@article{ScorcellettiKaraZangeetal.2022,
  author    = {Scorcelletti, Matteo and Kara, Serhan and Zange, Jochen and Jordan, Jens and Semler, Oliver and Sch{\"o}nau, Eckhard and Rittweger, J{\"o}rn and Ireland, Alex and Seefried, Lothar},
  title     = {Lower limb bone geometry in adult individuals with X-linked hypophosphatemia: an observational study},
  series = {Osteoporosis International},
  volume    = {33},
  journal   = {Osteoporosis International},
  number    = {7},
  doi       = {10.1007/s00198-022-06385-z},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324655},
  pages     = {1601-1611},
  year      = {2022},
  abstract  = {Summary We assessed lower-limb geometry in adults with X-linked hypophosphatemia (XLH) and controls. We found large differences in multiple measures including femoral and tibial torsion, bowing and cross-sectional area and acetabular version and coverage which may contribute to clinical problems such as osteoarthritis, fractures and altered gait common in XLH. Purpose Individuals with X-linked hypophosphatemia (XLH) are at risk of lower-limb deformities and early onset of osteoarthritis. These two factors may be linked, as altered biomechanics is a risk factor for osteoarthritis. This exploratory evaluation aims at providing clues and concepts for this association to facilitate future larger-scale and longitudinal studies on that aspect. Methods For this observational study, 13 patients with XLH, aged 18-65 years (6 female), were compared with sex-, age- and weight-matched healthy individuals at a single German research centre. Femoral and hip joint geometry, including femoral and tibial torsion and femoral and tibial shaft bowing, bone cross-sectional area (CSA) and acetabular version and coverage were measured from magnetic resonance imaging (MRI) scans. Results Total femoral torsion was 29° lower in individuals with XLH than in controls (p < 0.001), mainly resulting from lower intertrochanteric torsion (ITT) (p < 0.001). Femoral lateral and frontal bowing, tibial frontal bowing, mechanical axis, femoral mechanical-anatomical angle, acetabular version and acetabular coverage were all greater and tibial torsion lower in individuals with XLH as compared to controls (all p < 0.05). Greater femoral total and marrow cavity CSA, greater tibial marrow cavity CSA and lower cortical CSA were observed in XLH (all p < 0.05). Discussion We observed large differences in clinically relevant measures of tibia and particularly femur bone geometry in individuals with XLH compared to controls. These differences may plausibly contribute to clinical manifestations of XLH such as early-onset osteoarthritis, pseudofractures and altered gait and therefore should be considered when planning corrective surgeries.},
  language  = {en}
}
@phdthesis{Jordan2008,
  author    = {Jordan, Jens},
  title     = {Reachable sets of numerical iteration schemes : a system semigroup approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28416},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {We investigate iterative numerical algorithms with shifts as nonlinear discrete-time control systems. Our approach is based on the interpretation of reachable sets as orbits of the system semigroup. In the first part we develop tools for the systematic analysis of the structure of reachable sets of general invertible discrete-time control systems. Therefore we merge classical concepts, such as geometric control theory, semigroup actions and semialgebraic geometry. Moreover, we introduce new concepts such as right divisible systems and the repelling phenomenon. In the second part we apply the semigroup approach to the investigation of concrete numerical iteration schemes. We extend the known results about the reachable sets of classical inverse iteration. Moreover, we investigate the structure of reachable sets and systemgroup orbits of inverse iteration on flag manifolds and Hessenberg varieties, rational iteration schemes, Richardson's method and linear control schemes. In particular we obtain necessary and sufficient conditions for controllability and the appearance of repelling phenomena. Furthermore, a new algorithm for solving linear equations (LQRES) is derived.},
  subject      = {Nichtlineare Kontrolltheorie},
  language  = {en}
}