Emergent behaviors in RBCs flows in micro-channels using digital particle image velocimetry

Abstract

The key points in the design of microfluidic Lab-On-a-Chips for blood tests are the simplicity of the microfluidic chip geometry, the portability of the monitoring system and the ease on-chip integration of the data analysis procedure. The majority of those, recently designed, have been used for blood separation, however their introduction, also, for pathological conditions diagnosis would be important in different biomedical contexts. To overcome this lack is necessary to establish the relation between the RBCs flow and blood viscosity changes in micro-vessels. For that, the development of methods to analyze the dynamics of the RBCs flows in networks of micro-channels becomes essential in the study of RBCs flows in micro-vascular networks. A simplification in the experimental set-up and in the approach for the data collection and analysis could contribute significantly to understand the relation between the blood non-Newtonian properties and the emergent behaviors in collective RBCs flows. In this paper, we have investigated the collective behaviors of RBCs in a micro-channel in unsteady conditions, using a simplified monitoring set-up and implementing a 2D image processing procedure based on the digital particle image velocimetry. Our experimental study consisted in the analysis of RBCs motions freely in the micro-channel and driven by an external pressure. Despite the equipment minimal complexity, the advanced signal processing method implemented has allowed a significant qualitative and quantitative classification of the RBCs behaviors and the dynamical characterization of the particles velocities along both the horizontal and vertical directions. The concurrent causes for the particles displacement as the base solution-particles interaction, particle-particle interaction, and the external force due to pressure gradient were accounted in the results interpretation. The method implemented and the results obtained represent a proof of concept toward the realization of a general-purpose microfluidic LOC device for in-vitro flow analysis of RBCs collective behaviors.

Fig. 1.

(a) The Y-junction geometry, the rectilinear microfluidic channel width w = 320 μm and length l = 16 mm. (b) The zoom of the microfluidic chip positioned under the microscope. (c) Five frames showing the RBCs sample distribution per experiment: a uniform distribution in the experiments with A ∈{0, 10, 100}; the RBCs grouped in specific zones with A ∈{0.1, 1}.

Fig. 2.

The DPIV analysis from the RBCs flow movies to the RBCs time-varying velocity vectors maps V(t). In the velocity vectors maps the arrows display the RBCs velocity in directions and magnitudes.

Fig. 3.

Examples of the three RBCs flow patterns identified {Weak Activity, Vorticity, Alignment} represented by their velocity vectors maps. The velocity profiles are shown in three microchannel sections {A, B, C}.

Fig. 4.

(a) The map that establishes the relation between the RBCs flow patterns and the RBCs velocities along the horizontal (|〈V_x(t)〉|) and vertical (|〈V_y(t)〉|). The x-axis and the y-axis report respectively the |〈V_y(t)〉| and the |〈V_x(t)〉| values in [mm/s], whereas the color codes the behaviors: “0” for the Weak Activity, “0.5” for the Vorticity and “1” for the Alignment. (b) The three scattering plots related to (|〈V_y(t)〉|, |〈V_x(t)〉|) for the experiments A ∈{0; 0.1; 10}. All these experiments reach the Alignment.

Fig. 5.

Histograms of the range of variation and standard deviation of the signals (a) 〈V_x(t)〉 and (b) 〈V_y(t)〉 in the six experiments.

Fig. 6.

The velocities signals (〈V_x(t)〉, 〈V_y(t)〉) for all the five experiments A ∈{0; 0.1; 1; 10; 100} obtained by a spatial averaging the relative matrices (〈V_x(t)〉, 〈V_y(t)〉) and plotted using a color-coded representation in a time window of 1 s. The signals (〈V_x(t)〉, 〈V_y(t)〉) were normalized in the range [−1; 1]. (a) Comparison of 〈V_x(t)〉 trends: particles displacements toward the left direction for positive values (red arrow) and the right direction for negative values (blue arrow). (b) Comparison of 〈V_y(t)〉 trends: the positive values are for movements toward the wall_2 (down), and the negative for movements toward the wall_1 (up). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7.

The trends of velocity along the horizontal axis 〈V_x(t)〉 for the experiments A ∈{0.1; 10; 100} in a time interval of 10 s. The red line reproduces the trend of the periodic pressure wave at f = 0.1 Hz detected for A ∈{10; 100}. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8.

The spectra of 〈V_x(t)〉 (a) for the PBS flow and the five experimental conditions A ∈ {0; 0.1; 1; 10; 100}. The frequencies components at f ∈{5; 17.5} Hz have been selected as the most significant being highly sensitive to the experimental conditions and at the same time dominant at least in one experiment. They correspond to the time periods respectively T ∈ {0.2; 0.06} s. (b) A zoom of the spectra in the range f ∈[0.08; 10] Hz.

Fig. 9.

Histograms of the amplitude of the peaks in the 〈V_x(t)〉 spectra per experiment (a) f = 5 Hz; (b) f = 17.5 Hz.

Fig. 10.

Histograms of the amplitude of the peaks in the 〈V_y(t)〉 spectra per experiment (a) f = 5 Hz; (b) f = 55 Hz.

Fig. 11.

The signals (〈V_xL〉, 〈V_xR〉) are plotted respectively in red and blue lines in a time window including two periods of 0.2 s. The arrows evidence the significant periods: solid arrow T = 0.2 s, dotted arrow T = 0.06 s. (a) A = {0}. (b) A = {0.1}. (c) A = {1}. (d) A = {10}. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 12.

The spatial velocity maps obtained by the temporal average of the velocity matrices V_x(t) and V_y(t) per A ∈ {0, 0.1; 1; 10; 100}. The right column (a) is for |〈V_x〉| and the left column (b) is for |〈V_y〉|. A color-coded threshold was used.