title: Simulation of Stem Cells in Shear Thinning Bioinks
Creators: name: Müller, Sebastian Johannes
Publisher: name: University of Bayreuth
Year: 2018
Subjects: subject: Simulation
subject: shear thinning
subject: bioinks
subject: 3d bioprinting
subject: cell simulation
subject: 500
subject: 530
subject: 620

description: Facing the world’s growing demand on tissue and organ transplants, the research and development of methods of treatment in the field of regenerative medicine is a great challenge of our time. Very promising among techniques to fabricate biological tissues are additive manufacturing processes, i. e. the 3D printing of organs and tissues. Special printing methods and tailored bioinks, i. e. mixtures of cells and fluids with certain properties, allow the fabrication of three dimensional structures in a reproducible, controlled and automated manner. Besides biochemical properties of these inks, e. g. their compatibility with living cells, the rheological properties play an important role: Hydrodynamic forces occurring during the printing process can damage or even destroy the cell before it is incorporated into the 3D structure. Those shear forces are especially present inside the printer nozzle, where a transition from no-slip to free-slip boundary conditions happens and, thus, the flow profile strongly changes. To now level the different flow profiles in front of and behind the nozzle, fluids with shear thinning properties can be utilized as media for the cell. For these liquids, large shear rates result in a low viscosity, making the fluid flow better in the vicinity of a channel wall. Small shear rates, instead, make the fluid increasingly viscous and decelerate the flow in the channel center. Altogether, this results in a broad velocity profile, which reduces the shear forces for cells in the channel center. Measuring cell deformations during a real printing process is challenging and would require a lot of experiments with different cell types and bioink formulations. At this point, simulations can help to look closely inside the system. Reducing the system to its geometry, the rheological model for the fluid and the elastic model for the cell, the behavior of cells in bioinks can be studied in detail. Therefore, the simulation software ESPResSo has been extended with several shear thinning viscosity models during this thesis. Using the Lattice Boltzmann method, it is possible to calculate shear rates locally and, thus, the extension does not affect its advantageous parallelization capability. Furthermore, the respective GPU version has been extended, providing immense simulation speed up – especially for smaller systems. For validating this method, analytical solutions to the Navier-Stokes equations are derived using the power-law and the truncated power-law viscosity model to subsequently compare them with the simulated data. Afterwards, spherical cells – representing stem cells – are simulated in a cylindrical channel containing shear thinning fluid. The flow behavior and the cell deformation are investigated using different methods. Contrary to the primary assumption, it appears that the average deformation of the cell increases with increasing shear thinning strength. The expected effect, however, is solely observed for high shear thinning and centered cells. As the cell deviates from a central position, it deforms at least as much as in a Newtonian fluid. That is a consequence of the higher shear rates near the channel wall and those, in turn, stem from the broad velocity profile. Finally, simulations are performed in a system modeling a 3D printer nozzle. Combining both no-slip and free-slip boundary algorithms, the flow is studied at the transition. Afterwards, a spherical cell is included, starting at different radial offsets in the channel, and its deformation is analyzed with respect to the shear thinning strength of the liquid. The same behavior as before is observed – the higher the shear thinning, the greater deforms the cell during the transition. Even in the channel center, where the cell is significantly less deformed in front of the transition, it is stretched more in lateral direction while passing through it. The relaxation towards the cell’s original shape after the transition also takes longer, which is a consequence of the incorporated viscosity model that causes large viscosities to occur in the free-slip region. The greater deformation during the transition, however, can be explained considering the ratio of viscous fluid forces and the cell’s elastic restoring forces in this simulation setup. Although the flow profiles in front of and behind the transition are more similar for increased shear thinning, there exist radial flow components pulling on the cell. Due to the capillary number being up to twice as large as in the Newtonian fluid, the cell is deformed accordingly stronger. Those effects will probably reduce in a wider channel, where this radial flow is concentrated more towards the region around the boundary. To summarize, it is shown that the expected decreasing deformation for cells in shear thinning fluids can only be observed for cells located in the plateau region of the flow. In contrast, the deformation of a cell passing the nozzle transition is significantly larger than in a Newtonian fluid, irrespective of its radial position. All simulations in this thesis were performed with the extended version of ESPResSo [1]. Images from simulations were created using the visualization software ParaView [2] and they were arranged using GIMP [3] and the LATEX package TikZ. Data analysis was performed using custom scripts and functionalities of the software Gnuplot [4]. Gnuplot was further used to create all plots shown in the present work.