Modeling and computation of growth in soft biological matter

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Wrinkling phenomena emerging from mechanical instabilities in inhomogeneously growing soft biological tissue can evoke a wide variety of surface morphologies. Applications range from undesired folding of asthmatic airways, via wrinkling of skin, to brain convolutions, which maximize the number of neurons and minimize their distance. Here, we study growth-induced loss of stability primarily using the example of cortical folding during brain development. On the one hand the brain still remains our least understood organ. On the other hand brain growth involves both growth-induced mechanical instabilities and mechanically-induced biological growth with a morphogenetically growing superficial gray matter layer and a stretch-induced growing white matter substrate. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, in the first phase of the project we have established a preliminary computational model of brain growth, which provides first insights into growth-induced primary and secondary instabilities: Moderate growth in the outer layer generates a regular pattern of sinusoidal wrinkles; further continuing growth induces secondary instabilities associated with advanced wrinkling modes - the surface bifurcates into increasingly complex morphologies. During the second phase of the project, we will refine our model regarding more realistic constitutive equations and growth laws. For this purpose, we will supplement our computational investigations with biomechanical testing of brain tissue. We will incorporate temporal and regional variations in material properties with close consideration of the corresponding microstructure. Such experimental studies will not only allow for realistic simulations of brain development but could also revolutionize computational modeling of brain tissue in general. Accordingly, our project related work could additionally contribute to the medical treatment of diseases such as brain tumors and the prevention of injuries such as traumatic brain injury. With our computational model we will explore major aspects of healthy and pathologic brain development. As brain structure closely correlates with brain function, malformations of cortical development are common causes of mental diseases such as epilepsy and developmental delay. The computational model can bridge the scales from largely studied disruptions on the cellular level towards form and function on the organ level. It can explain why cortical malformations emerge. Understanding the underlying mechanisms of brain development will enhance early diagnostics of cortical malformations and ultimately facilitate treatment and prevention of mental disorders.