BB17: Brain mechanics, cortex folding, and pattern formation in growing tissues

Background

The function of the brain is closely associated with its shape. However, the development of the forms in the brain and the important physical ingredients are not well understood. There is interest in understanding the mechanics of brain matter during cerebral swelling and clinical therapies that can be applied in an attempt to prevent long-term tissue damage.

Techniques and Challenges

It has been hypothesised that mechanical forces and axonal tension play roles in folding [1]. However, the presence of axons in the tissue presents a modelling challenge. We are developing a constitutive model for brain tissue that explicitly accounts for fibres embedded within a viscoelastic matrix as an extension to an existing model [2]. We have developed our model within a variational framework that enables three-dimensional numerical computation using the finite-element method. We are also developing lower-dimensional models to aid understanding of the underlying mechanisms of folding and quantifying the large-scale response of the tissue when subjected to localised swelling.

Results

We have validated our model and are considering more complicated geometries. Furthermore, we have conducted finite-element simulations of tissue deformation induced by swelling in a two-dimensional slice of brain tissue confined by a rigid boundary and enclosing a fixed volume of incompressible fluid. We have also shown how stress distribution and tissue deformation is modified when a small segment of the outer rigid wall is removed and replaced by a no-stress condition (see figure) as a model for the treatment used for cerebral oedema.

The Future

We intend to calibrate the parameters in our model against experimental data. The model will then be used to consider the growth of a sample of tissue and examine the anisotropic response induced by the presence of the embedded fibres. Furthermore, we intend to investigate the conditions under which the surface of the tissue can exhibit folding and examine how the pattern formed by these folds is linked to the structure of the fibres.

References

[1] van Essen D.C.: A tension-based theory of morphogenesis and compact wiring in the central nervous system, Nature 385, 313-318, 1997

[2] El Sayed T., Mota A., Fraternali F., Ortiz M.: A variational constitutive model for soft biological tissues, Journal of Biomechanics 41(7), 1458-1466, 2008