Size-corrected BMD decreases during peak linear growth: Implications for fracture incidence during adolescence

Peak adolescent fracture incidence at the distal end of the radius coincides with a decline in size-corrected BMD in both boys and girls. Peak gains in bone area preceded peak gains in BMC in a longitudinal sample of boys and girls, supporting the theory that the dissociation between skeletal expansion and skeletal mineralization results in a period of relative bone weakness. Introduction: The high incidence of fracture in adolescence may be related to a period of relative skeletal fragility resulting from dissociation between bone expansion and bone mineralization during the growing years. The aim of this study was to examine the relationship between changes in size-corrected BMD (BMDsc) and peak distal radius fracture incidence in boys and girls. Materials and Methods: Subjects were 41 boys and 46 girls measured annually (DXA; Hologic 2000) over the adolescent growth period and again in young adulthood. Ages of peak height velocity (PHV), peak BMC velocity (PBMCV), and peak bone area (BA) velocity (PBAV) were determined for each child. To control for maturational differences, subjects were aligned on PHV. BMDsc was calculated by first regressing the natural logarithms of BMC and BA. The power coefficient (pc) values from this analysis were used as follows: BMDsc = BMC/BA(pc). Results: BMDsc decreased significantly before the age of PHV and then increased until 4 years after PHV. The peak rates in radial fractures (reported from previous work) in both boys and girls coincided with the age of negative velocity in BMDsc; the age of peak BA velocity (PBAV) preceded the age of peak BMC velocity (PBMCV) by 0.5 years in both boys and girls. Conclusions: There is a clear dissociation between PBMCV and PBAV in boys and girls. BMDsc declines before age of PHV before rebounding after PHV. The timing of these events coincides directly with reported fracture rates of the distal end of the radius. Thus, the results support the theory that there is a period of relative skeletal weakness during the adolescent growth period caused, in part, by a draw on cortical bone to meet the mineral demands of the expanding skeleton resulting in a temporary increased fracture risk.

Synthesis of monocyclic and linear polystyrene using the reversible coupling/cleavage of thiol/disulfide groups

By carefully controlling the concentration of alpha,omega-thiol polystyrene in solution, we achieved formation of unique monocyclic polystyrene chains (i.e., polymer chains with only one disulfide linkage). The presence of cyclic polystyrene was confirmed by its lower than expected molecular weight due to a lower hydrodynamic volume and loss of thiol groups as detected by using Ellman's reagent. The alpha,omega-thiol polystyrene was synthesized by polymerizing styrene in the presence of a difunctional RAFT agent and subsequent conversion of the dithioester end groups to thiols via the addition of hexylamine. Oxidation gave either monocyclic polymer chains (i.e., with only one disulfide linkage) or linear multiblock polymers with many disulfide linkages depending on the concentration of polymer used with greater chance of cyclization in more dilute solutions. At high polymer concentrations, linear multiblock polymers were formed. To control the MWD of these linear multiblocks, monofunctional X-PSTY (X = PhCH2C(S)-S-) was added. It was found that the greatest ratio of X-PSTY to X-PSTY-X resulted in a low M-n and PDI. We have shown that we can control both the structure and MWD using this chemistry, but more importantly such disulfide linkages can be readily reduced back to the starting polystyrene with thiol end groups, which has potential use for a recyclable polymer material.

Solution properties of star and linear poly(N-isopropylacrylamide)

The LCST transitions of novel N-isopropylacrylamide ( NIPAM) star polymers, prepared using the four-armed RAFT agent pentaerythritoltetrakis(3-(S-benzyltrithiocarbonyl) propionate) (PTBTP) and their hydrolyzed linear arms were studied using H-1 NMR, PFG-NMR, and DLS. The aim was to determine the effect of polymer architecture and the presence of end groups derived from RAFT agents on the LCST. The LCST transitions of star PNIPAM were significantly depressed by the presence of the hydrophobic star core and possibly the benzyl end groups. The effect was molecular weight dependent and diminished once the number of repeating units per arm >= 70. The linear PNIPAM exhibited an LCST of 35 degrees C, regardless of molecular weight; the presence of both hydrophilic and hydrophobic end groups after hydrolysis from the star core was suggested to cancel effects on the LCST. A significant decrease in R-H was observed below the LCST for star and linear PNIPAM and was attributed to the formation of n-clusters. Application of a scaling law to the linear PNIPAM data indicated the cluster size n = 6. Tethering to the hydrophobic star core appeared to inhibit n-cluster formation in the lowest molecular weight stars; this may be due to enhanced stretching of the polymer chains, or the presence of larger numbers of n-clusters at temperatures below those measured.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.