A bead-spring-chain model including hydrodynamic-interaction effects is used to calculate the rheological properties of dilute polymer solutions undergoing steady shear flow. The hydrodynamic fluctuations are explicitly taken into account within the context of the recently developed Gaussian approximation for the hydrodynamic interaction. In this Gaussian approach expressions for the non-Newtonian stress tensor at arbitrary shear rate are calculated. For short chains, the shear-rate–dependent predictions for the viscometric functions are presented. Also, the Brownian dynamics simulation technique is applied to determine exact rheological behavior of the model. Comparing the simulation results to the corresponding predictions of the Gaussian, consistent-averaging, and preaveraging approximations the validity and the superiority of the Gaussian method is clearly demonstrated.

The Brownian dynamics simulation technique is used to calculate exact rheological properties of the Hookean-dumbbell model with hydrodynamic interaction. The simulation results for steady shear flow are compared to the corresponding predictions of the preaveraging approximation, the consistent-averaging approximation, and the Gaussian approximation developed in the preceding article. Our calculations of the viscometric functions of the Hookean-dumbbell model are performed for various hydrodynamic-interaction tensors.

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Stereotactic frame systems are widely used in neurosurgery. The accuracy of frame devices is considered as a gold standard to which the accuracy of new frameless stereotactic navigation systems is compared. The purpose of this study is to develop a general approach for the prediction of the application accuracy of stereotactic systems. The approach will be applied to the frame-based biopsy performed with three frame devices: Leksell G, Cosman-Roberts-Wells ͑CRW͒, and Brown-Roberts-Wells ͑BRW͒. A work-flow analysis will be carried out demonstrating that the accuracy relevant for a clinical application comprises several error sources including imaging, target and entry point selection, image to frame coordinates registration, and the setting of mechanical parameters of the frame. These error sources will be postulated to obey a Gaussian distribution probability density. The linear, i.e., Gaussian, error propagation, will be used to link all error contributions thus to calculate the cumulative accuracy of the frame used in the application. Although the Gaussian approach is an approximation, it allows for an analytical treatment of the accuracy. Both the accuracy at the target point and the accuracy of the probe needle guidance along the planned trajectory have been investigated. Of great significance is the relationship found between accuracy, pixel dimension, and image slice thickness, the latter being the dominant factor for slices of more than 1.5 mm thickness, yielding inaccuracies larger than 1.5 mm. For target points the predictions for the application accuracy have been compared to the results of measurements, showing good agreement with the experimental data. © 1999 American Association of Physicists in Medicine. ͓S0094-2405͑99͒01803-9͔

A mechanical polymer model including hydrodynamic-interaction and excluded-volume effects is used to predict universal rheological and diffusive properties of dilute polymer solutions. For steady shear flow, explicit expressions for the shear-rate-dependent hydrodynamic-interaction contribution to the stress tensor and polymer diffusion tensors are obtained by employing a perturbation scheme. In the limit of long chains, these contributions are calculated systematically by using renormalization-group methods. The universal shear-rate-dependent predictions for the polymer contribution to the viscosity, the first normalstress coefficient, the ratio of the second to the first normal-stress coefficient, and the polymer diffusion tensor are presented and discussed for good and for solvents.