A Generalization of Mordell to Ternary Quadratic Forms

Mordell in 1958 gave a new proof of the three squares theorem. We generalize those techniques to characterize the integers represented by the remaining six "Ramanujan-Dickson ternaries" as well as three other ternary forms.Comment: 17 page

The Influence of High-Impact Exercise on Cortical and Trabecular Bone Mineral Content and 3D Distribution Across the Proximal Femur in Older Men: A Randomized Controlled Unilateral Intervention.

Regular exercisers have lower fracture risk, despite modest effects of exercise on bone mineral content (BMC). Exercise may produce localized cortical and trabecular bone changes that affect bone strength independently of BMC. We previously demonstrated that brief, daily unilateral hopping exercises increased femoral neck BMC in the exercise leg versus the control leg of older men. This study evaluated the effects of these exercises on cortical and trabecular bone and its 3D distribution across the proximal femur, using clinical CT. Fifty healthy men had pelvic CT scans before and after the exercise intervention. We used hip QCT analysis to quantify BMC in traditional regions of interest and estimate biomechanical variables. Cortical bone mapping localized cortical mass surface density and endocortical trabecular density changes across each proximal femur, which involved registration to a canonical proximal femur model. Following statistical parametric mapping, we visualized and quantified statistically significant changes of variables over time in both legs, and significant differences between legs. Thirty-four men aged mean (SD) 70 (4) years exercised for 12-months, attending 92% of prescribed sessions. In traditional regions of interest, cortical and trabecular BMC increased over time in both legs. Cortical BMC at the trochanter increased more in the exercise than control leg, whereas femoral neck buckling ratio declined more in the exercise than control leg. Across the entire proximal femur, cortical mass surface density increased significantly with exercise (2.7%; p 6%) at anterior and posterior aspects of the femoral neck and anterior shaft. Endocortical trabecular density also increased (6.4%; p 12% at the anterior femoral neck, trochanter, and inferior femoral head. Odd impact exercise increased cortical mass surface density and endocortical trabecular density, at regions that may be important to structural integrity. These exercise-induced changes were localized rather than being evenly distributed across the proximal femur.This research was financially supported by a National Osteoporosis Innovative Award, Medical Research Council UK Interdisciplinary Bridging Award, and a Loughborough University Scholarship. KESP acknowledges support of the Cambridge NIHR Biomedical Research Centre.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1002/jbmr.249

Brief high impact exercise increased cortical mass and trabecular density at regions predictive of femoral neck and trochanteric fracture [Abstract]

Brief high impact exercise increased cortical mass and trabecular density at regions predictive of femoral neck and trochanteric fracture [Abstract

The influence of high impact exercise on cortical and trabecular bone mineral content and 3D distribution across the proximal femur in older men: a randomised controlled unilateral intervention

Regular exercisers have lower fracture risk, despite modest effects of exercise on BMC. Exercise may produce localised cortical and trabecular bone changes that affect bone strength independently of BMC. We previously demonstrated that brief, daily unilateral hopping exercises increased femoral neck BMC in the exercise leg versus the control leg of older men. This study evaluated the effects of these exercises on cortical and trabecular bone and its 3D distribution across the proximal femur, using clinical computed tomography (CT). Fifty healthy men had pelvic CT scans before and after the exercise intervention. We used hip QCT analysis to quantify BMC in traditional regions of interest and estimate biomechanical variables. Cortical bone mapping localised cortical mass surface density and endocortical trabecular density changes across each proximal femur, which involved registration to a canonical proximal femur model. Following statistical parametric mapping, we visualised and quantified statistically significant changes of variables over time in both legs, and significant differences between legs. Thirty-four men aged 70 (4) years exercised for 12-months, attending 92% of prescribed sessions. In traditional ROIs, cortical and trabecular BMC increased over time in both legs. Cortical BMC at the trochanter increased more in the exercise than control leg, whilst femoral neck buckling ratio declined more in the exercise than control leg. Across the entire proximal femur, cortical mass surface density increased significantly with exercise (2.7%; P 6%) at anterior and posterior aspects of the femoral neck and anterior shaft. Endocortical trabecular density also increased (6.4%; P 12% at the anterior femoral neck, trochanter and inferior femoral head. Odd impact exercise increased cortical mass surface density and endocortical trabecular density, at regions that may be important to structural integrity. These exercise-induced changes were localised rather than being evenly distributed across the proximal femur. This article is protected by copyright. All rights reserved

Case Reports1. A Late Presentation of Loeys-Dietz Syndrome: Beware of TGFβ Receptor Mutations in Benign Joint Hypermobility

Background: Thoracic aortic aneurysms (TAA) and dissections are not uncommon causes of sudden death in young adults. Loeys-Dietz syndrome (LDS) is a rare, recently described, autosomal dominant, connective tissue disease characterized by aggressive arterial aneurysms, resulting from mutations in the transforming growth factor beta (TGFβ) receptor genes TGFBR1 and TGFBR2. Mean age at death is 26.1 years, most often due to aortic dissection. We report an unusually late presentation of LDS, diagnosed following elective surgery in a female with a long history of joint hypermobility. Methods: A 51-year-old Caucasian lady complained of chest pain and headache following a dural leak from spinal anaesthesia for an elective ankle arthroscopy. CT scan and echocardiography demonstrated a dilated aortic root and significant aortic regurgitation. MRA demonstrated aortic tortuosity, an infrarenal aortic aneurysm and aneurysms in the left renal and right internal mammary arteries. She underwent aortic root repair and aortic valve replacement. She had a background of long-standing joint pains secondary to hypermobility, easy bruising, unusual fracture susceptibility and mild bronchiectasis. She had one healthy child age 32, after which she suffered a uterine prolapse. Examination revealed mild Marfanoid features. Uvula, skin and ophthalmological examination was normal. Results: Fibrillin-1 testing for Marfan syndrome (MFS) was negative. Detection of a c.1270G > C (p.Gly424Arg) TGFBR2 mutation confirmed the diagnosis of LDS. Losartan was started for vascular protection. Conclusions: LDS is a severe inherited vasculopathy that usually presents in childhood. It is characterized by aortic root dilatation and ascending aneurysms. There is a higher risk of aortic dissection compared with MFS. Clinical features overlap with MFS and Ehlers Danlos syndrome Type IV, but differentiating dysmorphogenic features include ocular hypertelorism, bifid uvula and cleft palate. Echocardiography and MRA or CT scanning from head to pelvis is recommended to establish the extent of vascular involvement. Management involves early surgical intervention, including early valve-sparing aortic root replacement, genetic counselling and close monitoring in pregnancy. Despite being caused by loss of function mutations in either TGFβ receptor, paradoxical activation of TGFβ signalling is seen, suggesting that TGFβ antagonism may confer disease modifying effects similar to those observed in MFS. TGFβ antagonism can be achieved with angiotensin antagonists, such as Losartan, which is able to delay aortic aneurysm development in preclinical models and in patients with MFS. Our case emphasizes the importance of timely recognition of vasculopathy syndromes in patients with hypermobility and the need for early surgical intervention. It also highlights their heterogeneity and the potential for late presentation. Disclosures: The authors have declared no conflicts of interes

Mesothelioma and Radical Surgery 2 (MARS 2): protocol for a multicentre randomised trial comparing (extended) pleurectomy decortication versus no (extended) pleurectomy decortication for patients with malignant pleural mesothelioma.

INTRODUCTION: Mesothelioma remains a lethal cancer. To date, systemic therapy with pemetrexed and a platinum drug remains the only licensed standard of care. As the median survival for patients with mesothelioma is 12.1 months, surgery is an important consideration to improve survival and/or quality of life. Currently, only two surgical trials have been performed which found that neither extensive (extra-pleural pneumonectomy) or limited (partial pleurectomy) surgery improved survival (although there was some evidence of improved quality of life). Therefore, clinicians are now looking to evaluate pleurectomy decortication, the only radical treatment option left. METHODS AND ANALYSIS: The MARS 2 study is a UK multicentre open parallel group randomised controlled trial comparing the effectiveness and cost-effectiveness of surgery-(extended) pleurectomy decortication-versus no surgery for the treatment of pleural mesothelioma. The study will test the hypothesis that surgery and chemotherapy is superior to chemotherapy alone with respect to overall survival. Secondary outcomes include health-related quality of life, progression-free survival, measures of safety (adverse events) and resource use to 2 years. The QuinteT Recruitment Intervention is integrated into the trial to optimise recruitment. ETHICS AND DISSEMINATION: Research ethics approval was granted by London - Camberwell St. Giles Research Ethics Committee (reference 13/LO/1481) on 7 November 2013. We will submit the results for publication in a peer-reviewed journal. TRIAL REGISTRATION NUMBERS: ISRCTN-ISRCTN44351742 and ClinicalTrials.gov-NCT02040272