Introduction

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Erythropoietin (EPO) is a 34-kDa glycoprotein that is the primary hormone regulator of erythrocyte production. Recombinant human EPO (rhEPO) has been widely used clinically as an effective treatment of anemic patients with insufficient EPO production, e.g., end-stage renal disease. rhEPO is also approved for anemic patients suffering from neoplastic disease and acquired immunodeficiency with azidothymidine treatment.

Several pharmacokinetics/pharmacodynamics (PK/PD) models for EPO's stimulating effect on erythropoiesis have been developed (Brockmoller et al., 1992; Uehlinger et al., 1992; Bressolle et al., 1997). The PD response variables considered in EPO PK/PD models have been Hb, hematocrit, reticulocyte count, and serum soluble transferrin receptors. However, none of these previous studies have been considered under "physiologic conditions", i.e., investigating the PD of the response to the large endogenous EPO concentrations seen in hypoxemic episodes. Instead, the studies have been done using exogenous rhEPO under nonanemic conditions.

The goal of this investigation is to study the kinetic mechanisms underlying the PD of EPO through controlled physiologic experimentation, in which erythropoiesis was endogenously stimulated. A sheep model was employed to observe how the body naturally reacts to a large demand for hematopoiesis. The PD relationship between reticulocyte response and the endogenous EPO response was investigated under conditions of severe phlebotomy-induced anemia.

	Materials and Methods

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Study Animals. All surgical and experimental procedures received prior approval by the local institutional animal care review committee. Five healthy normal young adult sheep were selected. They were 2 months old and weighed 21.1 (±3.5) kg (mean ± S.D.) at the beginning of the experiments. The animals were housed in an indoor, light- and temperature-controlled environment. All animals were in good health. Jugular venous catheters were placed under anesthesia using pentobarbital. Intravenous ampicillin (1 g) was administered daily for the first 3 days.

Study Protocol. An increase in endogenous EPO was induced by controlled phlebotomy performed using the jugular venous catheter. Animals were bled until their Hb levels reached between 3.0 and 4.0 g/dl. To maintain a constant blood volume during the procedure, equal volumes of 0.9% NaCl solution was infused for each volume (~2000 ml) of blood removed. Each animal underwent two such phlebotomies given 4 to 6 weeks apart. EPO concentrations, reticulocyte counts, and Hb were measured from one to three samples per day drawn before and during the study period. EPO concentration was measured in plasma using a modification of the double antibody radioimmunoassay procedure as previously described (Widness et al., 1992). The number of reticulocytes was determined by flow cytometry (FACScan; Becton-Dickinson, San Jose, CA) as described by Peters et al. (1996). Plasma iron concentration was also monitored. No extra iron supplementation other than through food was given to any subjects in this study.

PK/PD Modeling. We applied a system analysis approach to analyze the PD (Cutler, 1978; Gillespie et al., 1988; Veng-Pedersen and Gillespie, 1988). In this approach we consider the rate of formation of reticulocyte, R, to depend on the EPO concentration, C_EPO:

(1)

The disposition of the reticulocyte (i.e., aging and maturation to become red blood cells) is considered to follow the superposition principle that forms the basis for the use of convolution in linear system analysis (Cutler, 1978). Accordingly, the relative reticulocyte count (RRC) depends on the EPO concentration according to the following convolution system analysis model:

(2)

The second term, A(t), in eq. 2 accounts for the initial steady-state reticulocyte count present before the EPO concentration increase due to the anemic condition created by the phlebotomy. Convolution is denoted by the asterisk (*) and UIR(t) is the unit impulse response function of the reticulocytes, which describes the average time course for appearance and disappearance of individual reticulocytes. UIR(t) equals 1, once the reticulocyte appears in the blood stream. Similarly, UIR(t) is zero before the reticulocyte appears in blood or after it has matured to a red blood cell. Accordingly, the time course described by the UIR is given by:

(3)

where T₁ is the time it takes new reticulocytes to first appear in the blood stream, T₂ is the time it takes a reticulocyte to mature to a red blood cell measured relative to the time the reticulocyte's first appears in the peripheral blood. The second term in eq. 2 is described by the following expression:

(4)

where RRC(0) is the RRC at t = 0, i.e., at the start of the phlebotomy. The initial steady-state count, RRC(0), is related to the basal EPO concentration C_EPO⁰ by:

(5)

Thus, eq. 2 may be written in a more explicit form as the final equation:

(6)

In addition to the relative (i.e., percentage) reticulocytes, the absolute reticulocyte index (ARI) was also analyzed. The ARI was defined as RRC(t) multiplied by the Hb level at the corresponding time (eq. 7). The parameter estimates from the model using ARI were compared with those from eq. 6, where RRC was used as the dependent variable.

(7)

Data Analysis. Equations 6 and 7 were fitted to the corresponding reticulocyte data using a Windows version of the general nonlinear regression program FUNFIT (Veng-Pedersen, 1977). A linear activation function was used to describe the formation rate of reticulocytes induced by EPO:

(8)

Initially, a more complex nonlinear activation rate function (e.g., a Michaelis-Menten equation) was investigated, but the Akaike information criterion (Akaike, 1974) indicated that eq. 6 was a more appropriate activation model than the model employing a nonlinear activation rate function. C_EPO⁰ and the reticulocyte counts [RRC(0) and ARI(0)] were predetermined by averaging two to three points before the ablation started. The EPO concentration in eqs. 6 and 7 was represented as a simple linear interpolation formed by connecting the EPO concentration data points by straight lines.

	Results

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EPO Concentrations and Reticulocyte Counts in Phlebotomized Sheep. Baseline characteristics of EPO concentrations and relative reticulocyte counts were determined as 18.3 ± 3.6 mU/ml and 0.81 ± 0.57%, respectively. Figure 1 illustrates the dynamic changes in the PD response variables after the phlebotomy. The anemia caused by phlebotomy (Hb < 4 g/dl) resulted in a rapid and immediate increase in endogenous EPO concentrations with peak concentrations ranging from 200 to 1400 mU/ml, from 0.5 to 3 days after the phlebotomy. The phlebotomy-induced EPO plasma concentrations returned to normal within 3 to 6 days after the start of the increase in EPO. The maximum relative percentage reticulocyte counts observed ranged between 9.3 and 14.1% at 2.5 to 5.1 days after the start of the phlebotomy. The increase in reticulocytes showed a delay with a lag time of 0.2 to 2.0 days from the commencement of phlebotomy. The elevated reticulocyte counts returned to baseline values at 10 to 15 days after the phlebotomy. The Hb levels lowered by phlebotomy recovered to the baseline by the time that the elevated reticulocytes returned to the normal range. None of the study animals showed significant iron deficiency, considering the observed ratio of plasma iron and total iron binding capacity throughout the experimental periods (0.37 ± 0.083; range, 0.31-0.50, n = 5).

View larger version (25K): [in this window] [in a new window]   Fig. 1.   Changes in EPO, reticulocytes, total Hb, and plasma iron resulting from a severe phlebotomy-induced anemia. The first phlebotomy was performed at day 0.

The Fitted Model and Parameter Estimates. The fitted model (eqs. 6 and 7) showed a good agreement with the observed data. Figure 2 provides representative plots of such fittings, and Tables 1 and 2 summarize the parameter estimates of the fitted PK/PD model. In Fig. 2, two examples of the curve fitting are shown, one with the best correlation (r = 0.992) and the other with the worst (r = 0.853) among the 10 data sets. Owing partly to the parsimony in the model, the parameter estimates showed relatively little variability with coefficients of variation less than 100%. The three estimated parameters T₁, T₂, and k summarize the kinetics, i.e., the onset of EPO action, the systemic lifespan of EPO induced reticulocytes, and the efficacy coefficient, respectively. The estimated means of T₁, T₂, and k are 0.47 days, 4.98 days, and 0.0099% · (mU/ml)¹ day¹ with standard deviations of 0.28, 1.31, and 0.0077, respectively. Accordingly, newly generated reticulocytes are first observed 0.47 day on average after EPO's activation of the hematopoietic progenitor cells and can be observed circulating in the peripheral blood for 4.98 days before maturating to red blood cells. The efficacy coefficient k represents an efficacy measure of EPO for the rate of formation of new reticulocytes.

View larger version (16K): [in this window] [in a new window]   Fig. 2.   Two representative plots of the model (eq. 6) fitted to the 10 data sets. The best fit (r = 0.992, left panel) and the worst fit (r = 0.853, right panel) are shown.

Fitting Using ARI Data. There was no significant difference found in the overall shapes of reticulocyte response to EPO as shown in Fig. 3, when ARI was used as the dependent variable in the model instead of percentage reticulocyte count. This was observed consistently among all ten phlebotomies of the five study animals. The sampling was not frequent enough near the peaks to accurately determine the difference in the two different modeling situations, i.e., one with percentage of reticulocytes and the other using the ARI. Correspondingly, the parameter estimates using eq. 7 with ARI also appeared to be similar to those from fitting eq. 6 to the data as shown in Tables 1 and 2.

View larger version (16K): [in this window] [in a new window]   Fig. 3.   Comparison of absolute and relative reticulocyte responses resulting from a phlebotomy in one animal.

	Discussion

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Linearity in Pharmacodynamic Response of EPO. In this study, the EPO concentrations resulting from severe phlebotomy-induced anemia are similar to those seen following s.c. EPO administration (Cheung et al., 1998). Within the endogenous range of EPO concentrations that the body could produce after this stimulus, the rate of reticulocyte formation was linearly related to the EPO concentration (eq. 8). This linearity was not expected, because most PD concentration-effect relationships are nonlinear and often well represented by an E_max or sigmoid E_max model. However, it is also recognized that a linear concentration range may exist as a part of nonlinear relationships, e.g., the sigmoid E_max model. In this modeling approach, the Akaike information criterion (Akaike, 1974) did not justify the inclusion of a nonlinear concentration-effect relationship. A deviation from PD linearity would likely have been observed if the EPO plasma concentrations had been higher.

Model Parameters. The proposed model provides information through the T₁ and T₂ parameters about the time course for the release of reticulocytes into the systemic circulation and the maturation of the reticulocytes into red blood cells. The transit time of human reticulocytes in blood is reported to be 1 to 2 days (Finch et al., 1977; Beutler et al., 1995), which was measured by injection of radiolabeled reticulocytes. The reported estimates of the circulating life span of reticulocytes are shorter than the corresponding T₂ estimates of 5 days we observed in sheep as assessed by our model. The exact reason is unknown, but it may be partly due to different analysis methodologies for the determination and the fact that our study was performed under anemia induced by phlebotomy, contrary to other studies. Possible interspecies differences may also exist. When the data in our study are visually compared with those in a human study by Breymann et al. (1996), the reticulocytes remained elevated for a significantly longer period relative to our EPO profiles in sheep.