Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

Accuracy of magnetic resonance imaging to detect cartilage loss in severe osteoarthritis of the first carpometacarpal joint: Comparison with histological evaluation

Background: Magnetic resonance imaging (MRI) is increasingly used for research in hand osteoarthritis, but imaging the thin cartilage layers in the hand joints remains challenging. We therefore assessed the accuracy of MRI in detecting cartilage loss in patients with symptomatic osteoarthritis of the first carpometacarpal (CMC1) joint. Methods: Twelve patients scheduled for trapeziectomy to treat severe symptomatic osteoarthritis of the CMC1 joint underwent a preoperative high resolution 3D spoiled gradient (SPGR) MRI scan. Subsequently, the resected trapezium was evaluated histologically. The sections were scored for cartilage damage severity (Osteoarthritis Research Society International (OARSI) score), and extent of damage (percentage surface area). Each MRI scan was scored for the area of normal cartilage, partial cartilage loss and full cartilage loss. The percentages of the total surface area with any cartilage loss and full-thickness cartilage loss were calculated using MRI and histological evaluation. Results: MRI and histological evaluation both identified large areas of overall cartilage loss. The median (IQR) surface area of any cartilage loss on MRI was 98% (82-100%), and on histological assessment 96% (87-98%). However, MRI underestimated the extent of full-thickness cartilage loss. The median (IQR) surface area of full-thickness cartilage loss on MRI was 43% (22-70%), and on histological evaluation 79% (67-85%). The difference was caused by a thin layer of high signal on the articulating surface, which was interpreted as damaged cartilage on MRI but which was not identified on histological evaluation. Conclusions: Three-dimensional SPGR MRI of the CMC1 joint demonstrates overall cartilage damage, but underestimates full-thickness cartilage loss in patients with advanced osteoarthritis