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WIREs Syst Biol Med
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Systems biology and mechanics of growth

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In contrast to inert systems, living biological systems have the advantage to adapt to their environment through growth and evolution. This transfiguration is evident during embryonic development, when the predisposed need to grow allows form to follow function. Alterations in the equilibrium state of biological systems breed disease and mutation in response to environmental triggers. The need to characterize the growth of biological systems to better understand these phenomena has motivated the continuum theory of growth and stimulated the development of computational tools in systems biology. Biological growth in development and disease is increasingly studied using the framework of morphoelasticity. Here, we demonstrate the potential for morphoelastic simulations through examples of volume, area, and length growth, inspired by tumor expansion, chronic bronchitis, brain development, intestine formation, plant shape, and myopia. We review the systems biology of living systems in light of biochemical and optical stimuli and classify different types of growth to facilitate the design of growth models for various biological systems within this generic framework. Exploring the systems biology of growth introduces a new venue to control and manipulate embryonic development, disease progression, and clinical intervention. WIREs Syst Biol Med 2015, 7:401–412. doi: 10.1002/wsbm.1312 This article is categorized under: Analytical and Computational Methods > Computational Methods Analytical and Computational Methods > Dynamical Methods
Axial growth of the eyeball. During myopia, the elongation of the eye causes the light to focus prior to reaching the retina. This shift of focus results in blurry vision and shortsightedness. Growth mechanics can illustrate this phenomenon.
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Length growth of a plant leaf. Initial configuration of the leaf (left) morphing into Rumex Crispus shape (right). The outermost edge of the leaf is subjected to growth; increasing growth value over time shown through the color scheme. The intersection of the two planar sections forms the stiff stem and grows slower than the outer edges. The intermediate material is softer than the stem and the edge, but does not grow. Simulation of the Rumex Crispus leaf is possible through fiber or lengthwise growth.
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Area growth of the intestinal lining. The development of ridges in the gut is caused by area growth in the radial and circumferential directions. The inner stiff mucosa layer is grown on a soft submucosa core. The instabilities that occur in an enclosed cylindrical geometry are characteristic of intestinal morphogenesis during embryonic development. The resulting surface patterns are directly comparable to clinical endoscopies.
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Area growth of the cerebral cortex. Morphologically driven brain development of growing external cortical layer on elastic subcortical core. The area growth of the expanding cortex triggers mechanical instabilities, which shape the characteristic folding pattern of our brain. As the surface grows, regions of high stress develop in regions of highest curvature. The brain can be simplified as a homogenous bilayered structure, in which existing or lacking folds are characteristic of healthy or diseased states.
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Volume growth of the airway wall. Patient‐specific branch of the human airway where the mucosal layer is subjected to isotropic growth and the outer submucosa layer is constrained. Growth‐induced instabilities are shown as the airway experiences an influx of cells, a biochemical bodily reaction to toxins and pollutants. The regions of high displacement are shown in red illustrating the obstruction of the lumen as disease‐driven growth folds the airway walls inwards.
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Volume growth of a tumor. Disease‐driven isotropic volume growth of a tumor inside a duct as in the case of breast cancer. The duct is assumed to be free to deform as the tumor grows. Assuming a homogeneous nutrients supply, the tumor grows homogeneously and isotropically, while its overall deformation is constrained by the wall of the duct. Tumor growth causes deformation of the mammary gland. According to this model, the duct‐tumor interface, the site of high stress concentrations indicated in red, suggests high risk of rupture.
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Kinematics of growth. Undeformed configuration β0, incompatible grown configuration, and deformed configuration βt. Line elements associated with λ, area elements associated with η, and volume elements associated with J are shown in the overall multiplicative decomposition of F = Fe ⋅ Fg.
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