Evaluation of a nonlinear Hertzian-based model reveals prostate cancer cells respond differently to force than normal prostate cells

• Published in: Microscopy research and technique 2013-01, Vol.76 (1), p.36-41
• Main Authors: Murphy, M.F., Lilley, F., Lalor, M.J., Crosby, S.R., Madden, G., Johnston, G., Burton, D.R.
• Format: Article
• Language: English
• Subjects: Actins - metabolism; AFM; Atomic force microscopy; Biomechanical Phenomena; Cancer; Cell Line; Hertz model; Humans; Indentation; Male; Mathematical models; Mechanical properties; mechanics; Microscopy, Atomic Force; Models, Theoretical; nonlinear; Nonlinear Dynamics; Nonlinearity; Polynomials; Prostate; Prostate - chemistry; Prostate - cytology; Prostate - metabolism; Prostatic Neoplasms - chemistry; Prostatic Neoplasms - metabolism; stiffness; Stress, Mechanical
• ISSN: 1059-910X; 1097-0029
• DOI: 10.1002/jemt.22132

Understanding how the mechanical properties of cells alter with disease may help with the development of novel diagnostics and treatment regimes. The emergence of tools such as the atomic force microscope (AFM) has enabled us to physically measure the mechanical properties of cells. However, suitable models for the analysis of real experimental data are either absent, or fail to provide a simple analysis tool in which experimental data can be analyzed quickly and reliably. The Hertz model has been widely used to study AFM data on living cells, however it makes assumptions that are untrue for cells, namely that cells behave as linear elastic bodies. This article presents and evaluates an alternative nonlinear Hertz model, which allows the Young's modulus to vary according to a second order polynomial function of indentation depth. Evaluation of the model revealed that prostate cancer cells (PC3) responded more uniformly to force compared to the normal PNT2 cells. Also, more energy (J) was needed to deform the normal prostate cells compared to the prostate cancer cells. Finally, the model described here suggests that overall the normal prostate cells behave in a more linear fashion to applied force compared to the prostate cancer cells. Microsc. Res. Tech., 2013. © 2012 Wiley Periodicals, Inc.