IVA in addition to BMD can change the osteoporosis management in 25% of clinical routine patients.

Vertebral fracture is one of the major osteoporotic fractures which are unfortunately very often undetected. In addition, it is well known that prevalent vertebral fracture increases dramatically the risk of future additional fracture. Instant Vertebral Assessment (IVA) has been introduced in DXA device couple years ago to ease the detection of such fracture when routine DXA are performed. To correctly use such tool, ISCD provided clinical recommendation on when and how to use it. The aim of our study was to evaluate the ISCD guidelines in clinical routine patients and see how often it may change of patient management. During two months (March and April 2010), a medical questionnaire was systematically given to our clinical routine patient to check the validity of ISCD IVA recommendations in our population. In addition, all women had BMD measurement at AP spine, Femur and 1/3 radius using a Discovery A System (Hologic, Waltham, USA). When appropriate, IVA measurement had been performed on the same DXA system and had been centrally evaluated by two trained Doctors for fracture status according to the semi-quantitative method of Genant. The reading had been performed when possible between L5 and T4. Out of 210 women seen in the consultation, 109 (52%) of them (mean age 68.2±11.5 years) fulfilled the necessary criteria to have an IVA measurement. Out of these 109 women, 43 (incidence 39.4%) had osteoporosis at one of the three skeletal sites and 31 (incidence 28.4%) had at least one vertebral fracture. 14.7% of women had both osteoporosis and at least one vertebral fracture classifying them as "severe osteoporosis" while 46.8% did not have osteoporosis not vertebral fracture. 24.8% of the women had osteoporosis but no vertebral fracture while 13.8% of women did have osteoporosis but vertebral fracture (Clinical osteoporosis). In conclusion, in 52% of our patients, IVA was needed according to ISCD criteria. In half of them the IVA test influenced of patient management either my changing the type of treatment of simply by classifying patient as "clinical osteoporosis". IVA appears to be an important tool in clinical routine but unfortunately is not yet very often use in most of the centers.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay