**Author details**

120 Viscoelasticity – From Theory to Biological Applications

level.

of a single large master curve, suggesting the reduced variable method, that is, the timemineral content superposition principle could be applicable. Fig. 20 shows the synthetic master curve constructed for bone specimens with different mineral contents. The synthetic curve looks smooth and the scatter of the data points is small. Fig. 21 shows the vertical shift factor, *b*m, plotted against the mineral content. The filled circles are taken from the mineral content dependence of the elastic modulus of bone after Katz (1971). Mineral content dependence of *b*m accords well with that of elastic modulus itself. This fact indicates that the superposition procedure was carried out correctly. Then, the result indicates the timemineral content superposition principle. A polymer-filler system has been considered to have the same reinforcing mechanism as the model discussed. But in the usual polymerfiller system, the time-filler-fraction superposition principle does not hold. The size of the commercially available filler is at least of the order of a few μm. By the analysis of the horizontal shift factor, the reinforcing effect depends on the filler-matrix surface area, not on the filler size. The mineral particle in bone, where the time-mineral content reduction was concluded to be applicable, has been recognized to be of the size of a few hundred Å at most. The reason why the time-filler fraction superposition principle does not hold in the polymer-filler system is deduced to be related to the very large filler size compared with the mineral particles in bone, as well as an adhesive weakness between filler and matrix. This fact leads to the suggestion that, in order to improve the relaxation properties of mineralresin composite as artificial bone, the mineral size should be reduced to, say, submicron

**Figure 20.** A master curve constructed by superimposing the relaxation modulus curves in Fig. 19. For the successful superposition, both the vertical and horizontal shifts were needed. (Sasaki et al., J.

Biomechanics 26, 77-83 (1993). With permission.)

Naoki Sasaki *Faculty of Advanced Life Science, Department of Interdisciplinary Sciences, Hokkaido University, Japan* 

#### **6. References**


Hasegawa, K., Turner, C. H., Burr, D. B. (1994) Contribution of collagen and mineral to the elastic anisotropy of bone. *Calcified Tissue International* 55, 381-386.

**Chapter 6** 

© 2012 Bhat et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Viscoelasticity in Biological Systems:** 

Supriya Bhat, Dong Jun, Biplab C. Paul and Tanya E. S Dahms

Over billions of years of evolution, living organisms have developed into complex biosystems, of which the basic unit is the cell. Cells have a complex molecular structure with a certain level of rigidity. Living cells, whether isolated or part of a larger collective, live under constant mechanical stress from their external environments. Cells have developed adaptive mechanisms to maintain homeostasis and viability, which interestingly follow the

Cell mechanical properties have myriad biological significance and so there has been significant interest in the past decade to measure the response of cells to external mechanical signals. Cellular mechanics and rheological properties (*e.g.* stress-strain relationships) are known to play a role in biological processes such as cell growth, stem cell differentiation, cell crawling, wound healing, protein regulation, cell malignancy and even apoptosis

A living cell is a complex dynamic system, far from static, which constantly undergoes remodeling to adapt to varying environmental conditions. The mechanical changes in cells under normal conditions and in response to external signals are highly complex and extremely difficult to measure *in vitro*. The interplay of cellular constituents enables adaptation to changing demands of mechanical strength and stability. The field of rheological science deals with the mechanical behavior of biological materials and over the past decade several rheological methods have been developed to quantify the mechanical

To understand cell mechanics we first need an appreciation of how cells operate in a mechanical context. Firstly, how do cells maintain their shape and flexibility to accommodate cellular requirements? Cell surface layers are strong, playing a crucial

and reproduction in any medium, provided the original work is properly cited.

behavior of cells in response to external conditions and forces.

**A Special Focus on Microbes** 

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/49980

basic principles of classical mechanics.

(programmed cell death) [1,2].

**1. Introduction** 

