Session F55: Brain Morphology and Mechanics: From Cortex Folding to Neuronal Growth to Compression Stiffening

How does the cortex get its folds? The role of tension-based morphogenesis

The cerebral cortex is a sheet-like structure that is convoluted to varying degrees in different species and, for human cortex, shows remarkable variability across individuals -- even in identical twins. This talk will discuss key biological events and physical forces involved in how the cortex gets its folds. The early stages of cortical morphogenesis are established by exquisitely regulated patterns of cellular proliferation and migration that place the right numbers of cells in an appropriate starting configuration. A major focus will be on the proposed role of mechanical tension in the next stages of morphogenesis. Does tension along apical dendrites of cortical pyramidal cells help make the cortex a sheet? Does tension along long-distance axons cause the cortex to fold? These are attractive but controversial ideas. I will suggest ways in which physicists can contribute critical models and analyses that may help distinguish the relative contributions of several mechanisms (differential proliferation, buckling of the cortical sheet, and tension-based cortical folding). Physicists can also help in evaluating the degree to which cortical circuits reflect principles of compact wiring and the putative role of tension-based morphogenesis in wiring length minimization.   

Gyrification from constrained cortical expansion

The convolutions of the human brain are a symbol of its functional complexity. But how does the outer surface of the brain, the layered cortex of neuronal gray matter get its folds? In this talk, we ask to which extent folding of the brain can be explained as a purely mechanical consequence of unpatterned growth of the cortical layer relative to the sublayers. Modeling the growing brain as a soft layered solid leads to elastic instabilities and the formation of cusped sulci and smooth gyri consistent with observations across species in both normal and pathological situations. Furthermore, we apply initial geometries obtained from fetal brain MRI to address the question of how the brain geometry and folding patterns may be coupled via mechanics.   

Elastic instabilities in a layered cerebral cortex: A revised axonal tension model for cortex folding

Despite decades of research, there is still no consensus regarding the mechanism(s) driving cerebral cortex folding. Two different mechanisms---axonal tension based on efficient wiring of the neurons and differential growth-induced buckling---are the prevailing hypotheses, though quantitative comparison with data raises issues with both of them. I will present a model for the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a 'flat' cortex configuration becomes unstable and periodic undulations emerge, i.e. a buckling instability occurs, to presumably initiate folds in the cortex. This model builds on the original axonal tension model for cortex folding based on the efficient wiring of neurons but with no buckling mechanism and allows one to understand why small mice brains exhibit no folds, while larger human brains do. Finally, an estimate of the bending rigidity constant for the cortex can be made based on the critical wavelength to quantitatively test this revised axonal tensional model.   

Effects of surface asymmetry on neuronal growth

Understanding the brain is of tremendous fundamental importance, but it is immensely challenging because of the complexity of both its architecture and function. A growing body of evidence shows that physical stimuli (stiffness of the growth substrate, gradients of various molecular species, geometry of the surrounding environment, traction forces etc.) play a key role in the wiring up of the nervous system. I will present a systematic experimental and theoretical investigation of neuronal growth on substrates with asymmetric geometries and textures. The experimental results show unidirectional axonal growth on these substrates. We demonstrate that the unidirectional bias is imparted by the surface ratchet geometry and quantify the geometrical guidance cues that control neuronal growth. Our results provide new insight into the role played by physical cues in neuronal growth, and could lead to new methods for stimulating neuronal regeneration and the engineering of artificial neuronal tissue.   

COMPRESSION STIFFENING OF BRAIN AND ITS EFFECT ON MECHANOSENSING BY GLIOMA CELLS

The stiffness of tissues, often characterized by their time-dependent elastic properties, is tightly controlled under normal condition and central nervous system tissue is among the softest tissues. Changes in tissue and organ stiffness occur in some physiological conditions and are frequently symptoms of diseases such as fibrosis, cardiovascular disease and many forms of cancer. Primary cells isolated from various tissues often respond to changes in the mechanical properties of their substrates, and the range of stiffness over which these responses occur appear to be limited to the tissue elastic modulus from which they are derived. Our goal was to test the hypotheses that the stiffness of tumors derived from CNS tissue differs from that of normal brain, and that transformed cells derived from such tumors exhibit mechanical responses that differ from those of normal glial cells. Unlike breast and some other cancers where the stroma and the tumor itself is substantially stiffer than the surrounding normal tissue, our data suggest that gliomas can arise without a gross change in the macroscopic tissue stiffness when measured at low strains without compression. However, both normal brain and glioma samples stiffen with compression, but not in elongation and increased shear strains. On the other hand, different classes of immortalized cells derived from human glioblastoma show substantially different responses to the stiffness of substrates \textit{in vitro }when grown on soft polyacrylamide and hyaluronic acid gels. This outcome supports the hypothesis that compression stiffening, which might occur with increased vascularization and interstitial pressure gradients that are characteristic of tumors, effectively stiffens the environment of glioma cells, and that \textit{in situ}, the elastic resistance these cells sense might be sufficient to trigger the same responses that are activated \textit{in vitro} by increased substrate stiffness.