I have recently started as a new post-doc at the School of Mathematics at the University of Manchester (working with Dr Igor Chernyavsky, Prof Oliver Jensen, and Dr Paul Brownbill on mathematical modelling of the fluid flow and oxygen uptake in the placenta). I have been kindly invited to speak at the internal Biomechanics Seminar at the School of Mathematics about my D.Phil. work from Oxford. Below you can find the abstract and slides of my presentationfrom Monday 23rd January 2017.
Growth Laws in Morphoelasticity
A. Erlich1, D.E. Moulton1, A. Goriely1 & R. Chirat2
1 Mathematical Institute, University of Oxford
2 Université Lyon 1
Many living biological tissues are known to grow in response to their mechanical environment, such as changes in the surrounding pressure. This growth response can be seen, for instance, in the adaptation of heart chamber size and arterial wall thickness to changes in blood pressure. Moreover, many living elastic tissues actively maintain a preferred level of mechanical internal (residual) stress, called the homeostasis. The tissue-level feedback mechanism by which changes of the local mechanical stresses affect growth is called a growth law within the theory of morphoelasticity, a theory for understanding the coupling between mechanics and geometry in growing and evolving biological material.
In this presentation we will discuss techniques to analyse growth laws that are biologically plausible, and explore issues of heterogeneity and growth stability. We present two models based on homeostasis-driven growth laws.
Firstly, we discuss the growth dynamics of tubular structures, which are very common in biology (e.g. arteries, plant stems, airways). We model the homeostasis-driven growth dynamics of tubes which produces spatially inhomogeneous residual stress. We show that the stability of the homeostatic state non-trivially depends on the anisotropy of the growth response. The key role of anisotropy may provide a foundation for experimental testing of homeostasis-driven growth laws.
Secondly, we apply our theoretical framework to the growth of Ammonites’ seashells. We demonstrate how homeostasis-driven growth produces seashell morphology that is consistent with observation and that cannot readily be captured with previous models.