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PHARMACOKINETICS AND PHARMACODYNAMICS |
From the Department of Pharmaceutical Sciences, School Pharmacy and Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, New York (Dr Ramakrishnan, Dr Jusko) and the Johnson & Johnson Pharmaceutical Research & Development, LLC, Raritan, New Jersey (Dr Cheung, Dr Wacholtz, Dr Minton).
Address for reprints: William J. Jusko, PhD, 565 Hochstetter Hall, Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY 14260.
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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24 hours), and the bioavailability of SC rHuEpo increased with dose (ranging from 46%-100%). A catenary cell production and loss model with a feedback down regulation component was used to fit the reticulocyte data yielding estimates of the stimulatory capacity (Smax), sensitivity (SC50), and life span parameters. These parameters were used for simulations of RBC and Hb profiles. An SC50 of 27 to 61 IU/L was estimated indicating that low physiological plasma rHuEpo concentrations were sufficient to produce pharmacological effects. No marked sex-dependent differences in clinical responses to rHuEpo therapy were found despite baseline differences. Realistic pharmacokinetic and physiological models accounted for clinical responses from a wide array of dosing conditions with rHuEpo. The rationale for greater efficacy of SC administration of rHuEpo compared to IV was ascertained.
Key Words: Recombinant human erythropoietin • erythropoietin • pharmacokinetics • pharmacodynamics • dosing
Recombinant human Epo (rHuEpo) has proven beneficial for treating renal anemia as well as anemia of other chronic disorders, including autoimmune diseases, malignancies, and AIDS. Evidence from clinical trials indicates that anemia associated with cancer chemotherapy generally responds well to a standard rHuEpo regimen of 150 IU/kg SC 3 times a week (tiw).3,4 Several dosage recommendations have been made for surgery patients depending on the type of surgery and practicality of an autologous blood donation program. In patients scheduled for major orthopedic surgery, 3 weekly 600 IU/kg SC doses of rHuEpo, with the last one on the day of the surgery, have been suggested.5 We present here pharmacokinetic/pharmacodynamic (PK/PD) modeling from 4 comparable, placebo-controlled, parallel-group studies in healthy subjects who were administered single rHuEpo doses of 300 to 2400 IU/kg as well as multiple doses of 600 IU/kg/wk and 150 IU/kg/tiw for 4 weeks.
Our goal was (1) to describe a pharmacokinetic model to account for serum rHuEpo concentrations in healthy volunteers following intravenous (IV) and subcutaneous (SC) dosing and (2) to characterize the pharmacodynamics of SC rHuEpo causing increased reticulocyte, red blood cell (RBC) numbers, and hemoglobin (Hb) concentrations in blood. The first objective was to fit data from 5 single IV and 8 single SC dose levels simultaneously using a complex kinetic model. Second, a cell production and loss model was applied to quantitate the pharmacodynamic data to estimate the SC50 and other stimulation parameters. We included a physiological feedback adaptation component in our model to explain rebound and palliative effects. Simulations were performed to describe the pharmacokinetics, dynamics, and tolerance effects of rHuEpo after multiple SC dosing. Third, sex differences in hematological responses on multiple dosing were assessed.
There is a wealth of pharmacokinetic and clinical data for rHuEpo, some in healthy volunteers but mostly in patients evaluating doses required to maintain a specific hematocrit.3 Dose recommendations have been proposed based on noncompartmental analysis and qualitative examination of the information gathered in these studies. Development of a general pharmacokinetic/dynamic model that can quantitatively describe serum rHuEpo concentrations and reticulocyte, RBC, and Hb concentrations after administration of different doses of rHuEpo would help to predict rHuEpo responses under diverse dosing conditions and provide improved understanding of the major determinants of such effects.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Analytical Methods
The serum rHuEpo concentrations after SC dosing were measured using an established and validated radioimmunoassay with a limit of quantification of 7.8 mIU/mL, as described originally by Egrie et al9 and by Cheung et al.6 Hematocrit and hemoglobin were measured by conventional clinical methods. Reticulocyte counts were measured using flow cytometry. The mean data were used for all analyses.
Pharmacokinetic Analysis
The measured rHuEpo concentrations after rHuEpo administration were corrected for baseline values because the radioimmunoassay cannot distinguish between endogenous Epo and rHuEpo. The baseline Epo concentration for each subject was determined by averaging any predose values. This value was subtracted from the postdose values at each time point to obtain the corrected serum rHuEpo concentration. The mean of the corrected concentrations for all subjects was used for data analysis.
Model
From preliminary analysis of the IV data, a 1-compartment model was found to be adequate. The disposition of rHuEpo has been reported to be nonlinear mainly because of a dose-dependant decrease in clearance.8,9 Therefore, the Michaelis-Menten function was used to describe rHuEpo disposition. The IV data for rHuEpo concentrations (CEPO = Ap/Vd) versus time were fitted with
 | (1) |
where Ap is the amount of rHuEpo in the body, Vmax is the capacity of the elimination process, Km is the affinity constant or the plasma rHuEpo concentration at which the elimination rate reaches one-half Vmax, and Vd is the volume of distribution.
The absorption of rHuEpo from the SC formulation was described by 2 absorption components: a zero-order absorption (ko) from time zero to 
followed by first-order absorption (ka) beginning at time . The differential equations for the model (Figure 1) are as follows:
 | (2) |
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The rHuEpo was assumed to be 100% bioavailable on IV administration. The bioavailability after SC dosing is represented by the parameter F. The fraction of the dose associated with ka is denoted by Fr. Accordingly, the amount of rHuEpo associated with the first-order process is given by F • Fr • Dose, whereas that absorbed by the zero-order process is given by F • (1 - Fr) • Dose.
All fittings were done using the ADAPT II software.10 Estimation of parameters was done using least squares fitting by the maximum likelihood method, and the extended least squares variance model used is given by
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where Vi is the variance of the ith data point, 
is the vector of structural parameters, 
1 and 2 are the vectors of variance parameters, ti is the ith time, and M(, ti) is the ith predicted value.
Simultaneous fitting of the mean data from the 8 single SC doses and 5 IV doses was done. During initial fittings, Vmax, Km, Vd, ka, Fr, and variance parameters were kept constant across doses, whereas and F were allowed to vary with dose. Results indicated that could be fixed as 44 hours up to the 1350-IU/kg single dose, whereas for the higher 2 doses, a longer of 60 hours was optimal. Bioavailability (F) was found to increase proportionately with dose and was described by a linear equation (r2 = 0.9713):
 | (3) |
For linear regression, the F-value for the 450-IU/kg dose was excluded as it appeared to be an outlier. Final fittings were done using equation (3) to set F-values across doses. This made it possible to describe all the data using a single set of parameters for Vmax, Km, Vd, ka, Fr, and the variance parameters.
The pharmacokinetics of 600 IU/kg/wk rHuEpo administered for 4 weeks was simulated using parameters obtained from the simultaneous fitting of the data from the 8 single doses. Only the and Fr values were estimated. For the 150-IU/kg/tiw regimen, the F, , and Vd values were estimated.
Deconvolution
Because the nonlinearity associated with disposition of rHuEpo was found to be modest, deconvolution analysis was done to obtain initial estimates of absorption rates and bioavailability for each single SC dose. The plasma concentration-time profile of the 150-IU/kg IV dose was used for obtaining the monoexponential unit disposition function. The response was numerically deconvolved against this function to obtain the input function using the program PCDCON.11 Responses were described by an interpolating cubic spline function. A plot of cumulative amount absorbed versus time gave an estimate of the input rate and overall amount absorbed. The fraction of the administered dose bioavailable from the SC dose was calculated as F = cumulative amount absorbed to 408 h/dose. A spline program12 was also used to obtain AUC values.
Pharmacodynamic Analysis
The mean cell numbers obtained by averaging the counts of all subjects per group at each time point were used for all fittings. The baseline Epo concentration (Cbs) for each dose group was fixed as the mean of the measured predose Epo values for that group of subjects. It was assumed that administration of rHuEpo does not cause alterations in the production of endogenous Epo; therefore, this baseline value Cbs was added to the concentration predicted by the PK model Cp(t), which was then used as a forcing function for the pharmacodynamicanalysis. The reticulocyte data for the 8 dose levels were simultaneously fitted. It was assumed that the predose cell numbers reflected steady-state reticulocyte values, and so these were used as the baseline cell counts. For the red blood cells, the mean of the 48- and 96-hour values was fixed as baseline.
Life span parameters obtained from single-dose estimation for rHuEpo were fixed for further multiple-dose fittings. The Smax and SC50 were estimated for the reticulocyte response after the 600-IU/kg/wk multiple-dose regimen. As reported later in Table III, these parameters do not seem to change appreciably considering the variability in the responses. The difference may simply reflect the fact that this was a different clinical study. Moreover, this set of parameters could also adequately characterize the 150-IU/kg/tiw regimen. The reticulocyte data for males and females were analyzed separately to obtain values of potency and sensitivity parameters for comparison. Furthermore, the RBC and Hb responses were simulated based on the parameters generated for each gender using the reticulocyte data.
Model
rHuEpo is known to stimulate the production and release of reticulocytes from the bone marrow, leading to increased reticulocyte, RBC, and Hb counts in the blood. A cell production and loss model developed by us for monkeys13 was extended to describe the changes in cell numbers with time after rHuEpo administration in humans. An extra component accounting for a feedback mechanism was employed (Figure 1) to account for the drop in cell counts below baseline seen upon single dosing and the modest palliation of multiple-dose effects. This was done by assuming that reticulocytes cause a feedback inhibition of their own production by reducing the production rate of cells in the P1 compartment.
According to our model, under baseline conditions, the cell numbers are maintained constant due to a balance between stimulation by the endogenous Epo and an inhibition by steady-state reticulocyte levels. An increase in reticulocyte numbers disturbs this balance by causing the inhibition to predominate, leading to a decrease in the production rate of progenitor cells. This ultimately forces the reticulocyte levels to return to original levels. Because there is a chain of events before a stimulated precursor cell can give rise to a reticulocyte, there is a time lag before the inhibition can be realized in the form of reduced reticulocyte numbers. Moreover, there is a possibility that there might be a series of transduction processes before the reticulocyte can cause a reduction in the rate of formation of precursor cells. Also, the inhibition might actually occur at cell stages (early progenitor cells) prior to P1. This was handled in the model by introducing a delay time TP0, which accounts for these transduction delays. This time lag causes the reticulocyte levels to fall below baseline upon single dosing and can lead to tolerance effects on multiple dosing. The inhibition was modeled using a nonlinear function with Imax set to 1, as it was assumed that sufficiently high reticulocyte counts could completely suppress their own production.
The differential equations for the model are as follows:
 | (4) |
where
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where Smax is the maximum possible stimulation of reticulocyte production by rHuEpo, and SC50 is the plasma concentration of rHuEpo causing one-half maximum stimulation.
Figure 2 outlines the process of erythropoiesis, and the life spans of each precursor cell (TP1 and TP2), reticulocyte (TR), and red blood cell (TRBC) are indicated. The compartments reflect the pools of erythroid progenitor cells (P1), erythroblasts (P2), reticulocytes (R), red blood cells (RBC), and hemoglobin (Hb) in the blood. Stimulation of erythropoiesis by the administered rHuEpo (Cp(t)) is given by the nonlinear function (S(t)) acting on production of both precursor cell types in the marrow. The Smax and SC50 are assumed to be the same for both types of cells.
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The baseline conditions (steady-state levels) are defined as
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As a result, the initial condition itself defines the steady-state levels.
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The baseline equation is given as
 | (5) |
The differential equations describing the RBC responses are
 | (6) |
The change in hemoglobin levels was modeled by simply using a proportionality factor Hbcell, which represents the hemoglobin content per cell (reticulocyte or RBC).
 | (7) |
where Ncells(t) represents the total number of reticulocytes and RBC at time t. The RBC life span, TRBC, was fixed to be 120 days, and the Hb content per cell was set as 29.5 pg/cell based on literature values.14,15 Both reticulocytes and RBC are assumed to contribute to the overall Hb content of blood.
All fittings were done using the ADAPT II program10 with the maximum likelihood method, and the variance model chosen was the same as for the pharmacokinetic analysis.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Plots of AUC versus dose for the different single SC doses showed a greater than proportional increase in AUC with increasing dose.6 This indicates that CL, bioavailability, or both are changing with dose. Elimination of rHuEpo was found to be only very mildly nonlinear. On the other hand, F was found to increase linearly with dose (Figure 5) and turned out to be the main factor responsible for the disproportionate increase in AUC with SC dose.6 At the 2 highest doses, reduced CL was also contributing to the nonlinearity. Table II lists the F-values for all the doses obtained by deconvolution and by fitting the data from individual doses to the proposed model. The estimates obtained using both methods are similar, indicating that the pharmacokinetic model can adequately account for the nonlinearity due to changing values of F.
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Data profiles and simulations of rHuEpo concentrations versus time for the 150-IU/kg/tiw and 600-IU/kg/week multiple-dosing regimens are shown in Figure 6. The pharmacokinetic model with most of the parameters fixed to the values obtained from fittings of the single doses was used to describe the multiple-dosing data. For the regimen of 150 IU/kg/tiw, the Vd had to be increased to 0.119 L/kg, and decreased to 10 hours. For the 600-IU/kg/wk dosing, F was set as 0.25 and as 32.15 hours. Reasons for these differences other than interstudy variation are not clear.
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Pharmacodynamics
Figure 7 shows the mean reticulocyte numbers versus time profiles for all single SC doses. The reticulocytes slightly increase compared to predose levels immediately at the first sampling point. This level is maintained for 3 to 4 days, after which they steadily start rising until the peak is reached around 200 to 300 hours. Then, counts start declining to reach baseline levels by day 22 (528 hours).
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The model fittings for the single doses of rHuEpo are also shown in Figure 7. Parameter estimates obtained by fitting the pharmacodynamic equations to the data are presented in Table III. An SC50 value of 26.53 IU/L and an Smax of 4.25 were estimated. The feedback inhibition component of the model captures the tolerance phenomenon evidenced by the modest fall in reticulocyte counts below baseline upon single dosing, as well as the drop in response and stabilization to a lower level upon multiple dosing. The estimated time for TP0 is higher than the reticulocyte life span TR. This might suggest the possibility that reticulocyte remnants or the newly formed RBC are causing this feedback inhibition.
The pharmacodynamic data for some rHuEpo dose levels are quite variable. This is reflected by inconsistencies in the extent of stimulation with increasing doses. For instance, the 600- and 1200-IU/kg doses produce slightly higher numbers of cells compared to the 900- and 1350-IU/kg doses. However, the pattern of return to baseline seems to be similar across doses. In any case, the model seems to acceptably capture the trend of responses, considering the variable nature of the data and the fact that 1 single set of parameters could adequately describe the pharmacodynamic data from all doses. It would be possible to obtain better fittings of the data from each dose level by allowing Smax and SC50 to vary for each group. This would be reasonable because these were parallel dose groups; however, the parameters would have to be averaged for purposes of generalization.
Figures 8 and 9 show the data and simulations for the changes in reticulocyte, RBC, and Hb counts in males and females after multiple SC dosing of rHuEpo. The pharmacodynamic responses for both dosage regimens were captured over the period of dosing. Table III lists the stimulation parameters estimated for both sexes. At first appearance, the data give an impression that males and females exhibit different dynamic responses to rHuEpo treatment despite having similar pharmacokinetics. However, their baselines for the responses are different. The model estimated slightly different Smax values in males upon multiple dosing, and the SC50 for multiple dosing in both sexes was higher than that upon single dosing. However, the percent coefficient of variation (CV%) values were large for these parameters.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Most of the bioavailable dose after SC dosing of rHuEpo was rapidly absorbed within 2 to 3 days by the zero-order component (Figure 4). The first-order absorption rate ka accounts for a slow, continuous release of rHuEpo from the SC site. A similar dual-absorption process model was used to characterize the absorption kinetics of another macromolecule, IL-10, following SC dosing.19 The cause of the incomplete and nonlinear bioavailability of SC rHuEpo is not known. The protein IL-10 exhibits only 42% bioavailability on SC dosing, with loss assumed to be due to the effects of proteolytic enzymes. In turn, these enzymes may be saturable at higher concentrations of peptide or protein substrates. The dual-absorption process may be due to the role of the lymphatics in controlling access of macromolecules after SC dosing. The rapid early absorption phase may be caused by leakage of a major part of the dose into local blood vessels, whereas the later phase may be related to slow entry via the lymphatic system. A similar pharmacokinetic model describes the time course of plasma concentrations of rHuEpo in monkeys.13 It was not possible to use a Michaelis-Menten degradation process to account for the incomplete bioavailability. This was also found to be true in monkeys.13 Factors controlling absorption and loss of Epo from the SC absorption site need further study.
Pharmacodynamics
Our PK/PD model with feedback regulation effectively captures the response patterns for all the dosage regimens of the 2 formulations in both sexes. A kin of 0.007 x 1010 cells/L/h in males and 0.02 x 1010 cells/L/h in females was obtained, which translates to 0.084 x 1011 and 0.24 x 1011 cells/day, assuming a blood volume of 5 L. It is not clear if these differences are meaningful. However, these values are consistent with findings that 1% of all RBC are destroyed daily and replaced by reticulocytes in healthy humans, yielding an erythrocyte production rate (k0)of 2 x 1011 cells/day.20,21 The estimated Smax was 4 to 8, which indicates that rHuEpo can produce a maximum 5- to 9-fold increase in the zero-order production rate of reticulocytes, a relatively modest degree of stimulation that accounts for the slow and limited rise in blood RBC.
The bone marrow in a normal individual is known to be capable of 6 to 8 times the normal output of erythrocytes with maximum stimulation.22 The Smax of 4 to 8 estimated by our model conforms to this. The SC50 of 22 to 60 IU/L obtained reflects the plasma rHuEpo concentration needed to cause half-maximal stimulation. As long as rHuEpo plasma concentrations are maintained above this value, the cell counts should remain above baseline. Normal erythrocytic progenitor cells, regardless of origin, express less than 1000 Epo receptors on the cell surface. Binding of Epo to this receptor causes signal transduction events, which ultimately lead to stimulation of the differentiation and proliferation of erythrocytic progenitors in the bone marrow.2 The low SC50 value obtained reflects the fact that low numbers of receptor sites on erythropoietic cells may be readily saturated so that high doses with rapid delivery may lead to considerable wastage of the bioavailable rHuEpo. An increase in dose or slower delivery facilitates rHuEpo levels being maintained above the SC50 for a longer time, and so there is an increase in the extent and duration of stimulation of reticulocyte production. This concept explains the results of 2 clinical studies23,24 that show that SC rHuEpo is more effective than IV dosing for stimulating production of erythrocytes. Despite lower bioavailability, the SC doses with prolonged absorption result in more efficient stimulation of RBC production, as found in the literature23,24 and in these studies.
Negative feedback control of production of Epo by the circulating red cell mass has been observed in rats.25 However, we did not see any rebound effects for total Epo concentrations, which suggested that the tolerance effects seen in reticulocyte responses might have been caused by other regulatory mechanisms. Our model predicts a tolerance phenomenon irrespective of whether feedback was assumed to initiate from the cells in the P1, P2, R, or RBC compartment. Owing to lack of more specific data on the various cells that might be involved in the control process, we chose the reticulocytes as the primary regulators of counterregulation. Lindemann26 reported data for the inhibitory effect of hemolysates and compounds from intact RBC on Epo-induced erythropoiesis in mice. Birkhill et al27 showed that transfusion polycythemia depressed bone marrow activity and reduced production of reticulocytes in normal men. These studies support our choice of the latter cell populations to be involved in the regulation.
There are significant differences in baseline hemoglobin levels between men and women, despite the fact that their steady-state endogenous Epo levels do not differ. Androgens have been implicated in a direct regulation of erythropoiesis. Alterations within the physiologic range of testosterone have been reported to cause changes in Hb level without altering plasma Epo levels.28 This is supported by in vitro studies in mice proerythroblasts, which demonstrate that with Epo present as a cofactor, androgens can stimulate proliferation of erythroid progenitor cells.29 On the other hand, physiologic levels of estrogens can exert an inhibitory effect on erythropoiesis at the marrow level.30 Hence, it was of particular interest for us to investigate if responses to rHuEpo therapy would differ with sex. As seen from Table III, the results from our PK/PD model suggest that there may not be appreciable sex differences in clinical responses to rHuEpo therapy. The SC50 values estimated were similar between men and women, and although the Smax for females was half of that for males in the multiple-dosing situations, it had high CV% and was similar to that obtained from the single-dose study. Of interest is that a recent review indicates that clinical studies have reported that women with end-stage renal disease undergoing hemodialysis require higher doses of rHuEpo to attain a hematocrit (Hct) equivalent to that of men.31
In conclusion, the physiologically mechanistic PK/PD model applied here characterizes an extensive array of experimental data and demonstrates the importance of dose, dosage regimen, and route of administration in controlling rHuEpo responses. It uses a difficult-to-implement modeling tool—namely, cell life spans—in a type of meta-analysis using data largely generated under similar clinical and analytical conditions. This type of model could be used as a valuable tool for assessing pathophysiological factors in patients and designing optimal rHuEpo doses and administration times for various conditions.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Submitted for publication March 29, 2004; Revised version accepted June 19, 2004.
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REFERENCES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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D. N. McLennan, C. J. H. Porter, G. A. Edwards, S. W. Martin, A. C. Heatherington, and S. A. Charman Lymphatic Absorption Is the Primary Contributor to the Systemic Availability of Epoetin Alfa following Subcutaneous Administration to Sheep J. Pharmacol. Exp. Ther., April 1, 2005; 313(1): 345 - 351. [Abstract] [Full Text] [PDF]
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—, male subjects; o---, female subjects.
