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- Klinik und Poliklinik für Unfall-, Hand-, Plastische und Wiederherstellungschirurgie (Chirurgische Klinik II) (7)
- Lehrstuhl für Orthopädie (4)
- Abteilung für Funktionswerkstoffe der Medizin und der Zahnheilkunde (1)
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- Institut für diagnostische und interventionelle Radiologie (Institut für Röntgendiagnostik) (1)
- Medizinische Klinik und Poliklinik I (1)
The subject of this thesis is the rigorous passage from discrete systems to continuum models via variational methods.
The first part of this work studies a discrete model describing a one-dimensional chain of atoms with finite range interactions of Lennard-Jones type. We derive an expansion of the ground state energy using \(\Gamma\)-convergence. In particular, we show that a variant of the Cauchy-Born rule holds true for the model under consideration. We exploit this observation to derive boundary layer energies due to asymmetries of the lattice at the boundary or at cracks of the specimen. Hereby we extend several results obtained previously for models involving only nearest and next-to-nearest neighbour interactions by Braides and Cicalese and Scardia, Schlömerkemper and Zanini.
The second part of this thesis is devoted to the analysis of a quasi-continuum (QC) method. To this end, we consider the discrete model studied in the first part of this thesis as the fully atomistic model problem and construct an approximation based on a QC method. We show that in an elastic setting the expansion by \(\Gamma\)-convergence of the fully atomistic energy and its QC approximation coincide. In the case of fracture, we show that this is not true in general. In the case of only nearest and next-to-nearest neighbour interactions, we give sufficient conditions on the QC approximation such that, also in case of fracture, the minimal energies of the fully atomistic energy and its approximation coincide in the limit.
Background
Laxatives are among the most widely used over-the-counter medications in the United States but studies examining their potential hazardous side effects are sparse. Associations between laxative use and risk for fractures and change in bone mineral density [BMD] have not previously been investigated.
Methods
This prospective analysis included 161,808 postmenopausal women (8907 users and 151,497 nonusers of laxatives) enrolled in the WHI Observational Study and Clinical Trials. Women were recruited from October 1, 1993, to December 31, 1998, at 40 clinical centers in the United States and were eligible if they were 50 to 79 years old and were postmenopausal at the time of enrollment. Medication inventories were obtained during in-person interviews at baseline and at the 3-year follow-up visit on everyone. Data on self-reported falls (≥2), fractures (hip and total fractures) were used. BMD was determined at baseline and year 3 at 3 of the 40 clinical centers of the WHI.
Results
Age-adjusted rates of hip fractures and total fractures, but not for falls were similar between laxative users and non-users regardless of duration of laxative use. The multivariate-adjusted hazard ratios for any laxative use were 1.06 (95% confidence interval [CI], 1.03-1.10) for falls, 1.02 (95% CI, 0.85-1.22) for hip fractures and 1.01 (95% CI, 0.96-1.07) for total fractures. The BMD levels did not statistically differ between laxative users and nonusers at any skeletal site after 3-years intake.
Conclusion
These findings support a modest association between laxative use and increase in the risk of falls but not for fractures. Its use did not decrease bone mineral density levels in postmenopausal women. Maintaining physical functioning, and providing adequate treatment of comorbidities that predispose individuals for falls should be considered as first measures to avoid potential negative consequences associated with laxative use.