Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Poor performance of microbiological sampling in the prediction of recurrent arthroplasty infection

During a two-stage revision for prosthetic joint infections (PJI), joint aspirations, open tissue sampling and serum inflammatory markers are performed before re-implantation to exclude ongoing silent infection. We investigated the performance of these diagnostic procedures on the risk of recurrence of PJI among asymptomatic patients undergoing a two-stage revision. A total of 62 PJI were found in 58 patients. All patients had intra-operative surgical exploration during re-implantation, and 48 of them had intra-operative microbiological swabs. Additionally, 18 joint aspirations and one open biopsy were performed before second-stage reimplantation. Recurrence or persistence of PJI occurred in 12 cases with a mean delay of 218 days after re-implantation, but only four pre- or intraoperative invasive joint samples had grown a pathogen in cultures. In at least seven recurrent PJIs (58%), patients had a normal C-reactive protein (CRP, < 10 mg/l) level before re-implantation. The sensitivity, specificity, positive predictive and negative predictive values of pre-operative invasive joint aspiration and CRP for the prediction of PJI recurrence was 0.58, 0.88, 0.5, 0.84 and 0.17, 0.81, 0.13, 0.86, respectively. As a conclusion, pre-operative joint aspiration, intraoperative bacterial sampling, surgical exploration and serum inflammatory markers are poor predictors of PJI recurrence. The onset of reinfection usually occurs far later than reimplantation.