Association of all-cause mortality with pre-dialysis systolic blood pressure and its peridialytic change in chronic hemodialysis patients

Background Pre-dialysis systolic blood pressure (pre-HD SBP) and peridialytic SBP change have been associated with morbidity and mortality among hemodialysis (HD) patients in previous studies, but the nature of their interaction is not well understood. Methods We analyzed pre-HD SBP and peridialytic SBP change (calculated as post-HD SBP minus pre-HD SBP) between January 2001 and December 2012 in HD patients treated in US Fresenius Medical Care facilities. The baseline period was defined as Months 4–6 after HD initiation, and all-cause mortality was noted during follow-up. Only patients who survived baseline and had no missing covariates were included. Censoring events were renal transplantation, modality change or study end. We fitted a Cox proportional hazard model with a bivariate spline functions for the primary predictors (pre-HD SBP and peridialytic SBP change) with adjustment for age, gender, race, diabetes, access-type, relative interdialytic weight gain, body mass index, albumin, equilibrated normalized protein catabolic rate and ultrafiltration rate. Results A total of 172 199 patients were included. Mean age was 62.1 years, 61.6% were white and 55% were male. During a median follow-up of 25.0 months, 73 529 patients (42.7%) died. We found that a peridialytic SBP rise combined with high pre-HD SBP was associated with higher mortality. In contrast, when concurrent with low pre-HD SBP, a peridialytic SBP rise was associated with better survival. Conclusion The association of pre-HD and peridialytic SBP change with mortality is complex. Our findings call for a joint, not isolated, interpretation of pre-HD SBP and peridialytic SBP change.

Medical Image Zooming by Using Rational Bicubic Ball Function

This chapter deals with image processing in the specific area of image zooming via interpolation. The authors employ bivariate rational cubic ball function defined on rectangular meshes. These bivariate spline have six free parameters that can be used to alter the shape of the surface without needed to change the data. It also can be used to refine the resolution of the image. In order to cater the image zomming, they propose an efficient algorithm by including image downscaling and upscaling procedures. To measure the effectiveness of the proposed scheme, they compare the performance based on the value of peak signal-to-noise ratio (PSNR) and root mean square error (RMSE). Comparison with existing schemes such as nearest neighbour (NN), bilinear (BL), bicubic (BC), bicubic Hermite (BH), and existing scheme Karim and Saaban (KS) have been made in detail. From all numerical results, the proposed scheme gave higher PSNR value and smaller RMSE value for all tested images.

Galerkin method with splines for total variation minimization

Total variation smoothing methods have been proven to be very efficient at discriminating between structures (edges and textures) and noise in images. Recently, it was shown that such methods do not create new discontinuities and preserve the modulus of continuity of functions. In this paper, we propose a Galerkin–Ritz method to solve the Rudin–Osher–Fatemi image denoising model where smooth bivariate spline functions on triangulations are used as approximating spaces. Using the extension property of functions of bounded variation on Lipschitz domains, we construct a minimizing sequence of continuous bivariate spline functions of arbitrary degree, d, for the TV- L2 energy functional and prove the convergence of the finite element solutions to the solution of the Rudin, Osher, and Fatemi model. Moreover, an iterative algorithm for computing spline minimizers is developed and the convergence of the algorithm is proved.