Characterizing the transport of nano- and microscopic particles (e.g., flow of blood cells in vessels and active movement of vesicles along microtubules in cells) is important for understanding many biological processes. A variety of techniques have been proposed to quantify the dynamics of particle flow, including particle image velocimetry (PIV) and Doppler optical coherence tomography (DOCT). PIV, which involves continuous imaging of particles to analyze the speed and direction of the flow pattern, is limited to sparse tracer particles. DOCT utilizes low coherence interference and Doppler frequency shift analysis to detect the blood flow in blood vessels, and currently, the time resolution of ODT is mainly limited by the necessity to record hundreds of holograms for each swept wavelength. Fluorescence correlation spectroscopy (FCS), especially the dual-focus FCS proposed in recent years, has also proven to be a valuable tool for the quantitative assessment of particle flow. In dual-focus FCS, the fluorescence signals from the two foci are registered as a function of time; then, time autocorrelation analysis of the intensity yields quantitative information about diffusion and flow. However, both FCS and dual-focus FCS require either intrinsically fluorescent particles, or particles labeled with fluorescent moieties. The unavoidable photobleaching sets limits to its application and calls for techniques not relying on fluorescence.

The refractive index (RI) is an intrinsic optical parameter related to the electrical permittivity of the material. The RI of biological particles, subcellular organelles or cells differ from their (usually aqueous-based) surrounding biofluid and, therefore, the RI can provide the necessary contrast against the background. Once fluorescence contrast is replaced by phase contrast, we can quantitatively access the dynamics of flowing microparticles using the concept of dual-focus FCS but in a label-free manner. Centering on the above ideas, Prof. Peng Gao's research group from Xidian University and Prof. G Ulrich Nienhaus's research group proposed and demonstrated two-beam phase correlation spectroscopy (2B-CS) as a label-free approach for the quantification of particle flow, such as in-vivo blood flow or particle flow through a standard microfluidic chip.

In 2B-CS, digital holography microscopy (or other quantitative phase microscopy approaches) was used to perform quantitative phase imaging for flowing particles continuously. Then, the phase fluctuation time traces are acquired from the DHM holograms, and correlation analysis yields information on concentration and velocity of flowing particles. 2B-CS overcomes photobleaching and phototoxicity issues inherent in fluorescence-based approaches, and thus can be widely applied in many fields including biomedicine. The authors utilized 2B-CS to realize the in vitro measurement of rat blood cell density and in vivo measurement of zebrafish blood flow velocity. The relevant research results were published in Photonics Research, Volume 11, No. 5, 2023(Lan Yu, Yu Wang, Yang Wang, Kequn Zhuo, Min Liu, G. Ulrich Nienhaus, Peng Gao. Two-beam phase correlation spectroscopy: a label-free holographic method to quantify particle flow in biofluids[J]. Photonics Research, 2023, 11(5): 757).

Figure 1 Principle of 2B-CS. (a) Sketch of the microfluidic channel illuminated by a perpendicular light beam. The sample flowing through the microchannel is monitored by phase imaging. (b)-(d) The workflow of 2B-CS. (e) ACFs and CCF curves calculated from the phase-time traces.

The workflow of 2B-CS for the quantification of particle flow: First, acquiring the holograms of flowing particles continuously by digital holography microscopy (DHM). Second, acquiring the phase fluctuation time traces in two selected circular areas in the phase images. Third, the correlation curves from phase fluctuation time traces are calculated, and the further correlation analysis yields information on the concentration and velocity of flowing particles. After comparing the correlation analysis using the intensity image sequence and phase image sequence, it is confirmed that the contrast provided by the phase of the flowing particles can provide the correlation curves with significantly-enhanced amplitude and signal-to-noise ratio (SNR).

2B-CS was applied to measure the density of rat blood cells in vitro. Fresh rat blood from a rat was extracted and diluted with PBS at a volume ratio of 1:100. Once the diluted blood was pumped in, and flowed in a microfluidic channel, 280 holograms were taken. 2B-CS analysis reveals the density of the rat blood cells is 4.7 ± 1.9×10⁶ µL^-1 (mean ± s.d.), and the average diameter of rat blood cells was 4.6 ± 0.4 µm (mean ± s.d.), as shown in Figure 2.

Figure 2 2B-CS measurement in density and size of rat RBCs. (a) The workflow of in-vitro 2B-ΦCS measurement on rat blood. (b) Phase images of flowing RBCs at six different times (specified in the insets). (c, d) Histograms of (c) density and (d) diameter measurements.

In addition, 2B-ΦCS was utilized to monitor blood flow in live zebrafish embryos. 6000 holograms of the veins and arteries of zebrafish embryos were recorded continuously using DHM. The phase image of blood vessels can be reconstructed from the holograms. An exemplary phase image reconstructed from the hologram series (Figure 3) shows RBCs in a vein (posterior cardinal vein, PCV) and an artery (dorsal aorta, DA) in phase contrast. The correlation analysis of 2B-ΦCS on 15 zebrafish embryos reveals that the blood flow velocities arteries (red square) and veins (gray square) are 290 ± 110 μm s^-1 and 120 ± 50 μm s^-1, respectively.

Figure 3 In-vivo 2B-CS measurement of blood flow velocities in an artery and a vein of a zebrafish embryo. (a) The schematic DHM setup for 2B-CS measurement on blood cell flow in zebrafish vessels; (b) The autocorrelation and cross-correlation curves calculated from two phase-time trajectories extracted from vascular images; (c) Statistical chart of blood flow velocity in arteries and veins, respectively.

The authors highlighted their finding: 2B-CS utilizes the phase difference of particles against the surrounding media as the substitute for extraneous fluorescence labels. The correlation analysis on the phase images can quantitatively access the flow velocity, diameter, and concentration of flowing particles in a label-free manner. The potential of 2B-CS will be further enlarged when being combined with deep learning, for instance, to measure particles of different sizes simultaneously. The authors also envisage that this technology will be widely applied in many fields, including blood inspection and water quality monitoring.