Two-Beam Phase Correlation Spectroscopy: A label-free holographic method to quantify particle flow in (bio)fluids

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-ΦCS) 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-ΦCS, 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-ΦCS 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-ΦCS 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).

The workflow of 2B-ΦCS 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-ΦCS 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-ΦCS 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.

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.

The authors highlighted their finding: 2B-ΦCS 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-ΦCS 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.

相位相关光谱：无标记全息方法测量流动生物微粒

定量检测流动中的微粒（例如血管中流动的血细胞、沿着细胞内微管主动运输的囊泡）对于研究许多生命过程十分重要。人们提出了多种技术以测量流场中的微粒：包括粒子图像测速（PIV）、多普勒光学相干断层成像（DOCT）和荧光相关光谱(FCS)。PIV技术通过对粒子进行连续拍摄，以分析相邻两幅图像中粒子的平均位移来确定液体的流速和粒子的直径，该方法仅适用于稀疏的示踪粒子。DOCT利用低相干干涉和多普勒频移分析来检测组织深处血管内的血流情况，但是无法获得细胞的密度信息。

FCS，尤其是近年来提出的双焦点FCS，是检测流场中微粒的一个重要方法。在双焦点FCS中，当含有荧光标记微粒的液体流经两个焦点时，记录两个焦点内荧光信号；通过对两个焦点内荧光信号做自相关和互相关计算，可以实现对微粒流速和密度的测量。然而，传统的FCS和双焦点FCS都需对样品进行荧光标记。荧光标记则会对细胞活性产生较大影响，同时其光漂白和光毒性阻碍了对活体样品的长时间检测。

折射率是与材料介电常数相关的固有光学参数，复杂样品（如细胞）的折射率分布与其化学成分分布密切相关。研究发现，细胞内几乎所有亚细胞器的折射率均不同于细胞质的折射率，生物微粒（如血细胞等）的折射率也不同于其周围的液体背景。因此，利用定量相位成像可以高衬度地获得这些亚细胞器及生物微粒的图像。当我们利用相位衬度代替荧光衬度时，就可以通过传统双焦点FCS的方法在天然状态下获得流场中微粒动力学信息。

基于以上思路，西安电子科技大学郜鹏教授课题组和德国KIT的G. Ulrich Nienhaus教授课题组提出并验证了用于流动中的微粒检测的双光束相位相关光谱方法（2B-ΦCS）。在2B-ΦCS中，利用数字全息显微（也可以是其他定量相位显微方法）对连续流动的微粒进行定量相位成像。之后，通过对相位图像序列中两个相邻圆域内随时间变化的相位曲线进行自相关和互相关分析，在无需标记的前提下获得了微粒的流速、直径、浓度等信息。文中，作者利用2B-ΦCS实现了大鼠血细胞密度的体外测量和斑马鱼血液流速的在体测量。相关研究成果发表于Photonics Research 2023年第5期。

2B-ΦCS定量检测微粒浓度和流速的步骤：首先，通过数字全息显微系统连续采集流动微粒的相位图像序列，然后对图像序列中两个选定圆形区域的相位扰动进行相关计算，最后使用物理模型拟合相关曲线来获取微粒的浓度和流速。作者通过利用强度图像序列和相位图像序列，来进行相关分析的优劣比较，证明了利用相位图像序列可以显著提高自/互相关的幅度和信噪比。

应用1：使用2B-ΦCS对大鼠血细胞的密度进行体外测量。结合微流控通道，对稀释100倍的大鼠血液进行测量。280组测量结果的分布直方图显示大鼠的血细胞密度为4.7 ± 1.9 × 10⁶ µL^–1 (平均值±标准差)、血细胞平均直径为4.6 ± 0.4 µm (平均值±标准差)，如图2所示。

应用2：利用2B-ΦCS对斑马鱼胚胎血管内血流进行了动态测量。利用DHM连续记录了斑马鱼的静脉和动脉血管的6000帧全息图。从DHM的全息图中可以再现出血管的相位图像，在相位图像序列中分别选取两个圆形区域以覆盖斑马鱼的动脉和静脉血管。之后，对两个圆域内的相位-时间曲线进行相关分析，可以获得动脉和静脉中血细胞的流速。通过对15条斑马鱼进行测量，统计得到动脉和静脉的血液流速分别为290 ± 110 μm s^–1 和120 ± 50 μm s^–1，如图3所示。

研究团队表示：“2B-ΦCS利用微粒相位与其周围介质在折射率上的差异来提供衬度，可以在无需额外荧光标记的前提下，结合相关分析实现对微粒流速、直径、浓度等信息的高精度测量。尤其是，当该技术与深度学习相结合时，可以对不同尺度的微粒进行同时测量。未来，该技术有望在血液检测和水质检测中得到普遍应用。”