2.1.

Diffuse Correlation Spectroscopy

DCS is a noninvasive optical method that quantitatively measures tissue BF using speckle correlation techniques.^{39,40,42–46} Herein, aspects of this technique relevant to our study are highlighted; for additional details, the reader should consult comprehensive reviews and papers.^7,36–40 DCS measures the temporal intensity fluctuations of coherent near-infrared (NIR) light that has multiply scattered from moving red blood cells in tissue.^7,36,39,40 These fluctuations are quantified by computing the temporal intensity autocorrelation function of the collected light, whose transport through tissue is mathematically described by the correlation diffusion equation. ^39,40 The solution to the correlation diffusion equation depends on several parameters including tissue geometry, tissue absorption and reduced scattering coefficients (${\mu }_a$, ${\mu }_s^{\prime }$), and a tissue BFI [${\mathrm{cm}}^2/\mathrm{s}$]. In practice, BFI can be broken down further; it is the product of an effective diffusion coefficient ($D_B$) that characterizes red blood cell motion and another parameter ($\alpha$) that is proportional to the concentration of moving red blood cells. Note that the correlation diffusion equation solution has been compared to data across a wide range of sample length scales and tissue types, and it has been found to best match the measured signals when the mean-square displacement of the red blood cells is modeled diffusively.³⁶

To quantify BF with DCS, the measured intensity autocorrelation function from muscle is fit to the solution of the correlation diffusion equation in the semi-infinite geometry; from this fit, we extract BFI.^39,40,53,54 The tissue absorption and reduced scattering coefficients are required inputs for this fit. For the present study, we measured each subject’s baseline tissue absorption (${\mu }_{a0}$) and baseline reduced scattering (${\mu }_{s0}^{\prime }$) coefficient with a frequency-domain diffuse optical spectroscopy device (Sec. 2.4). Subsequent variations in tissue absorption with respect to baseline during the monitoring session were obtained from DOS intensity changes using the semi-infinite modified Beer-Lambert law^55,56 (see Sec. 2.5), with tissue scattering assumed to remain constant.

Although the BFI has nontraditional units for flow, we and others have shown that BFI is proportional to true tissue BF.^8,47–51,57

From Eq. (1), it is apparent that fractional/relative changes of tissue blood flow (rBF) compared to a baseline blood flow ${\mathrm{BF}}_0$ can be derived from corresponding changes in BFI, i.e.,

2.2.

Venous-Occlusion Diffuse Optical Spectroscopy

DOS is a well-known technique that uses diffuse NIR light to monitor tissue oxygen saturation and blood volume.^51,58,59 The technique of VO-DOS employs DOS to measure changes in blood volume during a venous occlusion, and this information permits estimation of absolute muscle BF.^26–35 The venous occlusion of skeletal blood vessels is made with a blood pressure cuff set above venous pressure, but below arterial pressure (e.g., the blood pressure cuff is inflated to $\sim 50\mathrm{mm}\mathrm{Hg}$). Practitioners assume that during such an occlusion, venous outflow draining the muscle is reduced to zero, but arterial inflow, accommodated by passive expansion of the muscle vasculature, is initially unaltered.

With zero outflow and constant inflow, the muscle blood volume initially increases at a constant rate, and the tissue BF in this case is readily modeled as being proportional to the rate of increase in blood volume. In practice, we measure the rate of increase in the concentration of total hemoglobin ([HbT]) with DOS, which is proportional to the rate of increase in blood volume. The tissue BF is then given by²⁹

2.3.

Instrumentation

For subject monitoring during arm-cuff occlusion experiments (Sec. 2.4), we utilized a custom-designed hybrid optical instrument that could continuously obtain continuous-wave DOS and DCS data (Fig. 1); the instrument is described in detail elsewhere.⁶⁰ Briefly, the DOS measurements employed five laser diodes (685, 730, 785, 808, and 830 nm; OZ Optics, Ottawa, Canada) coupled to an optical switch (DiCon Fiberoptics Inc., Richmond, California) to sequentially illuminate a single tissue location (S in Fig. 1) via a multimode fiber ($940\mu \mathrm{m}$ core diameter; OZ Optics). Multiply scattered light emerging at tissue location D in Fig. 1 was detected with a multimode fiber bundle (3.5 mm active area diameter; Dolan-Jenner Industries, Boxborough, Massachusetts) and was coupled to a photomultiplier tube (R928, Hamamatsu, Bridgewater, New Jersey).

Fig. 1

Schematic of the hybrid instrument for diffuse correlation spectroscopy (DCS) monitoring of blood flow and diffuse optical spectroscopy (DOS) monitoring of tissue total hemoglobin in the forearm. The optical probe head is comprised of four optical fibers that form one DCS source–detector separation pair (FS-FD, 2.5 cm) and one DOS source–detector separation pair (S-D, 2.5 cm). As a rough rule of thumb, the approximate depth of measurement below the skin is one third to one half the source-detector separation, i.e., 1.25 cm (for a more precise relation, see Ref. 61). A tourniquet system (Zimmer Inc., Warsaw, Indiana) is utilized to inflate an arm cuff to 50 mm Hg (shown in green) for venous occlusion and 180 mm Hg (shown in red) for arterial occlusion.

For DCS measurements, a continuous-wave, long-coherence-length, fiber-coupled laser (785 nm, DL785-100-SO, CrystaLaser Inc., Reno, Nevada) illuminated the tissue at location FS in Fig. 1 via a multimode optical fiber (200 μm diameter; OZ Optics). Detected light emerged at location FD in Fig. 1, and a single-photon counting avalanche photodiode (SPCM-AQ4C, Excelitas, Quebec, Canada) was coupled to this output light via a single-mode fiber ($5\mu \mathrm{m}$ diameter; OZ Optics). A commercial multi-tau hardware correlator (Correlator.com, Bridgewater, New Jersey) computed the intensity autocorrelation function of the detected DCS light in real time. For the DCS and DOS measurements, the source–detector separation was 2.5 cm, and the temporal resolutions were 2.5 and 3 s per measurement, respectively.

As an alternative to venous-occlusion calibration, we aimed to derive a population-averaged calibration coefficient [i.e., $\gamma$ in Eq. (1)] to convert DCS BFI directly to absolute BF. This idea was stymied, in part, by a mediocre correlation between absolute BF and BFI. We later realized that this mediocre correlation was in large part due to errors in our assumed baseline tissue optical properties for the subjects. To ameliorate these errors, we utilized a frequency-domain ISS Imagent (ISS Medical, Champaign, Illinois) for subject-specific measurement of baseline absolute absorption and reduced scattering coefficients at 830 and 785 nm; this frequency-domain spectroscopy measurement was carried out many days after the cuff-occlusion experiments on the same subjects (Sec. 2.4).

2.4.

Subjects and Protocols

Ten healthy adult volunteers (six men, four women, age $29.5\pm 3.8$) participated in this study after giving their written informed consent. All study procedures were approved by the institutional review board of the University of Pennsylvania. Each subject came to the University of Pennsylvania for four visits.

In the first visit, the subject lay supine with his/her right arm extended in a comfortable bed (note that all subjects measured in the study were right-handed, hence the right arm was their dominant arm). The optical probe was secured to the subject’s right forearm with an elastic neoprene strap at position A indicated in Fig. 2(b). A blood pressure cuff was placed around the right bicep. Two cuff ischemia trials were carried out in series; for the arterial occlusion (cuff ischemia) measurement, the blood pressure cuff was inflated to 180 mm Hg [indicated in red in Fig. 2(a)]. In the first trial, measurements of [HbT] were utilized to estimate absolute BF with the VO-DOS method at the baseline and postarterial-occlusion intervals [indicated in green with cuff pressure of 50 mm Hg in Fig. 2(a)]. In the second trial, the DCS BFI was continuously monitored. Since the absolute BF was measured twice at site A (baseline and postarterial-occlusion measurement), we use A to denote the baseline measurement and ${\mathrm{A}}^{\prime }$ to denote the postarterial-occlusion measurement. Thus, for each venous-occlusion measurement, a DCS calibration coefficient [$\gamma$; see Eq. (1)] is determined. This information enables us to assess the variability in $\gamma$ over a range of BF levels.

Fig. 2

Schematic of experimental protocols and measurement sites. (a) Visit 1, visit 2, and visit 3 measurement protocols for each subject. The blood pressure cuff is inflated to 50 mm Hg (shown in green) for 1 min to create a venous occlusion, and it is inflated to 180 mm Hg (shown in red) for 3 min to create an arterial occlusion. (b) Schematic of the four different probe positions (A, B, C, and D) for blood flow measurements on the forearm. In visit 1, A and ${\mathrm{A}}^{\prime }$ denote the baseline and postarterial-occlusion measurements, respectively. The visit 3 protocol is carried out three times, i.e., at positions B, C, and D.

The reproducibility of the cuff ischemia BF response between trials 1 and 2 in each subject was tested with DCS in a second visit (about two months later). As with the first visit, there were two cuff ischemia trials, and DCS BFI monitoring was done for both of them (i.e., VO-DOS measurements were not done).

During the third visit (almost a week later), we examined the variability in DCS calibration coefficient ($\gamma$) across multiple tissue sites in each subject. While the subject lay supine, the optical probe was attached to the right forearm [B in Fig. 2(b)] and a set of baseline VO-DOS and DCS measurements of BF were carried out sequentially [Fig. 2(a)]. To determine the effect of slight probe positional changes that could occur from subject motion (e.g., exercise), the probe was removed and reattached to roughly the same position on the forearm [C in Fig. 2(b)], and the VO-DOS/DCS measurements of BF were repeated to derive another $\gamma$. Note that comparison of $\gamma$ measurements at sites B and C to site A from visit 1 permits assessment of intrasubject $\gamma$ variability across different days. Finally, the probe was attached to a corresponding position on the subject’s left forearm [D in Fig. 2(b)] for another set of VO-DOS and DCS measurements (i.e., to examine variability between the left and right forearm).

During the fourth visit (about two months later), the baseline tissue optical properties (${\mu }_{a0}$, ${\mu }_{s0}^{\prime }$) on the right arm and left arm of each subject [i.e., at indicated positions in Fig. 2(b)] were measured at 830 and 785 nm using a multiple-distance frequency-domain technique.^62,63 Specifically, a commercial ISS Imagent connected to a multiple-distance probe (ISS Medical, $\rho =2$, 2.5, 3, 3.5 cm) was utilized. The instrument was calibrated using a solid silicon phantom (ISS Medical) with known optical properties^62,63 before the arm measurements. As we will show, these subject-specific measurements of absolute tissue optical properties substantially improved the correlation between absolute BF and DCS BFI. Thus, for applications where it is desirable to use the DCS BFI as a measure of absolute BF (i.e., without venous-occlusion calibration), it is optimal to measure absolute tissue optical properties concomitantly with DCS using a frequency- or time-domain DOS instrument.

2.5.

Data Analysis: Measurement of Blood Flow and Diffuse Correlation Spectroscopy Calibration Coefficient

As discussed in Sec. 2.2, VO-DOS BF is derived from the rate of change of [HbT] with respect to time following the onset of venous occlusion. The temporal changes in [HbT] are obtained from time-dependent multispectral DOS intensity measurements via the well-known semi-infinite medium modified Beer-Lambert law.^36,55,56 The semi-infinite medium differential path lengths utilized in the modified Beer-Lambert law were computed from the photon diffusion model,⁶⁴ using subject-specific estimates of baseline tissue absorption and reduced scattering coefficients.

To compute absorption at all five wavelengths (685, 730, 785, 808, and 830 nm), the baseline tissue oxyhemoglobin and deoxyhemoglobin concentrations were obtained first from the frequency-domain baseline tissue absorption measurements at 785 and 830 nm³⁶ (assuming 70% muscle water volume fraction⁶³). The average measured tissue optical properties at 785 and 830 nm, and the average computed tissue oxygen saturation and total hemoglobin, are shown in Table 1. These oxyhemoglobin and deoxyhemoglobin concentrations were used to compute tissue absorption at the other three wavelengths.³⁶ For baseline tissue scattering, we found the measured reduced scattering coefficients at 785 and 830 nm to be comparable. Therefore, the average of the two measurements was used as the baseline tissue scattering coefficient for all five wavelengths.

Table 1

Measured tissue optical properties in right and left arm (results reported as mean±SD; these averages are across the study population (N=10).

Figure 3 shows a temporal trace of [HbT] during venous occlusion in a representative subject. Absolute BF is obtained via Eq. (3), where the rate of change, $d[\mathrm{HbT}]/dt$, was estimated from the slope of the linear regression line fit to [HbT] during venous occlusion (e.g., solid red line in Fig. 3).

Fig. 3

Temporal [HbT] trace during baseline venous occlusion measurement of a healthy subject. $T_{\text{fit}}$ is the time interval (shaded green region) used for the linear regression fit of [HbT] (red solid line) during venous occlusion (VO).

Ideally, [HbT] will increase linearly following the onset of venous occlusion. In practice, however, the inflation of the arm cuff to 50 mm Hg is not instantaneous. Thus, the rate of increase in [HbT] is nonlinear at the earliest times, and then it settles to a steady rate of increase obtained at full cuff inflation. Eventually, the vasculature in the muscle approaches maximal dilation, resulting in an increase in venous blood pressure that reduces arterial inflow. At this point, [HbT] starts to level off toward a maximal value as arterial inflow drops to zero. As shown in Fig. 3, blood flow is determined from the slope of [HbT] during the temporal interval $T_{\text{fit}}$, just after the pressure is increased and where the rate of increase is linear. (We note that for some subjects, the linear regime for fitting had fewer data points than in Fig. 3, leading to greater experimental uncertainty.) This procedure provides a quantitative estimate of absolute muscle BF just prior to each venous occlusion performed. For example, in visit 1 (see Fig. 2), two venous occlusions were done, enabling the measurement of baseline absolute BF, ${\mathrm{BF}}_0$, and measurement of the peak BF achieved from the hyperemic overshoot following cuff ischemia, ${\mathrm{BF}}_{\mathrm{os}}$.

These measurements of absolute BF with VO-DOS are then combined with corresponding measurements of DCS BFI (Sec. 2.1) to calculate the DCS calibration coefficient, $\gamma$, via Eq. (1). Continuing with the visit 1 example, the baseline DCS BFI, ${\mathrm{BFI}}_0$, was obtained by averaging the measured BFI over times corresponding to baseline temporal fitting interval, $T_{\text{fit},0}$, in cuff ischemia trial 1 (i.e., that used for the baseline VO-DOS measurement of ${\mathrm{BF}}_0$, see Fig. 2). Similarly, ${\mathrm{BFI}}_{\mathrm{os}}$ was obtained by averaging the measured BFI over the times corresponding to overshoot fitting interval, $T_{\text{fit},\mathrm{os}}$, used for the VO-DOS measurement of ${\mathrm{BF}}_{\mathrm{os}}$. Two estimates of $\gamma$ are, therefore, obtained from visit 1: ${\gamma }_{\mathrm{A}}={\mathrm{BF}}_0/{\mathrm{BFI}}_0$ and ${\gamma }_{\mathrm{A}}={\mathrm{BF}}_{\mathrm{os}}/{\mathrm{BFI}}_{\mathrm{os}}$.

During a separate visit on a different day (visit 3), three estimates of $\gamma$, i.e., ${\gamma }_{\mathrm{B}}$, ${\gamma }_{\mathrm{C}}$, and ${\gamma }_{\mathrm{D}}$, were obtained from sequential baseline VO-DOS and DCS muscle measurements acquired at positions B, C, and D indicated in Fig. 2(b). Positions B and C on the right arm are roughly the same and similar to position A (i.e., the probe was removed from position B and then reattached in roughly the same position, C); position D is at the corresponding location on the left arm.

3.1.

Venous-Occlusion Diffuse Optical Spectroscopy Measures Resting Skeletal Muscle Blood Flow Accurately

We first establish that our VO-DOS protocol described in Sec. 2.5 produces reasonable estimates of resting skeletal muscle BF. For each subject, we acquired three measurements of resting skeletal muscle BF on the right (dominant) forearm [see Fig. 2(b)]. On average, across 30 VO-DOS measurements [$(3\text{positions})\times (10\text{subjects})$], the resting forearm muscle BF ($\text{mean}\pm \mathrm{SD}$) in the dominant arm was ${\mathrm{BF}}_0=1.53\pm 0.55\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$. The resting BF on the left (nondominant) arm was $1.61\pm 0.82\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$. The average resting BF across both right and left arms was $1.56\pm 0.54\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$. These measurements of resting BF in the forearm are consistent with previously published findings, which are summarized in Table 2.

Table 2

Comparison of our venous-occlusion diffuse optical spectroscopy (VO-DOS) measurements of resting blood flow in the forearm (bottom row) to other forearm resting blood flow estimates in the literature measured with VO-DOS and with venous-occlusion strain-gauge plethsmography (VO-SGP) (results reported as mean±SD; n/a, not applicable; N, number of subjects).

3.2.

Cuff Ischemia due to Arterial Occlusion Produces a Reproducible Response

Since we do not determine flow with simultaneous measurements of VO-DOS and DCS, we performed a second experiment to ensure that BF measured with the arterial arm-cuff ischemia model is repeatable (see visit 2 in protocol, Fig. 2). Figure 4 shows representative temporal dynamics of BFI estimated with DCS from a healthy male subject during two sequential cuff ischemia experiments. During the artery occlusions (denoted as AO1 and AO2), DCS-BFI decreases by $\sim 95\%$, and then it rapidly reaches a peak hyperemic overshoot above baseline following cuff deflation. The hemodynamics of the two arterial occlusions were characterized by the magnitudes of the peak hyperemic overshoot, $F_{\mathrm{AO}1}$ and $F_{\mathrm{AO}2}$, and the times to reach the peak overshoot, $T_{\mathrm{AO}1}$ and $T_{\mathrm{AO}2}$ [see Fig. 4(b), insets].

Fig. 4

Reproducibility of blood flow response following arm-cuff ischemia. (a) Protocol of the DCS measurement for assessing reproducibility of cuff ischemia response in visit 2. (b) Representative changes in DCS blood flow index (BFI) during two consecutive artery occlusions. These responses are characterized by their peak hyperemic magnitudes, $F_{\mathrm{AO}1}$ and $F_{\mathrm{AO}2}$, and the time durations from point of cuff deflation to hyperemic peak, $T_{\mathrm{AO}1}$ and $T_{\mathrm{AO}2}$ (indicated in insets).

In the 10 healthy subjects, the peak BF overshoot ($F_{\mathrm{AO}1}$, $F_{\mathrm{AO}2}$) and the time-to-peak overshoot ($T_{\mathrm{AO}1}$, $T_{\mathrm{AO}2}$) for the two arterial occlusions are in excellent agreement (Fig. 5). Figure 5(a) shows the comparison of the peak BF overshoot of two arterial occlusions, plotting the peak BF overshoot of the second arterial occlusion on the vertical axis against the peak BF overshoot of the first arterial occlusion on the horizontal axis. Figure 5(b) shows the analogous comparison of the time-to-peak overshoot of the two arterial occlusions. Both plots are highly linear ($R^2=0.99$) with a slope close to unity (0.98 for peak overshoot, 1.00 for time-to-peak). Thus, we conclude the BF response from sequential cuff ischemia experiments is reproducible. Interestingly, although the hyperemic response is reproducible for a single subject, its magnitude is highly heterogeneous across different subjects (Fig. 5). Similar heterogeneous responses to cuff ischemia were observed in the leg across both healthy subjects and patients with peripheral artery disease.^65,66

Fig. 5

Comparison of peak blood flow overshoot [$F_{\mathrm{AO}1}$, $F_{\mathrm{AO}2}$, (a) and (b)] and time-to-peak overshoot [$T_{\mathrm{AO}1}$, $T_{\mathrm{AO}2}$, (c) and (d)] of two artery occlusions in healthy adult subjects ($N=10$). The arterial occlusions, respectively, are denoted as AO1 and AO2. The hemodynamics of the two arterial occlusions were characterized by the magnitude of their peak hyperemic overshoot ($F_{\mathrm{AO}1}$, $F_{\mathrm{AO}2}$) and their time to reach the peak overshoot ($T_{\mathrm{AO}1}$, $T_{\mathrm{AO}2}$). Bland-Altman plots are shown in (b) and (d); the solid horizontal line indicates the mean difference between the two parameters computed across the study population, which is not significantly different than zero. The dotted lines indicate the 95% confidence interval (CI) limits for agreement.

3.3.

Agreement of Blood Flow Changes Measured by Diffuse Correlation Spectroscopy and Venous-Occlusion Diffuse Optical Spectroscopy

One aim of this paper is to compare BF dynamics during arm-cuff ischemia measured with VO-DOS and with DCS. Accordingly, in another set of measurements on the same subjects (visit 1 in Fig. 2), two sequential arterial occlusions were carried out wherein the BF response in the first occlusion (trial 1) was measured with VO-DOS, and the BF response in the second occlusion (trial 2) was measured with DCS [Fig. 6(a)]. Since the reproducibility of the cuff ischemia response has been validated (Sec. 3.2), it is reasonable to compare the BF dynamics measured with VO-DOS to the dynamics measured with DCS. Figure 6(b) displays the temporal traces of [HbT] and BFI during trials 1 and 2, respectively, in a representative healthy male subject. As before, the BF response was characterized by comparing the ratio of BF during postischemic hyperemia to a baseline value.

Fig. 6

Time traces of HbT and BFI during the entire measurement (visit 1). The best linear fit lines (black solid lines) are used for calculation of ${\mathrm{BF}}_0$ and ${\mathrm{BF}}_{\mathrm{os}}$. Green shaded and red shaded regions represent the VO and arterial occlusion (AO) periods, respectively. The purple shaded regions indicate the fit interval for determination of absolute blood flow (b) and the corresponding intervals for BFI averaging (c). For the representative subject, the baseline and hyperemia blood flows were estimated to be ${\mathrm{BF}}_0=1.17\pm 0.05\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$ and ${\mathrm{BF}}_{\mathrm{os}}=2.66\pm 0.35\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$. The corresponding DCS estimates of BFI were ${\mathrm{BFI}}_0=(6.08\pm 0.37)\times {10}^{-9}{\mathrm{cm}}^2/\mathrm{s}$ and ${\mathrm{BFI}}_{\mathrm{os}}=(1.46\pm 0.08)\times {10}^{-8}{\mathrm{cm}}^2/\mathrm{s}$. Thus, the subject’s relative hyperemic blood flow overshoot measured with DCS and with VO-DOS are ${\mathrm{rBFI}}_{\mathrm{os}}={\mathrm{BFI}}_{\mathrm{os}}/{\mathrm{BFI}}_0-1=1.39\pm 0.23$ and ${\mathrm{rBF}}_{\mathrm{os}}={\mathrm{BF}}_{\mathrm{os}}/{\mathrm{BF}}_0-1=1.28\pm 0.20$, respectively.

In trial 1, two venous occlusions were performed to estimate the baseline BF to be ${\mathrm{BF}}_0=1.17\pm 0.05\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$ and the blood flow during hyperemia to be ${\mathrm{BF}}_{\mathrm{os}}=2.66\pm 0.35\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$ [note that the errors in the BF estimates were calculated by bootstrap resampling of the data over the purple fitting interval in Fig. 6(b)]. As discussed in Sec. 2.5, the baseline and postocclusion DCS BFIs (i.e., ${\mathrm{BFI}}_0$, ${\mathrm{BFI}}_{\mathrm{os}}$) were averaged over corresponding time intervals during the venous occlusions of trial 1 [Fig. 6(b)]. For the representative subject in Fig. 6, the DCS measurements in trial 2 were ${\mathrm{BFI}}_0=(6.08\pm 0.37)\times {10}^{-9}{\mathrm{cm}}^2/\mathrm{s}$ and ${\mathrm{BFI}}_{\mathrm{os}}=(1.46\pm 0.08)\times {10}^{-8}{\mathrm{cm}}^2/\mathrm{s}$ ($\text{mean}\pm \mathrm{SD}$). These BFI values were obtained from within the purple averaging interval in Fig. 6(c). Thus, the subject’s relative hyperemic BF overshoot measured with DCS and with VO-DOS are ${\mathrm{rBFI}}_{\mathrm{os}}={\mathrm{BFI}}_{\mathrm{os}}/{\mathrm{BFI}}_0-1=1.39\pm 0.23$ and ${\mathrm{rBF}}_{\mathrm{os}}={\mathrm{BF}}_{\mathrm{os}}/{\mathrm{BF}}_0-1=1.28\pm 0.20$, respectively.

Figure 7(a) is a plot of ${\mathrm{rBF}}_{\mathrm{os}}$ measured with VO-DOS on the vertical axis against ${\mathrm{rBF}}_{\mathrm{os}}$ measured with DCS on the horizontal axis for all 10 subjects. A linear regression analysis [Fig. 7(a); solid red regression line, dotted green one-to-one line] and a Tukey mean-difference (or Bland-Altman) analysis^67,68 [Fig. 7(b)] show excellent agreement between the two techniques, per estimation of relative BF changes. The slope between relative BF measured by DOS (${\mathrm{rBF}}_{\mathrm{os}}$) and DCS (${\mathrm{rBFI}}_{\mathrm{os}}$) is 0.94 ($\pm 0.073$), and the Pearsons correlation coefficient is $R^2=0.95$. Further, the mean difference in relative BF of $-0.10\pm 0.45$ between the two techniques was not significantly different from zero ($P=0.2$).

Fig. 7

(a) Relative hyperemic blood flow overshoot from cuff ischemia measured by VO-DOS (vertical axis) and by DCS (horizontal axis) in $N=10$ healthy adults. The solid red line is the linear best-fit with the intercept forced at zero ($R^2=0.95$, $\text{slope}=0.94\pm 0.073$) and the dotted green line is the one-to-one line. ${\mathrm{rBFI}}_{\mathrm{os}}$ is the relative fractional DCS BFI change, i.e., ${\mathrm{BFI}}_{\mathrm{os}}/{\mathrm{BFI}}_0$; ${\mathrm{rBF}}_{\mathrm{os}}$ is the relative fractional VO-DOS blood flow change, i.e., ${\mathrm{BF}}_{\mathrm{os}}/{\mathrm{BF}}_0$. (b) Bland-Altman plot of the difference in ${\mathrm{rBFI}}_{\mathrm{os}}$ and ${\mathrm{rBF}}_{\mathrm{os}}$ versus the mean of these two parameters. The solid horizontal line indicates the mean difference between these two parameters computed across the study population ($N=10$), which is not significantly different from zero ($P=0.2$); the dotted lines indicate the 95% CI limits for agreement.

The observed agreement between the relative flow measured by VO-DOS and DCS in Fig. 7 suggests that the two techniques are sensitive to the same parameter, i.e., muscle BF. The data also further support the notion of using VO-DOS to calibrate DCS for accurate absolute BF monitoring in skeletal muscle.

3.4.

Calibration of Diffuse Correlation Spectroscopy Blood Flow With Venous-Occlusion Diffuse Optical Spectroscopy for Absolute Blood Flow

We found that the absolute BF measured with VO-DOS on the right arm significantly correlates with the absolute BFI measured with DCS [$R^2=0.63$, $n=30$, $P<0.01$, see Fig. 8(a)]. We estimate the DCS calibration coefficient [Eq. (1)] from the slope of the best fit line, i.e., $\gamma =(1.24\pm 0.15)\times {10}^8(\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1})/({\mathrm{cm}}^2/\mathrm{s})$; here, the error is the 95% confidence interval (CI). As an important practical consideration, the subject-specific measurement of baseline optical properties is required to achieve this level of correlation significance. By contrast, when baseline optical properties used to compute the DCS BFI were assumed (${\mu }_{a0}=0.17$ and ${\mu }_{s0}^{\prime }=6{\mathrm{cm}}^{-1}$),⁶⁹ the correlation was weaker [$R^2=0.15$, $n=30$, $P=0.032$, see Fig. 8(b)].

Fig. 8

Absolute blood flow measured by VO-DOS (vertical axis) compared to the blood flow index measured by DCS (horizontal axis) across $n=30$ measurements [$(\mathrm{A},\mathrm{B},\mathrm{C})\times 10\text{subjects}$]. The labels A, B, and C described in Fig. 2 correspond to three separate measurements on the dominant forearm in each subject using (a) measured optical properties and (b) assumed optical properties (i.e., ${\mu }_{a0}=0.17$, ${\mu }_{s0}^{\prime }=6{\mathrm{cm}}^{-1}$). The red solid line represents the best linear fit to the data. In both panels, the estimate of $\gamma$ is the slope of the best linear fit, and the error is the 95% CI for the slope.

The significant correlation in Fig. 8(a) suggests that the DCS BFI can be used as a surrogate for absolute BF, i.e., ${\mathrm{BF}}_{\mathrm{DCS}}\equiv (1.24\times {10}^8)\mathrm{BFI}$. Figure 9(a) is a plot of absolute BF measured with VO-DOS on the vertical axis against absolute ${\mathrm{BF}}_{\mathrm{DCS}}$ calculated from the measured BFI [using $(1.24\times {10}^8)\mathrm{BFI}]$ on the horizontal axis across $n=30$ measurements. A linear regression line [solid red line in Fig. 9(a)] and a one-to-one line [dotted yellow line in Fig. 9(a)] exhibit moderate correlation ($R^2=0.63$) between the two techniques; importantly, there exists considerable variability on a per-subject basis. The interquartile range (75th percentile to 25th percentile, $n=30$ measurements) of the fractional difference ${\mathrm{BF}}_{\mathrm{DCS}}/\mathrm{BF}-1$ is 44%, which is modestly smaller than the intersubject variability in BF of 75% [i.e., $\mathrm{BF}/{\mathrm{BF}}_{\mathrm{m}}-1$ has an interquartile range of 75%, where ${\mathrm{BF}}_{\mathrm{m}}$ is the mean BF across subjects (Table 2)]. Additionally, the Bland-Altman analysis of these data [Fig. 9(b)] reveals a mean difference in absolute BF of $0.1\pm 1.0\mathrm{mL}·100{\mathrm{mL}}^{-1}·{\min }^{-1}$, which is not significantly different than zero ($P=0.3$). By contrast to the relative BF results in Fig. 7, however, the mean difference estimated by the 95% CI of the absolute BF results is of order its mean [Fig. 9(b)]; this finding suggests substantial variability on a per-subject basis can exist and should be accounted for, whenever possible.

Fig. 9

(a) Absolute blood flow measured by VO-DOS (vertical axis; BF) and by DCS [horizontal axis; ${\mathrm{BF}}_{\mathrm{DCS}}=(1.24\times {10}^8)\mathrm{BFI}$, as determined from Fig. 8(a)] across $n=30$ measurements [$(\mathrm{A},\mathrm{B},\mathrm{C})\times 10\text{subjects}$]. The labels A, B, and C described in Fig. 2 correspond to three separate measurements on the dominant forearm in each subject using measured optical properties). The solid red line is the linear best-fit ($R^2=0.63$) and the dotted yellow line is the one-to-one line. (b) Bland-Altman plot of the difference in ${\mathrm{BF}}_{\mathrm{DCS}}$ and BF versus the mean of these two parameters. The solid horizontal line indicates the mean difference between these two parameters computed across $n=30$ measurements [$(\mathrm{A},\mathrm{B},\mathrm{C})\times 10\text{subjects}$]; the dotted lines indicate the 95% CI limits for agreement.

Thus, it is best to employ in situ calibration of DCS for absolute BF monitoring with VO-DOS on a per-subject basis. For in situ calibration, $\gamma$ is derived from the quotient of the absolute BF measurement with VO-DOS and the corresponding BFI measurement with DCS [see Sec. 2.5 and Eq. (1)]. For each subject, we utilized this approach to obtain five estimates of $\gamma$ that correspond to the five pairs of VO-DOS and DCS measurements made during visits 1 and 3 (Sec. 2.5). In visit 1 (Fig. 2), two subject-specific estimates of $\gamma$ corresponding to the baseline and hyperemic overshoot BF levels were obtained on the dominant arm: ${\gamma }_{\mathrm{A}}={\mathrm{BF}}_0/{\mathrm{BFI}}_0$ and ${\gamma }_{{\mathrm{A}}^{\prime }}={\mathrm{BF}}_{\mathrm{os}}/{\mathrm{BFI}}_{\mathrm{os}}$ for each subject. In a separate visit on a different day (i.e., visit 3), three subject-specific estimates of $\gamma$ were obtained: ${\gamma }_{\mathrm{B}}$ and ${\gamma }_{\mathrm{C}}$, acquired at roughly the same position on the dominant arm (the probe was removed and reattached between measurements), and ${\gamma }_{\mathrm{D}}$, acquired at the corresponding position on the nondominant arm.

The in situ measurements of ${\gamma }_{\mathrm{A}}$, ${\gamma }_{{\mathrm{A}}^{\prime }}$, ${\gamma }_{\mathrm{B}}$, ${\gamma }_{\mathrm{C}}$, and ${\gamma }_{\mathrm{D}}$ across subjects are shown in Fig. 10. Interestingly, although the median calibration coefficient is similar for different positions (and flow speeds) on the dominant arm, it is noticeably higher on the nondominant arm (Fig. 10). This observation suggests that the calibration technique can be sensitive to tissue heterogeneities (e.g., differences in tissue vascular structure between right and left arm, discussed further in Sec. 4).

Fig. 10

Box plots of the five DCS calibration coefficient measurements (${\gamma }_{\mathrm{A}}$, ${\gamma }_{\mathrm{A}’}$, ${\gamma }_{\mathrm{B}}$, ${\gamma }_{\mathrm{C}}$, ${\gamma }_{\mathrm{D}}$; see Sec. 2.5) measured on 10 healthy subjects. In both panels, the central mark is the median, the edges of the box are the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers, and the blue dots represent each subject measurement.

In Table 3, we quantitatively characterize the intrasubject variability in $\gamma$ over four paired comparisons across different flow levels ($R_{{\mathrm{A}\mathrm{A}}^{\prime }}$), slightly different positions ($R_{\mathrm{BC}}$), different days ($R_{\mathrm{ABC}}$), and different arms ($R_{\mathrm{BCD}}$). Both the weighted mean and median were computed for each comparison. The weight that each subject contributes in the weighted mean is set by the inverse of the subject’s variance for the particular variability parameter (see Table 3). To estimate the variance, the standard deviation of the variability parameter (i.e., obtained from the standard deviations of the appropriate $\gamma$ coefficients) was added in quadrature with the median of $R_{\mathrm{A}{\mathrm{A}}^{\prime }}$.⁷⁰ In this procedure, we thus regard the median of $R_{{\mathrm{A}\mathrm{A}}^{\prime }}$ as a minimum systematic error to prevent overweighting of particular subjects with small random error bars. To estimate the subject’s random error, the standard deviations in the absolute BF and BFI measurements were employed to compute the standard deviations in the $\gamma$ coefficients present in the variability parameter [Eq. (1)]. Here, the standard deviation of the measured slope $d[\mathrm{HbT}]/dt$ determined the standard deviation in BF, and the standard deviation in BFI was computed across the measurements in the appropriate venous occlusion time window (e.g., purple shaded regions in Fig. 6).

Table 3

Comparison of intrasubject variability in the calibration coefficient γ across different blood flow levels, positions, and days. Here, the weighted mean and median are computed over the study population (N=10). The weights used in computing the weighted mean and standard deviation are the inverse variances of the subject measurements (see main text).

As expected from our results in Fig. 7, intrasubject variability in $\gamma$ at different BF levels but at the same site and on the same day is small (first comparison in Table 3). Removing and reattaching the probe at a slightly different position on the right forearm had a larger effect on the measured $\gamma$ coefficient (second comparison in Table 3). The variability in $\gamma$ across different days was even more substantial (notice the large SD of $R_{\mathrm{ABC}}$). Finally, the fourth comparison in Table 3 is a complementary result to Fig. 10, indicating a systematic difference in the $\gamma$ coefficient between the dominant (right) and nondominant (left) arms.