Pharmacodynamics of Unfractionated Heparin During and After a Hemodialysis Session

Dialysis Pharmacodynamics of Unfractionated Heparin During and After a Hemodialysis Session Philippe Brunet, MD,1 Nicolas Simon, MD,2 Adriana Opris, MD,1 Valérie Faure, MD,1 Anne-Marie Lorec-Penet, PharmD,3 Henri Portugal, PharmD,3 Bertrand Dussol, MD,1 and Yvon Berland, MD1 Background: Anti-Xa activity is used as a clinical guide to anticoagulation with heparin, but heparin dosing regimens for hemodialysis were established before anti-Xa assays were developed; thus, the optimal regimen for heparin dosing was not determined. The aim is to confirm the interesting characteristics of unfractionated heparin pharmacokinetics for hemodialysis anticoagulation, provide insight into the hemorrhagic risk of hemodialysis patients, and determine the dose of unfractionated heparin and its adequate mode of administration. Study Design: Cross-sectional study of the pharmacokinetics of unfractionated heparin performed during and after a 4-hour midweek hemodialysis session. Setting & Participants: 35 long-term hemodialysis patients at the Sainte-Marguerite Unit of the Marseille University Hospital, Marseille, France. Predictor: Hemodialysis anticoagulation with continuous unfractionated heparin infusion at a dose of 50 IU/kg/session (25 IU/kg/h during the first hour, 12.5 IU/kg during the second and third hours, and stop during the last hour). Outcome & Measurements: Anti-Xa activity was monitored during the 10 hours after the beginning of the hemodialysis session. Levels of 0.3 to 0.7 IU/mL are considered sufficient for anticoagulation. Pharmacokinetics was determined by using a population approach (nonlinear mixed-effects modeling). The final model and corresponding parameter values (including interindividual and residual variability) were used to simulate 1,000 replicates. Results: No case of clotting was recorded. A pharmacokinetic model with 1 compartment and first-order elimination best fitted the data. Terminal half-life was 54 minutes. Median anti-Xa activities were 0.55 IU/mL at peak, 0.25 IU/mL at end of the 4-hour session, and less than 0.1 IU/mL at 90 minutes after the session. We simulated a continuous infusion of the dose of 50 IU/kg for 1, 2, 3, and 4 hours. Peak values were 1.1, 0.8, 0.6, and 0.5 IU/mL, respectively. Values at the end of the session were 0.12, 0.18, 0.3, and 0.5 IU/mL, respectively. Values became less than 0.1 IU/mL at 15, 60, 105, and 120 minutes after the session, respectively. Limitations: Interindividual variability in unfractionated heparin pharmacokinetics. Conclusions: Unfractionated heparin administered by means of a 3-hour continuous infusion for hemodialysis anticoagulation provided an efficient and safe effect that quickly disappeared after the end of the session. Am J Kidney Dis 51:789-795. © 2008 by the National Kidney Foundation, Inc. INDEX WORDS: Anticoagulation; anti-Xa; heparin; hemodialysis; population pharmacokinetics; nonlinear mixed effects modeling (NONMEM).

nfractionated heparin (UFH), discovered in 1920, was one of the main factors making hemodialysis (HD) treatment possible. UFH at doses for HD anticoagulation has a short half-life and should be administered by means of repeated bolus injections or continuous infusion. In 1970, low-molecular-weight heparins (LMWHs) were

U

introduced for HD anticoagulation.1 LMWHs have a longer half-life than UFHs, and their use in HD anticoagulation is very convenient because a single bolus injection at the start of the session can prevent clotting of the extracorporeal circuit during the entire session. Considering the interest in LMWHs, is there still a place for UFH

From the 1Centre de Néphrologie et de Transplantation Rénale Hôpital de la Conception, Assistance Publique-Hôpitaux de Marseille; 2Laboratoire de Pharmacologie Médicale et Clinique, Faculté de Médecine; and 3Laboratoire Central Hôpital SainteMarguerite, Assistance Publique-Hôpitaux de Marseille, AixMarseille Université, Marseille, France. Received May 30, 2007. Accepted in revised form December 26, 2007.

Address correspondence to Philippe Brunet, MD, Centre de Néphrologie et de Transplantation rénale, Hôpital de la Conception, 147 Bd Baille, 13005 Marseille, France. E-mail: [email protected] © 2008 by the National Kidney Foundation, Inc. 0272-6386/08/5105-0011$34.00/0 doi:10.1053/j.ajkd.2007.12.040

American Journal of Kidney Diseases, Vol 51, No 5 (May), 2008: pp 789-795

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in HD anticoagulation? Beyond its low price, UFH retains a major interest because it appears safer than LMWHs.2 Its short half-life allows the anticoagulant effect to readily disappear after the injection. Conversely, the half-life of LMWHs is dramatically increased in patients with renal failure.3 Thus, their effect remains for many hours after the end of the HD session.4,5 Moreover, UFH has formulations that can be used for continuous infusion, whereas LMWHs are formulated as only prefilled syringes and can be used for only bolus injections. It is well known that bolus injection leads to very high peaks of anticoagulation that are not necessary because the anticoagulation effect, expressed as anti-Xa activity, could be considered sufficient at 0.3 to 0.7 IU/mL.4,6 A metaanalysis of studies comparing LMWHs and UFH for HD anticoagulation showed that LMWHs did not improve bleeding events, vascular access compression time, or extracorporeal circuit thrombosis.7 A recent review of the safety of heparins in patients with end-stage renal disease suggested further careful evaluation of this area.8 The present study was undertaken to specify the pharmacokinetic parameters of UFH after a continuous injection during an HD session. Anti-Xa activity is used as a clinical guide to anticoagulation with heparin, but heparin dosing regimens for HD were established before anti-Xa assays were developed; thus, the optimal regimen for heparin dosing was not determined. The aim is to confirm the interesting characteristics of UFH pharmacokinetics for HD anticoagulation, provide insight into the hemorrhagic risk of HD patients, and determine the dose of UFH and its adequate mode of administration. Pharmacokinetics was determined by using a population approach by means of nonlinear mixed-effects modeling (NONMEM).

METHODS Study Design This is a cross-sectional study of the pharmacokinetics of UFH performed in a midweek HD session. Session duration was 4 hours. Dialyzer was the low-flux cellulose diacetate membrane Dicea 150 (Baxter, Maurepas, France) with an ultrafiltration coefficient of 11.4 mL/h/mm Hg; it was not reused. There was no heparin binding on this membrane. Blood flow rate was 250 mL/min, and dialysate flow was 500 mL/min. The extracorporeal circuit was rinsed with 2 L of heparinized saline (2,500 IU/L). Almost all this solution was discarded before the tubing was connected to the pa-

tient. Then UFH was started and infused by means of continuous infusion into the afferent line of the dialyzer. UFH doses were 25 IU/kg during the first hour and 12.5 IU/kg during the second and third hours. The infusion was stopped after the end of the third hour. Total dose was 50 IU/kg/session. Pharmacokinetic follow-up was carried out with repetitive measures of plasma anti-Xa activity. The sampling scheme designed for the population pharmacokinetic analysis used sparse sample times covering the full anti-Xa activity profiles. Three or 4 samples were retrieved per patient, with different sampling times between patients. Samples were retrieved during the session (t ⫽ 0 to 4 hours) and after the end of the session, up to 10 hours after the beginning of the UFH infusion.

Participants The source consisted of 110 patients undergoing longterm HD at the Sainte-Marguerite Unit of the Marseille University Hospital, Marseille, France. A random sample of 50 patients was constituted to obtain a minimal sample size of 30, determined by the necessities of pharmacokinetic modeling. Inclusion criteria were age older than 18 years, HD started for at least 3 months, routine use of UFH as anticoagulant, lack of residual renal function (anuria), and native arteriovenous fistula or synthetic graft as vascular access. Exclusion criteria were anemia with hemoglobin level less than 10 g/dL (⬍100 g/L), recent (⬍1 month) trauma, surgery, infectious disease, hemorrhagic disorder, current administration of heparin between HD sessions, and HD through a central venous catheter. The study was approved by the local ethics committee, and written informed consent was obtained from all participants.

Variables of Interest The main variable was anti-Xa activity, determined by using a chromogenic assay (STA Rotachrom heparin; Diagnostica Stago, Genevilliers, France). The lower limit of detection was 0.1 IU/mL, the standard curve was linear between 0.1 and 2 IU/mL, and intra-assay variance and day-to-day variation coefficients were 3.8% and 3.5%, respectively. Blood samples were collected in citrated tubes (BD Vacutainer, final citrate concentration 0.129 mol/L, Becton Dickinson, Le Pont-de-Claix, France). The samples obtained during the session were collected from the afferent tubing, and the postsession sample was obtained by using venipuncture. Separate experiments performed during HD sessions showed similar values for anti-Xa activities obtained from the afferent tubing or venipuncture. Residual anti-Xa activity before the patient was connected to the extracorporeal circuit was measured in some patients; it was undetectable. Other variables include clotting and bleeding, routinely evaluated from time to hemostasis after needle removal and from clotting of the dialyzer and blood tubing.

Analysis Methods Anti-Xa activity–time analysis was performed using NONMEM software (version V, level 1.0; GloboMax LLC, Hanover, MD).9 One- and 2-compartment pharmacokinetic models with intravenous (IV) administration and first-order elimination were tested to fit the data. An example of a

Pharmacodynamics of Unfractionated Heparin in Hemodialysis function corresponding to a 1-compartment with infusion and first-order elimination is given in Equation 1: Apred ⫽ (Dose ⁄ Tinf) · 1 ⁄ (CLpop) · [exp(⫺(CLpop ⁄ Vcpop) · T*) ⫺ exp(⫺(CLpop ⁄ Vcpop) · Time)]

(1)

where Apred is anti-Xa activity predicted by the model, Dose is dose administered, Tinf is length of infusion, Vcpop is volume of distribution, and CLpop is clearance; Vcpop and CLpop are kinetic parameters (Ppop) to be estimated. T* is defined as follows. T* ⫽ Time ⫺ Tinf for Time ⬎ Tinf T* ⫽ 0 for Time ⱕ Tinf The following random-effect models were used to describe the interindividual variability of kinetic parameters. Proportional model: Pj ⫽ Ppop(1 ⫹ ␩pj) Additive model: Pj ⫽ Ppop ⫹ ␩pj In these models, Pj is a kinetic parameter of the jth individual, Ppop is the population mean value of the parameter, and ␩pj is the interindividual error, distributed normally with zero mean and variance equal to interindividual variability. Residual error was modeled in 2 ways. Proportional error: Aobsij ⫽ Apredij ⫻ (1 ⫹ ␧ij) Additive error: Aobsij ⫽ Apredij ⫹ ␧ij In these models, Aobs ij and Apred ij are the ith observed and model-predicted anti-Xa activity in the jth patient, and ␧ij is the residual error, distributed normally with zero mean and variance residual variability.

Model-Building Procedure A first analysis was performed to find the base model that best defined the data. Models were described in terms of such pharmacokinetic parameters as clearance and volume of distribution. The assumption was made that pharmacokinetics was linear and thus parameters were constant. Model selection was based on goodness-of-fit plots (observed versus predicted anti-Xa activity, weighted residuals versus predicted, and weighted residuals versus time) and precision of the estimation. The base model estimated the pharmacokinetic parameters without covariates. After it was defined, the influence of each covariate on the pharmacokinetic parameters was tested. These covariates were sex, age, and body weight. We noted the plot of observed versus predicted anti-Xa activity, change in objective functions, and change in parameter variability. A decrease in the objective function value of at least 6.61 (␹2 distribution with 1 df for P ⬍ 0.01) relative to the base pharmacokinetic model was required for the addition of a single parameter in the model. Covariates

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that significantly reduced the objective function were then combined in a stepwise fashion until no further reduction of the objective function occurred (full model). An intermediate multivariate model was then obtained including all significant covariates. Finally, to keep only covariates with the largest contribution to predict anti-Xa activity in a final model, a change in the objective function of at least 10.82 (P ⬍ 0.001) was required for a parameter to be retained during backward stepwise multiple regression analysis. More detail on the model-building procedure is in the supplementary methods, which are provided as supplementary materials available online with this article at www.ajkd.org.

Anti-Xa Activity Simulation The final model and corresponding parameter values (including interindividual and residual variability) were used to simulate 1,000 replicates using the SIMULATION, SUBPROBLEM feature in NONMEM (Monte Carlo simulation). The following schemes of administration and dosing were simulated: (1) the administration scheme used in this study for visual predictive check, and (2) a constant and continuous heparin infusion with the total dose of 50 IU/kg infused during 1, 2, 3, or 4 hours.

Funding This study was part of routine patient follow-up and quality assurance process of the unit.

RESULTS Of the 50 potentially eligible patients, 35 were included and completed the study. Clinical characteristics are listed in Table 1. Total administered UFH dose was 3,053 ⫾ 571 IU/session. Figure 1 shows anti-Xa activity versus time for blood samples obtained during dialysis session and up to 6 hours after the end of the session. Plasma anti-Xa activity after UFH administration for dialysis anticoagulation followed a monoexponential elimination curve. A pharmacokinetic model with 1 compartment and first-order Table 1. Patient Clinical Characteristics No. of patients Sex (women/men) Age (y) Weight (kg) Medications Antiplatelet agents Oral anticoagulants Antihypertensive medications Bleeding and coagulation manifestations during the test session Time to hemostasis after needle removal (min) Clotting of dialyzer and blood tubing Access thrombosis

35 12/23 69 ⫾ 12 62.3 ⫾ 11.7 25 10 22

14 ⫾ 5 0 0

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Figure 1. Observed (open circle) and simulated anti-Xa activity (solid line, median; dotted lines, 90% populationpredicted interval) versus time in hemodialysis patients during and after a continuous infusion of unfractionated heparin (25 mg/kg/h during the first hour, and 12 mg/kg/h during the second and third hours of the hemodialysis session).

elimination best fitted the data, even if the weighted residuals versus time plot (Fig 2C) suggested underestimation of predications at t ⫽ 8 hours. Models were parameterized in terms of central volume of distribution and clearance. The proportional error model was the most appropriate model for intersubject variability. Residual variability was parameterized with a mixed model, additive and proportional. The covariates tested (age, weight, height, and sex) did not decrease the objective function and did not improve the fit. Table 2 lists pharmacokinetic parameter estimates for the final model. Terminal halflife was 54 minutes. Population pharmacokinetic parameter estimates of the final model were used to simulate different administration schemes. We first modeled the administration scheme used in this study (Fig 1). Median anti-Xa activity showed that the effective anti-Xa activity of 0.3 IU/mL was attained after 25 minutes. A plateau of 0.55 IU/mL was attained after 1 hour and maintained until the end of the infusion after 3 hours. At the end of the session, at 4 hours, median anti-Xa activity was 0.25 UI/mL and became less than 0.1 IU/mL 90 min after the end of the session. The proportion of patients achieving anti-Xa activity of 0.3

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IU/mL was 10% at 15 minutes, 63% at 30 minutes, and greater than 90% from 45 minutes to 3 hours. It was 65% at 3 hours 30 minutes and 36% at 4 hours. Large interindividual variability was observed, as shown in Fig 3. The protocols simulated were a continuous heparin infusion with the total dose of 50 IU/kg infused during 1, 2, 3, or 4 hours without modification of the infusion rate. Figure 4 shows results of the simulations. The 1-, 2-, 3-, and 4-hour infusions led to median peak anti-Xa activities of 1.1, 0.8, 0.6, and 0.5 IU/mL, respectively. The effective anti-Xa activity of 0.3 IU/mL was obtained after 15, 30, 45, and 60 minutes with the 1-, 2-, 3-, and 4-hour infusions, respectively. At the end of the session, median anti-Xa activities were 0.12, 0.18, 0.3, and 0.5 IU/mL with the 1-, 2-, 3-, and 4-hour infusions, respectively. The value of 0.1 IU/mL was obtained 15, 60, 105, and 120 minutes after the end of session with the 1-, 2-, 3-, and 4-hour infusions, respectively.

DISCUSSION The key finding of this article is the first report of UFH pharmacokinetics during HD using an anti-Xa assay and a population pharmacokinetics approach by using NONMEM. Plasma anti-Xa activity is the established method for assessing systemic exposure to UFH.3,4 Heparin pharmacokinetic models previously were based on the measurement of anticoagulation effect by using activated partial thromboplastin time, performed in plasma, and whole-blood activated thromboplastin time or activated coagulation time, bedside tests performed in whole blood.10-12 These tests were criticized because the reagents used are not standardized and there was wide variability among laboratories.4 The present study shows that UFH administered at a dose of 50 U/kg during an HD session follows 1-compartment distribution and a firstorder elimination curve with a half-life of 54 minutes. These results are in accordance with previous studies reporting that after IV injection of small doses of heparin, less than 5,000 U or 100 anti-Xa U/kg, the first-order kinetics predominates and disappearance of anti-Xa activity is exponential, with a half-life of 50 to 70 minutes,3,10,13,14 which does not change with the dose injected. The exponential disappearance of

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Figure 2. Goodness-of-fit plots for the final analysis of unfractionated heparin. (A) Population-predicted versus observed anti-Xa activity (solid line, line of identity). (B) Weighted residuals (WRES) versus predicted anti-Xa activity. (C) WRES versus time. (D) Individual predicted versus observed anti-Xa activity. ([A-D] dotted line, regression line).

anti-Xa activity is caused by the binding of heparin to endothelium.13 However, this binding is saturable, and at doses greater than 100 anti-Xa U/kg, elimination of UFH follows a zero-order kinetics. In this situation, half-life dramatically increases, and the rate of decrease in heparin activity after IV injection increases with the initial concentration of the drug.3,13 During HD, these high heparin doses are never used, and the zero-order component of elimination is negligible.15 We administered UFH during HD by using a continuous infusion followed by discontinuation of the UFH infusion 1 hour before the end of the session. This led to median plateau anti-Xa activity

of 0.5 and 0.6 IU/mL, with extremes values of 0.2 to 0.8 IU/mL (Fig 1), which were close to the recommended therapeutic range.4,6 Moreover, median anti-Xa activity was 0.25 IU/mL at the end of the session and became less than 0.1 IU/mL only 90 minutes after the end of session. This suggests that patients were no longer at risk of bleeding after the end of session. This is an important advantage when surgery or invasive procedures need to be performed after the session. Moreover, these data emphasize the benefit of UFH over some LMWHs, such as enoxaparin, which leads to anti-Xa activity of 0.4 and 0.1 IU/mL 6 and 20 hours after the end of session, respectively.2

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Brunet et al Table 2. Unfractionated Heparin Population Pharmacodynamic Parameters Estimated for the Final Model Parameters

Volume of distribution (mL) Clearance (mL/h) ␻2 ␻2CL (% CV) ␴2 ␴21 proportional (% CV) ␴22 additive (anti-Xa activity/mL)

Final Estimate

1,870 1,440

Estimation SE

97 87

95% CI

1,680-2,060 1,269-1,611

0.08 (28)

0.02

0.04-0.12

0.22 (47) 0.05

0.02 0.01

0.18-0.26 0.03-0.07

Note: N ⫽ 35 patients. Analysis allowed us to divide variability between interindividual and residual variability. Interindividual variability could be estimated only on the clearance. The data were best described with residual variability combining an additive and a proportional error. Abbreviations: CI, confidence interval; % CV, coefficient of variation expressed as percentage; ␻2, interindividual variability; ␴2, residual variability.

Other studies showed that administration of UFH by using continuous infusion was safer for HD patients than the bolus method. The latter led to high and excessive peak values of anti-Xa activity.4,16 In the general population, there is evidence that heparin administered by means of intermittent IV injection is associated with more bleeding than when it is administered by using the continuous IV route.4 In HD, the 1- or 2-bolus method produces variations in anticoagulation, which exposes patients to the risk of both hemorrhage and clotting of the extracorporeal circuit.17 In the literature, continuous administration generally was performed by

Figure 3. Spaghetti plot of anti-Xa activity versus time in 35 hemodialysis patients during and after a continuous infusion of unfractionated heparin (25 mg/kg/h during the first hour and 12 mg/kg/h during the second and third hours of the hemodialysis session). Note that observations are linearly connected, providing an insight of interindividual variability, but do not correspond to the real evolution of anti-Xa activity.

using a constant infusion during dialysis preceded by a predialysis loading dose. Mingardi et al17 proposed a continuous infusion with no priming dose, which led to effective anticoagulation. Wilhelmsson and Lins6 proposed discontinuation of the UFH infusion 30 to 60 minutes before the end of HD, which decreased the risk of bleeding from the needle sites. The model obtained from the pharmacokinetic analysis served to simulate various profiles of heparin administration and thus suggest some improvements in our current procedure. Although the protocol in current use in our unit is safe, it is not convenient because it requires modifying the heparin infusion rate at the end of the first hour of the dialysis session. This procedure induces potential errors because the nurse might forget to modify the infusion rate. Thus, using the pharmacokinetic model, we simulated different schemes of continuous UFH infusion with the same total dose of 50 IU/kg to avoid changes in the heparin infusion rate during the session. Peak activities obtained with the

Figure 4. Simulated anti-Xa activity according to different schemes of unfractionated heparin administration of the total dose of 49 IU/kg in 1, 2, 3, or 4 hours. For clarity, only median anti-Xa activities are shown.

Pharmacodynamics of Unfractionated Heparin in Hemodialysis

1- and 2-hour infusions were excessive and nonadapted to the objective of anti-Xa activity of 0.3 to 0.7 IU/mL during the HD session.4 Peak activities obtained with the 3- and 4-hour infusions were more appropriate. The 3-hour infusion was the best scheme because it led to adequate anti-Xa activity of 0.3 IU/mL at the end of the session. This protocol possibly is more convenient and safe than our usual protocol. Whatever the scheme of UFH administration, anti-Xa activity 2 hours after the end of the HD session was less than 0.1 IU. What is the ideal dose of UFH for HD? Heparin doses used in the present study were based on an empiric simplified prescription. Administered doses were at the lower level of the recommended range.16 Pharmacokinetic analysis suggested that these doses are efficient and safe. Most HD units also select heparin doses on an empirical basis, and no coagulation test is performed. This simplified prescription is based on data from classic pharmacokinetic models.16 Heparin doses are adapted according to dialyzer clotting or venous compression time. The limitation of the present study mainly is the wide variability in UFH pharmacokinetics from patient to patient.15 This was taken into account by pharmacodynamic models for determining individual heparin doses based on serial measurements of coagulation times over several dialysis treatments.10-12 These models are precise and can accurately predict adequate heparin dose for an individual patient. They can improve dialyzer efficiency and optimize the rate of reuse.12 However, their use is time consuming and expensive, and they are not convenient for routine use in dialysis units. In summary, this study shows that UFH administered by means of continuous infusion led to effective anti-Xa activity during the HD session for every patient. This mode of HD anticoagulation is particularly interesting for patients at risk of bleeding because it does not lead to excessive peak values of anti-Xa activity. It could be used in patients who will be exposed to invasive procedures after the HD session because its effect decreases steeply after the end of the infusion and is negligible after the end of the HD session.

ACKNOWLEDGEMENTS Support: None. Financial Disclosure: None.

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SUPPLEMENTARY MATERIALS Item S1: Supplementary methods. Note: The supplementary material accompanying this article (doi:10.1053/j.ajkd.2007.12.040) is available at www.ajkd.org.

REFERENCES 1. Schrader J, Valentin R, Tonnis HJ, et al: Low molecular weight heparin in hemodialysis and hemofiltration patients. Kidney Int 28:823-829, 1985 2. Guillet B, Simon N, Sampol JJ, et al: Pharmacokinetics of the low molecular weight heparin enoxaparin during 48 h after bolus administration as an anticoagulant in haemodialysis. Nephrol Dial Transplant 18:2348-2353, 2003 3. Boneu B, Caranobe C, Cadroy Y, et al: Pharmacokinetic studies of standard unfractionated heparin, and low molecular weight heparins in the rabbit. Semin Thromb Hemost 14:18-27, 1988 4. Hirsh J, Raschke R. Heparin and low-molecularweight heparin: The Seventh ACCP Conference on Antithrombotic and Thrombolytic Therapy. Chest 126:S188S203, 2004 (suppl 3) 5. Goudable C, Ton That H, Damani A, et al: Low molecular weight heparin half life is prolonged in haemodialysed patients. Thromb Res 43:1-5, 1986 6. Wilhelmsson S, Lins LE: Heparin elimination and hemostasis in hemodialysis. Clin Nephrol 22:303-306, 1984 7. Lim W, Cook DJ, Crowther MA: Safety and efficacy of low molecular weight heparins for hemodialysis in patients with end-stage renal failure: A meta-analysis of randomized trials. J Am Soc Nephrol 15:3192-3206, 2004 8. Sonawane S, Kasbekar N, Berns JS. The safety of heparins in end-stage renal disease. Semin Dial 19:305-310, 2006 9. Beal SL, Sheiner LB (eds). NONMEM Users Guides (1989-98). Hanover, MD, GloboMax LLC,1998 10. Farrell PC, Ward RA, Schindhelm K, Gotch F: Precise anticoagulation for routine hemodialysis. J Lab Clin Med 92:164-176, 1978 11. Smith BP, Ward RA, Brier ME: Prediction of anticoagulation during hemodialysis by population kinetics and an artificial neural network. Artif Organs 22:731-739, 1998 12. Ouseph R, Brier ME, Ward RA: Improved dialyzer reuse after use of a population pharmacodynamic model to determine heparin doses. Am J Kidney Dis 35:89-94, 2000 13. de Swart CA, Nijmeyer B, Roelofs JM, Sixma JJ: Kinetics of intravenously administered heparin in normal humans. Blood 60:1251-1258, 1982 14. Teien AN, Bjoornson J: Heparin elimination in uraemic patients on haemodialysis. Scand J Haematol 17:29-35, 1976 15. Kandrotas RJ, Gal P, Douglas JB, Deterding J: Pharmacokinetics and pharmacodynamics of heparin during hemodialysis: Interpatient and intrapatient variability. Pharmacotherapy 10:349-355, 1990 16. Ouseph R, Ward RA: Anticoagulation for intermittent hemodialysis. Semin Dial 13:181-187, 2000 17. Mingardi G, Perico N, Pusineri F, et al: Heparin for hemodialysis: Practical guidelines for administration and monitoring. Int J Artif Organs 7:269-274, 1984