Applying A-PTV to RBC suspension flows

Abstract In strongly confined flow geometries, red blood cells migrate normal to the flow direction, thereby altering the flow rheology of blood. Direct optical measurements can help to gain an improved understanding of these migration processes. In the present study, we demonstrate that astigmatism particle tracking velocimetry is a suitable 3D-particle tracking method that allows to directly measure both 3D concentration and velocity distributions of red blood cells in a flow. Red blood cells assume a non-spherical shape; therefore, the influence of their orientation on the reconstruction of the out-of-plane particle position is evaluated through a ray tracing approach of synthetic, astigmatic images. While for noise-free images, the resulting absolute out-of-plane reconstruction error $$\sigma _z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:math> is small for different red blood cell orientations ( $$\sigma _z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:math> = 0.98 $$\upmu \text {m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mtext>m</mml:mtext> </mml:mrow> </mml:math> ), it triples for experimentally relevant signal-to-noise ratios (SNR = 1.2). Reconstruction errors are compared to those of spherical particles. Overall, both the red blood cell orientation and the increase in signal-to-noise ratio induce similar out-of-plane reconstruction error values. Experimental analyses are also performed using both a red blood cell suspension system and a refractive index-matched suspension system of identical volume fraction ( $${1.5\,\mathrm{\%}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.5</mml:mn> <mml:mspace/> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> ). Comparing results from the red blood cell suspension flow with those of the particulate suspension under identical parameters for volume fraction, particle Reynolds number, and bulk Reynolds number, a similarity in lateral migration behavior is observed under the given conditions. The results indicate that the absolute out-of-plane reconstruction error in the red blood cell suspension system ( $$\sigma _z = {4.50\,\mathrm{{\upmu \text {m}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>z</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mn>4.50</mml:mn> <mml:mspace/> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mtext>m</mml:mtext> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> ) is approximately 1.5 times larger compared to the refractive index-matched system. Graphical Abstract