Assessment of deformation of human red blood cells in flow cytometry: measurement and simulation of bimodal forward scatter distributions

: Light scattering by single cells is widely applied for flow cytometric differentiation of cells. However, even for human red blood cells (RBCs), which can be modeled as homogeneous dielectric particles, the potential of light scattering is not yet fully exploited. We developed a dedicated flow cytometer to simultaneously observe the forward scattering cross section (FSC) of RBCs for orthogonal laser beams with incident wave vectors (cid:174) k 1 and (cid:174) k 2 . At a wavelength λ = 632.8 nm, bimodal distributions are observed in two-dimensional dot plots of FSC( (cid:174) k 1 ) vs. FSC( (cid:174) k 2 ), which result from the RBCs’ random orientation around the direction of flow, as well as from the distributions of their size and their optical properties. Typically, signals of 7.5 × 10 4 RBCs were analyzed. We actively oriented the cells in the cytometer to prove that orientation is the main cause of bimodality. In addition, we studied the wavelength dependence of FSC( (cid:174) k 1 ) using λ = 413.1 nm, 457.9 nm, 488 nm and 632.8 nm, covering both weak and strong light absorption by the RBCs. Simulations of the light scattering by single RBCs were performed using the discrete dipole approximation (DDA) for a range of sizes, orientations and optical properties to obtain FSC distributions from RBC ensembles. Using the axisymmetric biconcave equilibrium shape of native RBCs, the experimentally observed distributions cannot be reproduced. If, however, an elongated shape model is employed that accounts for the stretching of the cell by hydrodynamic forces in the cytometer, the features of the strongly bimodal measured frequency distributions are reproduced by the simulation. Elongation ratios significantly greater than 1 in the range of 1.5 to 2.5 yield the best agreement between experiments and simulated data. elements in dependence on orientation, size and Hb concentration of the RBC. Integration of the corresponding combinations of Mueller matrix elements over the photodetector’s solid angle provides the FSC of the cells. FSC histograms are obtained by direct Monte Carlo (MC) sampling of the distributions of orientation angle, cell size, Hb concentration. We compare simulations with stretched and undeformed RBC shape models to measurement data to assess the effect of deformation on the observed bimodality of the frequency channel of the cytometer and their elongated shape due to hydrodynamic forces. This interpretation was experimentally validated by actively orienting the erythrocytes using a steel capillary for the injection of RBCs in the sheath flow whose outlet was changed from a circular cross section to a flattened, oval cross section. For modeling and simulation, we applied the DDA to compute the light scattering cross sections of native, oriented RBCs for the specific instrumental conditions and hematological RBC indices, i. e., mean cellular volume, red cell distribution width and mean cellular Hb concentration, obtained using a hematology analyzer. Our results clearly indicate that the elongations of RBCs, and hence their rheological properties, are essential to explain the experimentally observed bimodal distributions. Numerical simulations based on a biconcave shape model with an axis of rotational symmetry that corresponds to the RBC shape in the absence of external forces are in strong disagreement with the experimental observations reported here. On the other hand, we were able to reproduce the main features of the measured bimodal distributions by accounting for the elongation of RBCs in the flow cell. We found that a length of about 17 µm corresponding to an elongation factor of 2.25 yielded the best match to measurements at velocities of 7 m s − 1 in the flow cytometer. Our results give a proof of principle that rheological properties of native erythrocytes can be derived from flow cytometric measurements. For this purpose, it is necessary to know the relevant characteristics of the instrument concerning the optical layout and the fluidic system in detail, i. e., the solid angle of observation, shape of the laser beam at the intersection point as well as the forces exerted on the cell during hydrodynamic focusing and while passing through the flow channel. The presented results provide an incentive to compare and combine the mathematical approach here that is based on accurate optical modeling with a modeling of rheological and mechanical properties of cells in a macroscopic flow geometry. To this end, our studies will be extended by systematic investigations of the influence of hydrodynamic forces when changing the velocity of the sheath flow. Furthermore, the proposed ad hoc shape model for deformed RBCs