Tim Odenthal

Analysis of initial cell spreading using mechanistic contact formulations for a deformable cell model.

Adhesion governs to a large extent the mechanical interaction between a cell and its microenvironment. As initial cell spreading is purely adhesion driven, understanding this phenomenon leads to profound insight in both cell adhesion and cell-substrate interaction. It has been found that across a wide variety of cell types, initial spreading behavior universally follows the same power laws. The simplest cell type providing this scaling of the radius of the spreading area with time are modified red blood cells (RBCs), whose elastic responses are well characterized. Using a mechanistic description of the contact interaction between a cell and its substrate in combination with a deformable RBC model, we are now able to investigate in detail the mechanisms behind this universal power law. The presented model suggests that the initial slope of the spreading curve with time results from a purely geometrical effect facilitated mainly by dissipation upon contact. Later on, the spreading rate decreases due to increasing tension and dissipation in the cells cortex as the cell spreads more and more. To reproduce this observed initial spreading, no irreversible deformations are required. Since the model created in this effort is extensible to more complex cell types and can cope with arbitrarily shaped, smooth mechanical microenvironments of the cells, it can be useful for a wide range of investigations where forces at the cell boundary play a decisive role.

Solving microscopic flow problems using Stokes equations in SPH

Abstract Starting from the Smoothed Particle Hydrodynamics method (SPH), we propose an alternative way to solve flow problems at a very low Reynolds number. The method is based on an explicit drop out of the inertial terms in the normal SPH equations, and solves the coupled system to find the velocities of the particles using the conjugate gradient method. The method will be called NSPH which refers to the non-inertial character of the equations. Whereas the time-step in standard SPH formulations for low Reynolds numbers is linearly restricted by the inverse of the viscosity and quadratically by the particle resolution, the stability of the NSPH solution benefits from a higher viscosity and is independent of the particle resolution. Since this method allows for a much higher time-step, it solves creeping flow problems with a high resolution and a long timescale up to three orders of magnitude faster than SPH. In this paper, we compare the accuracy and capabilities of the new NSPH method to canonical SPH solutions considering a number of standard problems in fluid dynamics. In addition, we show that NSPH is capable of modeling more complex physical phenomena such as the motion of a red blood cell in plasma.

Quantifying the mechanical micro-environment during three-dimensional cell expansion on microbeads by means of individual cell-based modelling.

Controlled in vitro three-dimensional cell expansion requires culture conditions that optimise the biophysical micro-environment of the cells during proliferation. In this study, we propose an individual cell-based modelling platform for simulating the mechanics of cell expansion on microcarriers. The lattice-free, particle-based method considers cells as individual interacting particles that deform and move over time. The model quantifies how the mechanical micro-environment of individual cells changes during the time of confluency. A sensitivity analysis is performed, which shows that changes in the cell-specific properties of cell–cell adhesion and cell stiffness cause the strongest change in the mechanical micro-environment of the cells. Furthermore, the influence of the mechanical properties of cells and microbead is characterised. The mechanical micro-environment is strongly influenced by the adhesive properties and the size of the microbead. Simulations show that even in the absence of strong biological heterogeneity, a large heterogeneity in mechanical stresses can be expected purely due to geometric properties of the culture system. Supplemental data for this article can be accessed online.

Immersed Boundary Models for Quantifying Flow-Induced Mechanical Stimuli on Stem Cells Seeded on 3D Scaffolds in Perfusion Bioreactors.

Perfusion bioreactors regulate flow conditions in order to provide cells with oxygen, nutrients and flow-associated mechanical stimuli. Locally, these flow conditions can vary depending on the scaffold geometry, cellular confluency and amount of extra cellular matrix deposition. In this study, a novel application of the immersed boundary method was introduced in order to represent a detailed deformable cell attached to a 3D scaffold inside a perfusion bioreactor and exposed to microscopic flow. The immersed boundary model permits the prediction of mechanical effects of the local flow conditions on the cell. Incorporating stiffness values measured with atomic force microscopy and micro-flow boundary conditions obtained from computational fluid dynamics simulations on the entire scaffold, we compared cell deformation, cortical tension, normal and shear pressure between different cell shapes and locations. We observed a large effect of the precise cell location on the local shear stress and we predicted flow-induced cortical tensions in the order of 5 pN/μm, at the lower end of the range reported in literature. The proposed method provides an interesting tool to study perfusion bioreactors processes down to the level of the individual cell’s micro-environment, which can further aid in the achievement of robust bioprocess control for regenerative medicine applications.