A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Menarche, menopause, and breast cancer risk: individual participant meta-analysis, including 118 964 women with breast cancer from 117 epidemiological studies.

BACKGROUND: Menarche and menopause mark the onset and cessation, respectively, of ovarian activity associated with reproduction, and affect breast cancer risk. Our aim was to assess the strengths of their effects and determine whether they depend on characteristics of the tumours or the affected women. METHODS: Individual data from 117 epidemiological studies, including 118 964 women with invasive breast cancer and 306 091 without the disease, none of whom had used menopausal hormone therapy, were included in the analyses. We calculated adjusted relative risks (RRs) associated with menarche and menopause for breast cancer overall, and by tumour histology and by oestrogen receptor expression. FINDINGS: Breast cancer risk increased by a factor of 1·050 (95% CI 1·044-1·057; p<0·0001) for every year younger at menarche, and independently by a smaller amount (1·029, 1·025-1·032; p<0·0001), for every year older at menopause. Premenopausal women had a greater risk of breast cancer than postmenopausal women of an identical age (RR at age 45-54 years 1·43, 1·33-1·52, p<0·001). All three of these associations were attenuated by increasing adiposity among postmenopausal women, but did not vary materially by women's year of birth, ethnic origin, childbearing history, smoking, alcohol consumption, or hormonal contraceptive use. All three associations were stronger for lobular than for ductal tumours (p<0·006 for each comparison). The effect of menopause in women of an identical age and trends by age at menopause were stronger for oestrogen receptor-positive disease than for oestrogen receptor-negative disease (p<0·01 for both comparisons). INTERPRETATION: The effects of menarche and menopause on breast cancer risk might not be acting merely by lengthening women's total number of reproductive years. Endogenous ovarian hormones are more relevant for oestrogen receptor-positive disease than for oestrogen receptor-negative disease and for lobular than for ductal tumours. FUNDING: Cancer Research UK.