dc.description.abstract
The role of computational simulations is ever increasing in the field of biomedicine.At the same time, as compared to „old“ engineering fields, such as mechanical orcivil engineering, the biomedical simulation field is still in its infancy, and severalchallenges need to be overcome so as to reach a maturity which would eventually leadto a deep transformation of the medical world. The present thesis deals with two of these challenges: (1) it is often unclear which theoretical basis should be employed for a biomedical simulation; (2) traditional simulations schemes often turn out as too expensive and clumsy in a biomedical context. These two challenges are dealt with byexample of one of the most intensively studied hierarchical structures in the biologicalrealm: bone; from the basic elemental, via the tissue, to the organ scale. This material class is introduced in Chapter Chapter 1 of the thesis.Chapter 2 is devoted to challenge (1): there is no agreement in the open literatureon how X-ray diffraction patterns would help in unraveling organizational features inthe ultrastructure of bone. As remedy, a comparatively inverse approach is introducedhere; starting with the representation of bone ultrastructure as a composite of alignedmineralized collagen fibrils embedded in a porous polycrystalline matrix, which has beenshown, over the last 15 years, to be fully consistent with many independent experimentsfrom various sources, such as Transmission Electron Microscopy, chemical tests (demineralization,ashing), ultrasonics, creep, strength, and poromechanical tests. Quantifyingthe characteristics of the aforementioned composite in terms of electron density distributions,and feeding the latter into a continnum electrodynamics theory which specifiesthe Maxwell equations for a Small Angle X-ray setting, indeed satisfactorily predictsmeasured X-ray diffraction patterns; and also lets us identify the previously discoveredidentitiy of extrafibrillar and extracollageneous mineral concentration together with axialpositional fluctuations of fibrils, as the key structural features of bone ultrastructure,which are reflected in SAXS measurements.Chapter 3 and 4 then turn towards challenge (2): While having become the goldenstandard in computational biomechanics, 3D Finite Element analyses of organs reconstrcutedfrom Computed Tomography may prove expensive with respect to time andressources, and more efficient alternatives are sought after, in particular when it comes tothe potential use of such computational tools in clinical setting. As one way it overcomethis challenge, Chapters 3 and 4 cover the development of advanced beam theories forbony organs: Based on the Principle of Virtual Power (PVP), stress resultants associatedto beam stretching/compression, bending, and free as well as restrained torsion are identified,and related, via equilibrium conditions, to each other. They are the basis for a 1DFinite Element method along the beam axis. Combination of the 1D equilibrium relationswith dimensionally reduced versions of the classical 3D equilibrium and compatibilityconditions of 3D continuum mechanics yields cross-sectional boundary value problemsfor shear and torsional warping modes, entering 2D Finite Element analyses. The coupled2D-1D approach delivers results which are as reliable as those from classical 3D FEanalyses, however, the new approach is, by at least one order of magnitude, more efficientfrom a computational viewpoint. The novel beam theories are applied and adapted to two4famous problems in bone biomechanics: murine bone structures altered through spaceflight (Chapter 3), and a human lumbar vertebra under physiological loads (Chapter 4).Chapter 5 re-applies the innovations driven by the biomedical field, back into civilengineering; tackling an largely uncovered field which only recently gained importan cedue to durability issues: the mechanics of tramway rails. Characterized (as the bones) byunusual, somewhat exotic cross sections, the mechanical behavior of grooved rails cannotbe assessed by classical beam theory – however, the methods developed in Chapters 3and 4 appear to provide some remedy. Namely, shear stress concentrations arising fromshear and torsional loading expected over the life time of a tramway rail, as predictedby these advanced beam theories, turn out to reliably identify the locations of durability failure initiation, as observed in situ.
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