A pharmacokinetic slide rule for more accurate drug treatment

Summary A slide rule has been devised which is based on the general mathematical models of pharmacokinetics. It permits calculation of exact dosage regimens for individual patients from certain basic parameters. First, from the patient's renal clearance, the proportionality constant characterizing renal excretion of a certain drug (a) and its non-renal rate constant of elimination (k _nr), the rate constant of total elimination (k _e) can be calculated. Second, fromk _e, the apparent volume of distribution (V _d) and the desired final mean concentration of a drug (c), exact values can readily be obtained for the loading dose (D*) and the dosage schedule, which consists of the maintenance dose (D), the dosing intervals () and the infusion rate for intravenous administration. In addition the slide rule provides information about the rate at which c is reached ifD alone is administered at , and the fluctuation in the concentration around c to be anticipated during . By use of this calculation, the slide rule facilitates the decision whether a loading dose should be given, and what dosage schedule is best suited to the therapeutic problem. It is possible, therefore, to calculate exact dosage regimens for individual patients, even for those with excretory dysfunction. The slide rule should also help physicians to comprehend the nature and significance of pharmacokinetic mechanisms.     

Variability in the Bioavailability of Phenytoin Capsules in Males and Females

Purpose. To determine inter-lot and intra-subject variability in the bioavailability of the 100 mg extended phenytoin sodium capsules. In addition, to determine the effect of gender and menstrual cycle on phenytoin bioavailability. Methods. Three different lots of extended phenytoin sodium capsules were given to 12 healthy male and 12 healthy female subjects in a crossover fashion. One of the lots was also given a second time to each subject. Plasma phenytoin was determined, using an HPLC assay, in samples collected over a 73-hr period after each dose. Results. The mean Cmax for the four administrations ranged from 1.71-1.79 g/ml and mean AUC(0-) values from ranged 53.0-54.1 g_*hr/ml. The elimination half-life was 3 hr shorter, and the AUC(0-) adjusted for the mg/kg dose was 30% lower for females. Average bioequivalence was demonstrated between the three lots for both Cmax and AUC(0-) based on the BE limit of 80-125%. Further, all confidence intervals of AUC(0-) fell within the limit of 90-111%. There were no differences in the confidence limits for Cmax and AUC(0-) determined separately for males and females. Also, there was no difference in the mean Cmax or AUC(0-) for females when analyzed as a function of the week of their menstrual cycle. Individual bioequivalence was demonstrated between three lots of phenytoin using the constant-scaled method, but not the reference-scaled method. Conclusions. There was very little difference in the bioavailability of the three lots of phenytoin. Females exhibited a lower AUC(0-) than males after adjustment of dose for body weight, but their inclusion in the study did not affect the assessment of bioequivalence. When dose was not adjusted for body weight, no difference in AUC(0-) was seen between males and females.     

Bioavailability assessment: Methods to estimate total area (AUC 0-∞) and total amount excreted (A e ∞ ) and importance of blood and urine sampling scheme with application to digoxin

Five methods are compared to estimate the total area under the digoxin plasma or serum concentrationtime curve (AUC0-) after a single dose of drug. To obtain accurate estimates of AUC0-, data required are concentrations at a sufficient number of sampling times to define adequately the concentration-time curve prior to the log-linear phase, and at least three, but preferably four or more equally spaced points in the terminal loglinear phase. One method (designated Method I) requires a digital computer; another (Method III) is the classical method (these two methods do not require equally spaced points in the loglinear phase). Method IIA is the accelerated convergence method of Amidon et al.; Methods IIB and IIC are modifications of this method, but incorporate usual and orthogonal least squares, respectively, which make them more accurate with real (noisy) data. Methods I and IICgave very comparable estimates of AUC0-. Results indicate that digoxin administered orally in aqueous solution was completely (100%) absorbed when bioavailability estimates were based on oral and intravenous AUC0- estimates and the actual doses, whereas formerly only about 80% absorption was reported, based on areas, under plasma concentration curves which were truncated at 96 hr. It is shown that the sampling scheme of blood can produce biased apparent bioavailability estimates when areas under truncated curves are employed, but an appropriate sampling scheme and application of method IIyield accurate bioavailability estimates. This is important particularly in those bioavailability studies where one is attempting to determine the appropriate label dose for a new fastrelease digoxin preparation relative to the label dose and bioavailability of currently marketed tablets. It is shown that the magnitudes and variability of apparent elimination rate constants and halflives of digoxin, estimated from urinary excretion data by the ^– method, depend on which value of A _e is used. The formerly reported greater interindividual variability of AUC data compared to At data for digoxin is explained in that the AUCs, but not the A_e,'s, involve the renal clearance, which exhibits considerable inter- and intraindividual variation.     

Simple Methods for Estimation of Mean Residence Time and Steady-State Volume of Distribution from Continuous-Infusion Data

The following equations are derived for amount of drug in the body (x _bss), volume of distribution (v _ss), and mean residence time in the body (t _b) at steady state during a continuous constant rate infusion of drug. x _bss = R/c _ss0 [c _ss - c(t)]dt = R₀ [1 - c(t)/c _ss]dt v _ss = x _bss/c _ss = R/c ² _ss0 [c _ss - c(t)]dt = R/c _ss0 [1 - c(t)/c _ss]dt t _b = x _bss/R = v _ss/CL = 1/c _ss0 [c _ss - c(t)]dt = ₀ [1 - c(t)/c _ss]dt where c(t) drug concentration in the systemic circulation at time t following the start of a constant-rate infusion, c _ss steady-state systemic drug concentration, and R infusion rate. The equations are based on the assumption that the rate of drug elimination is proportional to the systemic drug concentration. The equations provide the basis for simple methods that are presented for estimating x _bss, v _ss, and t _b directly from experimental data. More general relationships are also derived for cases where the continuous infusion is preceded by other modes of administration, e.g., a bolus loading dose followed by a constant-rate infusion.     

The effect of renal function on the pharmacokinetics of ranitidine

This open study evaluated the influence of renal function on the pharmacokinetics of ranitidine (50 mg iv infusion given over 6 min). Five groups, each of 8 subjects, 1 with normal renal function and 4 with different degrees of renal impairment were studied.Renal function was assessed in each patient by ⁵¹Cr-EDTA (glomerular filtration rate, GFR), creatinine clearance (GFR) and N-methylnicotinamide clearance (reflecting glomerular and tubular function). Sixteen blood samples (5 ml) taken up to 48 h post dose from each subject were analysed for plasma ranitidine concentrations by reversed phase HPLC.Patient groups with renal impairment had significantly increased AUC and t_1/2 with corresponding decreases in CL_p and _z when compared with normal subjects. There was also a significant increase in t_max but not in C_max. There was a high linear correlation between the degree of renal impairment and ranitidine clearance.In patients with GFR 20 ml min^–1, the AUC mean ratio (compared with normal subjects) was up to 4.6 while for patients with GFR 20–50 ml min^–1, the average AUC ratio was 2.6. It is recommended that the dose of ranitidine is halved in patients with GFR 20 ml min^–1.     

Subclassification of presynaptic 5-HT autoreceptors in the human cerebral cortex as 5-HT1Dβ receptors

Human cerebral cortical synaptosomes were used to determine the 5-hydroxytryptamine (5-HT) receptor subtype to which the inhibitory presynaptic 5-HT autoreceptor belongs. The synaptosomes preincubated with [³H]5-HT were superfused and tritium overflow was stimulated by high K⁺. The K⁺-evoked tritium overflow, which was Ca²⁺-dependent but tetrodotoxin-resistant, was concentration-dependently inhibited by the nonselective 5-HTlD_1D/1D receptor agonist, 5-carboxamidotryptamine. Ketanserin at a concentration which should block the 5-HT_1D but not the 5-HT_1D receptor failed to antagonize the inhibitory effect of 5-carboxamidotryptamine. In contrast, the non-selective 5-HT_1D/1D receptor antagonist, methiothepin, at a concentration which should block both the 5-HT_1D and the 5-HT_1D receptor abolished the effect of 5-carboxamidotryptamine. It is concluded that the presynaptic 5-HT autoreceptor, which has previously been classified as 5-HT_1D, belongs to the 5-HT_1D subtype.     

Simple model to explain effects of plasma protein binding and tissue binding on calculated volumes of distribution,apparent elimination rate constants and clearances

Summary A simple pharmacokinetic model, incorporating linear plasma protein binding, linear tissue binding, and first order elimination of free (unbound) drug, was studied. If Cl_p is the plasma clearance, V_f is the true volume of distribution of free drug, is the apparent elimination rate constant, is the fraction of the drug which is free in plasma, f is the fraction of the drug which is free in the entire body, k_f is the intrinsic elimination rate constant for free drug, and A _TB ^o is the initial amount of drug which is bound to tissues, then the model indicates that the following relationships hold: (1) Cl_p = V_f k_f; (2) = f k_f; and V_dext = (/f) V_f. Only , and not f, can be measuredexperimentally. Dividing Cl_p by provides an estimate of the intrinsic clearance of free drug, V_fk_f. A plot of V_dext versus has an intercept equal to V_f, and the ratio of the slope/intercept is an estimate of A _TB ^o /A _f ^o , where A _f ^o is the initial amount of free drug (equal to V_f times initial concentration of free drug in plasma). Thus, an estimate of A _TB ^o may be obtained. Dividing the intrinsic clearance by V_f provides an estimate of k_f. Thus, theoretically, estimates of V_f, k_f, A _TB ^o and f may be obtained. The variables are not separated when is plottedversus , and curvature of such plots is expected; no useful information is obtained from such plots.Partly supported by Public Health Service Grant 5-P-11-GM 1559 and partly by Grant 1RO1AAOO683-O1A1 from the National Institute on Alcohol Abuse and Alcoholism, Rockville, Maryland.     

Compartment- and model-independent linear plateau principle of drugs during a constant-rate absorption or intravenous infusion

A simple general equation is derived to show the linear plateau principle under various conditions during or after a constant or changing rate of absorption or intravenous infusion. The time required to cause a certain fraction (f_t) of the total shift or change between the two steady-state plasma concentrations is equal to the time required for the cumulative (from time zero) plasma area, AUC_0t, to reach the same fraction of AUC₀ assumed to be obtained after an instantaneousintravenous dosing. The role of the terminal biological half-life and the importance of the earlydistribution phase and its exponential half-life or lives in the plateau principle are discussed.Clinical implications and applications to multiple dosage regimens are also discussed.     

Estimation of area under the curve for drugs subject to enterohepatic cycling

A physiologically realistic model is used to provide insight into the design of sampling protocols for accurate determination of AUC(0– ) for drugs subject to enterohepatic cycling. Through simulation of plasma concentration- time curves for such drugs it is found that (1) more than one peak is predicted after oral and intravenous administration of a single dose of drug, (2) the relative magnitude of peaks is dependent on the hepatic extraction ratio for both oral and intravenous drug administration, (3) the percent of the AUC(0– ) in later time intervals is also a function of the hepatic extraction ratio, and (4) present methods for the design of sampling protocols may not provide accurate estimates of AUC(0– ) (especially for highly extracted drugs), because (a) peaks are only evident at later times after intravenous administration when plasma sampling is less frequent, (b) much of the area occurs at later times, and (c) the amount of drug in the sampling compartment after oral administration is much lower than that after intravenous administration of drug and could be incorrectly interpreted as low bioavailability if sampling is not carried out for a long period of time. The types of oral and intravenous profiles predicted for highly extracted drugs are exemplified by data for naltrexone in the monkey.During the course of this work Theresa A. Shepard was supported by a fellowship from the American Foundation for Pharmaceutical Education.     

Preparation of Heptakis(2,6-di-O-ethyl)-β-cyclodextrin and Its Nuclear Magnetic Resonance Spectroscopic Characterization

Heptakis(2,6-di-O-ethyl)--cyclodextrin (DE--CyD) was prepared and its ¹H and ¹³C nuclear magnetic resonance (NMR) signals in DMSO-d₆ were unequivocally assigned by two-dimensional COSY and ROESY. The results on ¹H coupling constants indicated that all ethylated glucose units are in a ⁴C₁ chair conformation. The average spin-lattice relaxation times (T ₁) of ring carbons of DE--CyD were only slightly shorter, and their standard deviations from the mean T _l value were larger, than those of -cyclodextrin (-CyD) and heptakis(2,6-di-O-methyl)--cyclodextrin (DM--CyD), suggesting the presence of slightly irregular internal motion in the ethylated glucose units. The temperature dependence of chemical shift of DE--CyD in DMSO-d₆ suggested that the C3 hydroxyl protons may participate as proton donor in the intramolecular hydrogen bond to the C2 ethoxyl groups of neighboring glucose, and the intramolecular hydrogen bond of DE- and DM--CyDs is much stronger than that of -CyD, suggesting the stable macrocyclic ring structure of DE--CyD.     

Effects of a new antiarrhythmic compound [2-benzal-1-(2′ diisopropyl-amino-ethoxy-imino)-cycloheptane hydrogen fumarate] on the electrophysiological properties of mammalian cardiac cells

Summary Intracellular microelectrodes were used to study the effects of Th 494 [2-benzal-1-(2diisopropyl-amino-ethoxy-imino)-cycloheptane hydrogen fumarate; 1–100 mol/l) on transmembrane electrical activity of sinus node and Purkinje fibres of the rabbit as well as on atrial trabeculae and papillary muscles of the guinea pig.In the atrial and in the ventricular myocardium (32° C; driving rate 0.3–0.5 Hz) Th 494 exerted the following electrophysiological actions: no change of the resting potential nor of the amplitude of the action potential; concentration-dependent reduction of the maximum rate of rise (dV/dt)_max of the action potential; slight increase of the action potential duration at lower concentrations (1–20 mol/l), loss of the plateau at higher concentrations (above 20 mol/l). The isometric force of contraction was moderately reduced by Th 494 (about 20% reduction by 2 mol/l). The h -curve relating (dV/dt)_max of the action potential to the membrane potential, was depressed by Th 494 without being shifted along the voltage axis. The reduction of (dV/dt)_max was considerably more pronounced at higher driving frequencies. After interruption of stimulation for various periods, (dV/dt)_max of the first action potential attained a steady-state value in a two-exponential fashion, suggesting use-dependence as well as a change of the recovery kinetics of the fast Na⁺ channel by Th 494.In Purkinje fibres (37° C) Th 494 reduced (dV/dt)_max in a similar manner. The duration of the action potential was considerably decreased at the level of the plateau. In the primary pacemaker region of the sinus node (37° C) Th 494 moderately reduced the rate of diastolic depolarization and diminished at higher concentrations the amplitude of the action potential. All effects of Th 494 were only slowly reversible by drug-free perfusion.In view of its effects on (dV/dt)_max, Th 494 resembles quinidine in its potential-dependence, whereas its time-dependence bears greater similarity with lidocaine.     

Pharmacokinetics of fluconazole after oral administration in children with human immunodeficiency virus infection

The objective of this study was to determine the pharmacokinetics of fluconazole after oral administration in children with human immunodeficiency virus (HIV) infection. After an overnight fast, a single dose of either 2 mg·kg^–1 or 8 mg·kg^–1 was administered in a suspension; five children received 2 mg·kg^–1 and four 8 mg·kg^–1 (ages 5–13 years). Blood samples were collected at various times on day 1, and once daily on days 2–7 after the dose. Fluconazole serum concentrations were measured by gas chromatography. At the dose of 2 mg·kg^–1, the C_max, AUC (0–), and t_1/2 ranged from 2.3–4.4 g·ml^–1, 84.9–136 g·h·ml^–1, and 19.8–34.8 h, respectively. At the dose of 8 mg·kg^–1 the C_max, AUC (0–), and t_1/2 ranged from 5.4–12.1 g·ml^–1, 330–684 gh·ml^–1, and 25.6–42.3 h, respectively. When compared with published data in healthy adults, fluconazole achieved similar serum concentrations in the present group of children, indicating a nearly complete degree of absorption.     

Metabolism,Distribution, and Transdermal Permeation of a Soft Corticosteroid,Loteprednol Etabonate

The soft corticosteroid, loteprednol etabonate (chloromethyl 17-ethoxycarbonyloxy-11-hydroxy-3-oxoandrosta-1,4-diene-17-carboxylate), I, was designed based on the inactive metabolite approach. Accordingly, I should be metabolized by hydrolysis to the corresponding inactive cortienic acid derivative, II. The in vitro and in vivo metabolism of I indeed yielded mainly this inactive metabolite, which is more hydrophilic and thus readily eliminated from the body. Relatively high levels of I were found in tissues after intravenous administration of the drug in rats. The permeability of I through hairless mouse skin was comparable to what has been found for related hard steroids, without significant metabolism taking place in the skin.     

The availability of orally administered nortriptyline

Summary The availability of an orally administered drug may be defined as the fraction of the total dose that enters the blood. Three healthy subjects were given identical doses of nortriptyline hydrochloride (NT-HCl) by the oral and intramuscular routes. The availability was assessed by comparing the total areas under the NT plasma concentration-time curves produced by the two methods of administration. The concentrations of NT in plasma and blood were determined by gas chromatography — mass spectrometry and were found to be almost identical. The observed availability of NT in these subjects ranged between 56 and 70% (mean 64%). The availability predicted from the parenteral plasma levels (assuming an average hepatic blood flow of 1.7 l/min) differed from the observed availability in one subject, perhaps because of the known variation in liver blood flow between individuals. The gastrointestinal absorption of NT-HCl was complete, since the recovery of the main metabolite, 10-hydroxynortriptyline, was the same after the two routes of administration. Pharmacokinetic analysis of the data showed that there might exist interindividual differences in the apparent volume of distribution of NT, (V_d). There was no apparent relationship between the variations in availability of NT and steady-state plasma levels or the disposition plasma half-lives of the drug. The calculated (V_d) and (t 1/2) of NT for each subject were in good agreement with those obtained from a previous study of single oral does of NT.     

Pharmacokinetics and pharmacodynamics of etizolam are influenced by polymorphic CYP2C19 activity

Objective To study the effect of erythromycin on metabolism of quetiapine in Chinese suffering from schizophrenia.Methods Nineteen patients received multiple doses of quetiapine (200 mg, twice daily) with or without co-administered erythromycin (500 mg, three times daily). Blood samples were collected at specified time intervals for determination of plasma concentrations of quetiapine and some of its metabolites.Results With erythromycin co-administration: for quetiapine, maximal plasma concentration (C _max), area under concentration–time curve of 0– h (AUC_0–) and terminal-phase elimination half-life time (t _1/2) increased 68, 129 and 92%, respectively, and clearance (CL) and terminal elimination rate constant (K _e) decreased 52% and 55%, respectively; for quetiapine sulfoxide (QTP-SF), C _max, AUC_0– and AUC ratio decreased 64, 23, and 70%, respectively, and t _1/2 increased 211%; for 7-hydroxy-quetiapine (QTP-H), K _e and AUC ratio decreased 61% and 45%, respectively, and t _1/2 increased 203%; for 7-hydroxy-N-desalkyl-quetiapine (QTP-ND), C _max, AUC_0– and AUC ratio decreased 36, 40 and 71%, respectively.Conclusion Erythromycin has a noticeable effect on the metabolism of quetiapine. When quetiapine is co-administered with CYP3A inhibitors such as erythromycin, the dosing regimen should be modified according to quetiapine TDM.     

Application of the Wagner-Nelson absorption method to the two-compartment open model

This report considers the application of the Wagner- Nelson method to both one- and two- compartment open model data when there is no competing reaction at the absorption site. Equations are derived which show that application of the Wagner- Nelson method to data which obey the twocompartment open model with first-order absorption allows accurate estimation of not only the rate constant k_a but also the parameters of the two- compartment open model, namely k₁₂, k₂₁, and k_el. In the example given, this new method was more accurate than the classical feathering or back- projection method. The appropriate criterion for collapsing the two- to the onecompartment open model is given. In cases where the one-compartment open model applies, and absorption is first order but abruptly ceases after some time, it is shown that k_a may be accurately estimated by application of the Guggenheim method to the A_T/V values calculated for the absorption phase.Supported in part by Public Health Service Grant 5-P11-GM15559.     

Applications of a recirculatory stochastic pharmacokinetic model: Limitations of compartmental models

General equations for the time integral on [0, ) of the venous drug concentrationtime function after intravenous and oral drug administration are derived. A physiologically realistic stochastic recirculating model is applied in the derivations. The quotient of the intravenous drug dose and the integral on [0, ) of the resulting venous blood drug concentration function is equivalent to a summation of organ clearances only provided that drug elimination does not occur in the pulmonary system, and in general it is not equivalent to total body clearance. In general, mammillary compartmental models are not isomorphic with recirculating models. A necessary condition for isomorphism is that the pulmonary system be conservative toward the drug. Equations for the pulmonary first-pass effect derived via the compartmental analysis are invalid. A valid expression for the pulmonary first-pass effect is derived. General equations derived via compartmental analysis for the extent of hepatic metabolism and the hepatic first-pass effect are shown to be valid. A generally applicable expression for the advantage of close intraarterial drug administration is derived. The limitations of compartmental models for representing drug distribution and elimination are discussed, and the advantages of recirculating models are emphasized.     

Protein binding of digoxin in human serum

Summary The protein binding of digoxin in human serum was investigated using equilibrium dialysis and tritium-labelled digoxin. A constant protein bound fraction of about 30% was found over a wide range of concentrations of digoxin including therapeutic levels. Interpretation of the findings according to the law of mass-action showed an association constantK = 0.68·10^–5l/mol; and, the number of binding sites,n , indicating an almost infinite apparent maximum binding capacity and a very small affinity of human serum proteins for digoxin.Supported by the Schweizer Nationalfond zur Förderung der wissenschaftlichen Forschung.     

Activation of β2-adrenoceptors by isoprenaline and adrenaline enhances noradrenaline release in cortical kidney slices of young spontaneously hypertensive rats

Summary The aim of the present study was to investigate -adrenoceptor modulation of noradrenaline release from sympathetic nerves in superfused cortical kidney slices of 4-week-old spontaneously hypertensive rats (SHR) and age-matched controls (WKY). After preincubation with ³H-noradrenaline the kidney slices were electrically stimulated in superfusion chambers. The stimulation induced (S-I) outflow of radioactivity was mainly composed of unmetabolized 3H-noradrenaline in both strains and thus taken as an index of noradrenaline release. There was a frequency-dependent (1.25–20 Hz) increase in the S-1 outflow of radioactivity. At all stimulation frequencies tested S-I outflow of radioactivity was similar or even slightly lower in SHR than in WKY kidney slices in either the absence or presence of cocaine (10 mol/l). The non-selective -adrenoceptor agonists isoprenaline (0.l gmol/1) and adrenaline (0.01 and 0.1 mol/l) enhanced S-I outflow of radioactivity. The facilitatory effects of isoprenaline (0.1 mol/l) and adrenaline (0.1 mol/l) were blocked by the selective ₂-adrenoceptor antagonist ICI 118551 (0.1 mol/l) but not by the selective ₁-adrenoceptor antagonist atenolol (0.3 mol/l). The cell-permeable CAMP analogue 8-bromo-cAMP (300 mol/l) enhanced S-1 outflow of radioactivity to a similar extent in both SHR and WKY kidney slices. A combination of 8-bromo-cAMP (300 mol/l) and adrenaline (0.1 mol/l) did not enhance S-1 outflow of radioactivity to a greater extent than 8-bromo cAMP (300 mol/l) alone in both strains. However, the facilitatory effects of isoprenaline (0.1 mol/l) and adrenaline (0.1 mol/l) but not that of adrenaline (0.01 mol/l) were significantly greater in SHR than in WKY. The results suggest that stimulation of prejunctional ₂-adrenoceptors by adrenaline even in the absence of a-adrenoceptor blockade enhances noradrenaline release in kidney cortex of young SHR and WKY. This ₂-adrenoceptor mediated effect may possibly be dependent on cAMP formation. The greater facilitatory effects of isoprenaline (0.1 mol/l) and adrenaline (0.1 mol/l) in SHR as compared to WKY are in accord with receptor binding studies which show a higher density of ₂-adrenoceptors in SHR than in WKY kidney cortex.Abbreviations SHR Spontaneously hypertensive rats - WKY WistarKyoto rats - cAMP 3-5-cyclic adenosine monophosphate - S-I stimulation induced Send offprint requests to: L. C. Rump