NON-NEWTON FILTRATION EQUATION WITH SPECIAL MEDIUM VOID

This paper considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special medium void of the following form:where , ft is a smooth bounded domain in RN(N≥3), 0∈Ω, The result of asymptotic estimate of global solution depends on the best constant in Hardy inequality.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.

Accuracy of glomerular filtration rate estimation equations in patients with hematopathy

Renal dysfunction is a common side-effect of chemotherapeutic agents in patients with hematopathy. Although broadly used, glomerular filtration rate(GFR) estimation equations were not fully validated in this specific population. Thus, this study was designed to further assess the accuracy of various GFR equations, including the newly 2012 CKD-EPI equations. Referring to ^(99m)Tc-DTPA clearance method, three Scr-based(MDRD, Peking, and CKD-EPI_(Scr)), three Scys C-based(Steven 1, Steven 2, and CKD-EPI_(Scys C)), and three Scr-Scys C combination based(Ma, Steven 3, and CKD-EPI_(Scr-Scys C)) equations were included. Bias, P_(30), and misclassification rate were applied to compare the applicability of the selected equations. A total of 180 Chinese hematological patients were enrolled.Mean bias, absolute mean bias, P_(30), misclassification rate and Bland-Altman plots of the CKD-EPI_(Scr-Scys C) equation were 7.90 mL/minute/1.73 m^2, 17.77 mL/minute/1.73 m^2, 73.3%, 38% and 79.7 mL/minute/1.73 m^2, respectively.CKD-EPI_(Scr-Scys C) predicted the most precise eGFR both in lymphoma and leukemia subgroups. Additionally, CKDEPI_(Scys C) equation in the rGFR■90 mL/minute/1.73 m^2 subgroup and Steven 2 equation in the rGFR<90 mL/minute/1.73 m^2 subgroup provided more accurate estimates in each subgroup. The CKD-EPI_(Scr-Scys C) equation could be recommended to monitor kidney function in hematopathy patients. The accuracy of GFR equations may be closely related with GFR level and kidney function markers, but not the primary cause of hematopathy.

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results （Applicable Analysis, 92（2013）, 636-650） and the results of Zheng et al （Math. Meth. Appl. Sci., 36（2013）, 730-743）.

Existence, Uniqueness and Blow-up of Generalized Solutions to General Nonlinear Filtration Equations

In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.

QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION(Ⅰ)

This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution.

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.

Cake Filtration Equation Using tanⁿ<i>θ</i>Reduction Method

This study was completed by an extensive mathematical analysis. New equation to sludge filtration processes has been proposed for use in routine laboratory. The equation has been suggested to replace Ademiluyi’s cake filtration equation in view of the limitations of the latter. The new equation can be used for sludges whose compressibility factor is more than one but Ademiluyi’s cake filtration equation can only be used for sludges whose compressibility coefficient is less than one. The new sludge filtration equation was derived using tannθ reduction method. The generalized equation thus obtained resembles Ademiluyi’s equation in the mode of parameter combination except the presence of summation notation in the new equation.

NH_3-N Degradation Dynamics and Calculating Model of Filtration Bed Height in Constructed Soil Rapid Infiltration

The research on Constructed Soil Rapid Infiltration(CSRI) system is in its infancy at home and abroad.There are several details about the mechanism and application of CSRI system needed to be further studied.A major limitation in the current research is the absence of degradation dynamics of pollutants,and the height of filtration bed in CSRI system currently determined by empirical judgment lacks accuracy and logicality.To solve these two prob-lems,the soil column of CSRI system was utilized to treat domestic wastewater,meanwhile,the NH3-N degradation dynamics were studied according to the Monod equation,the research of Mann A T and the NH3-N degradation law.Then the mathematical model of filtration bed height was built based on NH3-N degradation dynamics equation in the soil column.It has been proven that within a limited range this model can calculate the appropriate height of filtration bed accurately in order to optimize technological parameters of hydraulic load and the concentration of influent NH3-N,improving the effluent quality of CSRI system.

Clinical use of estimating glomerular filtration rate equ-ations during pregnancy

Background: Kidney disease, even when mild, was once considered so major an impediment to successful pregnancy and so dangerous to the mother’s wellbeing. High-risk pregnancy mainly associated to renal impairment may occur in 10-20% of gestations and it is very important that renal function is closely monitored to prevent or minimize maternal and fetal complications. This study was designed to investigate the performance of Cockcroft-Gault CGeq and the simplified MDRDeq equations in healthy pregnant women to assess renal function. Methods: We studied 167 normal ambulatory pregnant women and kidney function was contemporaneously estimated through the CGeq and the simplified MDRDeq and calculated through the creatinine clearance (Ccr). Serum and urinary creatinine were assayed using Jaffé reaction method in the same AutoAnalyser. Results: When we compared calculated and estimated clearences for measurement of kidney function we observed that CGeq overestimated renal function (CGeq = 168.41 ± 38.80 ml/ min/1.73 m2, Ccr = 146.27 ± 30.49 ml/min / 1.73 m2, p < 0.001), MDRDeq underestimated renal function (Ccr = 146.27 ± 30.49 ml/min / 1.73 m2, MDRDeq = 129.15 ± 29.28 ml/min / 1.73m2, p < 0.001). Conclusions: Our results demonstrated that CGeq overestimated, MDRDeq underestimated significantly kidney function during gestation in healthy women and cannot be recommended to assess renal function in obstetric practice. Ccr remains a useful clinical tool in pregnant women until the development of a specific equation that considers the several important maternal renal physiological alterations and provides the measure of GFR the most unbiased and precise as possible.

Continuity of Some Classes of Functions Related to Degenerate Parabolic Equations and Its Applications

We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations.

The Choice Between Three Simple Methods for Glomerular Filtration Rate Assessment in Different Stages of Chronic Parenchymal Renal Diseases

Glomerular filtration rate （GFR） can be measured （mGFR） after intravenous application of indicators that are eliminated by kidneys or estimated （eGFR） using mathematic equations. We have compared eGFR obtained by the chronic kidney diseases epidemiology collaboration （CKD-EPI） and the Modification of diet in renal disease （MDRD） Study equations with GFR measured by technetium-99m diethylene triamine penta-acetic acid （99m^Te-DTPA） renal clearance in different stages of renal diseases in order that obtained results may contribute to more adequate choice of methods for the GFR assessment in relation to the type and stage of kidney disease. The study included a total of 189 participants with diabetes mellitus （DM）, glomerulonephritis （GN）, Balkan endemic nephropathy （BEN） and healthy subjects. 99m^Tc-DTPA clearance （ml/min/1.73 m^2） was calculated from the regression equation based on high correlation between distribution volume of radiopharmaceutical and clearance values obtained by multiple blood samples. For blood sample taken at 3 h and 4 h, clearance was calculated according to the equations： y = -0.0128x^2 ＋ 3.077x - 30.3, and y = -0.00628x^2 ＋ 2.066x - 19.3, where y is clearance, and x is distribution volume. MDRD-GFR （ml/min/l.73 m2） was calculated from equation： 186 × Scr^-1154 × age^-0.203 × 0.742 if female. CKD-EPI-GFR was calculated from equation： 141 × min（Scr/K, 1）^ α ×max（Scr/K, 1）^-1 209 × 0.993age × 1.018 if female, where Scr is serum creatinine, n is 0.7 for females and 0.9 for males, c~ is -0.329 for females and -0.411 for males, min indicates the minimum of Scr/K or 1, and max indicates the maximum of Scr/κ or 1. Irrespective of renal disease, both equations underestimated radionuclide clearance at mGFR 〉 90 ml/min/1.73 m^2 （91.7 ± 18.8 and 88.2 ± 22.0 vs. 121± 19.6, p〈0.0001） and at mGFR 60-89 ml/min/1.73 m^2 （67.1 ±19.9 and 65.8 ± 19.9 vs. 75.8 ± 9.2, p 〈 0.05 and p 〈 0.005）. They were also significantly lower than mGFR in DM patients with GFR 〉_ 90 ml/min/1.73 m^2. In patients with GFR 〉 60 ml/min/1.73 m^2, the median bias of CKD-EPI equation was lower and accuracy （percent of eGFR within 30% of mGFR, P30） was higher than that of MDRD equation. Nevertheless, in DM patients with GFR _〉 90 ml/min the accuracy of the former equation is significantly better than that of MDRD formula. Patients GFR 〈 60 ml/min had the similar bias and accuracy both eGFR equations. As CKD-EPI equation has lesser bias and improved accuracy than MDRD equation in patients with GFR 〉 60 ml/min, we suggest its use for prediction of GFR at higher renal function levels. However, underestimation of renal function by CKD-EPI equation seems not to be quite appropriate in diabetic patients with expected GFR above 90 ml/min because it may miss the patients with glomerular hyperfiltration. Thus, priority may be given to 99m^Tc-DTPA clearance method in the earlier stages of kidney diseases in type 1 diabetes mellitus. At last, in patients with expected GFR 〈 60 ml/min, it is better to monitor disease progression by estimating equations than by 99m^Tc-DTPA renal clearance, due to their simpler implementation.

HARNACK ESTIMATES FOR WEAK SOLUTIONS OF EQUATIONS OF NON-NEWTONIAN POLYTROPIC FILTRATION

An intrinsic Harnack estimate and some sup-estimates are established for nonnegative weak solutions of equations of non-Newtonian polytropic filtration ut -div(｜Dum ｜p-2Dum) =0, m(p- 1) ＜ 1, m＞0, p＞ 1.

Relative performance of two equations for estimation of glomerular filtration rate in a Chinese population having chronic kidney disease

Background The new Chronic Kidney Disease Epidemiology Collaboration （CKD-EPI） equation was developed to address the systematic underestimation of glomerular filtration rate （GFR） by the Modification of Diet in Renal Disease （MDRD） Study equation in patients with relatively well-preserved kidney function.Performance of the new equation in the Chinese population is unknown.The goal of the present study was to compare performance of these two equations in Chinese patients with chronic kidney disease （CKD）.Methods We enrolled 450 Chinese patients （239 women and 211 men） with CKD in the present study.The renal dynamic imaging method was used to measure the referenced standard GFR （rGFR） for comparison with estimations using the two equations.Their overall performance was assessed with the Bland-Altman method and receiver-operating characteristics （ROC） analysis.Performance of the two equations in lower and higher estimated GFR （eGFR） subgroups was further investigated.Results Both eGFRs correlated well with rGFR （r=0.88,0.81,P〈0.05）.In overall performance,the CKD-EPI equation showed less bias,higher precision and improved accuracy,and was better for detecting CKD.In the higher-eGFR subgroup,the CKD-EPI equation corrected the underestimation of GFR by the abbreviated MDRD equation.Conclusions The CKD-EPI equation outperformed the abbreviated MDRD equation not only in overall performance but also in the subgroups studied.For the present,the CKD-EPI equation appears to be the first-choice prediction equation for estimating GFR.

Analysis of chronic kidney disease staging with different estimated glomerular filtration rate equations in Chinese centenarians

Background: Accurate estimation of the glomerular filtration rate (GFR) and staging of chronic kidney disease (CKD) are important. Currently, there is no research on the differences in several estimated GFR equations for staging CKD in a large sample of centenarians. Thus, this study aimed to investigate the differences in CKD staging with the most commonly used equations and to analyze sources of discrepancy. Methods: A total of 966 centenarians were enrolled in this study from June 2014 to December 2016 in Hainan province, China. The GFR with the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Berlin Initiative Study 1 (BIS1) equations were estimated. Agreement between these equations was investigated with the k statistic and Bland-Altman plots. Sources of discrepancy were investigated by partial correlation analysis. Results: The k values of the MDRD and CKD-EPI equations, MDRD and BIS1 equations, and CKD-EPI and BIS1 equations were 0.610, 0.253, and 0.381, respectively. Serum creatinine (Scr) explained 10.96%, 41.60% and 17.06% of the variability in these three comparisons, respectively. Serum uric acid (SUA) explained 3.65% and 5.43% of the variability in the first 2 comparisons, respectively. Gender was associated with significant differences in these 3 comparisons (P<0.001). Conclusions: The strengths of agreement between the MDRD and CKD-EPI equations were substantial, but those between the MDRD and BIS 1 equations and the CKD-EPI and BIS 1 equations were fair. The difference in CKD staging of the first 2 comparisons strongly depended on Scr, SUA and gender, and that of CKD-EPI and BIS1 equations strongly depended on Scr and gender. The incidence at various stages of CKD staging was quite different. Thus, a new equation that is more suitable for the elderly needs to be built in the future.

The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption

The paper proves the nonexistence of the solution for the following Cauchy problem{ut=div(|■u^m|(p-2■u^(m)))^-λu^(q),u(x,0)=δ(x),(x,t)∈S_(T)=R^(N)×(0,T),x∈R^(N),under some conditions on m,p,q,λ,whereδis Dirac function.

Study on role of serum electrolyte combined with GFR evaluation equation in predicting the prognosis of severe obstructive renal injury

Objective: To study the predictive value of serum electrolyte combined with glomerular filtration rate (GFR) evaluation equation for prognosis of severe obstructive renal injury. Methods: A total of 69 patients with calculous obstructive renal impairment admitted to our hospital from May 2017 to December 2018 were selected as the research objects. Clinical data of the patients were collected, and according to the status of renal function impairment, they were divided into 37 cases of mild to moderate, 32 cases of severe, and 40 cases of health examination in the same period as the control group. The fasting serum of the subjects was separated in the morning, and the serum electrolytes and related indicators were detected by Olympus AV640 automatic biochemical analyzer, Scr-CysC GFR evaluation equation was used to calculate the GFR score of all subjects, the levels of serum sodium, potassium and GFR scores in patients with severe obstructive renal injury with different prognostic outcomes were analyzed, subject operating characteristic curve (ROC) of prognostic indicators in patients with severe obstructive renal impairment was drawn, and the prognostic values of serum Na+, K+, GFR score and their combination in patients with severe obstructive renal damage were analyzed. Results: Compared with the control group, the levels of UmAb, CysC, Scr, BUN, TC, serum sodium and potassium in mild to moderate group and severe group increased in turn, and the GFR score decreased in turn (P < 0.05). The serum sodium and potassium concentrations increased in turn and the GFR score decreased in turn at 1 month after operation (P < 0.05). Compared with the 1 day before operation, the serum sodium and potassium concentrations in mild group and severe group decreased and the GFR score increased 1 month after operation (P < 0.05). Compared with the good prognosis group, the serum sodium and potassium levels in patients with severe obstructive renal damage in the poor prognosis group increased significantly, and the GFR score decreased significantly (P<0.05). The results of ROC showed that the combined detection of Na + concentration, K+ concentration and GFR score had an AUC of 0.936 for predicting the prognosis and outcomes of patients with severe renal injury, which was significantly higher than that of the single detection (AUC of 0.796, 0.815 and 0.810, respectively). Conclusion: The serum sodium and potassium levels in patients with severe obstructive renal impairment are increased, and the GFR score is decreased. The combined detection of the three factors has certain reference value in predicting the poor prognosis of patients with severe obstructive renal impairment.

不同肾小球滤过率评估方程在HIV/AIDS患者早期肾损害中的应用

目的探讨3种肾小球滤过率(GFR)评估方程(CKD-EPI2009 Scr、CKD-EPl2012 Cys C、CKD-EPI2012 Scr-Cys C)评价HIV/AIDS患者肾功能的应用。方法选取2018年7月至2021年8月定期检测的HIV/AIDS患者144例,检测血肌酐(Scr)及胱抑素C(Cys C),用3种不同方程估算肾小球滤过率(eGFR),并进行比较。结果方程CKD-EPI2009 Scr结果明显高于CKD-EPl2012 Cys C及CKD-EPI2012 Scr-Cys C的结果,差异有统计学意义(P<0.05),而CKD-EPl2012 Cys C与CKD-EPI2012 Scr-Cys C结果一致,差异无统计学意义(P>0.05)。结论方程CKD-EPI2009 Scr有可能存在高估HIV/AIDS患者的GFR,建议使用CKD-EPl2012 Cys C或CKD-EPI2012 Scr-Cys C方程评估HIV/AIDS患者的肾小球滤过率。

Approximate Generalized Conditional Symmetries and Solutions for Nonlinear Filtration Equation with a Small Parameter

The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.

基于血清肌酐的肾小球滤过率估算值与^(99m)Tc-肾小球滤过率的相关性

目的分析肾小球滤过率(GFR)公式估算值(eGFR)与99锝-二乙烯三胺五醋酸(99mTc-DTPA)法测定值(99mTc-GFR)的相关性,探讨适合中国慢性肾脏病(CKD)住院患者eGFR的估算方法。方法选择1033例慢性肾脏病住院患者作为研究对象,99mTc-DTPA肾动态显像法测定99mTc-GFR,酶法检测血清肌酐(SCr)水平。采用Cockcroft-Gault公式、肾脏病膳食改良试验(MDRD)公式、简化MDRD公式、中国MDRD公式、中国简化MDRD公式及CKD-EPI公式计算并用体表面积(BSA)校正后得到eGFR,分别以C-GGFR、7GFR、aGFR、c-7GFR4、c-aGFR4和CKD-EPI-GFR表示。分析99mTc-GFR与eGFR的相关性。结果相关回归分析显示,C-GGFR、7GFR、aGFR、c-7GFR4、c-aGFR4和CKD-EPI-GFR与99mTc-GFR的相关系数(r)分别为0.805、0.797、0.783、0.791、0.777和0.800,与99mTc-GFR偏差值均值分别为-2.46、-14.24、-16.53、-20.92、-22.92和-13.56。患者99mTc-GFR与SCr水平呈近似双曲线的关系。结论在基于SCr的公式估算得到的eGFR中,C-GGFR与99mTc-GFR的相关程度最高。提示当以酶法SCr测定结果作为数据源时,C-G公式较适合中国CKD住院患者eGFR的估算。