BB21: The mechanics of growth and muscle contraction in tissues and organs
|Team Leader(s):||Prof. Alain Goriely, Dr Sarah Waters & Dr Derek Moulton
Cylindrical structures are common in many biological systems, from minuscule carbon nanotubes and the cytoskeleton, to blood vessels and the gastrointestinal tract . Our goal is to develop a framework to model the behaviour of multi-layered tubular structures subject to large deformations. We focus on the relationship between the growth of tissue layers and the resulting stress distribution. These are important factors to consider when predicting the onset of diseases such as asthma and atherosclerosis, which are characterised by growth and remodelling processes in the walls of airways and arteries, respectively [10/48].
Techniques and Challenges
How do the material properties, applied tractions and geometry of elastic rods influence their critical buckling pressure and mode of buckling? We make use of the theory of incremental deformations to examine their stability. Previous work in this field has considered spherical shells and hollow tubes: we consider 'solid' structures, which include neurons embedded in an elastic matrix and plant stems. For simple material response functions (e.g. neo-Hookean), we obtain the finite deformation exactly, though for more complex functions used to describe soft tissue, numerical schemes must be employed.
We have used a 3-dimensional elasticity approach in order to determine the critical axial growth of a slender elastic filament embedded in an elastic matrix. Using the Wentzel–Kramers–Brillouin (WKB) method allows estimation of the critical growth in terms of the material properties of the system. We have also considered the same problem using a rod-theory approach, assuming the matrix behaves as a Winkler foundation. By comparing the two approaches, we have obtained an estimate of the Winkler modulus parameter in terms of measurable properties of the system [13/25].
In the future, we will use our framework to study a number of biologically-relevant problems. These include the mechanism used by chameleons to project their tongues ballistically to catch prey and vibrations occurring in mammalian whiskers due to interaction with their surrounding environment.
[13/25] O'Keeffe S.G., Moulton D.E., Waters S.L., Goriely A.: Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix, Int. J. Nonlin. Mech.
[10/48] Moulton D.E., Goriely A.: Possible role of differential growth in airway wall remodeling in asthma, Journal of Applied Physiology
 Vandiver R., Goriely A.: Differential growth and residual stress in cylindrical elastic structures, Phil. Trans. R. Soc. 367:3607-3630, 2009