In this study we evaluate the influences of optical property assumptions on near-infrared diffuse correlation spectroscopy (DCS) flow index measurements. The optical properties, absorption coefficient (µa) and reduced scattering coefficient (µs′), are independently varied using liquid phantoms and measured concurrently with the flow index using a hybrid optical system combining a dual-wavelength DCS flow device with a commercial frequency-domain tissue-oximeter. DCS flow indices are calculated at two wavelengths (785 and 830 nm) using measured µa and µs′ or assumed constant µa and µs′. Inaccurate µs′ assumptions resulted in much greater flow index errors than inaccurate µa. Underestimated/overestimated µs′ from −35%/+175% lead to flow index errors of +110%/−80%, whereas underestimated/overestimated µa from −40%/+150% lead to −20%/+40%, regardless of the wavelengths used. Examination of a clinical study involving human head and neck tumors indicates up to +280% flow index errors resulted from inter-patient optical property variations. These findings suggest that studies involving significant µa and µs′ changes should concurrently measure flow index and optical properties for accurate extraction of blood flow information.
©2011 Optical Society of America
Near-infrared (NIR) light has been recently employed in the noninvasive acquisition of blood flow information from deep tissues (up to several centimeters), which is referred to as NIR Diffuse Correlation Spectroscopy (DCS) [1–4] or Diffuse Wave Spectroscopy (DWS) [5,6]. DCS measures relative change of tissue blood flow (rBF) which has been extensively validated in various tissues through comparisons with laser Doppler flowmetry (LDF) , Doppler ultrasound [8,9], power Doppler ultrasound [10,11], Xenon-CT , fluorescent microsphere measurement , arterial spin labeled magnetic resonance imaging (ASL-MRI) [14,15], and to literatures [1,4,16–18]. DCS also provides a blood flow index for comparisons of longitudinal measurements and inter-subject variations [11,13,19,20]. The probing depth of NIR DCS (several centimeters) is significantly larger than those (several millimeters) of similar optical modalities such as LDF [21–23], Doppler optical coherence tomography (DOCT) , photoacoustic tomography (PAT) , and optical micro-angiography (OMAG) . DCS is primarily sensitive to microvasculature rather than large blood vessels (e.g., Doppler ultrasound measurement), and does not require radiation exposure (e.g., PET, Xenon-CT). Systems based on DCS provide portability, allowing for bedside monitoring utilizing short acquisition time (varying from 6.5 ms to several seconds) without expensive instrumentation [17,27–29]. Due to these features, usages of DCS expand continuously into new applications in various deep organs/tissues such as muscle [15,28,30–33], tumor [10,11,19,20,29,34–36] and brain [4,5,7–9,12–14,16,17,27,37–41].
The use of NIR light for deep tissue measurements stems from the exploitation of a spectral region (650-950 nm) wherein light absorption of the biological tissue is relatively low. When using NIR spectroscopy (NIRS) to detect optical properties of deep tissues, a pair of source and detector fibers is usually placed along the tissue surface with a distance of a few centimeters. NIR light generated by a laser emits into tissues through the source fiber and is detected by a photodetector through the detector fiber. Photon migration in tissue is now known to be a diffusive process [2,7]. During this migration, photons encounter absorption and, more commonly, scattering events. The probabilities of these events are described by an absorption coefficient, μa, and a reduced scattering coefficient, μs′, also referred to as the optical properties, intrinsic to the probed tissue volume. The penetration depth of NIR light in biological tissues is approximately half of the source-detector separation. NIR DCS flow measurements are accomplished by monitoring speckle fluctuations of photons emitted at the tissue surface. In non-muscular tissues moving red blood cells (RBC′s) inside vessels are primarily responsible for these fluctuations [4,5,7–14,16,17,19,20,27,29,34–42], but complications such as tissue shearing and motion artifacts can arise for muscular tissues [28,32]. Blood flow indices and rBF can be calculated from the changes in the speckle patterns. Ensuing calculations of blood flow using DCS measurements include a dependence on the optical properties (μa and μs′) and are thus potentially influenced by variations thereof (see the details in Section 2).
DCS is not inherently capable of measuring absolute values of absorption and scattering coefficients. Solutions to this issue have typically been approached using two general methods: optical property assumptions or optical property measurements with separate instrumentation. Some studies have chosen to use the values of μa and μs′ from the literature [8,32], respective to the tissue type (e.g., brain or muscle), or assumed a constant μs′ while examining changes in μa [13,30,40]. These assumptions may be susceptible to deviations in optical properties that occur transiently, longitudinally, due to subject differences or from differences in literatures. A few of the recent studies have employed hybrid instrumentation allowing for measurement of both sets of information to extract accurate blood flow [9,19,29,43]. However, a generalization of potential flow index errors due to the inaccurate estimation of optical properties has not been investigated for the DCS flow measurements. In addition to optical properties, another potential influence on DCS flow indices is determined by selection of the laser wavelength.
Our lab has recently built a hybrid instrument capable of the simultaneous measurement of absolute μa, μs′ and flow indices at multiple wavelengths, through combining a commercial frequency-domain NIR tissue-oximeter, the Imagent (ISS, Inc., IL, USA) [44,45], and a custom-made NIR DCS flow-oximeter [31,33,41]. This newly developed hybrid instrument allows us to quantify the influences of optical properties on DCS flow indices measured at different wavelengths. In this study, homogeneous liquid phantoms with controlled variations of optical properties were created, attempting to isolate the influence of each optical property parameter (i.e., μa or μs′) on DCS flow indices. The usage of tissue-like phantoms for instrument calibration and experimental validation of NIRS and DCS techniques is common [2,4,44–51]. In DCS measurements, the dynamic scatterer motions (typically microvasculature RBC′s) are best modeled by Brownian diffusion as opposed to random ballistic flow, which has been determined empirically, but for reasons currently unknown [4,7,8,10,11,20,27,40]. An effective Brownian diffusion coefficient is calculated as the blood flow index when measuring in biological tissues and is usually distinct from the conventional Brownian diffusion coefficient predicted by Einstein . However, when utilizing liquid phantoms with Intralipid particles to provide Brownian motion, the two diffusion coefficients are expected to be equivalent. Through this special case using liquid phantoms, DCS flow indices calculated using measured or assumed optical properties can be compared to the Einstein prediction (as a true flow index) for Brownian particles suspended in liquid. Measurement errors are then determined through these comparisons for DCS flow indices at different wavelengths.
Simultaneous measurements of optical properties and blood flow indices are essential for extracting accurate hemodynamic information in tissues with transient, longitudinal and inter-subject differences in optical properties. To this end, we show a clinical study using the hybrid instrument to accurately quantify tissue optical properties and blood flow indices in head and neck tumors. The measurement errors in tumor blood flow indices induced by potential inaccurate estimations of tissue optical properties are ultimately discussed and compared to the phantom study results to determine the in vivo applicability thereof.
2. Methods and materials
2.1. Diffuse correlation spectroscopy (DCS) for blood flow measurement
DCS flow indices are quantified by a dual-wavelength DCS system  with two long coherence length continuous-wave (CW) NIR laser sources at 785 and 830 nm (100 mW, Crystalaser, Inc., NV, USA). The DCS sources emit light alternately into the tissue via two multi-mode optical fibers bundled at the same location on the tissue surface (see Fig. 1a ). Four detector fibers are tightly bundled and placed on the tissue surface at a distance of 1.5 cm away from the source fibers, and each is connected to a single photon-counting avalanche photodiode (APD) (PerkinElmer Inc., Canada). The outputs of 4 APDs are sent to a 4-channel autocorrelator board (Correlator.com, NJ, USA) producing normalized light intensity temporal autocorrelation functions (g2) which are averaged to improve the signal-noise-ratio. The averaged g2 from DCS is related to the normalized electric field temporal autocorrelation function (g1) through the following Siegert relation :
where τ is the delay time, is the position vector, and β depends on laser stability and coherence length and the number of speckles detected.
Scatterer motion is directly associated with the unnormalized electric field temporal autocorrelation function (G1) which obeys a correlation diffusion equation, derived rigorously elsewhere [2,46] and defined as follows for homogeneous media using a CW source (steady state):
whereis the photon diffusion coefficient, v is the speed of light in the medium, is the wavenumber, is the source light distribution, andis the mean-square displacement of scatterers in time τ. The position vector, , denotes a general vector from a source to a point of detection. Note that G1 is the unnormalized version of g1, i.e., . Scatterer movement for particles undergoing Brownian motion results in, where DB is the effective Brownian diffusion coefficient. An α (0–1) term is added to account for not all scatterers being dynamic and is defined as the ratio of moving scatterers to total scatterers. The combined term, αDB, is referred to as the blood flow index in biological tissues and is commonly used to calculate the relative blood flow (compared to the baseline flow index before physiological changes). In contrast to tissue samples where scatterers may be static (e.g., organelle, mitochondria) or dynamic (moving RBC), all scatterers in liquid phantom solutions (see Section 2.4) are considered dynamic with α ≈1 and the flow index is thus reported as simply DB. The homogeneous CW solution to Eq. (2) for semi-infinite geometry is
where ρ is the source-detector separation, S0 is source intensity, , , , , , and n ≈ 1.33 (for tissues and phantoms) [7,46,54,55]. The Reff term accounts for the mismatch between the medium and the air indices of refraction with n being the ratio between them.
For semi-infinite geometry, the collimating laser source at (0, 0, 0) and detector at (ρ, 0, 0) are placed on the tissue surface with z = 0 (see Fig. 1b). This solution (Eq. (3)) involves an extrapolated zero boundary condition including an isotropic source at z = z0 and negative isotropic imaging source at z = −(z0 + 2zb). The position vector, , from Eq. (2) considers the point source at (0, 0, z0) and the negative imaging source at (0, 0, −(z0 + 2zb)). The superposition of solutions to these two sources using infinite geometry provides the resulting Eq. (3) where now the semi-infinite boundary is modeled by the scalar parameter, ρ. Further details can be found elsewhere [46,55].
Flow index calculations begin with using Eq. (1) to first determine the β. Using the g2 data at earliest τ and letting g1 ≈ 1 (i.e.,) lead to . Using DCS measured , calculated β and Eq. (1), is calculated for all τ. Equation (3) is then used with the unknown parameter αDB (flow index) to fit the g1 derived from DCS measurements (see Fig. 1c). For a complete frame of DCS data acquisitions at two wavelengths, two flow indices are obtained sequentially.
2.2. Frequency-domain spatially resolved NIRS for tissue optical property measurement
Quantification of absolute μa and μs′ is performed by a frequency-domain multi-distance spatially resolved spectroscopy, i.e., the Imagent. Two wavelengths (780 and 830 nm) of a four-wavelength (690, 750, 780 and 830 nm) Imagent system are chosen to match the DCS lasers available (785 and 830 nm). The Imagent emits sinusoidally modulated light into tissue through 8 optical fibers (4 per wavelength) placed at four pre-determined distances (2.0, 2.5, 3.0, and 3.5 cm) from a detector fiber bundle connected to a photomultiplier tube (PMT) (see Fig. 1a). Source light is modulated at 110 MHz resulting in detected AC, DC and Phase (φ) information from multiple distances. A simplified solution based on semi-infinite geometry for the photon diffusion equation exposes linear relationships between φ, logarithmic AC or logarithmic DC and spatial distances [44,45]. From the fitting slopes (SAC, SDC, Sφ) of the linear relationships μa and μs′ can be extracted at each wavelength. Different source-detector separations generally provide measurements at different depths/regions based on diffusion theory . However, the depth/regional difference has minimal effect on measurement of optical properties of homogeneous phantoms.
2.3. Brownian motion of spherical particles in liquid phantoms
As mentioned earlier, when using liquid phantoms with Intralipid particles to provide Brownian motion, the effective Brownian diffusion coefficient (flow index) measured by DCS is expected to be equivalent to the conventional Brownian diffusion coefficient predicted by Einstein . In the present study, DCS flow indices are compared to Einstein diffusion coefficients for the estimation of measurement errors. The Brownian diffusion coefficient as defined by the Einstein-Stokes formula for spherical particles in liquid is
where kB is the Boltzmann constant, T is the phantom temperature, R is the radius of the spherical particles and η is the viscosity . In order to obtain the temperature and viscosity parameters, a temperature sensor (Physitemp, NJ, USA) is attached near the optical probe and viscosity is measured using a viscometer (Brookfield, MA, USA). Viscosity is reported in units of cP (centipoise), where 1 cP = 1 mPa∙s (millipascal∙second) = 0.001 kg∙m−1s−1 . The radius of Intralipid particles is estimated as 196 nm (see Section 2.5).
2.4. Liquid phantoms with varied optical properties
Liquid phantoms are comprised of distilled water, India ink (Black India 44201, Higgins, MA, USA) and Intralipid (30%, Fresenius Kabi, Uppsala, Sweden). India ink is used to manipulate the absorption coefficient of the phantom, μa (λ), where λ is the laser source wavelength. India ink is first diluted to a 10% solution with distilled water. The 10% ink solution (instead of pure ink) is used to create phantoms. Intralipid provides particle Brownian motion and control of the reduced scattering coefficient of the phantom, μs′ (λ). Setup of the liquid phantom is shown in Fig. 1b. A hybrid fiber-optic probe is placed on the surface of the liquid phantom solution contained inside a glass aquarium. A custom-made probe holder attached to a lab stand holds the probe at the center of the solution to simulate a semi-infinite geometry.
For creating phantoms with μa variation, a list of μa (λ) and a constant μs′ (λ) are chosen (see details in Section 2.5). The μa (λ) and μs′ (λ) of distilled water, 10% ink solution, and 30% Intralipid are first determined. These values in combination with titration equations provide the necessary volumes of water, ink and Intralipid to achieve desired phantom optical properties . The subscripts “ink”, “Intralipid”, and “water” are used in this paper to denote 10% ink solution, 30% Intralipid, and distilled water, respectively. The μa ink (λ) is derived from spectrometer (Beckman Coulter, CA, USA) measurements. Since the 10% ink solution is out of the measurable range of the spectrometer, further dilution is performed to get a 0.025% ink solution for spectrometer absorbance measurements. Absorbance measured from multiple 0.025% ink solution samples are averaged and converted to the μa ink (λ) . The μa water (λ) is taken from the literature . The μa Intralipid (λ) is assumed to be equivalent to that of water. Distilled water and 10% ink solution are both assumed to have no contributions to the phantom μs′ (λ), i.e., μs′water (λ) = μs′ink (λ) = 0 cm−1. The μs′ (λ) of 10% Intralipid is calculated using a Mie theory approximation . The theory and details including the Intralipid particle radius and refractive index were described in the original derivation  which has been extensively used for quantification of Intralipid-based liquid phantoms [2,7,57,60,61]. For 30% Intralipid used in this study, μs′Intralipid (λ) is the μs′ (λ) of 10% Intralipid multiplied by a factor of three .
2.5. Phantom experimental protocols and data analysis
μa variation. In this protocol, variation of µa was induced while maintaining a constant µs′. Thirteen steps were performed to cover µa (830 nm) from 0.05 to 0.20 cm−1 with a step size of 0.0125 cm−1 (i.e., µa (830 nm) = 0.05, 0.0625, 0.075, …, 0.20 cm−1) and µs′ (830 nm) = 10 cm−1. Prior to beginning the Imagent requires calibration to a phantom of known optical properties. During this process, corrections are made to account for the efficiency of optical coupling among the lasers/detector, optical fibers, and phantom [45,62]. The Imagent was calibrated to a liquid phantom of equivalent composition and optical properties at the midpoint (step 7) of the experimental range, i.e., µa (830 nm) = 0.125 cm−1 and µs′ (830 nm) = 10 cm−1. The combined probe was then placed upon a liquid phantom at the lowest optical property step, i.e., µa (830 nm) = 0.05 cm−1. For each of 13 steps the following actions were taken. Desired volume of ink solution was added to the liquid phantom, mixed, and allowed to stabilize for 10 minutes. Viscosity data was attained during this time by extracting three 500 µl samples. The three samples were carefully taken from the left, right and middle of the solution (at the surface) to minimize spatial variations without submerging the pipette. Room light was then turned off and the experimental setup was covered with black plastic to reduce ambient light. Measurements were taken by the hybrid optical instrument and temperature sensor for a 5 minute interval.
μs′ variation. Variation of μs′ immediately followed the performing of μa variation experiments. Between experiments the phantom from μa variation was disposed of and replaced with a new initial phantom for μs′ variation. The hybrid probe was cleaned with alcohol pads and repositioned on the surface of the second phantom for μs′ variation study. Neither Imagent nor DCS were shut down between protocols. Variation of µs′ was induced while maintaining a constant µa. A scattering range of µs′ (830 nm) from 4 to 16 cm−1 with a step size of 1 cm−1 (i.e., µs′ (830 nm) = 4, 5, 6, …, 16 cm−1) and µa (830 nm) = 0.125 cm−1 was performed over thirteen steps. The volume of Intralipid required to increase μs′ as desired could potentially reduce μa as well as influence the level of probe submersion. To remedy the first difficulty, ink was added with the Intralipid to maintain the µa of the phantom. For the second, an equivalent amount of phantom solution was removed after being mixed at each step. Viscosity, temperature and hybrid optical measurements were taken similarly to those during μa variation.
Data analysis and presentation. Each 5 minute interval measurement involves post calculations of interval averages of μa and μs′ at each wavelength along with the temperature, sample average of viscosity, and three diffusion coefficients (DB′s). Data between intervals (i.e., adding/taking solution, stirring) are excluded from data analysis. The µa and µs′ are measured by Imagent using the spatially resolved (slope) method (see Section 2.2) and averaged over the 5 minute interval. The averaged µa and µs′ are then used as known parameters in fitting DCS measured g2′s using Eq. (1) and (3) to produce two distinct DCS DB′s, which are distinguished with subscripts describing the optical property values used for calculation of DB. The first DCS DB (DB-mid) is calculated with the averaged µa and µs′ measured from the middle interval, i.e., µa (830 nm) = 0.125 cm−1 and µs′ (830 nm) = 10 cm−1, serving as the diffusion coefficient ignorant of optical property variation. Using the constant µa and µs′ from the middle interval results in overestimations of µa and µs′ during early intervals and underestimations at later intervals, thus causing errors in calculation of flow indices. The second DCS DB (DB-dynamic) is calculated using the averaged µa and µs′ measured from the corresponding interval, providing the best evaluations of DCS flow indices. These DCS DB calculations are repeated for both sets of wavelengths. The optical properties from the Imagent measurements at 830 and 780 nm are used in calculations of DCS DB ′s at 830 and 785 nm, respectively. The influence of wavelength mismatch (5 nm) between 780 and 785 nm is considered to be minor. The third DB (DB-Einstein) is calculated using Eq. (4) with the estimated particle radius, interval averaged temperature and three sample averaged viscosity. The estimated particle radius of 196 nm is determined to exhibit the least errors between the measured DCS flow indices (DB-dynamic) and calculated DB-Einstein at the calibration point (step 7). This estimation falls within the range of Intralipid particle size reported in the literatures [2,59].
Measurement errors are characterized by calculating percentage errors between the measured values and predictions. P-values from Student t-tests are included for comparisons of measurement errors and the criterion for significance is p < 0.05. Results are presented in figures and tables to visualize measurement variations, differences between expected and obtained values, and the optical property influences on DCS flow indices. Data are depicted as mean ± standard deviation (SD) in tables and SD is illustrated by error bars in figures.
2.6. In vivo quantification of head and neck tumor hemodynamics
The possible errors of assuming constant optical properties in calculation of flow indices may be more readily visualized through analysis of real tissue measurements. In order to evaluate such influences in in vivo measurements, tissue hemodynamic properties of head and neck tumors in 10 patients were measured using a hybrid optical instrument similar to that in the phantom study. Institutional review board (IRB) approval was given by the University of Kentucky and consent forms were obtained before subject participation. Only subjects with Stage III-IVb Squamous Cell Carcinoma of the Head and Neck (SCCHN) were included. Neck lymph nodes measuring more than 1 cm and clinically thought to be involved by tumor were selected to study.
The Imagent used 690 and 830 nm source wavelengths whereas DCS used 785 and 854 nm lasers. Other wavelengths used for phantom studies were not available for the tumor study. Thus, data from 830 nm for Imagent and 854 nm for DCS are analyzed for this tumor study as these wavelengths provide the best match. By contrast, the second pair of wavelengths (785 nm versus 690 nm) is excluded for data analysis due to the significance of wavelength mismatch (95 nm). The Imagent source-detector separations used (2.0, 2.5, 3.0, and 3.5 cm) are identical to the phantom study. DCS utilized 3 detector fibers at 1.5, 2.4, and 2.8 cm separations from the two source fibers. The probe was held by hand and secured on the subjects in the center of the area identified as tumor node while tumor optical properties and DCS flow data were obtained for ~2 minutes. DCS data from the 2.8 cm separation are examined, comparable to the tissue region/depth probed by the Imagent. Using different sets of optical properties measured by the Imagent, four DCS flow indices for each of 10 subjects are calculated and then averaged over the 2-minute measurement interval. The μa and μs′ are averaged over the measurement duration (2 minutes) for each subject and used in calculating the first DCS blood flow index (αDB-dynamic), which is considered as a true flow index. The minimum, mean and maximum μa and μs′ over 10 subjects are determined and used for calculating the respective remaining three DCS blood flow indices (αDB-min, αDB-mean, and αDB-max respectively) for comparisons with the true flow index (αDB-dynamic). Data in figures are presented by interval mean ± SD, where SD is depicted by error bars.
3.1. μa variation
In order to evaluate the influence of µa variation on flow indices, thirteen steps of liquid phantoms were performed to cover µa (830 nm) from 0.05 to 0.20 cm−1 with a step size of 0.0125 cm−1 while maintaining a constant µs′ (830 nm) = 10 cm−1. For each step/interval of measurements over 5 minutes, the means and SDs of viscosity (from three samples), temperature and calculated DB-Einstein are displayed as data sets (means) and error bars (SDs) in Fig. 2 . DB-Einstein (see Fig. 2c) is calculated using the measured temperature (see Fig. 2b) per interval along with the associated viscosity (see Fig. 2a) and estimated particle radius (196 nm).
The interval means and SDs (error bars) of μa, μs′, DB-Einstein, DB-mid, and DB-dynamic throughout the 13 steps of μa variation are displayed in Fig. 3 . The measured values of μa (see Figs. 3a and 3d) and μs′ (see Figs. 3b and 3e) at two wavelengths by the Imagent are compared to predictions calculated using spectrometer and Mie theory for the evaluation of measurement errors, respectively. Two DCS flow indices (DB-mid and DB-dynamic) are compared to the DB-Einstein (as a true flow index) for both wavelengths (see Figs. 3c and 3f). The DB-mid or DB-dynamic at each wavelength is calculated using the DCS measurement with averaged µa and µs′ from the middle interval [µa (830 nm) = 0.125 cm−1 and µs′ (830 nm) = 10 cm−1] or from the corresponding interval.
3.2. μs′ variation
Similar to µa variation, a scattering range of µs′ (830 nm) from 4 to 16 cm−1 with a step size of 1 cm−1 was performed over thirteen steps while maintaining a constant µa (830 nm) = 0.125 cm−1. Results for μs′ variation are plotted in a similar fashion as μa variation (see Section 3.1). The means and SDs (error bars) of viscosity (three samples), temperature and calculated DB-Einstein throughout μs′ variation are shown in Fig. 4 . The interval means and SDs of μa, μs′, DB-Einstein, DB-dynamic, and DB-mid are displayed in Fig. 5 .
3.3. Quantification of μa and μs′ influences on flow indices
Influence of μa and μs′ variations on DB-Einstein . Table 1 lists the means ± SDs and coefficients of variation (CVs) for viscosity, temperature, and DB-Einstein over the entire range of μa and μa ′ variations, calculated based on the data shown in Figs. 2 and 4. The CV is defined as a percentage of SD/mean, indicating the variation of the mean values over steps. The CVs of temperature, viscosity, and DB-Einstein are less than 2.2%, indicating the minor influences of μa and μa ′ variations on these variables. The DB-Einstein is thus used as a true flow index to evaluate the DCS flow measurement errors.
Mean measurement errors in μa, μs′ and DCS flow indices . Table 2 lists the means ± SDs of absolute percentage errors in measurements of μa, μs′, and DCS flow indices (DB-dynamic and DB-mid) over the entire range of μa and μa ′ variations, calculated based on the data shown in Figs. 3 and 5. Absolute percentage error is defined as (|Estimate-True|/True) X 100%. For μa and μs′, the Imagent measured values are considered estimates while the spectrometer and Mie theory, respectively, are used as true values. For flow indices, DB-dynamic and DB-mid are considered estimates and DB-Einstein as true. The measurement errors for μa, μs′, and DB-dynamic are small, averaging less than ~7%, whereas those of DB-mid are found to be larger, averaging up to 12.89% and 49.63% for μa and μs′ variations, respectively. The influences of μs′ variation can be seen to produce greater percentage errors on flow indices than those of μa variation. In Table 2, mean measurement errors between wavelengths are also compared using 2-sample unequal variance, two-tailed t-tests with significant differences considered for p-value < 0.05 and denoted with * prefix. Significant differences in mean measurement errors between wavelengths are found in μa (p = 0.01) during μa variation and in μs′ (p = 0.04) during μs′ variation. These differences between wavelengths are most likely associated with the intrinsic feature of the instrument (Imagent) in detection accuracy at different wavelengths. No significant differences in mean measurement errors between wavelengths are found for both DB-dynamic and DB-mid.
Table 3 provides p-value results for comparisons of the mean measurement errors of DB-dynamic and DB-mid at two wavelengths during μa and μs′ variations. It is apparent that there are significant (though it is borderline at 785 nm during μa variation) differences between the measuring (DB-dynamic) and assuming (DB-mid) variables; DB-dynamic is more accurate (with less measurement errors, see Table 2) than DB-mid. The much lower p-values for μs′ variation as compared with those for μa variation again suggest μs′ as a greater influence factor on DCS flow indices.
Influence of μa and μs′ variations on DCS flow index . Visualization of the influence of optical property assumptions at both wavelengths is shown in Fig. 6 , overlaying the results from both μa and μs′ variations over 13 steps (see Figs. 3 and 5). The percentage errors for μa during μa variation and for μs′ during μs′ variation are defined as [(μa –mid − μa -dynamic)/μa -dynamic] X 100% and [(μs′-mid − μs′-dynamic)/μs′-dynamic] X 100%, respectively. The subscripts “mid” and “dynamic” correspond to assumed constant (middle-interval) and dynamic optical properties. For both variations, the percentage DB error between DB-mid and DB-dynamic for each interval is defined as [(DB-mid − DB-dynamic)/DB-dynamic] X 100%. Larger estimation errors in optical properties (μa and μs′) generate larger percentage DB errors. Variations in μs′ have a greater influence on percentage DB errors compared to variations in μa. Trends in overestimation and underestimation of flow indices due to variations in μa or μs′ are different. Overestimating and underestimating μa results in overestimating and underestimating flow indices, respectively, opposite of the trend for μs′. Data for both wavelengths are in good agreement and show only minor differences.
3.4. Influence of tissue optical properties on head and neck tumor blood flow index
The means ± SDs of measured tumor optical properties (μa and μs′) and blood flow indices (αDB-dynamic, αDB-min, αDB-mean, and αDB-max) along with corresponding percentage errors for 10 patients with head and neck tumors are shown in Fig. 7 . Patients are shown in order of increasing αDB-dynamic (as true flow index), designated with a black line, for comparison of trend differences when using optical property assumptions (i.e., αDB-min, αDB-mean, and αDB-max). Note that the patient numbers represent indices to illustrate the trend rather than actual patient numbers corresponding to the measurement sequence. The mean optical properties over subjects are: μa (830 nm) = 0.12 ± 0.03 cm−1 and μs′ (830 nm) = 7.80 ± 2.64 cm−1. Maximum and minimum optical properties out of all subjects at 830 nm are indicated using the red and blue dots, respectively, in Figs. 7a and 7b. DCS blood flow indices calculated using DCS data at 854 nm with different optical properties are represented in Fig. 7c. Without considering the tissue optical property influence, the trends of flow indices (αDB-min, αDB-mean, and αDB-max) are not the same as the true flow index (αDB-dynamic). Percentage αDB errors are calculated between the αDB-dynamic (true) and the estimated αDB-min, αDB-mean, and αDB-max. Large ranges of percentage errors are found for αDB estimates: αDB-min from −8.07 to 278.15%, αDB-mean from −39.48 to 149.01%, and αDB-max from −70.26 to 22.59%. The tendency to overestimate or underestimate the blood flow indices follow the same trends as shown for μs′ variation in Fig. 6, supporting that μs′ has a greater influence on DCS flow indices than μa.
4. Discussion and conclusions
4.1. μa and μs′ variation influences on DB-Einstein
The Einstein-Stokes formula calculation, Eq. (4), provides the Einstein diffuse coefficient (DB-Einstein) for spherical particles moving in liquid phantoms. The DB-Einstein is determined by the temperature and viscosity of the liquid as well as the particle radius of Intralipid in the liquid phantoms. Only slight variations are exhibited in overall average temperature (CV < 1.1%), viscosity (CV < 2.2%), and DB-Einstein (CV < 2.2%) during both μa and μs′ variations, as seen in Table 1 and Figs. 2 and 4. The particle radius of Intralipid should not change during both μa and μs′ variations. The changes in temperature are likely due to room temperature increase over the ~4.5 hour experimental durations. These include contributions by heat from equipment in the confined room. The cause of small variations in viscosity is likely due to the measurement variations by the viscometer. With these small variations in temperature and viscosity, it is thus expected that the derived DB-Einstein from Eq. (4) is stable over the large variations of optical properties.
On the other hand, increases of μa (ink concentration) during μa variation are expected to have no contribution to DB-Einstein, as ink provides no particle motion. Similarly, increases of μs′ (Intralipid concentration) during μs′ variation do not show significant influence on DB-Einstein, which is expected as all scatterers (Intralipid particles) provide equivalent motion in liquid phantoms and the ratio of moving scatterers to all scatterers (α) remains unchanged (α = 1). Due to the independence of optical properties and high stability throughout, DB-Einstein is considered reasonable as the true flow index for spherical particles moving in liquid phantoms.
4.2. Measurement errors of μa, μs′, and DB-dynamic
In agreement with expectations, ink contributes only to increasing the absorption of the phantom during μa variation. Additions of equivalent amounts of ink per interval resulted in linear increases in μa for both Imagent wavelengths (see Figs. 3a and 3d). Only minimal variations occurred in μs′ at both wavelengths during μa variation (see Figs. 3b and 3e). Calibration at the midpoint [μa (830 nm) = 0.125 cm−1, μs′ (830 nm) = 10 cm−1] may influence the variation patterns seen in Imagent measurements. Intralipid contributes linearly to μs′ increases, as expected, during μs′ variation for both Imagent wavelengths (see Figs. 5b and 5e). The μa stayed relatively constant with minimal variations during μs′ variation (see Figs. 5a and 5d). Measured μa and μs′ during both experiments are consistent with predictions from spectrometer measurements and Mie theory, respectively. More specifically, the μs′ measurement errors were less than 6% (see Table 2) for both experiments and wavelengths, which are comparable to those obtained from the literature using the Mie theory estimation (see Section 2.4) . Overall, average measurement errors of μa and μs′ were small during μa (< 4%) and μs′ (< 6%) variations (see Table 2), which are in agreement with those found in previous studies using frequency-domain spatially resolved NIRS [44,45]. For μa variation, significant difference was found between measurement errors of μa at 780 and 830 nm. For μs′ variation, there was significant difference between measurement errors of μs′ at 780 and 830 nm. These differences are likely attributable to the intrinsic instrument (Imagent) feature in detection accuracy at separate wavelengths.
Average measurement errors for DB-dynamic (< 7%) compared to DB-Einstein at both wavelengths are similar to those obtained for optical properties (< 6%) during both experiments (see Table 2), suggesting the influence of optical properties on DB.
4.3. Resulting DB errors from optical property assumptions
When using assumed constant optical properties (i.e., middle-interval μa and μs′) to calculate DB-mid, mean DB-mid measurement errors during μa (~13%) and μs′ (~50%) variations (see Tables 2 and 3) were significantly higher than those of DB-dynamic (~7%). It is evident that the influence of μs′ on the DCS flow index is much greater than that of μa. This result is further supported by the great difference in p-values, where p-values during μs′ variation are much less than p-values during μa variation (see Table 3). Also, looking at Fig. 6, the range of DB percentage errors for inaccurate estimations of μs′ is much wider than that for μa. This result is expected due to DCS flow indices being derived from light speckle fluctuations, originated from photon phase shifts by dynamic scatterers. Upon examination of the K2 definition (see Eq. (3)), μs′ should have a more significant influence than μa given the μs′2 term along with the much larger scattering over absorption (i.e., μs′ >> μa) in biological tissues and the liquid phantoms. No significant difference was found between wavelengths in DB-dynamic and DB-mid measurement errors during both experiments (see Table 2). This indicates that wavelength may not be a critical factor in determining the importance of optical property influence on DB measurement, although further investigations using a large range of wavelengths are needed for making a solid conclusion. The trends of DB estimation errors when using DB-mid were found to be different between the μa and μs′ variations (see Figs. 3c, 3f, 5c, 5f and 6). For μa variation, overestimated or underestimated μa results in overestimated or underestimated DB. By contrast, for μs′ variation overestimated or underestimated μs′ results in underestimated or overestimated DB. Extreme examples of incorrect estimations of DB can be seen in Fig. 6. Overestimation errors of μa up to ~+150% during μa variation resulted in percentage errors up to ~+40% and underestimation errors up of ~−40% resulted in percentage errors up to ~−20%. When overestimation errors of μs′ reach up to ~+175% during μs′ variation, DB percentage errors were up to ~−80%. For underestimation errors of μs′ up to ~−35%, DB percentage errors reach up to ~+110%. Note that these estimation errors in optical properties and resulting DB may be affected by the selection of phantom properties for calibration.
4.4. In vivo tumor study data in comparison to phantom study results
In the tumor study, measured μa and μs′ show large variations between subjects (see Figs. 7a and 7b). The range of variations, μa (830 nm) from 0.07 to 0.16 cm−1 and μs′ (830 nm) from 5.35 to 13.1 cm−1, is within the range studied using liquid phantoms. The influence of the μs′ variations on flow indices was found to be greater than that of μa, supporting the phantom study results. This is exemplified by the trends shown in Fig. 7c. The overestimation of optical properties (using maximum μa and μs′) leads to underestimation of DCS flow index (αDB-max) and underestimation (using minimum μa and μs′) leads to overestimation of DCS flow index (αDB-min). These are in agreement with the trends of DB estimation errors using inaccurate μs′ in liquid phantoms (see Figs. 5c, 5f and 6). Percentage αDB errors range greatly, from ~−70% up to ~ +280%, depending on optical properties assumed. Errors in flow indices (see Fig. 7d) produce an incorrect observation of trends in the αDB magnitudes among patients (see Fig. 7c). It is evident that lack of consideration for optical property influences can lead to invalid results in similar studies.
The advent of DCS technology as a safe and quick alternative for measurement of blood flow in deep tissues has brought the need to further investigate potential errors, notably by the assumption of constant optical properties, μa and μs′. The flow index produced by DCS measurement is based on a solution to the correlation diffusion equation which includes parameters of μa and μs′. Utilizing a novel hybrid optical equipment setup, capable of measuring all three parameters of interest (i.e., flow index, μa, and μs′), with liquid phantom experimental protocols has made it possible to perform this investigation. The present study evaluates the influences of tissue optical properties on DCS flow indices through isolated variations of μa and μs′ in liquid phantoms. It is found that the particle motions in liquid phantoms are not influenced by the variations in optical properties, and the usage of Einstein particle Brownian motion coefficient (DB-Einstein) as true flow index is reasonable for comparison with DCS flow indices. During μa and μs′ variations, μs′ has a much greater influence on DCS flow indices than μa, regardless of the wavelengths used. Studies involving significant μa and μs′ changes should concurrently measure flow index and optical properties for accurate extraction of blood flow information in tissue. The flow index errors resulted from the optical property assumptions in the tumor study elicit such need for concurrent monitoring of optical properties. Incorporation of laser sources at wavelengths beyond those tested in this study may be the subject of future investigation. The range of optical properties tested in the phantoms may also be extended to encompass a wider variety of tissues.
The authors would like to thank the University of Kentucky Research Foundation and NIHR01 CA149274 for funding support. We also thank Daniel Kameny, Jacqueline Sims, Karen Meekins, and Laura Reichel for their assistance in recruitment of patients.
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