Laurie J. Garred

Simple Kt/V formulas based on urea mass balance theory

&NA; The ratio Kt/V (K is patient clearance, t dialysis time, V urea space) has become the standard measure of dialysis adequacy. In this article simple Kt/V equations are developed theoretically from the urea mass balance equation. Two approximations lead to the most precise equation: where R is the post to pre dialysis urea ratio, BW/V is the amount of fluid removed during dialysis (&Dgr;BW) expressed as a fraction of urea distribution space (V) at dry body weight (BW), and t is dialysis length in hours. A second equation arises with V approximated as 58% of BW. One further approximation leads to a simpler but slightly less precise Kt/V formula: These and earlier published equations were tested with two sets of data: 1) 49 sessions involving 17 patients on maintenance dialysis and 2) 540 computer simulations spanning all likely values of Kt/V (0.6‐1.6), protein catabolic rate (0.6‐1.6), interdialytic weight gain (0‐4% of BW per day) and dialysis session length (2‐4 hr). The most precise formula (upper equation above) had a maximum error of 0.031 and 0.035 Kt/V units for the clinical and simulated data, respectively, whereas the lower equation was slightly less accurate with maximum Kt/V errors of 0.079 and 0.081, respectively. The proposed Kt/V equations are considerably more accurate than previously published formulas. ASAIO Journal 1994; 40:997‐1004.

Recombinant Human Erythropoietin: 18 Months' Experience in Hemodialysis Patients

It has been shown that the regular administration of erythropoietin (EPO) permits the correction of anemia in end-stage renal failure patients. We analyzed the effect of chronic administration of EPO in 13 stable, regularly dialyzed end-stage renal failure patients over an 18-month period. The effects of EPO were evaluated according to standard criteria including clinical status, blood pressure control, hematology and biochemistry data, protein nutritional status, and dialysis efficiency. Following a 2-week control period, EPO was administered intravenously (IV) after the dialysis session according to a two-phase protocol. The first period (correction phase) consisted of a stepwise EPO dose increment, starting at 3 x 24 IU/kg/wk and doubling the dose every 14 days according to hemoglobin response in order to achieve a target hemoglobin level of approximately 11.0 g/dL (110 g/L). In the second period (maintenance phase) EPO dose was optimized to maintain the hemoglobin level between 100 and 110 g/L (10.0 and 11.0 g/dL), by adjusting either the unit dose or the frequency of injection. Anemia was corrected in all patients within 11 weeks, with EPO dose increasing from 72 to 360 IU/kg/wk. The stabilization of hemoglobin was achieved with an average EPO dose of 275 IU/kg/wk (50 to 476 IU/kg/wk). Concomitantly, a subjective and clinical improvement was noted in all patients. The dialysis efficacy remained in an acceptable range throughout the study, falling significantly (approximately 10%) through the first 3 months of treatment to stabilize at an effective urea clearance of approximately 120 L/wk. The dietary protein intake calculated from urea kinetic modeling ranged between 1.1 and 1.2 g/kg/d.(ABSTRACT TRUNCATED AT 250 WORDS)

Direct determination of blood recirculation rate in hemodialysis by a conductivity method

Blood recirculation is one of the key factors of decreasing dialysis efficiency. Determination of recirculation rate (R) is necessary to optimize effective dialysis delivery and to monitor vascular access function. R can be directly measured by a conductivity method in paired filtration dialysis (PFD), a double-compartment hemodiafiltration system that permits direct access to plasma water via the ultrafiltration stream. Measurement of R, in this system, involves the first of two conductivity sensors integrated in a urea monitor (UMS, Bellco-Sorin, Mirandola, Italy), and two saline injections. The rise in conductivity (δC1) induced by a 2.7 ml bolus of hypertonic saline 20% (mg/dl) in the arterial line serves for calibration, and is followed by an equivalent injection into the venous line, giving rise to δC2. The ratio δC2/δC1 equals R. A comparison between R values obtained with this method and with the low-flow technique in 31 chronic dialysis patients during 138 PFD sessions is reported. Mean R ± SD by the conductivity method was 5.1 ± 2.0 and 5.7 ± 2.0% after 65 and 155 minutes of PFD (correlation coefficient, r = 0.75), whereas it was 6.4 ± 4.9% and 5.5 ± 4.6% after 30 sec of low blood pump flow for urea and creatinine markers, respectively (r = 0.35). After 120 sec of low flow, mean R increased to 9.0 ± 5.1 and 8.8 ± 4.6% for urea and creatinine, respectively (r = 0.45). Considerable discrepancies were found in R values measured simultaneously with the two blood markers. Statistically significant differences were found between the two measurement modalities (blood-side and conductivity); the correlation coefficients (r) varied between 0.28 and 0.41. The observed differences in mean R results do not seem considerable from a clinical perspective. The best agreement between blood-side and conductivity R measurements was obtained with Rcreat after 30 sec of low flow. Overall, a wider distribution was found in R values from blood-side determinations, most likely consequent to variability in the dosing method. The conductivity method appears more accurate and simple in assessing total R, and can be readily automated and integrated into the dialysis machine. The authors, therefore, recommend evaluation of R using methods not based on chemical blood concentration values.

Protein catabolic rate determination from a single measurement of dialyzed urea.

Protein catabolic rate (PCR, in g protein/kg/day) for anuric patients can be accurately determined without blood sampling by equating urea generation over 7 days to the urea dialyzed in the three dialyses of this period as measured by partial dialysate collection (PDC) or with a urea monitor. The feasibility of determining the weeks dialyzed urea from measurement of urea dialyzed in a single session, obviating the need to monitor three consecutive dialyses, was examined in a steady-state simulation of 540 anuric patients spanning the full range of dialysis parameters. It was found that the first, midweek, and last dialyses account for nearly constant fractions (37.9, 32.1, and 30.0%, respectively) of the weeks urea removal, leading to equations of the form: PCR = CU/BW + 0.17 where U is the grams of urea dialyzed in the first, midweek, or final dialysis of the week, C = 2.45, 2.89, or 3.10, respectively, and BW is the patients dry weight in kilograms. These equations were tested on 1312 weeks of PDC data gathered in 42 dialysis patients. Using the midweek U resulted in a mean absolute error in PCR < 0.05 g/kg/day when compared to PCR determined using all three of the weeks U values.

Simple equations for protein catabolic rate determination from pre dialysis and post dialysis blood urea nitrogen.

&NA; Several simple equations exist for Kt/V determination from pre dialysis (Cpre) and post dialysis (Cpost) blood urea. However, comparable equations have not been available for calculation of protein catabolic rate (PCR), an essential parameter for assessing patient status. Three simple formulas for PCR determination were developed from the urea mass balance equation for an anuric patient in protein steady state receiving thrice weekly dialysis. The simplest formula, PCR = 0.0076[Kt/V][Cpre + Cpost] + 0.17 relates PCR (in g protein/kg/day) to Kt/V and pre and post dialysis blood urea nitrogen measurements (in mg urea nitrogen/dl) for the midweek session. When tested for 540 simulated patients spanning a range of Kt/V (0.6‐1.6); PCR (0.6‐1.6 g/kg/day); dialysis duration t (2‐4 hrs) and interdialytic weight gain expressed as a percentage of dry body weight gained daily (0‐4%), this equation yielded a maximum error of less than ±5%, within the accuracy generally required for clinical needs. A more accurate formula, where Clm is the logarithmic mean of Cpre and Cpost, gave maximum errors in PCR estimation for the same 540 simulated patients of less than ±0.6%. Both formulas require a precise value of Kt/V. The equation below incorporates a very accurate simple Kt/V equation recently published by the authors, allowing PCR to be expressed in terms of Cpre, the ratio of Cpost to Cpre (R), the ratio of session ultrafiltration volume (&Dgr;BW) to urea distribution volume (V), and dialysis time (t, in min). This equation was accurate to within a maximum error of ±1% for the simulated patient group. These equations allow simple and accurate patient PCR determination, and should be used in conjunction with a simple formula for accurate Kt/V determination to guide end‐stage renal failure patient therapy. ASAIO Journal 1995;41:889‐895.

On-line dialysis quantification in acutely ill patients: preliminary clinical experience with a multipurpose urea sensor monitoring device.

Direct dialysis quantification offers several advantages compared with conventional blood urea kinetic modeling, and monitoring urea concentration in the effluent dialysate with an on-line urea sensor is a practical approach. Such a monitoring device seems desirable in the short-term dialysis setting to optimize and personalize both renal replacement therapy and nutritional support of acutely ill patients. We designed a urea monitoring device consisting of a urea sensor, a multichannel hydraulic circuit, and a PC microcomputer. The sensor determines urea from catalysis of its hydrolysis by urease in liquid solution during neutral conditions. Hydrolysis of urea produces NH4+, and creates an electrical potential difference between two electrodes. Each concentration determination of urea is the average value of 10 measurements; samples are diverted and measured every 7 min. Laboratory calibration of the urea sensor has demonstrated linearity over the range 2–35 mmol/L. Urea monitoring was performed throughout the treatment course, either on the effluent dialysate or ultrafiltrate in seven acutely ill patients treated by either hemofiltration (n = 5) or hemodiafiltration (n = 2). The slope of the concentration of urea in the effluent over time was used to calculate an index of the dialysis dose delivered (Kt/V), urea mass removal, and protein catabolic rate. In addition, samples of the effluent were drawn every 21 min, and sent to the central laboratory for measurement of urea concentrations using an autoanalyzer. Kt/V values also were calculated with Garreds equation using pre and post session concentrations of urea in blood. Concentrations of urea in the effluent determined by the urea sensor were found to be very close to those obtained from the central laboratory over a wide range of values (3 to 42 mmol/L). In addition, Kt/V values for both hemofiltration and hemodiafiltration, when calculated with concentrations of urea in the effluent obtained by the urea sensor, did not significantly differ from Kt/V values obtained from the laboratory concentrations of urea in the effluent. On-line urea sensor monitoring of the effluent suppresses the cumbersome task of total effluent collection, and the complexity of urea kinetic analysis. The multipurpose prototype described here represents a new, simple, and direct assessment of dialysis dose and protein nutritional status of acutely ill patients, and is suitable for various modalities. ASAIO Journal 1998; 44:184–190.

Urea kinetic modeling with a prototype urea sensor in the spent dialysate stream.

The authors have previously demonstrated the feasibility and accuracy of urea kinetic modeling (UKM) based on monitoring urea concentration in the spent dialysate stream (SDS) throughout the hemodialysis (HD) session. They describe here a prototype urea sensor for this purpose and initial experience with HD patients. The sensor is based on ammonium ion and reference electrodes housed in a cell through which the entire SDS passes. The two electrode tips are bathed in urease solution on one side of a dialysis membrane; the SDS flows along the adjacent side. Urea diffusing across the membrane from the SDS is converted by the urease into ammonium ion, which is measured by the electrode pair. For evaluation, the prototype flowthrough urea sensor was installed in the SDS of a Cobe Centry 3 HD machine for 36 HD sessions. Independent measurement demonstrated a linear relationship between mv output of the sensor and logarithm of SDS urea concentration. The use of SDS urea concentration time profiles obtained with this sensor to obtain accurate values of patient protein catabolic rate (PCR) and KT/V is illustrated. Incorporation of urea sensors such as this prototype into HD machines, will permit complete automation of UKM in the near future.

Diffusive-convective mass transfer rates for solutes present on both sides of a dialyzer membrane.

The transport (J) of waste products across dialyzer membranes is known to be proportional to the blood inlet concentration (Cbi) according to J = KCbi, where K is the clearance. For solutes present on both sides of the membrane, like sodium chloride, it has been shown1 that under certain conditions the transport rate will depend linearly also upon the dialysis fluid inlet concentration Cdi according to J = KbCbi − KdCdi. Kb and Kd are generalized clearances, which depend upon flow rates and membrane permeability but are independent of the concentrations. We have extended the results of Ross et al. in three ways. First, they only considered ultrafiltration (UF) that is equally distributed along the dialyzer. This is an unrealistic assumption, especially in hemodiafiltration and hemofiltration treatments with large UF rates (Quf) leading to large pressure drops along the dialyzer. Our approach allows for an arbitrary UF distribution. Second, it was possible to incorporate the more realistic model of Villaroel et al. for the local combination of diffusion and convection. Finally, we allow an arbitrary distribution of blood among the different fibers. All of these results are valid in both cocurrent and countercurrent configurations. With a sieving coefficient of 1, a good approximation for small solutes, we were also able to show that Kd = Kb − Quf, irrespective of the UF distribution along the dialyzer. This is an important result that, for example, provides a theoretical foundation for allowing a nonzero Quf in conductivity based clearance measurements.

Biophysics of intermittent renal replacement therapy

This chapter on the technical and theoretical aspects of intermittent renal replacement therapy is divided into three parts. First we present the equations and theory relating to mass and fluid transfer for the principle forms of intermittent therapy: hemodialysis, hemodiafiltration and hemofiltration. This is followed by a discussion of urea kinetics, treatment quantification as Kt/V, and urea generation rate determination in acute renal failure. In the final section, we develop a quantitative framework to guide prescription of intermittent therapy for the acute renal failure patient.

Intermittent renal replacement modalities and indications

Several dialytic therapies are available to treat acute renal failure (ARF) in the intensive care unit (ICU) setting [1]. The basic principle of any option is to provide adequate treatment in any circumstance without delaying renal recovery or adversely affecting patient outcome [2]. Renal replacement therapy for ARF management implicates two major prerequisites: its performance has to meet the specific metabolic and nutritional needs of acutely ill patients, and it has to be tolerated as well as possible, mainly to prevent further hemodynamic instability [3].