax to limit hyperextension/enforced extension of the knee for the duration of the protocol. First, baseline measures of resting-state wavelength-dependent absorption and reduced scattering coefficients (μ

_{a}(λ) and μ

_{s}’(λ), respectively) were made with NIRS by gently holding an optical sensor over the outstretched medial gastrocnemius (MG). Measurements were repeated 3 times, repositioning slightly between each measure to account for local inhomogeneities in the underlying tissue. Next, the optical sensor was secured to the MG using a flexible rubber band. Care was taken to ensure adequate sensor contact with the skin without applying excessive pressure that could induce significant hemodynamic perturbations [

36,

37]. Continuous monitoring of dynamic changes in hemoglobin concentration (NIRS) and blood flow index (DCS) was performed during a 2-min baseline, a 30-s venous occlusion (VO, 90 mmHg tourniquet pressure), a 2-min recovery, a 30-s arterial occlusion (AO, 250 mmHg tourniquet pressure [

15]), and a 5-min recovery period. The sensor was then removed, and participants were allowed to move their leg. This entire protocol was then repeated 5 times for a total of 5 arterial and 5 venous occlusions per measurement session. Upon completion of these 5 epochs, a final NIRS measure of resting-state μ

_{a} (λ) and μ

_{s}’(λ) were made by again gently manually holding the sensor over the MG and repositioning 3 times.

All optical data were acquired using a customized frequency domain NIRS oximeter (Imagent, ISS, Champaign, IL, USA) and an in-house-built DCS system. The NIRS device utilized eight source wavelengths (690, 730, 750, 775, 785, 800, 825, and 830 nm) modulated at 110 MHz and four photomultiplier tube detectors with gain modulation of 110 MHz + 5 kHz to achieve heterodyne detection at 5 kHz. The DCS device used an 852 nm long-coherence-length laser source (iBeam Smart, TOPTICA Photonics, Farmington, NY, USA), two four-channel single photon counting modules (SPCMAQ4C-IO, Perkin-Elmer, Montreal, QC, Canada), and an eight-channel hardware correlator (Flex05-8ch, correlator.com, NJ, USA). NIRS and DCS data were acquired simultaneously (21 Hz NIRS, 1 Hz DCS) by placing an 842 nm short pass filter (FF01-842/SP-32-D, Semrock, Rochester, NY, USA) in front of each NIRS detector to mitigate crosstalk of the DCS source on the NIRS detectors.

The participant interface consisted of a custom-made optical sensor containing five source-detector pairs-four for NIRS (2.0, 2.5, 3.0, and 3.5 cm) and one for DCS (2.5 cm). These separations were chosen to maximize depth penetration while still maintaining adequate signal-to-noise ratio. For NIRS, we used customized 2.5 mm fiber bundles for both source and detection (50 μm multimode fibers, NA 0.66, FTTIIG23767, Fiberoptics Technology, Pomfret, CT, USA). For DCS, we used a 1-mm source fiber (FT1000EMT, NA 0.39, ThorLabs, Newton, NJ, USA) and seven single-mode detector fibers (780HP, Thorlabs, Newton, NJ, USA) bundled together at the 2.5-cm separation. The detected autocorrelation curves from these seven detectors were averaged to improved signal-to-noise ratio. All fibers were embedded in a rigid black 3D printed holder.

The data analysis pipeline is outlined in

Figure 5 and described in depth in the following sections. Representative data obtained via this analysis pipeline is shown in

Figure 6. Measures of participant-specific, wavelength-dependent optical properties (μ

_{a}(λ) and μ

_{s}’(λ)) were estimated from multi-distance measures of AC attenuation and phase shift using the semi-infinite solution to the photon diffusion equation [

38] (

Figure 5A). The measured μ

_{s}’(λ) were fit to an empirical power law relationship

${\mathrm{A}\mathsf{\lambda}}^{-\mathrm{b}}$, where

$A$ is a scaling factor and

$b$ is the scattering power. The measured μ

_{a}(λ) were fit to the hemoglobin spectrum to estimate resting-state measures of oxy- and deoxy-hemoglobin concentrations (HbR and HbO, respectively), which were used to derive total hemoglobin (HbT = HbO + HbR), difference in hemoglobin (HbD = HbO − HbR), and tissue oxygen saturation (StO

_{2} = HbO/HbT * 100%). Water concentration was assumed to be 75%. We also estimated the wavelength-dependent differential pathlength factor (DPF(λ)) that accounts for the increase in photon pathlength due to multiple scattering events using the following formula [

39]:

These measurements were made at baseline (3 repetitions), during the 2-min baseline prior to venous occlusion at the start of each epoch, and upon completion of the 5 epochs (3 repetitions) for a total of 11 values that were averaged to yield a mean resting-state estimate of of μ_{a}(λ), μ_{s}’(λ), DPF(λ), A, b, HbO, HbR, HbT, HbD, and StO_{2}, denoted with subscript 0.

As outlined in

Figure 5B and shown in

Figure 6, continuous monitoring of dynamic changes in hemoglobin concentration with NIRS during occlusion epochs were estimated at each source-detector separation using the modified Beer–Lambert Law:

where AC(λ, r, t) is the AC amplitude of detected light measured at wavelength λ, source-detector separation, r, and time t; AC

_{0}(λ, r) is the mean AC amplitude measured at wavelength λ during a 1-min baseline at the beginning of each epoch prior to the venous occlusion; DPF(λ) is the wavelength-dependent differential pathlength factor obtained as described above (Equation (1)). Changes in hemoglobin concentrations (ΔHbO(r, t) and ΔHbR(r, t)) were derived from Δμ

_{a}(λ, r, t) at 690, 785, and 825 nm. Continuous measures of HbO(r, t), HbR(r, t), HbT(r, t), HbD(r, t), and StO

_{2}(t) were then quantified from these changes and the resting-state estimations obtained as described above (e.g., HbR(r, t) = HbR0 + ΔHbR(r,t)). Additionally, we estimated a continuous measure of oxygen extraction fraction (OEF):

Here, SaO

_{2} is the arterial oxygen saturation, and γ is the fraction of blood volume within the venous compartment of the tissue interrogated with our sensor [

26]. We assumed a constant SaO

_{2} of 100% and γ of 0.675 for all participants [

16,

26].

Continuous monitoring of dynamic changes in blood flow with DCS during occlusion epochs was estimated by fitting the measured intensity autocorrelation curves, g

_{2}(τ,t), for a blood flow index (BFI(t)) using the semi-infinite solution to the correlation diffusion equation and incorporating the measured resting-state μ

_{a0} and μ

_{s}’

_{0} extrapolated for 852 nm [

38]. Fits were constrained to g

_{2}(τ,t) > 1.05. Data for a given detector were discarded if the detected photon count rate was less than 5 kHz.

Muscle oxygen metabolism (VO

_{2}) was measured with three distinct approaches (

Figure 5C and

Figure 6). The first approach, which we dub VO

_{2AO}, estimates VO

_{2} (in units of mLO

_{2}/min/100 g) using the rate of hemoglobin deoxygenation during arterial occlusion [

15,

16,

17,

19,

20,

21,

22,

23]:

Here

$\frac{\mathrm{dHbD}\left(\mathrm{r},\mathrm{t}\right)}{\mathrm{dt}}$ is the slope of HbD(r,t) versus time during the arterial occlusion estimated via linear regression using fitlm in MATLAB 2020b. The factor of ½ accounts for the fact that HbD represents the difference between 2 slopes [

40]. The 4 accounts for the 4:1 ratio of oxygen to hemoglobin, MW

_{O2} is the molecular weight of oxygen (32 g/mol), ρ

_{O2} is the density of oxygen (1.429 g/L), and ρ

_{tissue} is the assumed density of the muscle tissue (1.04 kg/L) [

16].

The second approach, which we dub VO

_{2VO}, relates oxygen metabolism to the increase in deoxyhemoglobin during the venous occlusion [

18,

19,

22,

24,

26]:

Here

$\frac{\mathrm{dHbR}\left(\mathrm{r},\mathrm{t}\right)}{\mathrm{dt}}$ is the slope of HbR(r,t) versus time during the venous occlusion estimated via linear regression. This approach assumes that the arterial input is fully saturated (i.e., SaO

_{2} = 100%) [

16] such that its contribution to the rate of change of HbR is negligible. This linear regression was applied over two separate windows. The first window extended from the start of cuff inflation to 25 s after the start of inflation to account for individuals who had an immediate hemodynamic response to the venous occlusion and thus limit potential accumulation of blood in the venous compartments [

23]. The second window extended from when the cuff pressure reached 90 mmHg until the release of pressure to account for individuals who did not have an immediate hemodynamic response suggesting that the venous occlusion was not complete until the desired pressure of 90 mmHg was reached. The window with the greater slope was used to estimate VO

_{2VO} for that epoch.

The third approach, which we dubbed VO

_{2i}, combined the oxygen extraction fraction measured by NIRS with the blood flow index measured by DCS to estimate an index of metabolism using Fick’s law [

15,

16,

26,

27]:

Here Hgb is the blood hemoglobin concentration (assumed to be 14.1 g/dL) [

16], ρ

_{tissue} is the assumed density of the muscle tissue (1.04 kg/L) [

16], and A is the amount of oxygen that can bind to hemoglobin (1.34 mLO

_{2}/g Hb). This approach provides a continuous measure of metabolism without the need for vascular occlusions. To compare VO

_{2i}(r,t) with VO

_{2AO}(r) and VO

_{2VO}(r), VO

_{2i}(r,t) was averaged over a 15-s period just prior to the arterial and venous occlusions, respectively.

The venous occlusion also allows us to estimate muscle blood flow (BF) using the mean rate of increase in total hemoglobin concentration during occlusion [

15,

16,

18,

24,

33]. We capitalized on this additional information by comparing BF to BFI measured by DCS. We estimated BF using the following formula:

Here MW

_{Hb} is the molecular weight of hemoglobin (64.458 g/mol) [

41] and

$\frac{\mathrm{dHbT}\left(\mathrm{r},\mathrm{t}\right)}{\mathrm{dt}}$ is the slope of HbT(r, t) versus time estimated via linear regression. Similarly to the calculation of VO

_{2VO}, the linear regression was applied over two separate windows and the window with the greatest slope was used to estimate BF for that epoch. To compare BF(r) with BFI, BFI(t) was averaged over a 15 s period just prior to the venous occlusion, as well as during the full occlusion.

Data were reported as mean ± standard deviation unless otherwise stated. A Wilcoxon rank sum test was employed to test for sex differences in each measured parameter. A Wilcoxon signed rank test was used to test for differences in BF, VO

_{2AO}, and VO

_{2VO} between source-detector separations. Linear mixed effect models were used to examine linear relationships between VO

_{2i} and VO

_{2AO}/VO

_{2VO}, between BFI and BF, and between VO

_{2AO} and VO

_{2VO}. In these models, because multiple measurements were made on each subject, a subject-specific random slope was modeled in addition to a fixed effect intercept and slope. The significance of between-subject variation in the slope parameter was assessed by examining the significance of the random slope parameter at the 0.1 level of significance. This threshold was chosen based on the small sample size and the number of replicates. After adjusting for repeated measurements and between-subject variation, the fixed effect intercept and slope were examined. Further, we estimated a correlation coefficient (R) to aid in the interpretation of the strength of the linear relationship of the variables of interest in the presence of repeated measures [

42]. For the relationship between VO

_{2AO} and VO

_{2VO}, we also used Bland–Altman plots to graphically assess the agreement between the two variables [

43] and Lin’s concordance correlation coefficient (CCC) to quantify this agreement. The CCC is the product of Pearson’s R and a bias correction factor that reflects the degree that the linear association between two variables differs from 45 deg through the origin. Finally, coefficient of variation (CV, defined as the ratio of the standard deviation to the mean across multiple measurements within a single participant) and an intraclass correlation coefficient (ICC) [

44,

45] were used to assess intra-participant repeatability of all metabolism and blood flow measures, as well as resting-state HbT and StO

_{2}. To estimate ICC, we used a two-way mixed effect, absolute agreement model that assumes experimenters remain fixed across epochs and treats intra-participant measurements as random samples. Typically, ICC values greater than 0.75 are classified as excellent repeatability, ICC between 0.6 and 0.74 are classified as good repeatability, between 0.4 and 0.59 are classified as fair, and less than 0.4 are classified as poor reliability [

45].