Fig 1.
Impedance system based on the Coulter principle to count and size particles: The left image is a slice through the complete domain; the color image shows the map of electrical field in the aperture, the red ellipses representing a time lapse of an RBC flowing through the sensor, with the associated tension pulse along time depicted above.
It should be noted that the constriction depicted in the color picture is cylindrical, the RBC flowing over the symmetry axis.
Fig 2.
Numerical pipeline for the simulation of the RBC dynamics and of the associated electrical pulse in a Coulter counter.
(A) Simulation of the RBC elongation in an extensional flow, which reproduces the deformations occurring before the cell enters in the aperture. Proper boundary conditions are applied to reproduce the extensional flow seen by the RBC along its trajectory. The typical extensional rate in picture A is 5104 s−1. (B) Sequence of RBC shapes during the simulation of the RBC dynamics in the aperture, shown over the velocity field (without cell). The elongated cell depicted in A is used as the initial state of the RBC in the simulation shown in B. (C) Electrostatic simulations performed for each RBC shape issued from B. (D) Resistive pulse obtained by gathering the results of the electrostatic simulations of picture C.
Fig 3.
Numerical simulations of the RBCs dynamics and of the associated electrical pulses for different trajectories: (A) RBC trajectories inside the aperture (the aperture center is located at the origin of the coordinate system); (B) Resistive pulses; (C) RBCs dynamics in the aperture.
In picture B, cases 2 and 3 are not shown since no substantial variations are found between cases 1 and 4, in terms of pulse profiles. In all pictures of C, the first two RBC shapes are separated by 11 μs. The remaining shapes are displayed at 4 μs intervals.
Fig 4.
RBC orientations and resistance pulses as a function of the cell location inside the aperture, for different trajectories: (A) RBC orientation (is zero when the particle is aligned with the aperture axis); (B) Resistive pulses.
Fig 5.
Illustration of quantities derived from impedance pulses and required for calculating features ,
and
.
Fig 6.
Scatter plots of experimental measurements and numerical results in the () plane (A) and in the (
) plane (B).
Measurements from the experimental acquisition are depicted in red and the 10 numerical simulations with the reference parameters for the RBC and only changing the trajectory are represented by black triangles and linked with a black solid line to ease the visualization.
Fig 7.
Comparison of the simulated pulses with experimental measurements.
The numerical pulses are superimposed with experimental data (in red continuous line) that have the same and
, with a tolerance margin of ±1 μs and ±2% respectively. Graphs A, B, C, D, E and F correspond to the simulated cases 1, 5, 6, 7, 8 and 10, respectively.
Fig 8.
One-at-a-time sensitivity analysis of the effect of the shear modulus Gs, the reduced volume and the internal viscosity νin.
Pulses of pictures A, B and C correspond to trajectories 1, 6 and 10 of Fig 3, respectively. The settings for the different depicted cases is given in Table 1.
Table 1.
Summary of the parameters used in the simulations performed to study the effect of shape and rheology of particles on the pulses.
Each column corresponds to a series of simulations, for different trajectories. Cases ‘ref’, ‘Gs↗’, ‘νin↗’ and ‘’ are relevant for RBCs, while case ‘r-sph’ models a rigid sphere.
Fig 9.
Microscopic views of RBCs suspended in the HORIBA Medical electrolytic reagent (left picture) and in a SB3–12 solution at 100 mg.L−1 concentration (right picture).
Fig 10.
Dependence of () and (
) density maps to the morpho-mechanical characteristics of the cells.
Graph A and D are obtained without SB3–12 nor glutaraldehyde. Pictures B and E arise from the acquisition with 90 mg.L−1 SB3–12, while graphs C and F are derived from the acquisition with 0.5% glutaraldehyde. In pictures A, E and F, the gating used for the extraction of pulse signatures (Gates 1–6) and for assessing RBCs alteration (Gate 7 and 8) is shown. The colormaps derive from Gaussian kernel density estimations, while the black lines are density isolines derived from the actual distributions.
Fig 11.
Gate-wise comparison of the averaged pulses signatures.
Pictures A, B, C, D, E and F correspond to Gates 1, 2, 3, 4, 5 and 6 (see Fig 10), respectively. The grey area illustrates the confidence intervals (±2σ) derived from 22 samples withdrawn from healthy donors. Glutaraldehyde concentration of 0.5% and SB3–12 concentration of 90 mg.L−1 have been used.
Fig 12.
Variations of the pulse proportion inside Gate 7 and 8 (see Fig 10) as a function of glutaraldehyde and SB3–12 concentrations.
The boxplots arise from measurements from 22 healthy donors, without glutaraldehyde nor SB3–12.