Volterra Series in Pharmacokinetics and Pharmacodynamics

Nonparametric black-box modeling has a long successful history of applications in pharmacokinetics (PK) (notably in deconvolution), but is rarely used in pharmacodynamics (PD). The main reason is associated with the fact that PK systems are often linear in respect to drug inputs, while the reverse is true for many PK/PD systems. In the PK/PD field existing non-parametric methods can deal with linear systems, but they cannot describe non-linear systems. Our purpose is to describe a novel implementation of a general nonparametric model which can represent non-linear systems, and in particular non-linear PK/PD systems, The model is based on a Volterra series, which is an integral series expansion of the response of a system in terms of its kernels and the inputs to the system. In PK we are familiar with the first term of the Volterra series, the convolution of the first kernel of the system (the so-called PK disposition function) with drug input rates. The main advantages of higher order Volterra representations is that they are general representations and can be used to describe and predict the response of an arbitrary (PK/ PD) system without any prior knowledge on the structure of the system. The main problem of the representation is that in a non-parametric representation of the kernels the number of parameters to be estimated grows geometrically with the order of the kernel. We developed a method to estimate the kernels in a Volterra-series which overcomes this problem. The method (i) is fully non-parametric (the kernels are represented using multivariate splines), (ii) is maximum-likelihood based, (iii) is adaptive (the order of the series and the dimensionality of each kernel is selected by the method), and (iv) allows for non-equispaced observations (thus allowing a reduction of the number of parameters in the representation, and the analysis of, e.g., PK/PD observations). The method is based on an adaptation of Friedmans's Multivariate Adaptive Regression Spline method. Examples demonstrate the possible application of the approach to the analysis of different PK/PD systems.     

Dose proportionality of nadolol pharmacokinetics after intravenous administration to healthy subjects

Summary To support the increasing use of intravenous -blockers during cardiovascular emergency and surgery, dose proportionality of pharmacokinetics of nadolol was evaluated after intravenous administration of ¹⁴C-nadolol at doses of 1, 2 and 4 mg to nine healthy volunteers. There were no observed differences in the excretion or the pharmacokinetics of nadolol with respect to the dose administered. Over a 72-h period after drug administration, an average of about 60% of the dose was excreted in the urine and about 15% was excreted in the feces. The range of values for total body clearance (219 to 250 ml·min^–1), renal clearance (131 to 150 ml·min^–1), mean residence time (10.5 to 11.3 h), half-life (8.8 to 9.4 h), and steady-state volume of distribution (V_ss) (147 to 157 l) indicated that nadolol was extensively distributed and slowly cleared from the body. There was a linear correlation (r ²=0.97) between the area under the plasma concentration of nadolol versus time curve (AUC) and the dose. All pharmacokinetics parameters, except V_ss, were slightly, but significantly, different at the 4 mg dose. Superposition of the dose-normalized average concentrations indicated that despite these minor differences in parameters, the pharmacokinetic behavior of nadolol was linear with respect to dose. Urinary excretion of nadolol was dose independent.     

Pharmacokinetics of transdermal drug delivery

The pharmacokinetics of drug delivery from transdermal controlled-release devices consisting of (a) a membrane plus a reservoir or (b) a monolithic slab are examined. For the period when the devices act as if the drug reservoir were infinite, simple relationships for the steady-state slope and time lag are derived and studied. An analysis of the time region when depletion of the finite dose is obtained is used to estimate the useful device lifetime. Applications to patch design are discussed.     

Chronopharmacokinetics of indomethacin in rats

In order to establish the origin of the circadian variations in the kinetics of indomethacin (Indocid) observed in humans, a chronopharmacokinetic study was developed in rats. In a first experiment, 3 groups of 24 h fasted rats each received a single i.v. dose of 0.25 or 0.5 or 1 mg/kg b.w. of indomethacin, respectively, at 8 h. Thus it could be demonstrated that the pharmacokinetics of indomethacin were linear in the dose range studied and obeyed a two-compartment model. In a second experiment, 3 other groups of rats from same strain received a single i.v. dose of 0.5 mg/kg b.w. of indomethacin at 2 h, 14 h and 20 h, respectively. In the 4 groups of rats having received 0.5 mg/kg b.w. of indomethacin, it was observed that only the pharmacokinetic parameters which reflected the distribution process exhibited significant circadian variations. When the animals were dosed at 2 h (physiological rest time for rats) the initial plasma concentration (Co = 4.2 +/- 0.08 micrograms/ml) and the area under the curve (AUC = 13.6 +/- 0.5 h micrograms/ml) was significantly lower while the distribution volume (Vd/b.w. = 120 +/- 2 ml/kg) and the total metabolic clearance (ClT/b.w. = 25 +/- 1.1 ml/h/kg) were higher than those observed in rats dosed at 20 h (period of activity). The apparent elimination half-life was not significantly altered by the time of administration. These results are in good agreement with those that we have previously reported in humans orally dosed with indomethacin, and suggest that the mechanisms of the circadian changes of the pharmacokinetics of indomethacin are mainly related to alterations in the drug distribution.     

Properties of the Michaelis-Menten equation and its integrated form which are useful in pharmacokinetics

Some old equations are reviewed and some new equations have been derived which indicate certain properties of the Michaelis-Menten equation and its integrated forms. Simulated data which obey Michaelis-Menten kinetics have been plotted in various ways to illustrate special relationships. An equation is derived which accurately estimates the slope of the apparently linear decline (k_o)of concentrations from the values of C_o, K_m,and V_m.This indicates the hybrid nature of k_o.It is pointed out that if a metabolite is formed by Michaelis-Menten kinetics, then (a)one would not expect linear plots of cumulative amount of metabolite excreted in the urine vs. time, and (b)the plasma clearance of the drug will change with dose, and the plasma clearance of the drug would be expected to be different following administration of the same dose in a rapidly available and a slowly available dosage form. The distortion in parameter values when data arising from Michaelis-Menten kinetics are evaluated by classical linear pharmacokinetics is indicated.     

Molecular Adsorbent Recirculating System Therapy with Continuous Renal Replacement Therapy Enhanced Clearance of Piperacillin in a Pediatric Patient and Led to Failure to Attain Pharmacodynamic Targets

Molecular adsorbent recirculating system (MARS), an extracorporeal support device used in patients with liver failure, specifically removes albumin-bound molecules, including antibiotics. Case reports in adult patients showed that MARS enhances the clearance of piperacillin. However, for those patients, pharmacodynamic targets were achieved when piperacillin/tazobactam was administered as extended infusions over 3–4 hours. In contrast, piperacillin/tazobactam is typically given as short intermittent infusions in children. No reports describe the effect of MARS on piperacillin pharmacokinetics or pharmacodynamic target attainment in pediatric patients with liver failure. This case report describes the effects of MARS on piperacillin clearance and target attainment in a child with liver failure. It was noted that MARS, in conjunction with continuous renal replacement therapy (CRRT), enhanced the clearance of piperacillin when compared with CRRT alone (6.4–7.4 L/hr vs 3.0 L/hr). Pharmacodynamic targets were not attained during MARS-CRRT cycles with free piperacillin concentrations being above 64 µg/ml for < 50% of dosing intervals, the goal target. We performed simulation analysis to identify a dosing regimen to optimize target attainment. For this patient, doses 3 times what she received over 3-hour extended infusions and an additional dose within 5 hours of cycle initiation would have led to target attainment throughout the MARS-CRRT cycles.     

Steady-state pharmacokinetics of metronidazole in Crohn's disease

The pharmacokinetics of metronidazole (MTZ) were studied in six Crohn's disease patients after multiple oral daily doses of 250, 500, 750, and 1000 mg day-1. Pharmacokinetic indices were found to be independent of the dose administered. The half-life, volume of distribution and oral clearance of metronidazole were 9.5 +/- 2.1 h, 0.732 +/- 0.094 l kg-1 and 0.921 +/- 0.175 (ml min-1) kg-1 (mean +/- SD), respectively. A strong linear correlation (r = 0.95) was found between the volume of distribution of MTZ and the patients' total body weight. The percentage of dose of metronidazole excreted in urine as the intact drug and metabolites as well as glucuronic acid conjugates ranged from 34.7 +/- 7.4 to 58.9 +/- 5.2. Both plasma and urine data exhibited very large inter-patient variations. However, intra-patient variations were negligible. Strong positive linear correlations were observed between the dose and the areas under the plasma concentration versus time curves, peak plasma concentrations as well as cumulative urinary excretion of the drug and its metabolites. It is concluded that in Crohn's disease, the pharmacokinetics of MTZ and its metabolites are linear and that the drug concentrations are dependent on the total body weight.     

Pharmacokinetics of nilvadipine after single oral doses in healthy volunteers

Forty healthy male Caucasian volunteers were randomly assigned to five treatment groups to receive a placebo or a 4, 8, 12, 16 or 20 mg dose of nilvadipine. The drug was well tolerated by the subjects at all dose levels. Pharmacokinetic parameters for nilvadipine were determined using model-independent methods. There were no significant differences (p greater than 0.05) in the time to the maximum plasma concentration (Cmax) (tmax), the elimination half-life or the mean residence time among the five treatment groups. Up to doses of about 12 mg, there was a linear relationship between dose and Cmax or area under the plasma concentration-time curve (AUCO----infinity). At doses of 16 and 20 mg, the relationship between dose and Cmax or AUCO----infinity was no longer linear, suggesting that the pharmacokinetics of the drug after single oral doses greater than about 12 mg may be dose-dependent, probably due to concentration-dependent first-pass hepatic elimination of the drug.     

The pharmacokinetics of ameziniummetilsulfate in man. Single and repetitive oral administration of a therapeutically effective dose

The pharmacokinetics of the antihypotensive drug 4-amino-6-methoxy-1-phenyl-pyridazinium methyl sulfate (ameziniummetilsulfate, LU 1631, Regulton), in the following briefly called amezinium, has been investigated in 8 healthy volunteers. Plasma concentrations were determined by means of a high pressure liquid chromatographic method after single oral administration of a therapeutic dose (10 mg), during repetitive dosing (10 mg b.i.d., 13 days) and following the last dose. The results demonstrate for amezinium rapid absorption (half-life about 0.6 h), good tissue penetration (distribution) with about 3.0 h half-life and comparably slow elimination (half-life about 12.0 h). Considering the results before and after multiple dosing and those of earlier studies (using higher dosages), none of the kinetic parameters showed any indication of dose dependency or changes by chronic dosing. These properties and the characteristics of amezinium with respect to absorption, bioavailability and elimination are considered favourable for safe and effective handling of the drug.     

Clinical and pharmacokinetic results with a new ultrashort-acting calcium antagonist, clevidipine, following gradually increasing intravenous doses to healthy volunteers

AIMS: To investigate the tolerability and safety of clevidipine in healthy male volunteers during intravenous infusion at gradually increasing dose rates and to obtain preliminary information on the pharmacokinetics and pharmacodynamic effects of the drug. METHODS: Twenty-five subjects were enrolled in the study and twenty-one of them were included twice, resulting in a total of forty-six study entries encompassing 20 min infusions of clevidipine at target dose rates ranging from 0.12 to 48 nmol min-1 kg-1. Haemodynamic variables and adverse events were recorded throughout the study. Concentrations of clevidipine and its primary metabolite, H 152/81, were followed in whole blood, and the pharmacokinetics were evaluated by non-compartmental and compartmental analysis. An Emax model was fitted to the effect on mean arterial pressure (MAP) over heart rate (HR) and the corresponding blood concentrations of clevidipine. RESULTS: Clevidipine was administered up to a target dose rate of 48 nmol min-1 kg-1, where a pre-determined escape criterion was reached (HR>120 beats min-1 ) and the study was stopped. The most common adverse events were flush and headache, which can be directly related to the mechanism of action of clevidipine. There was a linear relationship between blood concentration and dose rate in the range studied. The median clearance value determined by non-compartmental analysis was 0.125 l min-1 kg-1. Applying the population approach to the sparse data on clevidipine concentrations, an open two compartment pharmacokinetic model was found to be the best model in describing the disposition of the drug. The population mean clearance value determined by this method was 0.121 l min-1 kg-1, and the volume of distribution at steady state was 0.56 l kg-1. The initial half-life, contributing by more than 80% to the total area under the blood concentration-time curve following i.v. bolus administration, was 1.8 min, and the terminal half-life was 9.5 min. At the highest dose rates, MAP was reduced by approximately 10%, and the HR reached the pre-determined escape criterion for this study (>120 beats min-1 ). CONCLUSIONS: Clevidipine is well tolerated and safe in healthy volunteers at dose rates up to at least 48 nmol min-1 kg-1. The pharmacokinetics are linear over a wide dose range. Clevidipine is a high clearance drug with extremely short half-lives. The effect of clevidipine on the blood pressure was marginal, probably due to a compensatory baroreflex activation in this population of healthy volunteers. A simple Emax model adequately describes the relationship between the pharmacodynamic response (MAP/HR) and the blood concentrations of clevidipine.     

Pharmacokinetic/pharmacodynamic evaluation of the NHE inhibitor eniporide

The aim of this study was to investigate the pharmacokinetics and pharmacodynamics of the new cardioprotective sodium/proton exchange (NHE-1) inhibitor eniporide in humans. Eniporide was administered intravenously to healthy volunteers in doses between 2.5 and 100 mg. Concentrations of parent drug and its metabolite were measured by HPLC, and the data were analyzed by noncompartmental and compartmental pharmacokinetic methods. Platelet-swelling time was determined in each subject as a biomarker to assess pharmacodynamic activity. Eniporide showed linear pharmacokinetics with an average half-life of approximately 2 hours. The mean total body clearance was 34.4 L/h. The mean volume of distribution (Vdss) was 77.5 L, and the mean residence time was 2.3 hours. An average of 43% of the dose was recovered unchanged from urine. A pharmacokinetic two-compartment model was found suitable to provide excellent curve fits of the measured plasma concentration profiles. Plasma concentrations of the major metabolite were lower than that of the parent drug. An average of 27% of the dose was found in urine as that metabolite. The effect on platelet swelling could be well characterized by a direct Emax model. The average concentration for half-maximum effect (IC50) was 12 ng/mL. Eniporide was found to have predictable linear pharmacokinetics in the investigated dose range. Platelet-swelling time was shown to be a reproducible individual biomarker for pharmacodynamic activity, with great potential for a surrogate that predicts clinical outcome, since this effect is mediated through the same mechanism of action (NHE-1 inhibition) as the desired cardioprotective activity. Pharmacokinetic/pharmacodynamic modeling allowed a first estimate of the degree of NHE inhibition in the investigated dose range.     

Drug disposition in three dimensions: an update on stereoselectivity in pharmacokinetics

Many marketed drugs are chiral and are administered as the racemate, a 50:50 combination of two enantiomers. Pharmacodynamic and pharmacokinetic differences between enantiomers are well documented. Because of enantioselectivity in pharmacokinetics, results of in vitro pharmacodynamic studies involving enantiomers may differ from those in vivo where pharmacokinetic processes will proceed. With respect to pharmacokinetics, disparate plasma concentration vs time curves of enantiomers may result from the pharmacokinetic processes proceeding at different rates for the two enantiomers. At their foundation, pharmacokinetic processes may be enantioselective at the levels of drug absorption, distribution, metabolism and excretion. In some circumstances, one enantiomer can be chemically or biochemically inverted to its antipode in a unidirectional or bidirectional manner. Genetic consideration such as polymorphic drug metabolism and gender, and patient factors such as age, disease state and concomitant drug intake can all play a role in determining the relative plasma concentrations of the enantiomers of a racemic drug. The use of a nonstereoselective assay method for a racemic compound can lead to difficulties in interpretation of data from, for example, bioequivalence or dose/concentration vs effect assessments. In this review data from a number of representative studies involving pharmacokinetics of chiral drugs are presented and discussed.     

Pharmacokinetics and pharmacodynamics of avitriptan during intravenous administration in healthy subjects.

Avitriptan, a selective 5-HT1-like receptor agonist, is an effective compound for the treatment of migraine headaches with a prolonged duration of response. A double-blind, placebo-controlled, parallel-group, ascending-dose study in 24 healthy subjects was designed to assess the safety, tolerance, pharmacokinetics, and pharmacodynamics of avitriptan. This antimigraine drug was administered as two consecutive constant-rate IV infusions at three dose levels (12.7, 25.3, and 38.0 mg), which were targeted to produce plasma concentrations in and above the therapeutic range. The best fitting of the plasma concentration-time data was obtained by using a triexponential function yielding a terminal t1/2 of 8 hours. The areas under the plasma concentration versus time curves were proportional to dose, indicating linear pharmacokinetics. Moreover, the clearance and steady-state volume of distribution values were independent of the dose. The change in pulse rate and supine systolic and diastolic blood pressure was determined as pharmacodynamic effects of avitriptan. A "threshold log-linear" model, which accounts for the linear increase in pharmacodynamic effect with the log of plasma concentrations when the latter was higher than a certain threshold value, adequately described the pharmacodynamic data. The threshold plasma drug concentrations for the pulse rate and the diastolic and systolic blood pressure were 14, 74, and 161 ng/ml, respectively. Overall, avitriptan has consistent, linear pharmacokinetics and increases systolic and diastolic blood pressure in a predictable manner at a higher plasma concentration. However, this drug does not produce a significant change in pulse rate at the dose levels (12.7-38 mg) evaluated in this study.     

肿瘤患者体内甘氨双唑钠及代谢产物甲硝唑单剂量和多剂量药代动力学及排泄率比较

目的　研究甘氨双唑钠 (CMNa)的单剂量和多剂量药代动力学 ,以评价CMNa的蓄积性。方法　 5名肿瘤病人 ,单次或每隔 1d连续 9次静脉滴注 70 0mg·m- 2 的CMNa液 ,分别在单次和第 9次静滴后设定时间点采血 ,用高效液相色谱 二极管阵列紫外法测定受试病人全血CMNa及其代谢产物甲硝唑浓度 ,对CMNa的血药浓度 时间数据进行了拟合 ,并对单剂量和多剂量的血药浓度 时间数据和药代动力学参数以及尿排泄率进行比较。结果　CMNa在病人体内分布及消除都很快 ,单剂量和多剂量静滴CMNa后血药浓度值和各药代动力学参数非常相近 ,没有明显差别。结论　甘氨双唑钠不会在肿瘤病人体内蓄积。     

Use of gamma distributed residence times in pharmacokinetics

The multiple dose pharmacokinetics of isotretinoin and its major blood metabolite, 4-oxo-isotretinoin, were studied in 10 patients with cystic acne and 11 patients with various keratinization disorders. Blood samples were obtained at predetermined times following the first dose, interim doses and the final dose. Blood concentrations of isotretinoin and 4-oxo-isotretinoin were measured by a specific and sensitive HPLC method. A lag time was usually observed prior to the onset of absorption following oral administration of the drug in a soft elastic gelatin capsule. Absorption then proceeded rapidly and maximum blood concentrations usually occurred within 4 h of drug administration. The harmonic mean half-life for the elimination of isotretinoin by the cystic acne patients was approximately 10 h after the initial dose and did not change significantly following 25 days of 40 mg b.i.d. dosing. Steady-state blood concentrations remained relatively constant after the fifth day of dosing. The harmonic mean elimination half-life in the patients with various disorders of keratinization was about 16 h. The results of the 2 studies suggest that no significant changes in the pharmacokinetics of isotretinoin occur during multiple dosing and that the multiple dose pharmacokinetic profile is predictable and can be described using a linear pharmacokinetic model. This suggests that the steady-state concentrations of isotretinoin can be predicted from single dose data.     

Biowaivers for oral immediate-release products: implications of linear pharmacokinetics

Bioequivalence of drug formulations plays an important role in drug development. Recently, the Biopharmaceutical Classification System (BCS) has been implemented for the purpose of waiving bioequivalence studies on the basis of the solubility and gastrointestinal permeability of drug substance. Using the rationale of the BCS, it can be argued that biowaivers can, however, also be granted on the basis of standard pharmacokinetic data. If a drug exhibits dose-linear pharmacokinetics and a sufficiently fast dissolution profile, it can be concluded that this drug appears to pose no problem with respect to absorption. It should be noted that a change of an immediate-release tablet formulation can only lead to a deviating rate and/or extent of absorption when release of the drug from the formulation is altered. Logically, the dissolution profiles of the different formulations should be equal to guarantee bioequivalency. Thus, both BCS and the alternative linear pharmacokinetics approach require an evaluation of dissolution profiles. The justification of BCS is found in the permeability classification of the compound, while those of the linear pharmacokinetics lie in the apparent lack of a permeability problem. For example, in this context P-glycoprotein-transported drugs form an interesting class of compounds, which may be treated likewise when complying to the aforementioned requirements. Furthermore, poorly soluble compounds may be less troublesome than expected. It is shown that linear kinetics can be explained by the solubilising activity of, for example, bile salts. In this instance, linear pharmacokinetics shows that elevated doses do not appear to exhibit a limiting role on the dissolution. Hence, a change in formulation without any effect on the dissolution profile is not expected to cause a change in availability. It is clear that the formulations to be compared should not contain excipients that display an effect on (presystemic) drug metabolism.     

Lipophilicity in trans-bilayer transport and subcellular pharmacokinetics

The aim of subcellular pharmacokinetics in drug design is to model drug disposition and response as a function of the properties of drugs and biosystems involved and the observation time. Biosystems are represented by systems of alternating membranes and aqueous phases that differ in acidity and contain low-molecular cell constituents, enzymes and other proteins. The resulting disposition models are combined with linear free-energy assumptions, drug/receptor binding kinetics and relationships between receptor binding and response to produce model-based quantitativestructure–(time–)activity relationships, QS(T)AR. This review summarizes the present status of subcellular pharmacokinetics with emphasis on passive trans-bilayer transport. In particular, mechanisms of transport are analyzed with respect to amphiphilicity and lipophilicity. The overall rate of transport is strongly governed by amphiphilicity, the tendency of drug molecules to adsorb to the bilayer/water interface. Depending on amphiphilicity, the time needed for a drug to cross a single bilayer ranges from seconds to days. The main advantage of the subcellular pharmacokinetic approach is that the resulting models, once calibrated for a given biosystem, provide a detailed recipe for tailoring the drug properties to ensure optimum disposition. This revised version was published online in August 2006 with corrections to the Cover Date.     

Interspecies scaling and comparisons in drug development and toxicokinetics

1. Methods of interspecies extrapolation using physiological models and allometric scaling have been reviewed with their possible application to drug development, both for candidate drug selection and the interpretation of toxicokinetic data. 2. Physiological models offer a mechanistic approach to extrapolation from one species to another, examining individual components which interrelate to produce the characteristics of the whole system. Tissues of interest are arranged in anatomical order based on blood circulation, and the disposition of a drug can be simulated with knowledge of tissue size (volume), tissue perfusion (blood flow), drug permeability, binding of the drug between the tissue and blood (partition), as well as elimination. Using this approach the behaviour of the drug under different conditions, such as dose route, disease state or animal species, can be predicted. 3. The alternative approach of allometric scaling is an empirical examination of relationships between size, time and its consequences. A regression of the logarithm of the pharmacokinetic parameter and the logarithm of the body weight of the animal species produces a linear relationship which enables the value of pharmacokinetic parameters in any animal species to be calculated from the product of an allometric coefficient and the body weight to a power function. 4. Whilst this technique gives acceptable predictions for the pharmacokinetics of those drugs eliminated renally, or which are blood flow-dependent, there is poor prediction for humans for low clearance drugs primarily eliminated by the mixed-function oxidase system. This appears to be a result of differences in maturation, and can be corrected for by including a brain weight or maximum life-span potential term into the allometric equation. 5. Of the two approaches described for extrapolation of pharmacokinetics between animal species, physiological models tend to be resource-demanding and costly, with more frequent failures, but can be invaluable for examining target organ exposure and for the targeting of drugs as in cancer chemotherapy. For routine drug development, however, allometric scaling is potentially more useful since it uses data which are routinely obtained and the calculations are relatively simple. 6. The problems of intraspecies scaling from high-dose data to low-dose predictions are discussed with respect to current models of dose levels. A new approach is proposed using a modified Hill equation based on drug exposure, which should allow for a more meaningful determination of the toxicity of a compound with different drug exposures.(ABSTRACT TRUNCATED AT 400 WORDS)     

Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. I. Derivations and theoretical analysis

The approach presented enables a model independent representation of the pharmacokinetics of drugs with a liner disposition and some drugs with a nonlinear disposition. The approach is based on a decomposition of the drug disposition into an elimination function q(c) and a distribution function h(t). The q function represents the net effect of all disposition processes which work toward a reduction in the systemic drug level. The h function represents the net effect of all disposition processes which slow down the rate of decline of the systemic drug level by returning drug from the peripheral environment to the systemic circulation. Several theorems relating q and h to the drug disposition are presented which uniquely define these functions mathematically. The disposition decomposition is of particular significance in three main areas of pharmacokinetics: (1) evaluation of drug absorption, (2) drug level predictions including steady state predictions, (3) and elucidation of drug disposition kinetics. The practical significance of the decomposition method in these three areas is discussed, and various procedures for the application of the method are proposed. The decomposition method represents a model independent alternative to pharmacokinetic models such as linear compartmental models, the recirculation model, and some physiologic models. This also includes nonlinear forms of such models, as long as the nonlinearity is due to a central nonlinear elimination. The greatest promise and significance of the disposition decomposition approach appears to be its application to nonlinear pharmacokinetics. In contrast to linear pharmacokinetics the kinetic analysis in such cases has been limited to model dependent methods employing specific pharmacokinetic models, due to the lack of model independent alternatives. The novel development presented offers such alternatives. For some applications these alternatives appear more rational in the sense that the analysis becomes more general and objective and may be based on fewer assumptions.     

Pharmacokinetic software for the health sciences: choosing the right package for teaching purposes

Computer assisted learning has an important role in the teaching of pharmacokinetics to health sciences students because it transfers the emphasis from the purely mathematical domain to an 'experiential' domain in which graphical and symbolic representations of actions and their consequences form the major focus for learning. Basic pharmacokinetic concepts can be taught by experimenting with the interplay between dose and dosage interval with drug absorption (e.g. absorption rate, bioavailability), drug distribution (e.g. volume of distribution, protein binding) and drug elimination (e.g. clearance) on drug concentrations using library ('canned') pharmacokinetic models. Such 'what if' approaches are found in calculator-simulators such as PharmaCalc, Practical Pharmacokinetics and PK Solutions. Others such as SAAM II, ModelMaker, and Stella represent the 'systems dynamics' genre, which requires the user to conceptualise a problem and formulate the model on-screen using symbols, icons, and directional arrows. The choice of software should be determined by the aims of the subject/course, the experience and background of the students in pharmacokinetics, and institutional factors including price and networking capabilities of the package(s). Enhanced learning may result if the computer teaching of pharmacokinetics is supported by tutorials, especially where the techniques are applied to solving problems in which the link with healthcare practices is clearly established.