Quantitative and mechanistic characterization of geometric features and patterns in biological systems

Abstract

In his pioneering work 'On Growth and Form' (1917), the Scottish scholar D'Arcy Thompson argued that physical forces and constraints were likely to play a decisive role in shaping the morphology of many living organisms, suggesting that a more mathematical approach to the study of natural patterns and structures was necessary for a scientific understanding of morphogenesis. Bold as they might have seemed to his contemporaries, these original ideas would later go on to be recognized as foundational in the fields of physical and mathematical biology, as evidence vindicating Thompson's conjectures steadily accumulated over the years. In this work, I have tried to follow the scientific doctrine exposed in 'On Growth and Form' in two ways: first, by showing how techniques from the fields of computer science and physics can be employed to study biological systems in a quantitative fashion, and second, by arguing that the pattern of minuscule crevices present on the skin of the African bush elephant (Loxodonta africana) is generated through a physical mechanism: cracking (tensile fracture). Passive image-based 3D reconstruction is an approach through which a digital 3D model of the geometry and color texture of an object can be generated from photographs of its surface. Widely researched and used in computer graphics, these methods have seldom been employed in the life sciences disciplines. In this thesis, I show how the two basic steps of this approach – scanning and reconstruction – can be combined into a single, automated system that is able to generate accurate and high-resolution 3D digital models of biological samples and specimens, including animals under anesthesia. Applications in paleontology and forensics are briefly discussed. Moreover, it is argued that this technology can be employed to reconstruct surface features with micrometric dimensions using a specialized, but simple and inexpensive, setup. It is increasingly recognized that mechanics may play an important role in the patterning of many living organisms. Understanding the way in which these processes influence biological shape frequently requires the use of numerical simulations, since analytical solutions cannot be found except in a very limited number of simple cases. In particular, the elastic response of physical shells - thin, surface-like structures that are curved in their stress-free state - has recently received considerable attention owing to its many applications: human skin, plant leaves, the peel of most fruits or the wings of bats are all examples of biological tissues that can be modelled as shells. In this work, I motivate and introduce a lattice-based framework for the simulation of the elasticity of these objects, and present a quantitative error analysis of its results. I argue that, in some circumstances, this approach may have advantages over the more traditional application of the finite element method. Due to their prodigious size and the frequently hot environments that they inhabit, maintaining thermal balance is a challenging task for elephants. Of the many mechanisms that are speculated to contribute to achieving this goal, evaporative cooling is considered to be one of the most important, and it has long been known that the African elephant's sculptured skin is likely to be an adaptation to enhance the efficiency of evaporative heat loss. In this thesis, I address the previously unanswered question of how the crevices that contribute to this carved appearance form. Using experimental and numerical data, I argue that these structures are in fact cracks in the stratum corneum of the animal, and that their generative process depends critically on the convoluted geometry and hyperkeratotic nature of the skin. Physical simulations confirmed this picture and, in addition, demonstrated that bending stresses play an important role in the formation and propagation of cracks, a characteristic that distinguishes this example from other common cracking patterns in which stretching is the dominant factor.