Numerical simulation of deformable particles in a Coulter counter

Abstract

In Coulter counters, cells counting and volumetry are achieved by monitoring their electrical print when they flow through a sensing zone. However, the volume measurement may be impaired by the cell dynamics, which may be difficult to control. In this paper, numerical simulations of the dynamics and electrical signature of red blood cells in a Coulter counter are presented, accounting for the deformability of the cells. In particular, a specific numerical pipeline is developed to overcome the challenge of the multi‐scale nature of the problem. It consists in segmenting the whole computation of the cell dynamics and electrical response in a series of dedicated computations, with a saving of one order of magnitude in computational time. This numerical pipeline is used with rigid spheres and deformable red blood cells in an industrial Coulter counter geometry, and compared with experimental measurements. The simulations not only reproduce electrical signatures typical of those measured experimentally, but also allow an analysis of the electrical signature in terms of the heterogeneity of the electrical field and dynamics of the particles in the measurement zone. This study provides a methodology for computing the sizing of rigid or deformable particles by Coulter counters, opening the way to a better understanding of cells signatures in such devices.

Impact of the membrane viscosity on the tank-treading behavior of red blood cells

“…The numerical framework used in this work is the YALES2BIO solver (https://imag.umontpellier.fr/ ~yales2bio/), dedicated to the simulation of RBC dynamics under flow and already used in several publications in the recent years [5,6,19,24,45,46]. It is based on a continuum framework both for the fluid and the membrane.…”

Detecting cells rotations for increasing the robustness of cell sizing by impedance measurements, with or without machine learning

“…Note that in the case of more spherical particles, the problem of rotation‐associated overestimation of the volume disappears. However, small electrical peaks [34,4,14] may be present at the corner of the orifice. The parameters of the ‐based filter could be modified to detect such peaks, as discussed in Section 3.2.…”

“…As reported in the literature [10,11], complex pulses shapes are obtained when deformable and aspherical particles flow near the aperture wall, while 'bell‐shaped' signatures are obtained for centered paths. Previously [14], we directly showed that RBCs deform and, most importantly, rotate when flowing near the wall, which induces a peak on the electrical pulse at the exact moment of the flow‐induced rotation. Golibersuch [13] also reported pulses presenting several peaks when the aperture is long enough to allow RBCs to rotate several times in the sensing region.…”

Numerical simulation of time-resolved 3D phase-contrast magnetic resonance imaging

“…The fluid velocity is predicted by solving the incompressible Navier-Stokes equations (NSE) that read: where u , p , ρ and μ are the velocity field, pressure field, constant density and constant dynamic viscosity of the fluid, respectively. To this aim, the NSE are discretized on a fixed numerical mesh and solved using the YALES2BIO solver [ 39 ] ( http://imag.umontpellier.fr/~yales2bio/ ), an in-house CFD solver dedicated to the simulation of blood flows in complex geometries at both macroscopic and microscopic scales [ 40 – 44 ]. The flow solver uses high-order finite-volume non-dissipative numerical methods to solve the NSE on unstructured meshes [ 45 ].…”