Effect of osteoporosis on bone mineral density and fracture repair in a rat femoral fracture model

Osteoporosis (OP) is one of the most prevalent bone diseases worldwide with bone fracture the major clinical consequence. The effect of OP on fracture repair is disputed and although it might be expected for fracture repair to be delayed in osteoporotic individuals, a definitive answer to this question still eludes us. The aim of this study was to clarify the effect of osteoporosis in a rodent fracture model. OP was induced in 3-month-old rats (n = 53) by ovariectomy (OVX) followed by an externally fixated, mid-diaphyseal femoral osteotomy at 6 months (OVX group). A further 40 animals underwent a fracture at 6 months (control group). Animals were sacrificed at 1, 2, 4, 6, and 8 weeks postfracture with outcome measures of histology, biomechanical strength testing, pQCT, relative BMD, and motion detection. OVX animals had significantly lower BMD, slower fracture repair (histologically), reduced stiffness in the fractured femora (8 weeks) and strength in the contralateral femora (6 and 8 weeks), increased body weight, and decreased motion. This study has demonstrated that OVX is associated with decrease in BMD (particularly in trabecular bone) and a reduction in the mechanical properties of intact bone and healing fractures. The histological, biomechanical, and radiological measures of union suggest that OVX delayed fracture healing. (C) 2007 Orthopaedic Research Society. Published by Wiley Periodicals.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Individual differences in trajectories of arithmetical development in typically achieving 5-to 7-year-olds

The arithmetical performance of typically achieving 5- to 7-year-olds (N = 29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear growth over the 18-month period, analysis of individual differences revealed a much more complex picture. Some children exhibited marked variation in performance across the seven tasks, including evidence of difficulty in some cases. Individual growth patterns also showed differences in developmental trajectories between children on each task and within children across tasks. The findings support the idea of the componential nature of arithmetical ability and underscore the need for further longitudinal research on typically achieving children and of careful consideration of individual differences. (C) 2009 Elsevier Inc. All rights reserved.