Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI.

Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments 'plasma' and 'interstitial volume' and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge-Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter v e shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.

Probing highly confined optical fields in the focal region of a high NA parabolic mirror with subwavelength spatial resolution.

Parabolic mirrors with a high numerical aperture can be conveniently used to produce highly confined optical fields in the focal region. Furthermore, these fields can have interesting polarization behaviour due to the high numerical aperture. In particular, if the mirror is illuminated with a size matched radially polarized or azimuthally polarized doughnut mode, the electric field has in the focal region almost exclusively a longitudinal or a transverse polarization component. Such field distributions are interesting for applications in confocal or near-field optical microscopy. Here we present experimental results where we have probed some of these field distributions by raster scanning a fine gold tip in nanometer steps through the focal region and detecting the scattered light intensity. The measured intensity patterns are compared with corresponding vector-field calculations.

Confocal microscopy with a high numerical aperture parabolic mirror.

A novel high-resolution stage scanning confocal microscope for fluorescence microscopy and spatially resolved spectroscopy with a high numerical aperture (NA 1) parabolic mirror objective is investigated. A spatial resolution close to the diffraction limit is achieved. As microscopic fluorescent test objects, dye-loaded zeolite microcrystals (diameter approx. 0.4 microm) and single fluorescent molecules were used. Confocal fluorescence images show a spatial resolution of .x = 0.8 . both at room temperature and at 1.8 K. Imaging of a quasi-point light source and focusing by the parabolic mirror were investigated experimentally and theoretically. Deviations between the theoretical results for a perfect parabolic mirror and the experimental results can be attributed to small deviations of the mirror profile from an ideal parabola.

Torque-velocity relationships and muscle fiber composition in elite female athletes.

The relationship between the predominance of fast and slow muscle fibers of the vastus lateralis and "in vivo" torque velocity properties in 22 female athletes was studied. Fiber types were classified according to the histochemical myofibrillar adenosine triphosphatase technique at a basic pH. Maximal extensor troques were recorded at 30 degrees from full extension at four selected velocities. While results confirm earlier reports on muscle fiber type and performance, an additional finding was that as knee extension velocities increased from 0 to 95 degrees/s angle specific extensor torque production did not decline as seen in in vitro muscle preparations. The difference in extensor torque between 0 and 96 degrees/s appeared far more critical than the differences observed between 96 and 288 degrees/s. Significant differences in torque were seen at 96, 192, and 288 degrees/s in thos with greater than 50% and less than 50% slow-twitch fibers. When expressed per kilogram of body weight the subjects with greater than 50% fast-twitch fiber produced the greatest torque at 192 degrees/s. These results suggest that the velocity at which torque begins to decline in vivo is related to the proportion of slow-twitch fibers in the vastus lateralismuscle.