Introduction

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Cardiac glycosides are widely used in the treatment of congestive heart failure because the inhibition of Na⁺/K⁺-ATPase (sodium pump), which serves as a functional receptor for digitalis, results in an increase in positive inotropy. Binding of digitalis drugs, such as digoxin, to the catalytic -subunit inhibits the sodium pump and increases intracellular Ca²⁺ availability for contractile proteins. The cardiac actions of digitalis glycosides and the "pump-inhibition hypothesis" have been critically reviewed (Eisner and Smith 1992; Levi et al., 1994). In the rat, consecutive inhibition of the ₂- and the ₁-isoforms of Na⁺/K⁺-ATPase with high and low affinity, respectively, for ouabain, induces positive inotropism over a wide dose range (Grupp et al., 1985; Sweadner, 1993; McDonough et al., 1995; Schwartz and Petrashevskaya, 2001). Despite fundamental new insights obtained in the last decades at the enzyme and cellular level by biochemical and electrophysiological studies, however, there is limited knowledge about the functional role of Na⁺/K⁺-ATPase isoforms in the intact heart. Although recent evidence suggests that the ₂-isoform may have a special function in the regulation of intracellular Ca²⁺ (Blaustein and Lederer, 1999; James et al., 1999), implying that only this single isoform mediates the glycoside action, this view is still controversial (Gao et al.,1995; Kometiani et al., 2001; Schwartz and Petrashevskaya, 2001). To understand the role of uptake kinetics and the contribution of Na⁺/K⁺-ATPase isoforms to cardiotonic effects of cardiac glycosides, we investigated the pharmacokinetics and pharmacodynamics of digoxin in the isolated perfused rat heart. Although findings from an intact, perfused organ are more likely to reflect processes occurring in vivo than are results from isolated cells or membrane preparations, to our knowledge, a kinetic analysis of uptake and receptor binding of cardiac glycosides with the aim to explain the time course of the positive inotropic effect in the intact heart has so far not been reported. Specific questions are: how is the transient kinetics of receptor binding related to that of the positive inotropic effect? Is functional receptor heterogeneity detectable in the intact heart? What are the characteristics of the transcapillary and trans-sarcolemmal transport processes?

A prerequisite to understanding the kinetics and dynamics of cardiac glycosides is a mechanistic and quantitative description of the processes involved. We therefore developed an integrated pharmacokinetic/pharmacodynamic (PK/PD) model of digoxin uptake, receptor binding, and inotropic response in the heart. The model included the barriers represented by the capillary and sarcolemmal membranes. One unique property of drug-receptor interaction is saturability, which implies the nonlinearity of the system. By using both the information provided by the outflow concentration-time profile and the time course of left ventricular pressure following three doses of digoxin in the isolated perfused rat heart, the results of PK/PD analysis support the view that two receptor populations are involved and provide evidence for a permeability-limited, transcapillary exchange process.

	Experimental Procedures

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Perfused Rat Heart. Hearts (wet weight, 1.05 ± 0.04 g) from adult male Sprague-Dawley rats (300-350 g; n = 12) were perfused with a Krebs-Henseleit bicarbonate buffer at 37°C with 60 mm Hg pressure (Weiss and Kang, 2002). Left ventricular (LV) pressure was monitored by means of a water-filled latex balloon placed in the left ventricle and connected to a pressure transducer. The chest was opened, an aortic cannula filled with perfusate was rapidly inserted into the aorta, and retrograde perfusion was started with an oxygenated perfusate. The perfusate consisted of Krebs-Henseleit buffer solution, pH 7.4, containing 118 mM NaCl, 4.7 mM KCl, 2.52 mM CaCl₂, 1.66 mM MgSO₄, 24.88 mM NaHCO₃, 1.18 mM KH₂PO₄, 5.55 mM glucose, and 2.0 mM sodium pyruvate, including 0.1% bovine serum albumin. A catheter was inserted into the pulmonary artery and connected to an autosampler. The balloon was inflated with water to create a diastolic pressure of 5 to 6 mm Hg. After stabilization, the system was changed to constant flow condition, maintaining a coronary flow of 8.8 ± 0.3 ml/min. The hearts were beating spontaneously at an average rate of 275 beats/min. Coronary perfusion pressure, left ventricular pressure, and heart rate were measured continuously. A physiological recording system (Hugo Sachs Elektronik-Harvard Apparatus GmbH, March-Hugstetten, Germany) was used to monitor left ventricular systolic pressure (LVSP), left ventricular end-diastolic pressure (LVEDP), and maximum and minimum values of rate of left ventricular pressure development (dP/dt_max and dP/dt_min). Left ventricular developed pressure was calculated as LVDP = LVSP  LVEDP. This investigation conformed with the Guide for the Care and Use of Laboratory Animals published by the National Institutes of Health (National Institutes of Health Publication 85-23, revised 1996). Experiments were approved by the Animal Protection Body of the state of Sachsen-Anhalt, Germany.

Materials. [³H]Digoxin (17 Ci/mmol) and digoxin were purchased from PerkinElmer Life Sciences (Boston, MA) and Sigma Chemie (Deisenhofen, Germany), respectively. All other chemicals and solvents were of the highest grade available.

Experimental Protocol. Hearts were allowed to equilibrate for 20 min with Krebs-Henseleit solution. Digoxin was dissolved in dimethyl sulfoxide (DMSO) and diluted with the same amount of 70% ethanol. The mixture was attenuated with 0.45% NaCl solution. The final concentration of DMSO and ethanol in vehicle was 0.5 and 0.35%, respectively. Digoxin solution was made by mixing a labeled (5 µCi/ml) compound with an unlabeled (0.32 µmol/ml) one. The final doses (0.1, 0.2, and 0.3 µmol) were administered as 1-min infusions, permutating the sequence of doses with an interval of 15 min (six permutated blocks in 12 hearts). Infusion was performed into the perfusion tube close to the aortic cannula using an infusion device. Outflow samples were collected every 5 s for 3 min and every 30 s for the next 7 min (total collection period, 10 min). The outflow samples were kept frozen at 20°C until analysis. In each heart, control-matched experiments were performed with the vehicle: 0.3, 0.6, and 0.9 ml of vehicle (19, 38, and 57 µmol of DMSO and 22, 44, and 66 µmol of ethanol) were infused in the same way, and the cardiac response was measured. For determination of [³H]digoxin, the outflow sample (50 µl) was transferred to a vial and 4 ml of cocktail was added. After mixing vigorously, the radioactivity was measured with a liquid scintillation counter (PerkinElmer Instruments, Shelton, CT).

PK/PD Model and Data Analysis. The cardiac distribution spaces of digoxin, i.e., the vascular, interstitial, and cellular, were represented by compartments. The model structure is shown in Fig. 1; the corresponding differential equations that describe changes in the amounts of digoxin in the mixing, capillary, interstitial, and cellular compartments as well as the two compartments representing the two saturable binding sites after infusion of digoxin (dosing = RATE) at the inflow side of the heart perfused at flow Q (single-pass mode) are given by eqs. 1 to 6. As suggested by independent experiments with the vascular marker Evans blue (data not shown), a lag time t₀ and an additional compartment with volume V₀ (in series with the capillary compartment) were introduced to account for the delayed drug appearance and mixing in nonexchanging elements of the system, respectively. [Initial estimates of the parameters t₀ and V₀ were obtained by fitting the outflow curve of Evans blue (1-min infusion) to a model consisting of only one additional compartment representing the vascular space.] The subscripts are "vas" for the vascular, "is" for the interstitial, and "cell" for the cellular compartments. Note that the measured outflow concentration C_out(t) = D_vas(t)/V_vas is the concentration in the vascular compartment.

(1)

(2)

(3)

(4)

(5)

(6)

(Note that the lag time t₀ was part of the FORTRAN program used in ADAPT II.)

View larger version (20K): [in this window] [in a new window]   Fig. 1.   Kinetic model of cardiac digoxin uptake and inotropic response with vascular, interstitial, and cellular compartments and two distinct sarcolemmal binding sites, R1 and R2.

i

i

(7)

(8)

(9)

(10)

	Results

Top Abstract Introduction Experimental Procedures Results Discussion References

Outflow Concentration. The averaged outflow concentration-time curves after infusion of three doses of digoxin for 1 min are shown in Fig. 2. The curves reached a plateau within about 20 s, and the rapid decay upon cessation of infusion was followed by a slower terminal phase. The recoveries of digoxin in the outflow perfusate (up to 10 min) were 97.8 ± 2.4, 96.5 ± 4.4, and 96.6 ± 5.7% for doses of 0.1, 0.2, and 0.3 µmol, respectively.

View larger version (19K): [in this window] [in a new window]   Fig. 2.   Outflow concentration-time profiles in rat hearts for a 1-min infusion of three doses (0.1, 0.2, and 0.3 µmol) of digoxin (average ± S.E.M.; n = 12).

Cardiac Performance. Figure 3 shows the average inotropic response-time profiles as a percentage of the difference to the vehicle effect corresponding to the outflow curves (Fig. 2). Treatment with digoxin resulted in an increase in LVDP at 1 min (i.e., end of infusion) to 9.6 ± 5.1, 16.2 ± 3.6, and 27.0 ± 3.4% of the vehicle level for doses of 0.1, 0.2, and 0.3 µmol, respectively, and recovered within about 10 min. Consistent with the increase in LVDP, the maximal rate of pressure development (dP/dt_max) increased to 9.3 ± 6.2, 15.4 ± 4.2, and 26.2 ± 4.2% of the vehicle level, respectively. These inotropic effects of digoxin were significant at the p < 0.05 level by one-way repeated measurement analyses of variance. The decrease in heart rate (1.7 ± 0.3, 3.5 ± 2.0, and 4.2 ± 1.9%) was not significant, whereas coronary vascular resistance significantly increased with maximum values of 11.2 ± 4.1, 23.8 ± 4.2, and 44.0 ± 7.6% of the vehicle level, respectively, at the end of infusion. There was no change in left ventricular end-diastolic pressure. The corresponding response to vehicle infusion was as follows: LVDP and coronary vascular resistance were increased by 9.2 ± 3.7, 10.5 ± 4.3, and 15.7 ± 3.5%, and 9.2 ± 3.4, 13.2 ± 7.3, and 18.3 ± 5.6% at the end of infusion of 0.3, 0.6, and 0.9 ml of vehicle [mixture of DMSO (63.3 µmol/ml) and ethanol (73.3 µmol/ml)], respectively.

View larger version (25K): [in this window] [in a new window]   Fig. 3.   Positive inotropic effect of digoxin (LVDP in the percentage of vehicle value) in rat hearts for a 1-min infusion of three doses (0.1, 0.2, and 0.3 µmol) of digoxin (average ± S.E.M.; n = 12).

PK/PD Analysis. Figure 4 shows a representative set of outflow and response data (three consecutive doses in one heart) together with the lines obtained by a simultaneous model fit. It is apparent that the PK/PD model perfectly fitted the data; the PD predictions are concordant with the observed time course of positive inotropy. The model was conditional identifiable, and parameter estimates (mean ± S.D.; n = 12), obtained with ADAPT II, are reported in Table 1 together with the precision of the estimates. Cardiac kinetics of digoxin was characterized by transport across the capillary barrier and specific binding to two distinct extracellular sites, R₁ and R₂. Cellular uptake of digoxin was not detectable under the present experimental conditions.

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Representative fit of time course of digoxin outflow concentration (top) and positive inotropic effect (bottom) obtained in one heart by the PK/PD model for three consecutive doses of 0.1 (left), 0.2 (middle), and 0.3 (right) µmol infused over 1 min.

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2

View larger version (10K): [in this window] [in a new window]   Fig. 5.   Contribution of high-affinity (R2) and low-affinity (R1) pumps to the maximal effect at the end of infusion, i.e., eiRDi/E (percentage) (cf. eq. 8).

View larger version (11K): [in this window] [in a new window]   Fig. 6.   Effect data shown in Fig. 4 refitted by an alternative model in which the effect is solely induced by the high-affinity receptor system, R2 (i.e., e1 = 0 in eq. 8). The model fails for the 0.3-µmol dose (left).

	Discussion

Top Abstract Introduction Experimental Procedures Results Discussion References

To quantify the PK and PD of digoxin in the present work, a mathematical model of transcapillary exchange, receptor interaction, and effectuation of digoxin in the intact rat heart was built. Although it was necessary to postulate two sarcolemmal binding sites to explain the PK data, the identification of the ratio of high- to low-affinity binding sites was only possible by simultaneous fitting of both PK and PD data. Note that in contrast to conventional PK/PD modeling, in which drug-receptor interaction does not influence PK (i.e., mass balance) (Breimer and Danhof, 1997; Mager and Jusko, 2001), specific binding was an important determinant of digoxin distribution kinetics in the rat heart. To obtain reliable parameter estimates, we utilized a priori information on digoxin receptor binding determined in vitro (Noel and Godfraind, 1984). Incorporating the ratios of binding parameters, K_A,2/K_A,1 and R_tot,1/R_tot,2, the results of Bayesian modeling were satisfactory both in terms of the capability of the model to describe the data (Fig. 1) and in terms of parameter estimation (Table 1). Only the rate constants of high-affinity binding (k₂ and k₂) are poorly estimated (CV >50%). (Note that a formal proof of identifiability is a complicated mathematical undertaking, especially for nonlinear models, which was in our opinion beyond the scope of this paper.)

Although multiple studies have characterized the expression of Na⁺/K⁺-ATPase isoforms (₁, ₂, and ₃) in the heart of various species (Blanco and Mercer, 1998; James et al., 1999; Lelievre et al., 2001), their functional role in mediating the effect of digitalis drugs on cardiac contractility is still controversial (James et al., 1999; Kometiani et al., 2001; Schwartz and Petrashevskaya, 2001). The results of this study suggest that the kinetics and inotropic response of digoxin in the normal rat heart are mediated by a mixture of two receptor subtypes, a low-affinity/high-capacity binding site (R₁) and a high-affinity/low-capacity binding site (R₂), which account for 89.4 ± 0.4 and 10.6 ± 0.4% of the total number of receptors (R_tot,1 + R_tot,2), respectively. The fact that the myocardium of the adult rat heart contains two sodium pump subunits exhibiting low (₁) and high (₂) affinity for glycosides, whereby ₂ comprises only 10 to 25% of the sodium pumps (Lucchesi and Sweadner, 1991; Askew et al., 1994), indicates that R₁ and R₂ are identical to the ₁- and ₂-isozymes, respectively. The low percentage of functionally active, high-affinity binding sites (11%) and the ratio of affinity constants (K_A,2/K_A,1 = 13.7) are not much different from the values of 13 and 18% found for ouabain binding in microsomes from normal rat heart (Vér et al., 1997). Although our results are in accordance with the general view that the positive inotropic action of cardiac glycosides is primarily mediated by inhibition of the ₂-isoform (McDonough et al., 1995), the PK and PD data could not be explained without the assumption of a low-affinity/high-capacity receptor (₁). For the maximum effect at the end of infusion, the dominating role of the ₂-isoform (R₂) decreases with increasing dosage, whereas the contribution of the low-affinity system (₁) increases (Fig. 5). If the parameters e₁ and e₂ in eq. 8 are interpreted as effects per unit of digoxin-receptor complex, this effect-related sensitivity is significantly higher for the high-affinity receptor population (R₂). Our PD model (eq. 8) is analogous to the weighted sum of low- and high-affinity-mediated effects used by Gao et al. (1995) to describe Na⁺/K⁺-pump currents in cardiac ventricular myocytes. Interestingly, in these experiments, the onset of receptor blockade was also much more rapid than the offset. Thus, in agreement with the latter results and the recent discussion (Kometiani et al., 2001; Schwartz and Petrashevskaya, 2001), our findings do not support the hypothesis (James et al., 1999) that only the inhibition of the ₂-isoform by cardiac glycosides would induce the positive inotropic effect. In view of the underlying discussion regarding the dose dependence of the specific role of these two isoforms (Schwartz and Petrashevskaya, 2001), we further tested the performance of an alternative model in which only one receptor, R₂, mediates the positive inotropic effect (R₁ remains part of the PK model). As shown in Fig. 6, such a model fails to describe the high-dose PD data (0.3 µmol), suggesting that the low-affinity/high-capacity isoform (₁) significantly contributes to the effect at higher dose levels (p < 0.05).

In view of the fact that we have obtained only indirect information on digoxin binding processes, the term "receptor" as used here is mainly based on the ability of the model to predict the time course of the inotropic effect. The proportionality between effect and receptor occupation (eq. 8) suggests that the time dependence of signal transduction (Mager and Jusko, 2001) was negligible. Finally, it is important to note that our model explains the PD of digoxin without postulating a cellular mechanism of action (Sagawa et al., 2002). Although such an effect cannot be excluded, a significant contribution appears unlikely in view of the negligible cellular digoxin uptake during the 1-min infusion period. It should be noted that the positive inotropic and vasoconstrictive effects of the vehicle are probably produced by DMSO (Shlafer et al., 1974), since ethanol does not influence cardiac function in this dose range (Kojima et al., 1993).

The new information provided by this study about cardiac uptake kinetics of digoxin is also of importance for a critical appraisal of the pharmacodynamic results discussed above. The myocardial uptake was barrier-limited due to the relatively low transcapillary permeation clearance of digoxin (compared with perfusate flow). If entry into the heart is by passive diffusion through interendothelial clefts, one would expect a CL_vi value ~0.7-fold less than that for sucrose (the square root of the ratio of molecular weights of sucrose and digoxin, 0.7, accounts for the different diffusion coefficients). Although our estimate appears concordant with a value of 5.1 ml/min measured for sucrose in rats (Caldwell et al., 1998), a bias due to model misspecification (compartment approximation versus distributed model) has to be taken into account. However, the digoxin-to-sucrose ratio of capillary permeation clearances should be less biased when the clearances are estimated with the same model (i.e., assuming a well mixed vascular compartment). Applying a reduced model consisting only of a vascular and interstitial compartment to sucrose impulse data (bolus injection), a value of 2.90 ± 0.37 ml/min (n = 5) was obtained (W. Kang and M. Weiss, unpublished results). This suggests that transcapillary exchange of digoxin is primarily via diffusion through gaps between the endothelial cells. A steady-state ratio of interstitial-to-vascular concentration of 0.53 is predicted by eq. 10, assuming a volume ratio, V_vas /V_is, of 0.38 (Dobson and Cieslar, 1997). This concentration gradient has to be taken into account when comparing in vitro results with those obtained in the intact heart. No quantitative information could be extracted from the data on the trans-sarcolemmal transport process of digoxin. The nearly complete recovery of injected dose and the sensitivity analysis indicate that the cellular accumulation of digoxin in the 1-min infusion experiment was too small to be detectable with our method. Note that such a low uptake rate appears consistent with receptor-mediated endocytosis as a possible uptake mechanism (Núnez-Durán et al., 1988; Eisner and Smith, 1992).

The PK/PD model was selected according to the principle of parsimony as a minimal mechanistic model (Fig. 1), which is in accordance with the information content of the outflow and effect data. The mathematical model, although greatly simplified as a description of a complex process, offers a means to pose hypotheses concerning cardiac PK and PD of digoxin. Although a satisfactory fit to the experimental data is not proof of its correctness, the predictive power of the model is encouraging in view of the ability to accurately predict the time course of inotropic response from receptor occupancy and the principal consistency with previous results on receptor binding obtained in vitro. We suggest that theoretical models of this kind are valuable tools to bridge the gap between studies at the molecular level and the functioning of organ systems. Nevertheless, one must be cautious in its interpretation and extrapolation. The assumption of homogeneous compartments is a limitation of the model (e.g., it does not account for flow heterogeneities). However, the integration of a pharmacological effect excludes the use of a spatially distributed model.

In summary, the present PK/PD modeling approach provides information about the mechanism of drug action, which is unavailable from equilibrium studies. This methodology for the nondestructive measurement of membrane transport and receptor binding kinetics in intact hearts provides, for the first time, an integrated description of cardiac kinetics and dynamics of digitalis drugs. It is possible that a model such as this may resolve some of the controversy regarding the functional role of Na⁺/K⁺-ATPase isoforms. Passive transcapillary uptake followed by binding to two distinct sarcolemmal receptor populations determines cardiac kinetics and, in accordance with the pump inhibition hypothesis, also the inotropic effect of digoxin.