1.

Introduction

Laser Doppler flowmetry (LDF) can be used to measure perfusion [fraction of red blood cells (RBCs) times their average speed] in the microcirculation. Conventional LDF measures perfusion in arbitrary units, by calculating the first moment of the Doppler spectrum.¹ By considering the complete distribution of Doppler frequencies and not only the first moment, a speed-resolved perfusion measure can be obtained. Using this approach typically involves a decomposition of the LDF photodetector power spectrum. Liebert et al.² developed a calculation scheme based on light transport simulations where the scattering phase function anisotropy value of the medium was varied until the modeled and measured spectra matched. The calculations were evaluated in the single Doppler-shift regime using highly diluted milk flowing in tubes.³ No independent validation of the anisotropy value was performed. Later, this model was expanded to account for multiple Doppler shifts.⁴ However, evaluation measurements in the multiple Doppler-shift regimes using a flow phantom showed that it was not possible to estimate the speed distribution in detail due to system noise.

A similar approach, in which the LDF power spectrum is decomposed into three speed components, was proposed by Larsson and Strömberg.⁵ Validation measurements were performed using both single- and double-tube flow phantoms perfused with a diluted microsphere solution. It was concluded that it is possible to estimate speed and concentration changes and to differentiate between flows with different speeds. This method was also evaluated for measurements on highly diluted blood, where a Gegenbauer-kernel (Gk) scattering phase function was found to be appropriate for modeling RBC light scattering.⁵ Fredriksson et al.⁶ further developed the photon transport simulation and processing method, which could then also model undiluted blood. The flow model for evaluation included plastic tubes and polyacetal plastic mimicking tissue scattering. The speed-resolved LDF system was later refined⁷ and used in vivo by Fredriksson et al.⁸ to separately study the effect in capillaries from those in larger microvascular vessels by speed-resolved perfusion. For the first time, it was demonstrated that type 2 diabetes is associated with an increased shunt flow.⁸ However, to make the LDF perfusion measures fully quantitative, additional information on the optical properties of local tissue is needed.⁹

Analyzing spatially resolved steady-state diffuse reflectance spectra (DRS) using either inverse modeling or direct methods based on trained algorithms has proven to be a successful way of estimating the optical properties of local tissue.^10,11 Instruments that combine LDF and DRS have previously been presented.¹² However, the main purpose of these instruments has not been to make quantitative perfusion measures but to be able to simultaneously measure the blood oxygen saturation.

Fredriksson et al.¹³ showed that, by having a multimodal optical instrument that combines spatially resolved DRS and LDF, both blood perfusion and blood amount measures can be made absolute, e.g., in the unit $\%\mathrm{RBC}\times \mathrm{mm}/\mathrm{s}$ for perfusion. The core of this instrument is an inverse Monte Carlo (MC) algorithm that makes use of an adaptive tissue model common to both the LDF and DRS techniques. The optimal tissue model is estimated using a fast optimization routine in which simulated LDF and DRS spectra are fitted to measured spectra in real time. Blood perfusion, oxygen saturation, and amount of RBCs are then given in absolute units directly from the optimal model.¹³ This enhanced perfusion and oxygen saturation (EPOS) system considers intraindividual and interindividual variations in the skin’s optical properties as well as variations over time.

The output parameters given from the EPOS system (speed-resolved perfusion, oxygen saturation, and tissue fraction of RBCs), as well as intrinsic model parameters (tissue scattering, vessel diameters, and epidermal thickness), have previously been evaluated using MC simulations.¹³ Of these parameters, tissue scattering, epidermal thickness, oxygen saturation, and tissue fraction of RBCs were evaluated using the state-of-the-art physical multilayer solid silicon phantoms, as well as liquid phantoms with known parameters.¹⁴ MC simulation enables the evaluation of perfusion under well-controlled conditions, including situations in which hundreds or thousands of discrete blood vessels are included in the model. However, since the analysis algorithm is based on inverse MC simulations, an independent validation on physical phantoms is desired to assess the accuracy in the speed-resolved measurement.

Therefore, the aim of this study was to evaluate the speed-resolved perfusion components, i.e., the relative amount of perfusion within each speed region, separated by absolute speeds in the unit mm/s. This was done using the EPOS system in a well-controlled setup on a physical blood-flow phantom.

2.

Method

2.1.

Single Doppler Shift and the Optical Doppler Spectrum

When a light wave is scattered by a moving RBC in tissue, a small frequency shift, a Doppler shift, occurs. The size of a single Doppler shift $\mathrm{\Delta }f$, arising from light scattered by an RBC with velocity $\mathbf{v}$ can be expressed as

Eq. (1)

$$\mathrm{\Delta }f=\mathbf{v}·\mathbf{q}=\frac{2nv}{\lambda }\sin \left(\frac{\theta }{2}\right)\cos \phi ,$$

where $\mathbf{q}$ is the difference between the incoming and the scattered wave vector, ${\mathbf{k}}_{\mathrm{i}}$ and ${\mathbf{k}}_{\mathrm{s}}$, $v=|\mathbf{v}|$, $\lambda$ is the laser wavelength, $\phi$ is the angle between $\mathbf{v}$ and $\mathbf{q}$, $n$ is the refractive index of the medium, and $\theta$ is the scattering angle (Fig. 1). Thus, it can be concluded that the single Doppler shift is directly dependent on the speed of the RBC and the scattering angle.

Fig. 1

Vectors and angles involved in a single Doppler shift.

In tissue, the probability distribution of the scattering angle is given by the scattering phase function. A commonly used phase function for biological tissue is the Henyey–Greenstein phase function described by the anisotropy factor $g=⟨\cos \theta ⟩$. However, the scattering phase function is very different for RBCs compared to tissue ($g\sim 0.99$ and $\sim 0.8$, respectively) and the two-parametric Gk phase functions have been found to more accurately describe scattering from RBCs.¹⁵ The Gk phase function contains the two parameters $g_{\mathrm{Gk}}$ and ${\alpha }_{\mathrm{Gk}}$ and is identical to the Henyey–Greenstein phase function for ${\alpha }_{\mathrm{Gk}}=0.5$.¹⁶ The choice of phase function is important for LDF since it determines the distribution of Doppler shifts and hence affects the conventional perfusion estimate.⁵ In Fredriksson et al.,¹⁷ the Gk phase function was determined at 780 nm for whole blood, giving $g_{\mathrm{GK}}=0.948$ and ${\alpha }_{\mathrm{Gk}}=1$ resulting in an anisotropy factor of 0.991, which agrees with the results in Kienle et al.¹⁵

The distribution of Doppler shifts forms the optical Doppler spectrum, i.e., the distribution of light intensity as a function of frequency shift. For a Gk phase function with ${\alpha }_{\mathrm{Gk}}=1$, the single shifted optical Doppler spectrum for a specific speed $v$ can be calculated analytically when assuming a random angle $\phi$ between the light and the direction of blood flow.¹⁸ The width of this optical Doppler spectrum will scale linear to the speed $v$, according to Eq. (1). In the presence of RBCs moving at different speeds, the optical Doppler spectrum will constitute a superposition of single-speed optical Doppler spectra.

In real tissue not all light will be Doppler-shifted, whereas some will be shifted multiple times. The degree of Doppler-shifted light and the distribution of multiple Doppler shifts affect both the magnitude and the shape of the optical Doppler spectrum of the light that propagates through tissue. Consequently, the tissue fraction of RBCs and the optical properties of the static tissue will indirectly affect the optical Doppler spectrum as they both affect the number of interactions with moving RBCs.¹⁹ With knowledge on the tissue fraction of RBCs and their speed distribution, the optical properties of the tissue and the detector layout, these effects can all be modeled as outlined in Secs. 2.3.1 and 2.3.2.

2.4.

Measurement System

The measurements were performed using a PeriFlux 6000 EPOS system (Perimed AB, Järfälla, Stockholm, Sweden), and implementing the method outlined in Sec. 2.3. The system consisted of a PF 6040 laser Doppler unit (including a laser light source at 780 nm and an optical bandpass filter), a PF 6060 spectroscopy unit, a broadband white light source (Avalight-HAL-S, Avantes BV, The Netherlands), and a fiber-optic probe.²⁴ The PF 6060 spectroscopy unit contained two spectrometers (AvaSpec-ULS2048L, Avantes BV, The Netherlands) and an optical notch filter suppressing wavelengths $790\pm 20\mathrm{nm}$ to minimize influence from the laser light source on DRS spectra. The fiber-optic probe included two emitting fibers and three detecting fibers (one for LDF spectra and two for DRS spectra). The LDF-detecting fiber was placed 0.8 mm from the LDF laser-light emitting fiber and the two DRS detecting fibers were placed at distances of 0.4 and 1.2 mm from the DRS white-light-emitting fiber [Fig. 2(a)]. The diameter of the DRS coupling fibers was $200\mu \mathrm{m}$, and the diameter of the LDF was $125\mu \mathrm{m}$. All fibers had a numerical aperture of 0.37 and were made of fused silica. The face of the probe is shown in Fig. 2(a).

Fig. 2

(a) Face of the probe with source–detector geometry. The central black region with fibers includes two LDF fibers, $D=125\mu \mathrm{m}$ (striped: emitting, black: detecting) and three DRS fibers, $D=200\mu \mathrm{m}$ (striped: emitting, gray: detecting). (b) Schematic view of the flow phantom. Gray structures are made of silicone and the gap between the silicone slabs and the tubes are filled with ultrasound gel. Measurements are in millimeter.

3.

Results

The accuracy of using the nominal tube diameter for converting balance data to flow speed was assessed by introducing an air bubble into the tube. The measured conversion factor was $51889\mathrm{mm}/\mathrm{g}$, which deviates by 2.8% from the theoretical factor. The theoretical conversion factor was used throughout the results section.

Even though the flow phantom is a nonhomogeneous tube phantom, the bio-optical model used in the EPOS system managed to accurately fit an LDF Doppler power spectrum to the measured validation data. Three examples taken from measurement 1, covering a tube flow speed from 1.0 to $15\mathrm{mm}/\mathrm{s}$, are depicted in Fig. 3(a). Similarly, there was a good agreement between measured and fitted DRS spectra for both source–detector separations used by the EPOS system, as demonstrated by the example depicted in Fig. 3(b).

Fig. 3

(a) Three examples from measurement 1 of measured (solid) and fitted (dotted) LDF spectrum covering the range from 1.0 to $15\mathrm{mm}/\mathrm{s}$. (b) Example of measured (solid) and fitted (dotted) DRS spectrum for the short- and long-fiber separation in the EPOS system, taken at the same time point as the $5.0\mathrm{mm}/\mathrm{s}$ LDF spectrum example. The fitting error was within 3% for both separations and without any systematic deviations.

The results from the two flow-phantom MC simulations strongly indicate that the direction of the RBCs impacts upon the result. The simulated Doppler power spectrum from the two models showed that there was a decreased width in the Doppler spectrum when the flow was aligned with the tube direction, compared to when it had a random direction (Fig. 4). Analyzing the width of the Doppler spectra, as described in Sec. 2.8, where an exponential decay function is fitted to the simulated spectra, showed that the tube direction flow needs to be increased by 27.8% to mimic the Doppler spectra from a random direction flow. To account for this effect, the theoretically expected speed components, as shown in Fig. 4, are scaled accordingly.

Fig. 4

Simulated Doppler power spectrum assuming laminar flow (parabolic speed distribution), with the RBC velocity vectors in the tube direction (red) or random direction (blue). Dotted lines show fitted exponential decay functions.

The validation measurements resulted in flow speeds that continuously decreased from 32 to $0.63\mathrm{mm}/\mathrm{s}$ (measurement 1) and from 26 to $0.20\mathrm{mm}/\mathrm{s}$ (measurement 2). The LDF perfusion increases linearly with the flow speed. Hence, to properly compare the magnitude of the three different speed components, each component was normalized by the total perfusion, calculated as the sum of the three components. This normalization also effectively removed dependencies on variations in the RBC tissue fraction that were observed during the experiments due to sedimentation in the syringe.

The results show that with increasing flow speed, the speed components for higher speeds become successively more dominant (Fig. 5). The measured speed components agree well with the theoretical components calculated by assuming laminar flow (see Sec. 2.6), after correction for the assumption of random velocity vector direction. The weighted RMS errors for the three normalized speed components are given in Table 1.

Fig. 5

Normalized speed components versus the flow speed in the tube for (a) measurement 1 and (b) measurement 2. The dotted lines mark the theoretically expected speed component assuming a laminar flow in the tube direction.

Table 1

Weighted RMS error for each of the three speed components at both measurements and the average.

4.

Discussion

In this study, we have demonstrated that a multimodal optical system integrating LDF and DRS, with an individually adapted tissue model analyzed using an inverse MC technique, can accurately differentiate moving RBCs into three speed components separated by absolute flow speeds in the unit mm/s. This result adds to our previous validation, performed using MC simulated data, of a multilayered skin tissue containing a large number of discrete blood vessels of different sizes ranging from 6 to $400\mu \mathrm{m}$ in diameter.¹³ The previous study showed that our inverse algorithm could compensate for both intraindividual and interindividual variations in optical and geometrical properties as well as different blood vessel sizes, positions, and directions, to enable a quantitative assessment.

Flow phantoms, consisting of either perfused microtubes^1,5,6,15,32 or moving layers,^9,33–35 have previously been used for the calibration and evaluation of the LDF technique. The results from some of these studies have shown that MC simulations can accurately predict the LDF Doppler spectrum and that the Doppler power spectrum depends on the scattering phase function and the degree of multiple Doppler shifts. However, using solid moving layers where the scattering material has a phase function that deviates significantly from that of RBCs is a major drawback for this type of flow phantoms, as the results will not mimic those from real tissue. With tube phantoms, it is possible to overcome this by using blood as a moving scatterer. In this study, we have used undiluted human blood, which results in a more realistic validation, compared to previous studies in which diluted blood was used.^5,6

Constructing and using flow phantoms that mimic real tissue pose a challenging task. By selecting a tube with a diameter of $150\mu \mathrm{m}$, we were able to model the larger vessels in the microcirculation. When attempting the same with smaller tube sizes, the flow resistance was too large to reach the higher flow speeds without either breaking the tube connections or having a major blood plasma leakage in the phantom.

The validation measurements were performed by initially perfusing the tube with the maximal speed of up to $32\mathrm{mm}/\mathrm{s}$. When a stable flow was reached, the syringe pump was turned off. This gave an exponentially decreasing flow speed with minimal variations in RBC concentration. To reduce sedimentation and coagulation effects at slow speeds, the validation measurement time was limited to a maximum of 20 min. This resulted in a minimal flow speed of down to $0.20\mathrm{mm}/\mathrm{s}$ by the end of the experiment. This range of flow speeds covers the majority of the range of speeds that can be found in the microcirculation.

When analyzing measured data, the EPOS method assumes that successive Doppler shifts are independent. In tissue, this is a valid assumption since RBCs move in random directions in a complex vessel network of different sizes of vessels oriented in random directions. However, this is not true in the physical model, which consists of five aligned 0.15-mm-diameter tubes. In the physical model, the velocity vectors of all RBCs were directed along the tubes. MC simulations, as depicted in Fig. 4, show that a Doppler spectrum from a flow in the tube direction is narrower than, but similarly shaped to, a Doppler spectrum generated from a random direction flow. By increasing the speed of the tube direction flow by 27.8%, a close match to the random direction Doppler spectra was achieved. This directional effect can be compensated by either modifying the Doppler spectra in the inverse MC algorithm or scaling the reference speed by 27.8% when calculating the theoretical speed components. We chose the latter because we do not want to change the algorithm that is being validated.

Compared to the tissue model used by the inverse MC algorithm, the flow phantom is significantly less homogeneous, containing a nonscattering layer of polytetrafluoroethylene tubing material and ultrasound gel. This nonscattering layer does not affect the inverse MC algorithm’s ability to find a solution with a negligible misfit. The accuracy of the output parameters, RBC tissue fraction, and oxygen saturation has been evaluated elsewhere¹⁴ and was not within the scope of consideration when designing the flow phantoms in this study. Furthermore in that study, the intrinsic model parameter, the reduced scattering coefficient, was evaluated. It should be emphasized that due to the inhomogeneous distribution of RBCs in the flow phantom, in relation to that in the tissue model and in real tissue, we did not evaluate the accuracy of the RBC tissue fraction dependency in the perfusion (cf. the unit $\%\mathrm{RBC}\times \mathrm{mm}/\mathrm{s}$). We evaluated the relative speed-resolved perfusion components, i.e., the relative amount of perfusion within each speed region and thus the absolute speed limits differentiating the components.

The inverse MC algorithm used in the EPOS system is based on an adaptive three-layered skin tissue model. The MC model includes vessel-packaging effects to compensate for blood being confined to vessels rather than being homogeneously distributed. The model also assumes that the blood is found in both dermal tissue layers. Obviously, this is not the case for the flow phantoms used in this study, where all the blood is confined to the five tubes located at a depth of 0.60 mm. Still the inverse algorithm is capable of accurately modeling the measured LDF Doppler power spectra (Fig. 5).

5.

Conclusion

The validation measurements were performed on average flow speeds in the range from 0.20 to $32\mathrm{mm}/\mathrm{s}$, covering the nominal ranges for all three LDF speed components. Comparing the measured and theoretical speed components shows that the EPOS system is capable of accurately decomposing the LDF power spectrum into three speed components, differentiated by absolute flow speed, with a weighted average RMS error ranging from 2.9% to 8.1%. The presented results strongly support the claim that the EPOS system can quantitatively measure speed-resolved perfusion differentiated by absolute speeds in the microcirculation. Applied to skin tissue, this enables a differentiation between flow compartments having different flow speeds and could prove to be a valuable tool for studying microcirculatory function or dysfunction in greater detail.