Quantitative blood flow velocity imaging using laser speckle flowmetry

Abstract

Laser speckle flowmetry suffers from a debated quantification of the inverse relation between decorrelation time (τc) and blood flow velocity (V), i.e. 1/τc = αV. Using a modified microcirculation imager (integrated sidestream dark field - laser speckle contrast imaging [SDF-LSCI]), we experimentally investigate on the influence of the optical properties of scatterers on α in vitro and in vivo. We found a good agreement to theoretical predictions within certain limits for scatterer size and multiple scattering. We present a practical model-based scaling factor to correct for multiple scattering in microcirculatory vessels. Our results show that SDF-LSCI offers a quantitative measure of flow velocity in addition to vessel morphology, enabling the quantification of the clinically relevant blood flow, velocity and tissue perfusion.

Figures

Figure 1. Overview of acquisition and analysis steps for quantitative laser speckle flowmetry.

A modified SDF-LSCI videomicroscope enables consecutive multi-exposure laser speckle imaging and SDF-imaging of the same microcirculation area. The acquisition and analysis steps are supported by our theoretical modelling and experimental validation, as described in this Article.

Figure 2. Multiple scattering scaling factor.

Scaling factor Α(N) = α/α1 = τc,1/τc, is calculated using our model for autocorrelation g1(τ) based on Mie-Percus-Yevick scattering in human blood for Hct = 30% (upper solid orange line) and Hct = 45% (lower solid red line). As a practical guideline, A(N) from our MPY model can approximately be fitted by A(N) = 1.1 N(2/3), which gives an error <10% for the range plotted for both hematocrits. Dashed lines represent Α(N) for Lorentzian (grey) and Gaussian (black) models for g1(τ). All scaling factors are calculated using a normal distribution for the number of scattering events in the vessel pN(n), with mean N and variance determined by the Percus-Yevick pair correlation function (Supplementary equation 6).

Figure 3. Multi-exposure curves and fits.

Multi-exposure speckle contrast values (data points) and corresponding fit of Supplementary equation (12) (dashed lines) for 9 different flow velocities for 2 μm polystyrene spheres (2.5 vol%). Speckle contrast K is calculated according to Supplementary equation 12.

Figure 4. Influence of scatterer size on α.

(a) 1/τc plotted against V for 6 different scatterer sizes (polystyrene microspheres diameter = [0.6–10 μm]), together with a linear fit (dotted lines) to the data points with weights τc. The slope of the linear fit is α. No error bars are plotted for clarity, the average standard error on τc was 4% ± 2% (max. error 12%). (b)α versus scatterer diameter, error bars are 95% CI intervals from linear fit in (a). Also plotted is the theoretically derived α (solid line) using Mie-Percus-Yevick scattering theory and the number of scattering events N in the flow tube (diameter d 0.2 ± 0.03 mm) as obtained from Monte Carlo simulations (N = 1.2μsd), N ranged from [2–15] for [0.6–10 μm] spheres. The shaded area represents the uncertainty in α due to error margins in optical properties of the scatterers.

Figure 5. Influence of scatterer volume fraction on α.

Measured α versus (a) scatterer volume fraction, (b) scattering properties (scattering coefficient μs and average number of scattering events N in the flow tube with diameter d 0.2 ± 0.03 mm, N = 1.2μsd) and (c) theoretically derived α for all measured samples. Error bars are 95% CI intervals from linear fit on 1/τc vs. V.

Figure 6. In vivo determination of α.

1/τc versus V for RBCs in vivo, for (a) chick embryo and (b) human microcirculation. The top panels (green open circles) show 1/τc estimated by a multi-exposure curve fit (Supplementary Section IIId, equation 12) and τc,offset correction (Supplementary equation (13)21). The bottom panels show 1/τc,1 rescaled for the average number of scattering events N, using model based Α(N) = α/α1, and 1/τc,1 = (1/τc)/Α(N). In both (a,b) one data point was excluded as an outlier (not shown). Vertical error bars represent 95% CI of the multi-exposure curve fit and horizontal error bars represent the standard deviation in reference flow velocity measurements from conventional SDF images. The slope, or α1, is 0.20 ± 0.07 (95% CI) and 0.39 ± 0.15 for chick embryo respectively human RBCs, and the theoretical prediction for α1 is 0.27 respectively 0.38.

Figure 7. Human microcirculatory flow velocity mapping.

(a) Conventional SDF image where the contrast is based on absorption differences between RBCs and tissue. Flows below 2 mm/s can be measured by RBC tracking. (b) 1/τc map of the same microcirculation region obtained with multi-exposure SDF-LSCI after correction for τc,offset, contrast is obtained by perfusion dynamics. (c) Map of LSCI-derived blood flow velocities after correction for τc,offset and A(N), and masking of selected blood vessel contours. The scale bar is 100 μm.