Introduction

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Verapamil is a calcium-channel antagonist that can reduce the strength and rate of contraction of cardiac muscle (Cohen et al., 1987; Satoh et al., 1979; Raschack, 1976) and the tone of vascular smooth muscle (Nawrath and Raschack, 1987; Golenhofen and Lammel, 1972). It has been used clinically to treat hypertension, myocardial ischemia and tachyarrhythmias, the latter often by intravenous bolus administration or short infusion. Early studies of this type of administration showed a delay between the concentration of verapamil in venous blood and its effects on A-V conduction in some circumstances (McAllister and Kirsten, 1982) but not others (McAllister et al., 1977). Attempts to account for this delay (hysteresis) by measuring the myocardial concentrations of verapamil have had mixed success. In dogs, verapamil concentrations in direct myocardial biopsies were linearly related to myocardial effects, but with some suggestion of hysteresis (Keefe and Kates, 1982). In humans, the direct effects of verapamil on the heart showed hysteresis when compared with the myocardial concentrations determined by a mass balance method (Powell et al., 1990).

Several developments have contributed to the understanding of these earlier studies, and suggest the following hypotheses. First, like many other drugs (Huang et al., 1993; Upton et al., 1996), it can be hypothesized that the myocardial effects of verapamil are directly related to its concentration in the myocardium. Second, it is now clear that the enantiomers of verapamil can differ in their kinetics and dynamics (Eichelbaum et al., 1984), and that these differences can be species specific (Laethem et al., 1995). It could be hypothesized that this alone could account for the hysteresis observed in some studies in which only racemic verapamil was assayed. Third, it could be hypothesized that recent insights into the kinetics of bolus administration (Upton, 1996), when applied to verapamil, would provide greater insight into the relationship between verapamil dose and duration of injection and the amount of verapamil entering the heart. Important processes in bolus kinetics are the mixing of drug with venous blood and cardiac output (Upton and Huang, 1993), the kinetics of the first-pass passage of the drug through the lungs (Roerig et al., 1989) and the kinetics and dynamics of the drug in its target organ, in this case the heart (Upton, 1996; Huang et al., 1993). Indeed, descriptions of initial bolus kinetics that do not include these processes but consider bolus administration as the addition of a drug to a central compartment often perform poorly, with very unreliable estimates of the central volume (Keefe and Kates, 1982).

In this paper, we examine these hypotheses by measuring the enantiomer-specific lung, heart and systemic kinetics of verapamil, and its myocardial dynamics, in a conscious chronically instrumented sheep preparation. We identify the determinants of the myocardial concentrations and effects of verapamil and propose a physiologically based pharmacokinetic-pharmacodynamic model of the process [analogous to our previous work with propofol (Upton and Ludbrook, 1997; Ludbrook and Upton, 1997)]. Simulations with the model are used to provide important insights into the dose requirements of verapamil.

	Methods

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The study protocol was approved by the institutional Animal Ethics Review Committee. Seven adult merino ewes weighing approximately 50 kg were prepared with chronic intravascular catheters and Doppler flow probes to allow drug administration, cardiovascular function monitoring and the measurement of blood flows.

Animal Preparation

The method for preparing the sheep has been described in detail elsewhere (Huang et al., 1992). Sheep were prepared under anesthesia with ultrasonic Doppler flow probes on the left main coronary artery (for measurement of an index of left myocardial blood flow) and the trunk of the pulmonary artery (for measurement of cardiac output). The calibration of these flow measurements also has been described previously (Huang et al., 1992). Intravascular catheters were placed via the right carotid artery or jugular vein in the ascending aorta (for arterial blood sampling and placement of a left ventricular manometer catheter), inferior vena cava (for drug administration), the coronary sinus (after ligation of the hemiazygous vein for sampling myocardial effluent blood) and in the pulmonary artery (for blood sampling). All the surgical procedures were performed by sterile technique. After they recovered from anesthesia, the sheep were placed in mobile metabolic crates and their catheters were flushed continuously with heparinized (5 IU/ml) 0.9% saline at a rate of 3 ml/hr, with a gas-powered system (Runciman et al., 1984). All animals had free access to food and water.

Hemodynamic Measurements

On an experimental day, the following hemodynamic measurements were made by methods reported previously (Huang et al., 1992). Myocardial blood flow and cardiac output were derived from the output of the Doppler flow probes. An index of myocardial contractility was derived from the LV dP/dt_max recorded by use of an acutely placed micromanometer catheter in the left ventricle. Mean arterial blood pressure was measured with a pressure transducer on one of the arterial catheters. These hemodynamic parameters were recorded with an analog-to-digital card (Metrabyte DAS 16-G2) and a personal computer (486 based IBM compatible). A quadrapolar electrocardiogram was recorded from electrodes placed on each leg of the sheep and on a high-frequency response chart recorder (Devices 4 channel). This electrocardiogram was later analyzed to determine the heart rate and PR interval to give an index of the rate of A-V conduction.

Study Design and Pharmacokinetic Measurements

Studies were conducted in seven sheep prepared as described above. After the placement and the calibration of the hemodynamic measurement devices, sheep were allowed to "settle down" for approximately 30 min before base-line measurements of the hemodynamic parameters were recorded. The sheep were administered 10-mg doses of verapamil hydrochloride (Isoptin 5 mg/2 ml, Knoll AG, Germany) diluted with 0.9% saline (total volume, 20 ml) as a 2-min i.v. infusion into the right atrium. During the experiments, the sheep were partially supported in a comfortable sling inside their metabolic crates to prevent them from lying down during the study, which would influence the hemodynamic measurements. After the start of the verapamil infusion, the hemodynamic parameters were recorded continuously for the next 30 min, and pulmonary artery, arterial and coronary sinus blood samples (1 ml) were taken at 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 7, 8, 9, 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5 and 30 min by methods reported previously by our laboratory (Huang et al., 1991).

Verapamil Assay

Verapamil was assayed by an high-performance liquid chromatography method based on enantiomer separation with an Chiral-AGP column (100 × 4.0 mm, ChromTech AB, Hagersten, Sweden), as described in the application notes for this column [ChromTech Application note no. 11 (1993), ChromTech AB, Hagersten, Sweden]. The whole-blood samples were collected into 10-ml glass tubes that contained 0.25 µg of (+)-mepivacaine as an internal standard and 25 µl of heparin (1000 IU/ml) as an anticoagulant. They were processed by extraction into diethyl ether under basic conditions, followed by acidic extraction into 200 µl of 0.005 N phosphoric acid. This acid phase (50 µl) was injected into the high-performance liquid chromatography which used a buffer containing 90% 0.01 N Na₂HPO₄ (pH 7.15) and 10% acetonitrile. Detection was by ultraviolet absorbance at 214 nm. A runtime of approximately 15 min separated the enantiomers of verapamil, and the limit of sensitivity was approximately 0.02 µg/ml. To determine whole-blood verapamil concentrations, five-point standard curves (range, 0.05-0.5 µg/ml) were prepared in drug-free whole blood taken from the animal immediately before the study. The mean R² values of the standard curves were 0.9992 (S.D. 0.0008) and 0.9996 (S.D. 0.0002) for the (+)- and ()-enantiomers, respectively.

Kinetic and Dynamic Analysis

In general terms, lung kinetic values were deduced from the pulmonary artery-arterial verapamil gradient and cardiac output, whereas heart kinetic values were deduced from the arterial-coronary sinus verapamil gradient and myocardial blood flow. Systemic kinetic values were deduced from the time course of the arterial verapamil concentrations. The dynamic effects of verapamil on myocardial contractility (LV dP/dt_max), myocardial blood flow and A-V conduction (PR interval) were compared with the concentrations of verapamil in arterial or coronary sinus blood. The complex relationships between these kinetic and dynamic processes were synthesized by physiological modeling as described below.

Modeling methods. The general modeling method was the hybrid modeling of kinetics and/or dynamics in separate regions (e.g., lung, heart) with empirical forcing functions to represent inputs into the region and curve-fitting of the output to determine model parameters (Upton, 1996). Curve-fitting was by a least squares method based on the maximization of MSC, which is essentially the Akaike Information Criterion scaled to compensate for data sets of different magnitudes (Wagner, 1993). In this context, values of about 5 are consistent with an extremely good fit of the data, whereas values of about 1 are consistent with a poor fit. No weighting was considered necessary because there was no evidence that the data were heteroscedastic. Models were constructed as a series of differential equations with the Scientist for Windows software package (Version 2, Micromath Scientific Software, Salt Lake City, Utah). Models were fitted to mean data for the seven sheep.

1.

A single flow-limited compartment with the mass balance equation modified for effluent rather than tissue drug concentrations, where Vlung is the apparent volume of the compartment representing the lung. (1) 2.  A single flow-limited compartment with first-order lung extraction (ERlung): (2) 3.  A membrane-limited model where "PS" is used to represent membrane permeability in keeping with standard principles of capillary exchange (Intaglietta and Johnson, 1978) and Cd is the verapamil concentration in the deep compartment of the lung with a volume given by Vdeep. (3) Heart models of each enantiomer. The process used was similar to that described above for the lung, but the arterial concentrations of verapamil and myocardial blood flow data were fitted to forcing functions and used as the inputs, and the coronary sinus concentrations were used as the output for parameter estimation. The structural models examined for each enantiomer were those described above for the lung, but to define the model in terms of parameters more relevant to the heart than the lungs, the flow-limited compartment with extraction was expressed alternatively as small first-order loss from the compartment: (4) Cart is the arterial verapamil concentration, Ccs is the coronary sinus verapamil concentration, Qh is myocardial blood flow, Vh is the apparent volume of the heart and kout is the rate constant of drug loss. The model was expressed in this form for comparison with the reported loss of some drugs from the surface of the heart into surrounding fluids (Huang and Upton, 1993).

View larger version (16K): [in this window] [in a new window]   Fig. 1.   The overall structure of the model. The model is composed of six compartments representing a venous mixing, lung, deep lung, heart and two tissue pools connected in a recirculatory manner through which the cardiac output (Qco) flows. The kinetics of the (+)- and ()-enantiomers of verapamil were treated separately in each compartment. The effects of verapamil on myocardial blood flow (Qh), myocardial contractility (LV dP/dtmax) and A-V conduction (PR interval) were treated as the sum of the effect of both enantiomers using the potency ratios shown in table 4.

(5)

(6)

(7)

(8)

(9)

Combined kinetic-dynamic model for both enantiomers. Although data on the relationships between the concentrations of each enantiomer of verapamil and their combined effect on the heart from the previous sections are useful for choosing the concentration site best related to a drug effect, conclusions drawn from these data can be misleading if potency resides predominantly in one enantiomer, as for verapamil (Satoh et al., 1980). The combined kinetic-dynamic model was therefore structured as follows: After the administration of racemic verapamil, the kinetics of each enantiomer was handled separately in each organ of the model as described above. The measured drug effects were assumed to be the sum of the effect caused by the concentration of each enantiomer at the effect site of relevance, with the difference in potency accounted for by differences in the EC₅₀ of each enantiomer. The following equations are an example, and have been used to relate the LV dP/dt_max changes (dpdt) to the coronary sinus concentrations of each enantiomer [C_csm for the ()-enantiomer, C_csp for the (+)-enantiomer]. E_max is the maximum drug effect, EC_{50 m} and EC_50p are the concentrations at which half the maximum effect is achieved for the ()- and (+)-enantiomers, respectively, and P is the potency ratio ()/(+).

(10)

This equation requires the estimation of only three parameters (E_max, EC_50m and base line) from the concentration and effect data. The literature was examined to determine the known potency ratios (/+) of the enantiomers of verapamil for their effects on myocardial blood flow, myocardial contractility (e.g., LV dP/dt_max) and A-V conduction (e.g., PR interval). The potency ratio for changes in myocardial blood flow has been reported to be between 1.5 and 3 (Satoh et al., 1979, 1980); we used a value of 2. A potency ratio of 10:1 was used for LV dP/dt_max, based on data in experimental dogs (Satoh et al., 1980; Chiba et al., 1978; Kaumann and Serur, 1975). For PR interval, potency ratios of 3 to 10:1 have been reported (Kaumann and Serur, 1975; Glorr and Urthaler, 1983; Chiba et al., 1978); to be conservative, we used a value of 4:1.

Implications of the Model

Two simulations were performed to illustrate some of the uses of the final kinetic-dynamic model. First, the model was used to analyze the effect of altering the duration of injection (from 10 to 480 sec) of a fixed dose of verapamil on the time course of its arterial and coronary sinus concentrations (and therefore effects of PR interval and contractility). Second, it was used to analyze the dose requirements for verapamil to achieve approximately the same time course of effect for a variety of physiological states. For this, the model was used to predict the time course of the effect of verapamil (10 mg) on changes in PR interval for 60 min under normal conditions of cardiac output (Q_co) and myocardial blood flow (Q_h). A curve-fitting routine was then used to determine the dose and duration of injection of verapamil best able to duplicate the same time course of effect over a range of values of Q_co and Q_h.

	Results

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Blood concentration differences between the enantiomers of verapamil. The time courses of the concentrations of each enantiomer of verapamil in pulmonary artery, arterial and coronary sinus blood were superficially similar and are shown in figure 2. However, 95% confidence limit analysis of the ratios of the (+) over the () concentrations showed that concentration of the (+) was 10 to 20% greater than that of the () for each site at some stage during the 30-min study period (fig. 3), which suggests that an enantiomer-specific analysis was necessary. The times of the peak arterial, pulmonary artery and coronary sinus concentrations were 2, 2 and 4.5 min, respectively, and did not differ between enantiomers.

View larger version (31K): [in this window] [in a new window]   Fig. 2.   The means and standard errors of the concentrations of (+)-verapamil (top) and ()-verapamil (bottom) observed in pulmonary artery (open squares), aortic (filled circles) and coronary sinus (open triangles) blood after administration of 10 mg of the racemate during 2 min starting from time zero.

View larger version (23K): [in this window] [in a new window]   Fig. 3.   The time course of the mean and 95% confidence limits of the ratio of the (+) over the () concentrations of verapamil in blood from the arterial, coronary sinus and pulmonary artery sampling sites. If there were no differences in the kinetics of the enantiomers, this ratio would be 1. In fact, the 95% confidence limits of the data do not include 1 for some time points, which suggests enantiomeric differences in kinetics.

Lung kinetics of verapamil. The parameters and "goodness of fit" of the various models are shown in table 1. The flow-limited model was a poor fit of the data, principally because less verapamil left the lungs than entered during the experimental period. This could be addressed by adding a first-order extraction term of 22 to 26%, but a better fit was achieved by sequestering this "missing drug" in a relatively large "deep distribution" compartment in the membrane-limited model. This provided an excellent fit of the data (fig. 4) and good estimates of parameters. The ratio of permeability (PS, approximately 2 l/min) over flow (cardiac output, approximately 5.6 l/min) of approximately 0.3 places this model in the category that is both flow and membrane limited (Piiper and Scheid, 1981). The volume of this deep compartment differed between enantiomers.

View this table: [in this window] [in a new window]   TABLE 1 Lung kinetic models The parameters of the flow-limited (flow), flow-limited with extraction (flow + ER) and membrane-limited (membrane) lung kinetic models for each enantiomer. Goodness of fit is given by the R2 value and the MSC (see the text). A higher MSC indicates a better fit. The data are shown as the mean and upper and lower 95% confidence limits. An asterisk indicates that the value for the (+)-enantiomer was statistically different from that for the ()-enantiomer by comparison of the mean with the 95% confidence limits.

View larger version (20K): [in this window] [in a new window]   Fig. 4.   The line of best fit (solid line) of the membrane-limited model of lung kinetics for the (+)-enantiomer to the observed arterial (+)-verapamil concentrations (mean, open circles; 95% confidence limits, dotted lines).

Myocardial kinetics of verapamil. All three models were good descriptions of the data, with general agreement that the volume of the heart was about 1.1 l (table 2). A subtle improvement was gained by including the first-order loss, which was relatively small. However, this loss was not consistent with distribution into a deep compartment of the membrane-limited model, which gave a slightly worse fit and under-determined parameters (table 2). The first-order loss model provided a good fit of the data (fig. 5) and was used for the subsequent systemic modeling, this loss may be caused by diffusion of verapamil from the surface of the heart into pericardial fluid, which has been reported for other drugs (Huang and Upton, 1993). The differences in myocardial kinetics between the enantiomers were insignificant (table 2).

View larger version (18K): [in this window] [in a new window]   Fig. 5.   The line of best fit (solid line) of the single flow compartment with small first-order loss model of myocardial kinetics for the ()-enantiomer to the observed coronary sinus ()-verapamil concentrations (mean, open circles; 95% confidence limits, dotted lines).

Systemic kinetics of verapamil. For the (+)-enantiomer, the volumes (mean ± S.D.) of tissue pool 1, tissue pool 2 and the total clearance where 10.09 ± 2.28 l, 51 ± 66 l and 2.82 ± 0.87 l/min, respectively. For the ()-enantiomer, these values were 9.87 ± 2.49 l, 38 ± 15 l and 2.70 ± 0.77 l/min. With the exception of the volume of tissue pool 2 for the (+)-enantiomer, these were precise estimates, and the MSC was relatively good (2.92 for the (+) and 3.01 for the ()) for each enantiomer.

Pharmacodynamic effects of verapamil. Verapamil had profound effects on the heart (fig. 6). LV dP/dt_max decreased to 45% of base line at 3 min, whereas myocardial blood flow and PR interval increased to 213% and 141% of base line, respectively. Its hemodynamic effects were less pronounced. Cardiac output was increased transiently to a maximum of 122%, but was only statistically increased for a period from 0.5 to 2 min, whereas blood pressure was decreased transiently to a minimum of 90% of base line for a similar period. Heart rate was increased significantly from 1 to 6 min, with a peak increase of 131% of base line at 3.5 min.

View larger version (20K): [in this window] [in a new window]   Fig. 6.   The time courses of myocardial blood flow (Qh), the maximum rate of change of left ventricular pressure (LV dP/dtmax) and PR interval after the intravenous administration of 10 mg of racemic verapamil for 2 min (mean, open circles; 95% confidence limits, dotted lines). The solid line is the best fit of effect delay models relating the effect to the arterial ()-verapamil concentrations (Qh) and the coronary sinus ()-verapamil concentrations (LV dP/dtmax and PR interval) as given in table 3. The dashed line is the best fit of the combined dynamic models for both enantiomers without the small effect delay for these sites (table 4).

Pharmacokinetic-pharmacodynamic relationships. The effect delay half-lives for various concentrations and effects are shown in table 3. The changes in Q_h were well related to the time course of the arterial concentrations of each enantiomer, whereas the changes in PR interval were well related to the time courses of their coronary sinus concentrations. The LV dP/dt_max data were problematical in that the analysis showed they were slightly delayed relative to the arterial concentrations, but preceded the coronary sinus concentrations by a smaller amount (table 3), although the coronary sinus concentrations were substantially delayed relative to the arterial. This may have been because the time course of LV dP/dt_max did not have a well defined minimum value, and was at its minimum for a period of 2 to 3 min. Hysteresis analysis was conducted by quantitating the area under the curve of the ascending and descending limbs of concentration-effect plots (Huang et al., 1993). This showed that hysteresis was considerably smaller for the coronary sinus concentrations than for the arterial, so in subsequent analysis the changes in LV dP/dt_max were assumed to be a function of the coronary sinus (and therefore myocardial) concentrations.

View this table: [in this window] [in a new window]   TABLE 3 Effect delay half-lives The effect delay half-lives () of myocardial blood flow (Qh), the maximum rate of rise of left ventricular pressure (LV dP/dtmax) and A-V conduction (PR interval) relative to arterial and coronary sinus blood. The data are shown as the mean and upper and lower 95% confidence limits. A negative effect half-life indicates that the effect preceded the concentration indicated. An asterisk indicates that the value for the (+)-enantiomer was statistically different from that for the ()-enantiomer by comparison of the mean with the 95% confidence limits.

Combined kinetic-dynamic model. An E_max model was the most appropriate dynamic model for the combined effects of each enantiomer on Q_h, LV dP/dt_max and PR interval, giving the highest value of the MSC with precise estimation of parameters (table 4). The fits of the best models to the effect data are shown in figure 6.

View this table: [in this window] [in a new window]   TABLE 4 Combined effect model parameters The parameters of the best dynamic models for changes in myocardial blood flow (Qh), the maximum rate of rise of left ventricular pressure (LV dP/dtmax) and A-V conduction (PR interval) relative to arterial (Qh) and coronary sinus blood (LV dP/dtmax and PR interval) for both the (+)- and ()-enantiomers based on the potency ratios shown. An example of the equations of the dynamic models is shown in the text. The data are shown as the mean and upper and lower 95% confidence limits.

Implications of the model. The effect of altering the duration of administration of the same dose is shown in figure 7. The peak coronary sinus concentrations were delayed behind the end of injection by nearly 3 min for a 10-sec injection, but only 1 min for a 480-sec injection. For durations between 10- and 240-sec injections, the peak concentrations were within 95% of each other, whereas the value was 90% for the 480 sec injection. More rapid injections were associated with high transient arterial concentrations (fig. 7).

View larger version (32K): [in this window] [in a new window]   Fig. 7.   The effect of duration of injection of racemic verapamil on the time course of the concentrations of the ()-enantiomer in arterial blood and the heart.

View larger version (19K): [in this window] [in a new window]   Fig. 8.   Model predictions of the dose and duration of injection of verapamil required to achieve an approximately equivalent increase in PR interval (during 60 min) for different physiological states. The model was used to predict the time course of the effect of verapamil (10 mg) on slowing A-V conduction (increases in PR interval) for 60 min under normal conditions of cardiac output (Qco) and myocardial blood flow (Qh). A curve-fitting routine was then used to determine the simultaneous dose and duration of injection of verapamil best able to duplicate the same time course of effect over a range of values of Qco (3, 6 and 9 l/min) and Qh (50, 100 and 200 ml/min)

	Discussion

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Keefe and Kates (1982) have previously modeled the myocardial disposition of verapamil in dogs, and Powell et al. (1990) have examined the myocardial uptake of verapamil in humans. However, the present data apparently are the first in which myocardial uptake has been examined in an enantiomer-selective manner.

A comparison of the kinetics of ()- and(+)-verapamil. By nature, 10 mg of racemic verapamil contains 5 mg of each enantiomer. Therefore, in the absence of enantiomer-specific kinetics, the time courses of the concentrations of each enantiomer will be the same. Figure 1 shows that in broad terms this was the case. Modeling, however, revealed differences in the extent of deep distribution of the enantiomers into the lungs (table 1). This may have been sufficient to account for the observed differences in the time courses of each enantiomer (fig. 3).

The kinetic role of the lung. The lung plays an important role in bolus kinetics (Chiou, 1979; Jones and Nicholas, 1981; Roerig et al., 1989), whereby it can act as a "capacitor" for a drug between the injection site and its target organ. The greater the storage capacity of the lung, the greater the ability of the lung to damp the rapidly changing pulmonary artery blood concentrations caused by bolus injection (Upton and Huang, 1993). This appears to be the case for verapamil, for which a membrane-limited model with significant distribution volumes was found. This is compatible with the significant uptake (50%) of verapamil reported for the human lung (Roerig et al., 1989).

Heart kinetics. The apparent volume of the heart for both ()- and (+)-verapamil was approximately 1.1 l. Given that the mass of the heart tissue drained by the coronary sinus in sheep has been measured as 216 ± 37 g (Huang, 1991), this apparent volume equates to a heart/blood partition coefficient of approximately 5.1, which is similar to the value of 6.2 reported in dogs (Keefe and Kates, 1982) and 7.05 in humans (Padrini et al., 1985).

Kinetic-dynamic relationships. The importance of the myocardial concentration of verapamil in determining the magnitude of its effects on myocardial contractility and conduction has been shown in vitro (Chiba et al., 1978; Raschack, 1976) and in vivo (Gloor and Urthaler, 1983), and it has been shown that it is the concentration of the unionized form that is important in determining effects (Cohen et al., 1987). These data support the results of the present study and the use of the myocardial concentrations as the determinant of myocardial effects in the model. The fact that the changes in myocardial blood flow were better related to the time course of the arterial concentrations is intriguing. This suggests that flow changes are dictated by the concentration of verapamil in the arteries and arterioles of the heart, which rapidly equilibrate with arterial blood, rather than in the tissue of the heart which equilibrate more slowly.

Dose implications. The predictions of the model provide insight into the determinants of the myocardial uptake of verapamil, but still must be confirmed experimentally. They suggest, however, that the myocardial concentrations of verapamil are relatively insensitive to the duration of injection of a given dose because of the "damping" of the injected peak in the relatively high distribution volumes of the lungs and heart. The common clinical practice of infusion of a given dose of verapamil for 5 min is confirmed by these data. For this duration of injection, the peak myocardial concentrations could be expected to occur between 1 and 2 min after the end of the infusion. Thus, when titrating verapamil against a clinical indicator, this is predicted to be the minimum interval between doses required so that another dose is not injected before the maximum effect of the previous dose has been manifested.