Effects of Embedded Beads Distribution on Cellular Traction Force Analysis

Many physiological processes can be affected by cellular traction force between cells and surroundings. Quantifying the magnitude and direction of cellular traction force can provide important information while cell migrating or in cell differentiation. Developments in three-dimensional (3D) traction force microscopy techniques with Finite Element Method, which measure the displacement of beads in whole substrate, make it accessible to measure traction force exerted by cell. However, the method is limited by the beads density and the technique of tracking beads in whole substrate. With special treatments, beads can be concentrated on the top surface of the polyacrylamide (PA) substrates. When the distribution of the beads is thin enough, it can be regarded as surface beads. In addition, it is easier to track the displacement and we can get higher resolution by using higher beads density. In the thesis, we get the displacements from the nodal solutions of simulated traction field, and put the x, y, and z component of displacements into three-dimensional regular grid. Then, we put the complete grid of displacement into finite element model to obtain traction field solution. Compared with the whole boundary condition, plane boundary condition can be readily applied to substrate and calculate better result. Following the same steps described above, we compare the two methods by solving traction field exerted by experimental cell data. In this thesis, we focus on the computational method, and develop a method to understand the influences of the beads density. We use simulations to find resolvable range for single focal adhesion and couple focal adhesion recovery under different beads density. We find that the lower beads density causes the recovered traction more dispersed and underestimated, and that also probably cause the deviation on the recovered position of tractions. We then construct mixed boundary method to calculated the cell traction force. For this condition, we applied displacement in the cell region and make traction free outside the cell region. For this case, we can obtain more accurate experimental result. In conclusion, we develop several analysis methods and compare their pros and cons, which provide helpful information for experimental conditions and a better understanding of the simulation results.