Estimating Force Fields of Living Cells – Comparison of Several Regularization Schemes Combined with Automatic Parameter Choice
In this paper we evaluate several regularization schemes applied to the problem of force estimation, that is Traction Force Microscopy (TFM). This method is widely used to investigate cell adhesion and migration processes as well as cellular response to mechanical and chemical stimuli. To estimate force densities TFM requires the solution of an inverse problem, a deconvolution. Two main approaches have been established for this. The method introduced by Dembo  makes a finite element approach and inverts the emerging LES by means of regularization. Hence this method is very robust, but requires high computational effort. The other ansatz by Butler  works in Fourier space to solve the problem by direct inversion. It is therefore based on the assumption of smooth data with little noise. The combination of both, a regularization in Fourier space, has been proposed  but not analyzed in detail. We cover this analysis and present several methods for an objective and automatic choice of the required regularization parameters.
KeywordsRegularization Parameter Fourier Space Temporal Derivative Regularization Scheme Human Epidermal Keratinocytes
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