Advertisement

Estimating Force Fields of Living Cells – Comparison of Several Regularization Schemes Combined with Automatic Parameter Choice

  • Sebastian Houben
  • Norbert Kirchgeßner
  • Rudolf Merkel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6376)

Abstract

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 [1] 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 [2] 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 [3] but not analyzed in detail. We cover this analysis and present several methods for an objective and automatic choice of the required regularization parameters.

Keywords

Regularization Parameter Fourier Space Temporal Derivative Regularization Scheme Human Epidermal Keratinocytes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dembo, M., Oliver, T., Ishihara, A., Jacobson, K.: Imaging the traction stresses exerted by locomoting cells with the elastic substratum method. Biophysical Journal 70, 2008–2022 (1996)CrossRefGoogle Scholar
  2. 2.
    Butler, J.P., Tolic-Norrelykke, I.M., Fabry, B., Fredberg, J.J.: Traction fields, moments, and strain energy that cells exert on their surroundings. American journal of physiology, Cell physiology 282, C595–C605 (2002), doi:10.1152/ajpcell.00270.2001 Google Scholar
  3. 3.
    Sabass, B., Gardel, M.L., Waterman, C.M., Schwarz, U.S.: High resolution traction force microscopy based on experimental and computational advances. Biophysical Journal 94, 207–220 (2008), doi: 10.1529/biophysj.107.113670CrossRefGoogle Scholar
  4. 4.
    Harris, A.K., Wild, P., Stopak, D.: Silicone rubber substrata: a new wrinkle in the study of cell locomotion. Science 208, 177–179 (1980), doi: 10.1126/science.6987736 CrossRefGoogle Scholar
  5. 5.
    Balaban, N.Q., Schwarz, U.S., Riveline, D., Goichberg, P., Tzur, G., Sabanay, I., Mahalu, D., Safran, S., Bershadsky, A., Addadi, L., Geiger, B.: Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nature Cell Biology 3, 466–472 (2001)CrossRefGoogle Scholar
  6. 6.
    Cesa, C.M., Kirchgeßner, N., Mayer, D., Schwarz, U., Hoffmann, B., Merkel, R.: Micropatterned silicone elastomer substrates for high resolution analysis of cellular force patterns. Rev. Sci. Instrum. 78, 034301-1–034301-10 (2007)CrossRefGoogle Scholar
  7. 7.
    Boussinesq, J.: Applications des potentiels a l‘etude de l‘equilibre et du mouvement des solides elastiques. Gauthier-Villars, Paris (1885)zbMATHGoogle Scholar
  8. 8.
    Landau, L.D., Lifshitz, E.M.: Lehrbuch der Theoretischen Physik: Elastizitaetstheorie, vol. 7. Akademie-Verlag, Berlin (1987); Deutsche UebersetzungGoogle Scholar
  9. 9.
    Merkel, R., Kirchgeßner, N., Cesa, C.M., Hoffmann, B.: Cell force microscopy on elastic layers of finite thickness. Biophysical Journal 93, 3314–3323 (2007)CrossRefGoogle Scholar
  10. 10.
    Tikhonov, A.N.: On the solution of ill-posed problems and the regularization method. Dokl. Akad. Nauk SSSR 151, 501–504 (1963)MathSciNetGoogle Scholar
  11. 11.
    Hansen, P.C.: Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review 34, 561–580 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Wahba, G.: Spline models for observational data. SIAM, US (1990)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sebastian Houben
    • 1
  • Norbert Kirchgeßner
    • 1
  • Rudolf Merkel
    • 1
  1. 1.Forschungszentrum Jülich, IBN-4JülichGermany

Personalised recommendations