Comparison of four basic models of indirect pharmacodynamic responses

Four basic models for characterizing indirect pharmacodynamic responses after drug administration have been developed and compared. The models are based on drug effects (inhibition or stimulation) on the factors controlling either the input or the dissipation of drug response. Pharmacokinetic parameters of methylprednisolone were used to generate plasma concentration and response-time profiles using computer simulations. It was found that the responses produced showed a slow onset and a slow return to baseline. The time of maximal response was dependent on the model and dose. In each case, hysteresis plots showed that drug concentrations preceded the response. When the responses were fitted with pharmacodynamic models based on distribution to a hypothetical effect compartment, the resulting parameters were dose-dependent and inferred biological implausibility. Indirect response models must be treated as distinct from conventional pharmacodynamic models which assume direct action of drugs. The assumptions, equations, and data patterns for the four basic indirect response models provide a starting point for evaluation of pharmacologie effects where the site of action precedes or follows the measured response variable.Glossary C _e Drug concentration at the hypothetical effect site - C _p Plasma concentration of drug - C _p(T_max) Plasma concentration of drug at the time of maximal response - D Dose - EC ₅₀ Drug concentration producing 50% of maximum stimulation at effect site - E _max Maximum effect attributed to drug - E _o Baseline effect prior to drug administration - IC ₅₀ Drug concentration producing 50% of maximum inhibition at effect site - K _el First-order rate constant for drug elimination - K _eo First-order rate constant for drug loss from effect site - K _in Zero-order rate constant for production of drug response - K _out First-order rate constant for loss of drug response - n Sigmoidicity factor of the sigmoid E_max equation - R Response variable - R_max Maximal (or minimal) response - R_o Initial response (time zero) prior to drug administration - t time after drug administration - T Infusion time - T_max Time to reach maximum effect following drug administration - V Volume of distribution Supported in part by Grant No. 24211 from the National Institutes of General Medical Sciences, National Institutes of Health.     

Disposition kinetics in dogs of diethyldithiocarbamate,a metabolite of disulfiram

Following the intravenous infusion of sodium diethyldithiocarbamate to dogs, the disposition kinetics of diethyldithiocarbamate (DDC), a metabolite of disulfiram, were assessed. Approximately 27% of the administered dose was S-methylated, this process exhibiting a mean first-order rate constant of 0. 0569 min^–1 (t_1/2=12.2 min), while the remainder was eliminated by other routes having a rate constant of 0.148 min^–1 (t_1/2=4.68 min). The methyl diethyldithiocarbamate (MeDDC) formed from DDC showed an elimination rate constant of 0.0141 min^–1 (t_1/2=49.2 min). These observations are discussed in the light of previous investigations where the presence of MeDDC has rarely been sought or reported. A few comparisons with prior studies, in which DDC or disulfiram was administered, are made by retrospective kinetic evaluation of published data. The results are discussed in relation to the duration of action of disulfiram in man.Glossary A plasma concentration intercept at the cessation of infusion (mass/volume) - A _T simplifying constant (mass/volume/time) - AUC _M area under the plasma concentration-time curve for MeDDC (mass × time/volume) - b time variable; equalst during infusion, equalsT after the cessation of infusion - B plasma concentration intercept at the cessation of infusion (mass/volume) - B _T simplifying constant (mass/volume/time) - C _D plasma concentration of DDC at any timet (mass/volume) - C _M plasma concentration of MeDDC, expressed as DDC, at any timet (mass/volume) - C _T plasma concentration of total DDC, expressed as DDC, at any timet;C _T=C_D+C_M (mass/volume) - C _t plasma concentration of total DDC, expressed as DDC, at any timet (mass/volume) - Cl _D total body clearance of DDC (volume/time) - Cl _M total body clearance of MeDDC (volume/time) - DDC diethyldithiocarbamate - f fraction of DDC that is methylated;f=K _DM/K _D - K _A apparent first-order rate constant (reciprocal time) - K _B apparent first-order rate constant (reciprocal time) - K _D apparent first-order rate constant for the elimination of DDC by all routes (reciprocal time) - K _M apparent first-order rate constant for the elimination of MeDDC by all routes (reciprocal time) - K _DE apparent first-order rate constant for the elimination of DDC by all routes except methylation (reciprocal time) - K _DM apparent first-order rate constant for theS-methylation of DDC (reciprocal time) - MeDDC methyl diethyldithiocarbamate - NaDDC sodium diethyldithiocarbamate (trihydrate) - Q zero-order infusion rate constant (mass/time) - Q ₁ zero-order infusion rate constant for the faster of two consecutive infusions (mass/time) - Q ₂ zero-order infusion rate constant for the slower of two consecutive infusions (mass/time) - t elapsed time since dosing (e.g., infusion) commenced - t elapsed time since the cessation of infusion - T duration of infusion (time) - T ₁ duration of the faster of two consecutive infusions (time) - T ₂ total duration of infusion when two consecutive infusions are administered (time) - V _D apparent volume of distribution of DDC - V _M apparent volume of distribution of MeDDC This work was supported by the Atkinson Charitable Foundation (Toronto, Ontario, Canada) and the Non-Medical Use of Drugs Directorate, Health and Welfare Canada (Grant No. 1212-5-206).     

Computer simulation of sulfobromophthalein kinetics in the rat using flow-limited models with extrapolation to man

A linear, flow-limited mathematical model of drug kinetics was used to simulate total sulfobromophthalein (BSP) kinetics in normal anesthetized rats during intravenous infusions and following rapid intravenous injections. Four parameters were used to characterize the distribution and biliary and urinary excretion of BSP: liver- to- plasma concentration ratio, extrahepatic tissue- to- plasma concentration ratio, liver clearance rate constant, and renal plasma clearance rate constant. The same parameters appear to characterize the kinetics of BSP in man through the successful application of scale- up techniques utilizing data from experiments in rats. Plasma levels of BSP corresponding to intravenous infusions and rapid intravenous injections in man are approximated by computer simulation.The notation used is that of Bischoff et al. (2) with a few additions C _p BSP concentration in plasma - C _l BSP concentration in liver - C _bi BSP concentration in bile compartmenti, i = 1,2,3 - C _m BSP concentration in extrahepatic tissue - V _p volume of plasma - V _l volume of liver - V _b volume of bile - V _m volume of extrahepatic tissue - Q _l plasma flow rate through liver - Q _m plasma flow rate through extrahepatic tissue - Q _b bile flow rate through biliary tract - R _l hepatic tissue-to-hepatic venous plasma concentration ratio of BSP - R _m extrahepatic tissue-to-extrahepatic venous plasma concentration ratio of BSP - k _l hepatic tissue elimination rate constant for BSP - k _k renal plasma clearance rate constant for BSP - f(t) infusion rate function - f _i volume of bile in the bile duct compartment as a fraction of the total bile volume V_b     

Combined recirculation of the rat liver and kidney: Studies with enalapril and enalaprilat

Combined recirculation of the rat liver (L) and kidney (IPK) at 10 ml min^–1 per organ (LK) was developed to examine the hepatorenal handling of the precursor-metabolite pair: [¹⁴C]-enalapril and [³H]enalaprilat. Loading doses followed by constant infusion of [¹⁴C]enalapril and preformed [³H]enalaprilat to the reservoirs of the IPK or the LK preparation was used to achieve steady stale conditions. In both organs, enalapril was mostly metabolized to its dicarboxylic acid metabolite, enalaprilat, which was excreted unchanged. At steady state, the fractional excretion for [¹⁴C]enalapril (FE=0.45 to 0.48) and preformed [³H]enalaprilat (FE{pmi}=1.1) were constant and similar for both the IPK and LK. The additivity of clearance was demonstrated in the LK preparation, namely, the total clearance of enalapril was the sum of its hepatic and renal clearances. However, the apparent fractional excretion for fanned [¹⁴C]enalaprilat, FE{mi} and the apparent urinary clearance were time-dependent and higher than the corresponding values for preformed [³H]enalaprilat in both the IPK and LK. The FE{mi} and urinary clearance values further differed between the IPK and LK. Biliary clearance of formed vs. preformed enalaprilat displayed the same discrepant trends as observed for FE{mi} vs. FE{pmi} for the LK. These observations on the time-dependent and variable excretory clearance (urinary or biliary) of the formed metabolite vs. the constant, and much reduced, excretory clearance of the preformed metabolite are due to dual contributions to formed metabolite excretion: the nascently formed, intracellular metabolite which immediately underwent excretion and the formed metabolite which reentered the circulation, behaved as a preformed species. When data for the IPK and LK preparations were modeled with a physiological model with parameters previously reported for the L and IPK, all data, including metabolite excretory clearances, were well predicted. Model simulations revealed that the apparent FE{mi} differed between the LK and IPK preparations when the liver was present as an additional metabolite formation organ; the apparent excretory (urinary orGlossary k⁰ infusion rate into the reservoir - C_R reservoir concentration - C_Out,k and C_Out,L venous concentrations for the kidney and liver - C_p,k and c_P,L concentrations in renal and hepatic plasma, respectively - C_k and C_L concentrations in kidney and liver tissue, respectively - C_U and C_Bile concentrations in urine and bile, respectively - CL _b ⁱⁿ andCL _b ^ef influx and efflux clearances, respectively, at the basolateral membrane of the renal tubular cell - C _l ⁱⁿ and CL _l ^ef influx and efflux clearances, respectively, at the luminal membrane of the renal tubular cell - CL _int,K ^m renal metabolic intrinsic clearance of the drug - CL _d ⁱⁿ and CL _d ^ef influx and efflux clearances, respectively, at the sinusoidal membrane - CL _int ^m,L hepatic metabolic intrinsic clearance of the drug - CL _int,L ^b biliary intrinsic clearance - V_R plasma reservoir volume - V_P,K and V_P,L plasma volumes of the kidney and liver, respectively - V_K and V_L tissue volumes of the kidney and liver, respectively - V_U and V_Bile volumes of urine and bile, respectively - Q_K and Q_L total renal and hepatic plasma flow rates, respectively - GFR glomerular filtration rate - Q_U and Q_Bile urine and bile flow rates, respectively - f_P, f_K, and f_L unbound fractions in plasma and kidney and liver tissue, respectively This work was supported by the Medical Research Council of Canada. I. A. M. de Lannoy was a recipient of the Ontario Graduate Scholarship from the Ontario Ministry of Health; K. S. Pang was a recipient of the Faculty Development Award, Medical Research Council.     

Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse laplace transform (FILT)

A dispersion model developed in Chromatographic theory is applied to the analysis of the elution profile in the liver perfusion system of experimental animals. The equation for the dispersion model with the linear nonequilibrium partition between the perfusate and an organ tissue is derived in the Laplace-transformed form, and the fast inverse Laplace transform (FILT) is introduced to the pharmacokinetic field for the manipulation of the transformed equation. By the analysis of the nonlinear least squares method associated with FILT, this model (two-compartment dispersion model) is compared to the model with equilibrium partition between the perfusate and the liver tissue (one-compartment dispersion model) for the outflow curves of ampicillin and oxacillin from the rat liver. The model estimation by Akaike's information criterion (AIC) suggests that the two-compartment dispersion model is more proper than the one-compartment dispersion model to mathematically describe the local disposition of these drugs in the perfusion system. The blood space in the liver, V_B, and the dispersion number D_N are estimated at 1.30 ml (±0.23 SD) and 0.051 (±0.023 SD), respectively, both of which are independent of the drugs. The efficiency number, R_N, of ampicillin is 0.044 (±0.049 SD) which is significantly smaller than 0.704 (±0.101 SD) of oxacillin. The parameters in the two-compartment dispersion model are correlated to the recovery ratio, F_H, mean transit time, ¯t_H, and the relative variance, ²/¯t_H ², of the elution profile of drugs from the rat liver.Notation A Cross-sectional area of the blood space - C(t, z) Concentration of drug (one-compartment dispersion model) - C(s, z) Laplace transform of C(t, z) - C ₁(t, z) Concentration of drug in blood space (two-compartment dispersion model) - C ₂(t, z) Concentration of drug in the liver tissue (two-compartment dispersion model) - C ₁ (s, z) Laplace transform ofC ₁(t, z) - D Axial or longitudinal dispersion coefficient - D _c(=D· A ²) Corrected dispersion coefficient - D _N Dispersion number - f _I(t) Input function with respect tot - f_I(z) Input function with respect toz - F_I(s) Laplace transform of f_I(t) - f_s(t) System weight function with respect tot - f_s(z) System weight function with respect to z - F_H Recovery ratio - k Partition ratio (distribution ratio) - k₁₂, k₂₁ Forward and backward partition rate constant in the central elimination two-compartment dispersion model - k ₁₂ ^p ,k ₂₁ ^p Forward and backward partition rate constant in the peripheral elimination two-compartment dispersion model - k_e Elimination (or irreversible transfer) rate constant - k _e ^p Elimination rate constant in peripheral elimination model - K_H Distribution constant - L Length of blood space in liver - M Amount of drug injected - m Coefficient related to the injected amount - p_h Mass transfer coefficient from perfusate to hepatic tissue - Q Flow rate of perfusate - R_N Efficiency number - s Laplace variable - t Time - ¯ t_H Mean transit time - Linear flow velocity of the perfusate - V _B(= L·A) Blood volume (sum of the sinusoid volume and the space of Disse) - v_h Apparent volume of distribution - V _H Anatomical volume of liver tissue - z Axial coordinate in the liver - (t) Delta function - Volume ratio of the anatomical liver tissue to the blood space - ² Variance of transit time - ²/¯t _H ² Relative dispersion to transit time - Partial derivatives     

双室模型药物静脉输注方案的数学探讨

静脉输注是临床上广泛用于抢救危重病例的一种有效的给药方法,缺点是开始输注时血药浓度偏低。为了使血药浓度迅即达到临床治疗的最佳有效血药浓度,有一种简便易行的方法是在开始时立即静注一个底药剂量,同时以恒定速度进行静脉输注,以维持该血药浓度。这种静脉输注方案的关键问题在于采用何种底药剂量和以何种速度静脉输注。对于双室模型的药物,1971年及1972年Boyes及Mitenko先后提出了两种不同的静脉输注方案。本文用组合曲线求组合常数的方法推导出了介于上述两种方案之间的一种新的静脉输注方案,给出了这种新方案的“血药浓度一时间”曲线公式,并从理论上证明这种方案的优越性。     

Dose-effect curves and relative biophasic drug levels: Elucidation of these concepts and the illustration of their use for the determination of bioavailability,rate of absorption,and time course of pharmacological response

The theoretical basis for the development of dose-effect curves, linear dynamic models, and relative biophasic drug levels as derived from pharmacological response intensity is presented. The presentation is kept sufficiently rigorous to demonstrate the theoretical soundness of the concepts, yet each concept is clearly explained and related to physical experimental variables so as to be physically meaningful. The use of these concepts for the determination of bioavailability, rate of absorption, and time course of drug action is demonstrated.Notation A _i amplitude coefficients for impulse response equations - BDA biophasic drug availability - CA cumulative amount of drug absorbed - C _p concentration of drug in the plasma - D magnitude of impulse input - D relative biophasic drug level - f(I) relative biophasic drug level (7) - G(s) transfer function for system - I intensity of pharmacological response - m _i time constant for impulse response equation - n number of compartments in the system - PDA physiological drug availability - Q _B biophasic drug level - RBA relative biophasic drug availability - s Laplace transform variable - SDA systemic drug availability - STD. standard dose - t time, the independent variable - u(t) unit impulse input - V _D volume of distribution - U(s) Laplace transform of unit impulse input - _t a function of time, defined by equation 1     

Effect of serum protein binding on pharmacokinetics and anticoagulant activity of phenprocoumon in rats

The relationship among serum protein binding, kinetics of elimination, distribution, and anticoagulant activity of phenprocoumon was investigated in 25 selected outbred Sprague-Dawley rats which differed in the extent of serum protein binding of this drug. In addition, the serum protein binding of phenprocoumon was altered in inbred Lewis rats by continuous treatment with tolbutamide. This drug was found to displace phenprocoumon from serum proteins without affecting its intrinsic clearance. The serum free fraction values (f_s)of the selected Sprague-Dawley rats ranged from 0.0053 to 0.0145. There were positive and linear correlations between f_s and the first-order elimination rate constant (k), f_s and total clearance (CL _total ),and f_s and the liver/plasma concentration ratio (L/P ratio) of phenprocoumon. The free fraction values in the liver tissue (f _I )showed twofold variations and were not related to f_s.The half-effective plasma concentrations (C _p50% )of total phenprocoumon (i.e., the concentrations necessary to inhibit the prothrombin complex synthesis rate by 50%) decreased with increasing f_s.The C_p50% values of total drug varied eightfold between the animals but those of free drug only 3.5- fold. The total anticoagulant effect per dose (AE/dose), as reflected by the magnitude of the area above the prothrombin complex activity vs. time curve in the plasma, varied only 1.5- fold between the rats and was not related to f_s.Continuous treatment of inbred Lewis rats with tolbutamide led to an increase of f_s (twofold), k (1.3-fold), V_d (1.5-fold), and CL_total (twofold). The intrinsic clearance (CL _intr )remained unaffected. There was no significant increase of f_L but a twofold increase of the L/P ratio. AE/dose and the C_p50% values of free drug in tolbutamide-treated rats were not significantly different from those of control rats. Thus an increase of the free fraction of phenprocoumon in the serum of rats is followed by a proportional increase of the total clearance. This prevents a concomitant rise of the free drug concentration. Consequently, the total anticoagulant effect per dose remains almost unaffected by about threefold variations in the serum free fraction values of this drug.This work was supported by the Deutsche Forschungsgemeinschaft: it is part of the Ph.D. thesis for D. T.     

Pharmacokinetics of sulfaethidole in the rat: Nonlinear multicompartment solution

Sulfaethidole distribution and elimination in the rat was studied over a 90-fold dose range. This experimental design produced marked nonlinearity in the binding of Sulfaethidole to proteins in both interstitial fluid and plasma. Using a multicompartmental model consisting of binding of Sulfaethidole to plasma and interstitial fluid proteins, Sulfaethidole distribution in the body could be simulated. Urinary and biliary elimination of Sulfaethidole depended on the unbound drug mass in the plasma and urine flow. The results confirm the central role of the unbound species in the distribution and elimination of drugs with marked binding to plasma proteins.Nomenclature A ₁ amount of drug in plasma (mg) - A ₂ amount of drug in interstitial fluid (mg) - A ₃ amount of drug in poorly perfused tissues (mg) - A ₄ amount of drug in highly perfused tissues (mg) - fu ₁ fraction of total drug in plasma unbound (dimensionless) - fu ₂ fraction of total drug in interstitial fluid unbound (dimensionless) - fb ₁₁ fraction of drug bound to first binding site on plasma protein (dimensionless) - fb ₁₂ fraction of drug bound to second binding site on plasma protein (dimensionless) - fb ₂₁ fraction of drug bound to first binding site on interstitial fluid protein (dimensionless) - fb ₂₂ fraction of drug bound to second binding site on interstitial fluid protein (dimensionless) - K _d,1 apparent dissociation constant of first binding site on protein (dimensionless) - K _d,2 apparent dissociation constant of second binding site on protein (dimensionless) - B _max,11 ^–1 inverse of maximal binding capacity of first binding site on plasma protein (ml/mg) - B _max ^12–1 inverse of maximal binding capacity of second binding site on plasma protein (ml/mg) - B _max,21 ^–1 inverse of maximal binding capacity of first binding site on interstitial fluid protein (ml/mg) - B _max,22 ^–1 inverse of maximal binding capacity of second binding site on interstitial fluid protein (ml/mg) - k ₁₂ fractional transport rate of unbound drug from plasma to interstitial fluid (h^–1) - k ₂₁ fractional transport rate of unbound drug from interstitial fluid to plasma (h^–1) - k ₂₃ fractional transport rate of unbound drug from interstitial fluid to poorly perfused tissues (h^–1) - k ₃₂ fractional transport rate of unbound drug from poorly perfused tissues to interstitial fluid (h^–1) - k ₁₀ fractional rate of elimination of unbound drug from plasma (h^–1) - k ₁₀ ⁰ value during the first 210 min - k ₁₀ ¹ value after 270 min, linearly increased between 210 and 270 min (Eq. 5) - fup _t fraction of instantaneous binding of drug between plasma unbound drug and highly perfused tissue (dimensionless) - V _p plasma volume (ml) - V _is interstitial fluid volume (ml)     

Clinical pharmacokinetics of procainamide infusions in relation to acetylator phenotype

The pharmacokinetics of procainamide was determined in 21 lidocaine-resistant patients who received the drug according to a pharmacokinetically designed double-infusion technique. Thirteen patients were phenotyped as slow acetylators, seven as fast, and one as intermediate. The total body clearances (Cl_T) of PA in slow and fast acetylators were 22.6 and 34.8 liters/hr, respectively. The fraction of PA cleared by the formation of NAPA in the corresponding acetylator group was 0.2 and 0.4. Renal impairment affected the pharmacokinetics of PA more profoundly as the Cl_Ts of PA in patients with and without renal impairment were 17.9 and 31.2 liters/hr, respectively. None of the calculated volumes of distribution was affected by acetylator phenotype or renal impairment. These data identify the contribution of at least two of the major factors accounting for variability in PA disposition in patients undergoing therapy.Glossary PA Procainamide - NAP A N-Acetylprocainamide - LI Loading infusion - MI Maintenance infusion - V _p Volume of central compartment for PA - V _t Volume of tissue compartment for PA - V _ss ^d Volume of distribution of PA at steady state - V _d Volume of distribution of PA during postdistributive phase - Cl₁₂ Intercompartmental clearance of PA - Cl _T Total body clearance of PA - Cl _R Renal clearance of PA - Cl _A Acetylation clearance of PA - Cl_AP Apparent acetylation clearance of PA - Cl _M Metabolic (nonacetylation) clearance of PA - C _PA Serum concentration of PA - C _t Tissue concentration of PA - C _PA ^ss Steady-state serum concentration of PA - V _n Volume of distribution of NAPA - Cl _N Renal clearance of NAPA - Cl₀ Nonrenal clearance of NAPA - Cl_BN Total body clearance of NAPA - C _NAPA Serum concentration of NAPA - C _N ^ss Steady-state serum concentration of NAPA This work was supported by Grants 20852 and 24211 from the National Institutes of General Medical Sciences, National Institutes of Health.     

Nonlinear elimination and hepatic concentration of conjugation- metabolite of valproate in guinea-pigs

The plasma clearance and metabolic rate characteristics of valproic acid (VPA) were studied using guinea-pigs placed on various (0.08-9 μmol ml^?1 = 11–1303 μg ml^?1) steady-state plasma concentrations (C_ss) by constant intravenous (i.v.) infusion. The total clearance (CL) was significantly decreased at plasma concentration of 0.61 μmol ml^?1 (88 μg ml^?1). The metabolic clearance of VPA was apparently biphasic. The maximum metabolic rate (V_max) and the Michaelis-Menten constant (K_m) for the primary (V_maxl, K_ml) and the secondary (V_max2, K_m2) pathways were V_maxl = 1.52 μmol min ^?1kg^?1, K_ml = 0.15 μmol ml^?1, V_max2 = 24.98 μmol min ^?1 kg^?1 and K_m2 = 11.70 μmol ml^?1, respectively. The K_ml value was within clinical therapeutic concentration range. The formation of conjugated VPA (cjVPA) metabolite in liver was shown to be saturable. Plasma protein binding of VPA was also nonlinear. The dose-dependent decrease in metabolic clearance was counterbalanced by the increased unbound fraction (f_u), resulting in a relatively constant apparent clearance of VPA over a wide concentration range. The hepatic concentration of VPA was not significantly different from the plasma unbound concentration, again over a wide concentration range. The biliary and hepatic concentrations of VPA were not significantly different; but the concentration ratio of cjVPA in bile compared with that of VPA in liver decreased against hepatic concentration of VPA, which suggests a saturable conjugation rate. The K_m value estimated from hepatic cjVPA production as a function of plasma VPA concentration was comparable with the K_ml value. These results implied that the primary metabolic parameters may describe the conjugation pathway which is nonlinear within the clinical therapeutic concentration range.     

DOSE-DEPENDENT DISTRIBUTION VOLUMES OF TOTAL AND UNBOUND VALPROATE IN GUINEA-PIGS: CONSEQUENCE OF NON-LINEAR PLASMA PROTEIN BINDING

The response of steady-state distribution volume (V_dss for total and V_dssu for unbound drug) of valproate (VPA) to dose-dependent plasma protein binding was studied in guinea-pigs. Various steady-state plasma concentrations of VPA were achieved by intravenous constant infusion. The concentrations of VPA in plasma (C_ss for total and C_uss for unbound drug) and various tissues (C_T) were determined. The V_dss and the V_dssu were estimated based upon the apparent tissue-to-plasma concentration ratio of VPA. The results showed that the plasma unbound fraction (f_u) of VPA increased significantly with dose. The V_dss was significantly increased with, while the V_dssu was significantly decreased against the increasing dose. The increase in V_dss with dose indicated an increase in tissue-to-plasma concentration ratio, which may be attributed to the increase in distribution of unbound drug from plasma to tissues subsequent to non-linear plasma protein binding. The decrease in V_dssu against the increasing dose indicated a decrease in tissue-to-unbound plasma concentration ratio, which suggests that the extravascular distribution of unbound VPA might be capacity limited and the tissue binding of VPA negligible.     

Drug pharmacokinetics and the carbon dioxide breath test

The interrelationship of the pharmacokinetics of a drug and the expiration of carbon dioxide formed as a metabolite have been studied. The pharmacokinetic characteristics of the drug that affect the usefulness of the carbon dioxide excretion as a measure of liver function were examined by means of computer simulations. The parent drug extraction ratio, fraction demethylated, volume of distribution, and absorption rate of an oral dosage form all contribute to the carbon dioxide breath test result. A drug that would be a useful substrate when the carbon dioxide breath test is used as a probe for changes in liver function should be at least 50% metabolized by demethylation, have a hepatic extraction ratio of 0.2–0.5, and be administered in a form that is rapidly absorbed.Appendix b. symbols CL _c net clearance of formaldehyde to carbon dioxide - CL _int,f intrinsic hepatic clearance of formation of formaldehyde from parent drug (bound and unbound to plasma proteins) - CL _int,p intrinsic hepatic clearance of total parent drug (bound and unbound to plasma proteins) - CL _sys,f systemic hepatic clearance of formation of formaldehyde from parent drug,Q _H CL _int,f /(Q _H +CL _int,p ) - CL _sys,p systemic hepatic clearance of parent drug,Q _H CL _int,p /(Q _H +CL _int,p ) - E extraction ratio,CL _int,p /(Q _H +CL _int,p - F I-E fraction escaping first-pass metabolism,Q _H/(Q _H +CL _int,p - fm fraction of parent drug metabolized by demethylation to formaldehyde,CL _int,f /CL _int,p - HCHO amount of formaldehyde - [HCHO] concentration of formaldehyde - _a absorption rate constant - M _i metabolite of P formed by routes other than demethylation - M ₁ metabolite of P formed by demethylation - P amount of parent drug in the body - [P] concentration of parent drug measured in arterial blood - P _A amount of parent drug at absorption site - P _L amount of parent drug in the liver - Q _H hepatic blood flow - V _F volume of distribution of formaldehyde - V _p volume of distribution of parent drug     

The effect of HPMC—a cholesterol-lowering agent—on oral drug absorption in dogs

The objective of this study was to evaluate the effects which hydroxypropylmethylcellulose (HPMC) may exert on oral drug absorption, in cases where this soluble fiber is administered to regulate blood lipid levels. Studies were conducted in vitro and in healthy female mongrel dogs using two different grades of HPMC, i.e. K8515 HPMC and ultra high molecular weight (UHMW) HPMC. The maximum plasma concentration, C_max, of paracetamol and both the C_max and the area under the concentration–time curve, AUC, of cimetidine were significantly decreased by the coadministration of 10 g of K8515 HPMC or 7.5 g of UHMW HPMC dissolved in 500 mL normal saline under fasting conditions. No statistically significant effects were observed on hydrochlorothiazide or mefenamic acid absorption. Based on in vitro data and previous studies it appears that reductions in gastric emptying and dissolution rate of paracetamol account for the effect observed in vivo. For cimetidine, a drug which can be absorbed from both the small and the large intestine, the indigestibility of HPMC in the colon in addition to the great reduction of dissolution rate led to reductions of both the C_max and AUC values. The long T_max values, even in the absence of HPMCs and the more modest reduction of the dissolution rate of hydrochlorothiazide by the HPMCs are thought to have precluded the observation of any significant alterations in the in vivo absorption profile. Owing to its erratic absorption, no statistically based conclusion could be drawn about the effects of coadministered HPMC on the oral absorption of the poorly soluble mefenamic acid. It is concluded that the effects of HPMCs on drug absorption in dogs are most pronounced for compounds with absorption profiles that are dependent on gastric emptying, i.e. compounds that are highly water soluble and that exhibit short T_max values. Compounds with long absorption profiles appear to be less susceptible to changes in absorption behavior due to coadministration of HPMCs. Copyright © 1998 John Wiley & Sons, Ltd.     

二室模型药物“静注十静滴”的给药方案计算

本文对静脉注射一定剂量,同时以一定速度恒速静脉滴注,提出了一类确定静注剂量和静滴速度的方法。按这类方法确定的给药方案用药时,可确保从用药一开始直至用药结束,血药浓度一直在有效血药浓度范围内变化。     

Formed and preformed metabolite excretion clearances in liver,a metabolite formation organ: Studies on enalapril and enalaprilat in the single-pass and recirculating perfused rat liver

Single-pass and recirculating rat liver perfusion studies were conducted with [¹⁴C]enalapril and [³H] enalaprilat, a precursor-product pair, and the data were modeled according to a physiological model to compare the different biliary clearances for the solely formed metabolite, [¹⁴C]enalaprilat, with that of preformed [³H]enalaprilat. With single-pass perfusion, the apparent extraction ratio (or biliary clearance) of formed [¹⁴C]enalaprilat was 15-fold the extraction ratio of preformed [³H] enalaprilat, an observation attributed to the presence of a barrier for cellular entry of the metabolite. Upon recirculation of bolus doses of [¹⁴C]enalapril and [³H]enalaprilat, the biliary clearance, estimated conventionally as metabolite excretion rate/midtime metabolite concentration, for formed [¹⁴C]enalaprilat was again 10-to 15-fold higher than the biliary clearance for preformed [³H]enalaprilat, but this decayed with perfusion time and gradually approached values for preformed [³H]enalaprilat. The decreasing biliary clearance of formed enalaprilat with recirculation was explained by the dual contribution of the circulating and intrahepatic metabolite (formed from circulating drug) to excretion. Physiological modeling predicted (i) an influx barrier (from blood to cell) at the sinusoidal membrane as the rate-limiting process in the overall removal of enalaprilat, (ii) a 15-fold greater extraction ratio or biliary clearance for formed [¹⁴C]enalaprilat over [³H]enalaprilat during single-pass perfusion, and (iii) the time-dependent and declining behaviour of the biliary clearance for formed [¹⁴C]enalaprilat during recirculation of the medium. In the absence of a direct knowledge of eliminating organs in vivo, this variable pattern for excretory clearance of the formed metabolite within the organ is indicative of a metabolite formation organ.Glossary C _R denotes the reservoir concentration - C _In andC _Out,L respectively, denote the input and output concentrations. - Q _L is the total hepatic plasma flow rate. - Q _Bile is the bile flow rate - f _p and f_L denote the unbound fractions in plasma and liver tissue, respectively - C_p is the concentration in renal plasma; C_L is the concentration in liver; - C _Bile is the concentration in bile. - v _R,V _p,V _L, andV _Bile denote the reservoir plasma, hepatic plasma, tissue, and bile volumes, respectively - CL _d ⁱⁿ andCL _d ^ef denote the influx and efflux clearances, respectively - CL _int,L ^m ,L represents the hepatic metabolic intrinsic clearance of the drug - CL _int,L ^b L denotes the biliary intrinsic clearance This work was supported by the Medical Research Council of Canada. I. A. M. de Lannoy was a recipient of the Ontario Graduate Fellowship from the Ontario Ministry of Health; K. S. Pang was a recipient of the Faculty Development Award, Medical Research Council, Canada.     

盐酸维拉帕米渗透泵片溶出度与人体生物利用度研究

溶出度按Weibull's分布处理得T_d=5.76 h,T₅₀=3.9 h,零级溶出速度常数K_t=9.9450,平均体外溶解时间MDT=5.391 h。测定8名健康受试者,单剂量口服,得C_max=76.2±16.7 ng/ml,T_amx=8.0 h,t_1/2=9.75 h,MRT=19.41 h,MAT=5.34 h,与Knoll公司SR片相比,F_rel=101.71%;与市售普通片相比,F_rel=96.16%。多剂量口服,得C_max=121.47±34.5 ng/ml,T_max=7.14 h。按Loo-Riegelman方程处理表明体内外显著相关。理论值与实测值基本相符。     

The clinical pharmacokinetics of phenytoin

Procedures for estimating the variability in dosage requirements of phenytoin to achieve steadystate plasma concentrations of 10–20 mg/liter and for estimating the plasma concentrations produced on a fixed dose are given. Further, a method is proposed for estimating the dosage required to achieve a desired steady-state plasma phenytoin concentration when a steady-state value on a known daily dose has been measured, A method is also described for estimating dosage requirements when two or more plasma concentrations have been measured. These methods are derived from data obtained on administering phenytoin in four to five different dosage regimens until steady state was achieved in each of nine volunteers. The drug was administered orally as a suspension every 8 hr, starting with about 100mg/day. The daily dose was increased in steps, and maintained at each daily dose rate for 6–14 days, or longer. Blood samples were drawn 4 and 8 hr after the last dose on 2 successive days at the end of each step and analyzed for phenytoin concentration. The average of these values was used to estimate the steady-state plasma concentration, C_pss. For each subject the C_pss values were fitted to a rearranged Michaelis-Menten equation C_pss =K_mR/(V_m-R). In this equation R is the dosing rate, V_m is the maximum rate of metabolism, and K_m is a constant equal to the plasma concentration at which the metabolism rate is one-half maximum. The average values found for V_m and K_m were 10.3 mg/kg/day and 11.54 mg/liter, respectively. The individual values of V_m and K_m appear to be constant over time, but there is considerable interindividual variability: coefficients of variation are 25% and 50%, respectively.Supported in part by grants (GM-16496, GM-01791, and GM-00001) from the National Institutes of Health. Dr. Martin was a recipient of a grant from the Swiss National Research Foundation.     

From piecewise to full physiologic pharmacokinetic modeling: Applied to thiopental disposition in the rat

Physiologically based pharmacokinetic modeling procedures employ anatomical tissue weight, blood flow, and steady tissue/blood partition data, often obtained from different sources, to construct a system of differential equations that predict blood and tissue concentrations. Because the system of equations and the number of variables optimized is considerable, physiologic modeling frequently remains a simulation activity where fits to the data are adjusted by eye rather than with a computer-driven optimization algorithm. We propose a new approach to physiological modeling in which we characterize drug diposition in each tissue separately using constrained numerical deconvolution. This technique takes advantage of the fact that the drug concentration time course, C_T(t), in a given tissue can be described as the convolution of an input function with the unit disposition function (UDF _T) of the drug in the tissue, (i.e., C _T (t)=(C _a (t)Q _r )*UDF _r (t) whereC _a(t) is the arterial concentration,Q _T is the tissue blood flow and * is the convolution operator). The obtained tissue unit disposition function (UDF) for each tissue describes the theoretical disposition of a unit amount of drug injected into the tissue in the absence of recirculation. From theUDF, a parametric model for the intratissue disposition of each tissue can be postulated. Using as input the product of arterial concentration and blood flow, this submodel is fit separately utilizing standard nonlinear regression programs. In a separate step, the entire body is characterized by reassembly of the individuals submodels. Unlike classical physiologic modeling the fit for a given tissue is not dependent on the estimates obtained for other tissues in the model. Additionally, because this method permits examination of individualUDF _s, appropriate submodel selection is driven by relevant information. This paper reports our experience with a piecewise modeling approach for thiopental disposition in the rat. Supported in part by Grant RO1-AG04594 from the National Institute of Aging and the Anesthesia/Pharmacology Research Foundation.     

On the accuracy of calculation of the mean residence time of drug in the body and its volumes of distribution based on the assumption of central elimination

1.?The steady state and terminal volumes of distribution, as well as the mean residence time of drug in the body (V_ss, V_β, and MRT) are the common pharmacokinetic parameters calculated using the drug plasma concentration–time profile (Cp(t)) following intravenous (iv bolus or constant rate infusion) drug administration.

2.?These traditional calculations are valid for the linear pharmacokinetic system with central elimination (i.e. elimination rate being proportional to drug concentration in plasma). The assumption of central elimination is not valid in general, so that the accuracy of the traditional calculation of these parameters is uncertain.

3.?The comparison of V_ss, V_β, and MRT calculated by the derived exact equations and by the commonly used ones was made considering a physiological model. It turned out that the difference between the exact and simplified calculations does not exceed 2%.

4.?Thus the calculations of V_ss, V_β, and MRT, which are based on the assumption of central elimination, may be considered as quite accurate. Consequently it can be used as the standard for comparisons with kinetic and in silico models.