title: Blood platelets in the microcirculation - a theoretical and computational study
Creators: name: Bächer, Christian
Publisher: name: University of Bayreuth
Year: 2021
Subjects: subject: Active membranes
subject: Rayleigh-Plateau instability
subject: anisotropic tension
subject: blood platelets
subject: blood platelet biogenesis
subject: blood flow
subject: (anti)margination
subject: cell mechanics
subject: fluid-particle interaction
subject: computational fluid dynamics
subject: biological physics
subject: 530

description: The blood cells called blood platelets play a crucial role in keeping the blood circulatory system intact. Circulating through the human body within the flowing blood, platelets are responsible for the quick stop of a bleeding. A prime property of the platelets is the margination, i.e., the adaption of a near-wall location in the flowing blood. However, the blood flow does not only facilitate their main function, but also contributes significantly to their highly efficient formation. The large number of 10^11 blood platelets forms daily in the bone marrow in a strongly flow-accelerated process. In addition to the external fluid forces, actively generated stresses in the cell cortex, a thin layer of cytoskeletal filaments and motor proteins tethered to the cell membrane, are important for the development of blood platelets. While simulations of passive elastic cells in flow are abundant, a combination with active cortex mechanics has so far not been addressed. In the present thesis, a simulation tool is developed, which allows such a combination. In a fully three-dimensional manner, the computational tool combines an arbitrarily deforming, elastic active cell cortex plus membrane with a dynamic coupling to a flowing liquid. By utilizing active gel and thin shell theory, the force balance equations are expressed on a triangulated membrane and forces resulting from active stresses are calculated using a parabolic fitting procedure. Suspending fluid flow dynamics as well as a two-way coupling of flow and membrane mechanics are achieved using a lattice-Boltzmann/immersed boundary scheme or the boundary integral method. On the same footing including the parabolic fitting procedure, a second three-dimensional simulation method is developed which considers an active cortex in the long time, i.e., viscous, limit. Here, a heterogeneous active stress distribution triggers flow inside the cell cortex. We numerically determine the flow velocity by globally solving the force balance equations by means of a minimization ansatz. Both simulation methods are extensively validated. A particular interesting feature of a cell cortex is the occurrence of anisotropic active stress. Based on the mathematical description it becomes clear that a cortical active stress is analogous to the surface tension of a liquid despite their fundamentally different origin. Therefore, the Rayleigh-Plateau instability, which is known to describe the break-up of a cylindrical liquid jet into droplets, has also been predicted to occur in the presence of a cortical active stress. However, the question arises how an anisotropic active stress, in contrast to the isotropic surface tension, alters this instability. We analytically derive dispersion relations for a fluid-fluid interface as well as a shear and/or bending elastic membrane under the influence of an anisotropic interfacial tension. Our theoretical analysis accompanied by numerical simulations uncovers a strong impact of the anisotropy on the instability, where fragment size decreases and instability dynamics becomes faster for dominating azimuthal tension. Most remarkably, the interplay of elasticity and tension anisotropy can restrict the instability and can render the interface stable. In blood platelet formation, progenitor cells trapped in the bone marrow develop long, finger-like membrane protrusions into blood vessels. These protrusions fragment into numerous platelets in the presence of blood flow. Using our developed simulation tool, we identify a biological Rayleigh-Plateau instability as the fundamental biophysical origin of the highly efficient formation of the blood platelets. We confirm the cortical activity as key ingredient for this fragmentation. In addition, we systematically study the influence of external blood flow, where we find a significant acceleration of the formation with increasing flow velocity in agreement with experiments. Simulations show that this acceleration is especially pronounced in a homogeneous flow field, which sheds light onto an efficient design of microfluidic devices for in vitro platelet production. In the presence of shear, we find an explanation for the formation of larger preplatelets, which are intermediate progenitors of blood platelets. While it is well known that released blood platelets are expelled towards the vessel wall in a process called margination in blood flowing through straight channels, their behavior in vessel networks is hardly understood. In this thesis, we investigate their flow behavior passing through a vessel bifurcation as well as a vessel confluence. While our simulations show that their distinct near-wall position is robust along a bifurcation, we observe platelets located within an additional (red blood) cell-free layer in the vessel center behind a confluence. By determining the shear induced diffusion coefficient, we are able to draw conclusions on platelet dynamics in a vessel network, where succeeding confluences would lead to a more continuous distribution of blood platelets across the vessel diameter. Therefore, the observed antimargination behind a confluence can explain differences in platelet distribution between the arterial part with abundant bifurcations and the venous part of the microcirculation with a lot of confluences previously found in vivo.