Three-Dimensional Cellular Traction Force Microscopy
Date Issued
2015
Date
2015
Author(s)
Lee, Hung-Huei
Abstract
While migrating, cells generate traction forces to the polyacrylamide substrate through complex adhesion mechanism. Measuring such forces, known as traction force microscopy, is of critical importance in understanding how cells interact with extracellular matrix. The polyacrylamide gel is indeed a viscoelastic material. However, cellular traction force analysis considering viscoelastic models becomes too complicated to tackle, and is beyond the scope of this study. In this thesis, we focus on the traction force under static condition; therefore, we assume that the gel is linearly elastic material and conduct the numerical analysis accordingly. Some analytical methods based on Boussinesq-Cerruti problem [1], such as two-dimensional Fourier-transform traction cytometry (FTTC) [2], have been widely used to reconstruct the cellular traction from substrate displacement field measured by confocal microscopy, and they often assume that cells exert only shear forces on an elastic flat substrate. However, recent studies indicated that cells on a planar substrate exert significant out-of-plane traction. Therefore, the out-of-plane component of the traction should not be neglected, and we found that neglecting the out-of-plane component results in considerable deviation from the more realistic traction force. Compared with the conventional FTTC method, finite element method (FEM) can be readily applied to substrates with complicated non-planar surfaces and those made of inelastic materials. In this thesis, we focus on the computational methods, and develop several kinds of methods to understand the difference between different methods. In order to understand the influences of beads density, which represent the quantity of data points, we use simulations to find resolvable range for single focal adhesion recovery under different beads density. In addition, we also investigate whole normal traction field recovery and find that the lower beads density causes the recovered traction more dispersed and underestimated, and that also probably causes the deviation on the recovered positions of tractions. While further adding the noises effects during the traction force reconstruction, we investigate the strain energy recovery and traction force recovery, and test the reliability of different methods for noises treatment. We find that noises increasing the traction deviations between bootstrap iterations. For 2D analysis methods, there are only about 20 Pa of standard deviations in shear tractions, thus we think both the FTTC and 2D FEM are consistent enough for noises treatment. Beside the analysis of normal tractions, due to the neglecting in z direction, 2D analysis methods tend to much more underestimate the strain energy than the recovered strain energy in 3D analysis, and this also confirm the significance for 3D methods. In conclusion, we develop several analysis methods and compare between different methods, and use various simulations to provide the direction for improvement and helpful information for a given experimental setup.
Subjects
Three-dimensional
Cellular traction force
Finite element method
Beads density
Noises effect
Traction force reconstruction
Strain energy recovery
Type
thesis
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