Przemyslaw Korohoda

Which equations should and which should not be employed in calculating eGFR in children

PURPOSE We assessed the reliability of calculating eGFR in children as compared to the iohexol disappearance test (GFR-I), which was performed 417 times in 353 children aged 2 and more. MATERIAL/METHODS eGFR was estimated with equations based on serum creatinine: Schwartz (1: eGFR-Scr), Cockroft-Gault (2: eGFR-CG) and MDRD (3: eGFR-MDRD), and on creatinine clearance (4: eGFR-U), or relying on serum cystatin C: Hoeck (5: eGFR-H), Bokenkamp (6: eGFR-B) and Filler (7: eGFR-F), and on the three Schwartz markers (8: eGFR-S3M). Mean relative error (RE), correlation (R), Bland-Altman analysis and accuracy of GFR-I were studied in all patients and in subgroups: at GFR<60ml/min/1.73m(2); in children aged ≤12 and >12. RESULTS The results by eGFR-Scr, eGFR-S3M demonstrated no statistical difference to GFR-I at GFR<60ml/min/1.73m(2), but underestimated eGFR at higher filtration values by 11.6±15.1% and 19.1±16.4, respectively (p<0.0000). The eGFR-B, eGFR-F and eGFR-MDRD equations illustrated important overestimation of reference GFR results (RE: 84±44.2%; 29.5±27.9%, 35.6±62%; p<0.0000 for all). The MDRD and C-G formulas showed statistically better consistency in children aged >12. A good agreement was achieved by the eGFR-H equation (5.1±21.9%; p<0.0000; R=0.78). CONCLUSIONS (1) Schwartz equations show a good conformity at GFR<60ml/min/1.73m(2), but underestimate the results at higher GFR values. (2) The Bokenkamp equation with original coefficient should not be employed in children. (3) The use of the Hoeck formula in all children and C-G and MDRD formula in children aged >12 is possible. (4) The error of eGFR calculations increases at higher GFR values.

Quantifying the discontinuity of haemodialysis dose with time-averaged concentration (TAC) and time-averaged deviation (TAD)

It is with great interest that we have read the analysis of Daugirdas et al. on the effects of spacing of discontinuous haemodialysis on weekly dose of dialysis [1]. The authors showed that (contrary to other measures) the change in maximum concentration (‘peak’) associated with intermittent dialysis and attained at the end of the long dialysis interval best captured the increase in the weekly dose, especially when changing from illto well-spaced treatments. Long before the introduction of equivalent renal clearance [2] and so-called standard Kt/V [3], Lopot et al. compared different modes of dialysis by computing the timeaveraged deviation (TAD) and plotted this measure against the time-averaged concentration (TAC) of urea [4,5]. For c (t), representing the time-dependent urea nitrogen concentration (in millimole per litre), and T, representing the duration of 1 week (10 080 min), TAC and TAD are given as

Generalized convolution as a tool for the multi-dimensional filtering tasks

In this paper the so-called generalized convolution, being in fact an adequate adaptation of the well known circular convolution concept to any invertible block-transform, is proposed, developed, and analysed. First the proposed idea is summarized for a one-dimensional case. Then it is extended to multidimensional problems. The presented generalized convolution concept is based on the earlier A-convolution. This idea is recalled at the beginning and a set of techniques for studying the dependence of the respective coefficients on the arbitrary transform, is suggested. The generalized convolution matrix, being an extension of that for the circular convolution, is introduced and adapted to an arbitrary invertible transform. The filtering problem is then defined and presented in the transform domain. The multidimensional analysis starts with two-dimensional problems, then it is continued with formulas for multidimensional filtering tasks. The paper is illustrated with examples computed for twenty carefully selected transforms. Among them are Haar, Hadamard, Hartley, Karhunen-Loeve and a family of 16 discrete trigonometric transforms.

Relationship between kinetics of albumin-bound bilirubin and water-soluble urea in extracorporeal blood purification

BACKGROUND The purpose of the study was to examine the relationship between urea and conjugated bilirubin kinetics during extracorporeal liver support (ELS) therapy and to determine the dose of therapy for urea and conjugated bilirubin as markers for water-soluble and protein-bound solutes, respectively. METHODS Kinetics of urea and bilirubin were described by standard two-compartment models with central clearance, constant intercompartment clearance, constant generation rate and constant volume. While the concentration of urea was assumed as equilibrated between compartments at the beginning of ELS therapy, the concentration of conjugated bilirubin between compartments was assumed to follow the partition of albumin between plasma and interstitial spaces. Treatment dose was calculated as removed solute mass and fractional solute removal. RESULTS Seven patients were studied during 15 treatments lasting at least 6 h. Bilirubin distribution volume of 14.8 ± 5.4 L was not different from urea extracellular water volume of 15.0 ± 2.8 L. The correspondence between models was used to predict the mass of bilirubin removed based on extracellular volume obtained from urea kinetics, average data from bilirubin kinetics, as well as selected treatment and patient information. The prediction of bilirubin mass removed based on this reduced information was not different from the mass of solute removed based on complete bilirubin kinetic analysis. CONCLUSIONS The correspondence between kinetics of urea and conjugated bilirubin can be used to identify the bilirubin distribution volume from urea kinetic analysis. This information is then useful to estimate and predict the solute removal of conjugated bilirubin in ELS.

Design of the mutually cancelling narrow passband and stopband filters — A case study

Design of narrowband digital filters taking into account time-frequency properties of input signals and the requirements of real-time application which sets heavy constrains for their dynamic characteristics is not easy task in practice. This article presents design and detailed analysis of the complementary pairs of notch-peak filters used in case of audio signals.

Modification of the Schwartz equations for children increases their accuracy at eGFR > 60 mL/min/1.73 m2

Abstract Aim: Estimation of eGFR in children with normal kidney function using the Schwartz equations results in underestimating real GFR. Materials and methods: We propose modification of three Schwartz equations – two based on creatinine concentration (eGFRScrBS bedside) and (eGFRScr) and one 3-marker based on creatinine, urea and cystatin C concentrations (eGFRS3M). The iohexol test (reference method) was performed 417 times in 353 children >2 years with mean GFR: 98 ± 31.6 ml/min/1.73m2. The assessment included also the Filler and Zappitelli equations. The modification was performed using methods: (1) based on equation, eGFRcor = a [eGFR − T] + T, where T = 50, if eGFR > T, and a equals for: eGFRScrBS 1.4043, for eGFRScr 2.0048, for eGFRS3M 1.2951, and (2) based on correction of all coefficients of the original equation. Results: For comparison of all the results and for children with GFR< 60, 60-90, 90-135 and > 135 ml/min/1.73m2 the correlation coefficient, relative error (RE) and root mean square relative error (RMSRE) was employed and revealed improvement of RE from 25.9 to 6.8 and 3.9% (depending on the correction method) for eGFRScr; from 19 to 8.1 and 3.9% for eGFRScrBS and: from 11.6% to 2.0 and 2.3% for eGFRS3M (respectively). The RMSRE values changed from 30 to 21.3 and 19.8% for eGFRScr, from 25.1 to 21.6 and 19.8% for eGFRScrBS and from 19.1 to 15.8 and 15.3 % for eGFRS3M. Conclusions: Modifications of Schwartz equations at GFR > 60 ml/min/1.73m2 significantly improves the accuracy of calculating eGFR. The 3-markers equation is more accurate and should be employed frequently.

Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis

Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue) indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.

Analysis of critical sampling effects revisited

In the paper, some specific problems occurring in analysis of critically sampled signals and their reconstruction are considered. These are the problems which are mostly omitted in the literature of the subject because they can lead to ambiguous results. Because of this reason, their explanation is hard and thankless. Here, we show how to find and verify the general description of the resulting signal by usage of Dirac delta and sinc, and Π functions.

Reference ranges and impact of selected confounders on classic serum and urinary renal markers in neonatal period

PURPOSE Renal injury in term and pre-term neonates may be an antecedent to chronic kidney disease in the childs further life. The aim of the paper was to compile a reference range for selected serum and urinary renal markers in the neonatal period for full-term (FT) and pre-term (PT) newborns. MATERIAL AND METHODS The prospective study included 23 FT infants (birth weight - BW≥2500g and gestational age - GA≥37Hbd) and 32 PT children (BW<2500g and GA<37Hbd) in good general condition, without acute kidney injury (AKI) or sepsis. Between the 4th and 28th DOL, urinary concentrations of the studied renal markers (uCr, uNa, uOsm) were determined on a daily basis, while serum creatinine (SCr) was assessed minimum every 48-72h. RESULTS The mean GA and BW of the FT and PT infants were respectively as follows: 38.5±1.7Hbd; 3433±495.2g and 32.7±2.6Hbd; 1836.7±419.8g. For serum glomerular (SCr, eGFR) and tubular markers (FENa, RFI), the median values with normal ranges were compiled. For urinary renal markers (uCr, uNa, uOsm) and those values standardized for kg of body weight, percentile tables for 4-28DOL were elaborated. CONCLUSIONS The study has resulted in determining the normal ranges of serum glomerular and tubular renal markers, as well as percentile tables of selected urinary renal parameters during the neonatal period. The percentile tables may prove to be helpful for further standardization of other urinary parameters per urinary creatinine in neonatal population.

Audio in-band signalling system based on a complementary pair of peak and notch equalizers

Slow rate, in-band signalling embedded into audio content of digital or analog radio broadcast network is common but demanding design challenge. In this paper a solution based on complementary pair of notch-peak filters for audio in-band signalling system is proposed. The concept is illustrated with a series of examples, verifying the basics of the idea and indicating possible traps and challenges the engineer utilizing the described system may encounter. The simulations were performed with Matlab and the accuracy of filters was tested with the SHARC signal processor.