TY - JOUR A1 - Scorcelletti, Matteo A1 - Kara, Serhan A1 - Zange, Jochen A1 - Jordan, Jens A1 - Semler, Oliver A1 - Schönau, Eckhard A1 - Rittweger, Jörn A1 - Ireland, Alex A1 - Seefried, Lothar T1 - Lower limb bone geometry in adult individuals with X-linked hypophosphatemia: an observational study JF - Osteoporosis International N2 - 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. KW - bone KW - femur KW - geometry KW - shape KW - XLH Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-324655 VL - 33 IS - 7 ER - TY - THES A1 - Jordan, Jens T1 - Reachable sets of numerical iteration schemes : a system semigroup approach T1 - Erreichbarkeitsmengen numerischer Iterations Schemata : ein Systemhalbgruppenansatz N2 - 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. N2 - Iterative numerische Algorithmen können als zeitdiskrete Systeme betrachtet werden. In dieser Arbeit werden Methoden der nichtlinearen Kontrolltheorie benutzt um iterative numerische Algorithmen zu analysieren. Hierzu wird ein Ansatz verfolgt der darauf basiert, dass Erreichbarkeitsmengen als Halbgruppenorbits interpretiert werden können. Im ersten Teil der Arbeit werden Werkzeuge zur systematischen Analyse von Erreichbarkeitsmengen allgemeiner nichtlinearer Kontrollsystme entwickelt. Dazu werden klassische Konzepte, wie geometrische Kontrolltheorie, Halbgruppenaktionen und semialgebraische Geometrie zusammengeführt. Desweiteren werden neue Konzepte, wie rechtszerlegbare Systeme und Abstoßungsphänomene, eingeführt. Im zweiten Teil der Arbeit werden diese Werkzeuge und dabei insbesondere der Halbgruppenansatz zur Untersuchung konkreter numerischer Algorithmen angewandt. Bekannte Ergebnisse über die Erreichbarkeitsmengen der klassischen inversen Iteration werden erweitert. Die Ergebnisse werden auf inverse Iteration auf Fahnenmannigfaltigkeiten und auf Hessenbergvarietäten erweitert. Untersucht wird zudem die Struktur der Erreichbarkeitsmengen der rationalen Iteration, der Richardsonmethode und von linearen Kontrollsystemen. Insbesondere werden notwendige sowie hinreichende Kriterien sowohl für Kontrollierbarkeit als auch für das Auftreten von Abstoßungsphänomenen bewiesen. Außerdem wird ein neuer Algorithmus zum Lösen linearer Gleichungssysteme vorgestellt. KW - Nichtlineare Kontrolltheorie KW - Numerische Mathematik KW - Systemhalbgruppen KW - Inverse Iteration KW - Abstoßungsphänomen KW - Systemsemigroups KW - inverse Iteration KW - repelling phenomenon Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-28416 ER -