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Multiscale poro-micromechanics of bone materials, with links to biology and medicine

Final Report Summary - MICROBONE (Multiscale poro-micromechanics of bone materials, with links to biology and medicine)

Modern computational engineering allows for reliable design of the most breathtaking high-rise buildings, but it has hardly entered the fracture risk assessment of biological structures like bones. Is it only an engineering scientists' dream to decipher mathematically the origins and the evolution of the astonishingly varying mechanical properties of complex hierarchical biological materials? Not quite: By means of micromechanical theories, we could show during the last decade, that “universal” elementary building blocks (which are independent of tissue type, species, age, or anatomical location) govern the elastic properties of bone materials across the entire vertebrate kingdom, from the supermolecular to the centimeter scale.
The project MICROBONE has driven forward these ground-breaking scientific developments, from the purely elastic case to the inelastic properties of bone; in particular creep (viscoelasticity) and strength (elastoplasticity). Through novel, strictly experimentally validated micromechanical theories, MICROBONE has focussed on predicting tissue-specific inelastic properties of bone materials, from the “universal” mechanical properties of the nanoscaled elementary components (hydroxyapatite, collagen, water), their tissue-specific dosages, and the “universal” organizational patterns they build up. Therefore, we have developed the first ever multiscale multisurface elastoplasticity theory for mineralized biological materials, translating irreversible sliding events between nano-crystals into elastoplastic behavior of bone material across all its hierarchical scales, the (extra-)fibrillar, the (extra-)cellular, the (extra-)vascular, and finally the macroscopic level. At the nano level, the source of plasticity is considered through an entirely new sliding interface-to-inelastic bulk upscaling theory.

The efficient algorithmic treatment of the aforementioned theory marks a new cornerstone in the discipline called “computational mechanics”. For experimental validation of the new multiscale bone models, we employed state-of-the-art methods such as ultrasonics, but in particular, we have developed novel and unusual experimental protocols, such as triaxial poromechanical testing, statistical nanoindentation for distinguishing undamaged from damaged material phases, or mechanical loading-unloading experiments on only micron-sized cylindrical samples. The latter were produced by means of a new variant of the focused ion beam technique, then transported by means of a micromanipulator and fixed on silicon wafers, and finally placed into a nanoindentation device and there subjected to loads through a flat punch. These unique and first-of-their kind experiments reveal a most interesting ductile-to-brittle behavior transition, as the length scale of the load application changes from one micron to some millimeters. Besides their fundamental impact on the general understanding of bone mechanics, these tests confirm a mathematically cast “building plan” inherent to all bone tissues, based on which we are able to predict not only the material’s strength, but also its poroelasticity, its creep properties, and the velocity and attenuation of fast and slow ultrasonic waves traveling through bone. Surprisingly, we discovered that such “building plans” can be even formulated beyond the mechanical interactions at different length scales: we could formulate mathematically cast rules for hydration-induced swelling and mineralization-induced shrinkage in collageneous tissues in general. Together with in vivo access to these dosages (e.g. through Computed Tomography - CT), these theories are expected lead to novel diagnostic possibilities: As final output, MICROBONE provided micromechanics-based Finite Element analyses for patient-specific bone failure risk assessment: We determined elasticity and strength “maps” throughout bony organs from micro-CT images, and successfully merged intravoxel bone micromechanics with CT-image-derived elastic Finite Element models, which critically drives forward fields such as biomaterial design or computer-aided surgery.

Most importantly, MICROBONE has linked the aforementioned suite of fully integrated theoretical, computational, and experimental tools for bone multiscale poro-physico-chemo-mechanics, to systems biology, i.e. to biological cell population models. This opens a new chapter in the investigation of bone mechanobiology, i.e. of how the “living material” bone changes its properties in reply to mechanical stimulation. With MICROBONE providing strains and pore pressures directly at the cellular level, we have triggered most interesting and stimulating interactions between the standardly very separated scientific disciplines of engineering mechanics and experimental cell biology. This holds the promise for unprecedented avenues in bone disease therapies.