Stability of finite difference deconvolution II: simulation studies

Theoretical analysis of the stability of finite difference deconvolution (FDD) indicates that if the cumulative amount function is used to characterize the drug input the method is stable for any sampling schedule for an intravenous unit impulse response function. The analysis also indicates that the method is stable for an oral unit impulse response only for well designed sampling schedules. This article confirms these results through numerical simulation experiments. It is shown that the assumption that the unit impulse response is error-free has an influence on the performance of FDD which is generally of no practical significance, except possibly for the first few points estimated. It is also shown that there is no significant interaction between the statistical error due to data noise and the deterministic algorithm error. The major source of error in practice is likely to be the data noise in the input response function. The simulations confirm that, with the estimated cumulative amount function as the quantity estimated and, with a well designed sampling schedule for the case of an oral unit impulse response, FDD is in practice an accurate and stable method with acceptable precision under a typical error disturbance. Copyright © 1998 John Wiley & Sons, Ltd.     

An algorithm and computer program for deconvolution in linear pharmacokinetics

The procedure of deconvolution to evaluate the rate and the extent of input from absorption data and data from intravenous administration is the most fundamental and least assumptive method of accurately evaluating drug absorption in linear pharmacokinetics. It is shown for linear systems that if the absorption response and the response from an intravenous infusion or bolus administration are both well approximated by a polyexponential function, then the rate of absorption can be expressed as a sum of exponentials. An algorithm and computer program are presented whereby the absorption function is uniquely defined from the model-independent parameters of the polyexponential expressions fitted to the absorption data and data from intravenous administration. Fitting a sum of exponentials to data has become a routine procedure in pharmacokinetics. The method presented therefore makes the previously complex task of deconvolution a simple procedure. The deconvolution approach is discussed in relation to conventional methods of evaluating drug absorption and appears to have some distinct advantages over these methods. The method is tested using simulated data and demonstrated using pentobarbital and cimetidine data from human subjects.     

Numerical deconvolution using system identification methods

A deconvolution method is presented for use in pharmacokinetic applications involving continuous models and small samples of discrete observations. The method is based on the continuous-time counterpart of discrete-time least squares system identification, well established in control engineering. The same technique, requiring only the solution of a linear regression problem, is used both in system identification and input identification steps. The deconvolution requires no a prioriinformation, since the proposed procedure performs system identification (including optimal selection of model order), selects the form of the input function and calculates its parametric representation and its values at specified time points.On leave from Eötvös Lorand University, Budapest, Hungary.     

大鼠口服尼莫地平吸收动力学性别差异研究

目的 :研究大鼠ig尼莫地平 (NMD)后体内药物动力学是否存在性别差异 ,并考察合用红霉素(Ery)后血浆中NMD变化。方法 :雌性和雄性大鼠单独igNMD或与Ery合用后 ,用HPLC法测定血浆中NMD的浓度。结果 :大鼠ig给药NMD(2 0mg·kg-1) ,雌鼠血浆中的NMD浓度显著高于雄鼠 (P <0 .0 5 ) ,其AUC值是雄鼠的 4 .4倍。合用Ery后 ,与单用比较 ,无论是雄鼠 ,还是雌鼠 ,血浆中NMD浓度显著升高 ,AUC值分别提高了 2 .0和 1.6倍。合用Ery ,NMD的性别差异仍然存在。雌鼠的浓度仍然高于雄鼠 ,AUC值是雄鼠的 3.4倍。结论 :NMD在大鼠体内口服吸收动力学存在性别差异 ,并且红霉素可以提高NMD在血浆中的浓度。     

国产药品说明书信息差异分析程序设计的探讨

建立一种分析国产药说明书信息差异的程序,可以帮助监管人员及时有效地识别药品说明书的信息差异,以督促企业尽快完善药品说明书。建立结构化的药品说明书库,并设计药品说明书比对程序和算法,采用余弦相似度文本分析法分析国产药说明书的信息差异,并与国家药品不良反应（ADR）监测中心建立相关链接,从而让药品说明书信息差异分析更加合理,能够有效提高我国相关制药企业完善药品说明书的效率。     

Semiparametric analysis of non-steady-state pharmacodynamic data

We present an approach to the analysis of pharmacodynamic (PD) data arising from non-steadystate experiments, meant to be used when only PD data, not pharmacokinetic (PK) data, are available. The approach allows estimation of the steady-state relationship between drug input and effect. The analysis is based on a model describing the time dependence of drug effect (E) on (unobserved) drug concentration (Ce) in an hypothetical effect compartment. The model consists of (i) a known model for the input rate of drug I(t), (ii) a parametric model; L(t, a) (a function of time t, and vector of parameters a), relating I to an observed variable X, (iii) a nonparametric model relating X to E. Ce is proportional to X. X(t) is given by I(X) * L(t, a)/AL, where L(t,)=e ^– ₁ ^t * _k=1 ^m , _2k e ^– _2k+1 ^t, _k=1 ^m _2k=1, AL= ₀ L(t) dt, and * indicates convolution.The nonparametric model relating X to Eis a cubic spline, a function of X and a vector of (linear) parameters . The values of and are chosen to minimize the sum of squared residuals between predicted and observed E. We also describe a similar model, generalizing a previously described one, to analyze PK/PD data. Applications of the approach to different drug-effect relationships (verapamil-PR interval, hydroxazine-wheal and flare, flecainide and/or verapamil-PR, and left ventricular ejection fraction) are reported.Work supported in part by Department of Health, Education and Welfare Grants AG03104, AG04594, and GM26691.     

Numerical deconvolution by least squares: Use of prescribed input functions

A new method for numerical deconvolution is described, for use in calculating drug input rates. The method is based on the least-squares criterion and is applicable when the input function can be assumed to take a prescribed form. In particular, an exponential input function and an input function derived from the cube-root dissolution law are considered. The stability of the method to data noise is shown by means of examples, using simulated data.     

Numerical deconvolution by least squares: Use of polynomials to represent the input function

A new method for numerical deconvolution is described, for use in calculating drug input rates. The method is based on the least-squares criterion and approximates the input rate by a polynomial function. Ill-conditioning of the normal equations is avoided by using orthogonal functions. The use of the method is illustrated by means of examples, using simulated data.     

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 linear 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 qfunction represents the net effect of all disposition processes which work toward a reduction in the systemic drug level. The hfunction 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 qand hto 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, and (3)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.     

Linear and nonlinear system approaches in pharmacokinetics: How much do they have to offer? I. General considerations

System approaches in pharmacokinetics are defined as generalizing and simplifying modeling approaches that mathematically model a general property of the pharmacokinetic system without modeling specifically the individual kinetic processes responsible for the general property considered. The rationale for the use of system approaches is discussed and the kinetic basis of some of the approaches is presented. An overview of the approaches is presented together with a comparison to classical approaches involving specific pharmacokinetic models. Examples are given from different application areas involving problems in linear and nonlinear pharmacokinetics and in pharmacodynamics. The advantages, disadvantages, and limitations of the system approaches are discussed. In several application areas the system approach offers some rational methods and procedures with distinct advantages over more traditional approaches.This work was in part supported by grant no. 1 RO1 DA04083-01 from NIH.Part II of this article will appear in theJournal of Pharmacokinetics and Biopharmaceutics, Vol. 16, No. 5; commentaries on both parts and a rebuttal by P.V.P. will appear in JPB, Vol. 16, No. 6.     

Species Difference in the Disposition of Liposomes Among Mice,Rats, and Rabbits: Allometric Relationship and Species Dependent Hepatic Uptake Mechanism

Purpose. The species difference in the pharmacokinetics of liposomes was investigated in mice, rats and rabbits. Methods. Liposomes were intravenously injected at doses of 1, 10 and 100 (nmol/g body weight), and the time courses of liposomes in blood, liver and spleen were measured. Pharmacokinetic parameters were regressed as a function of body weight (BW) and dose of liposomes (D). The uptake mechanism of liposomes was also examined with the isolated perfused liver between rats and mice. Results. Mean residence time increased with the increase of BW and D of liposomes. This increase of mean residence time resulted from the decreased total body clearance, which was principally explained by the species difference in the hepatic uptake clearance (CLh) of liposomes. The parameter CLh was regressed well by a multiple regression as a function of BW and D. In this analysis, an exponent for BW was around 0.5, which clearly indicates that smaller animals have higher uptake clearance per unit BW. Immunohistochemical analysis revealed that there was no significant difference in the density of Kupffer cells among these species. This suggest that the species difference in CLh resulted not from the density of Kupffer cells but from the uptake ability of Kupffer cells amoung species. In the isolated perfused liver, the hepatic uptake of liposomes was mainly explained by opsonin dependent uptake in rats, while opsonin independent uptake in mice. Conclusions. These quantitative and qualitative information on the species difference of liposome disposition will provide an useful information for constructing a drug delivery system using liposomes.     

Properties of the recirculation model: Calculation of the amount of drug in the body from blood concentration data,with application to absorption rate calculations

Compartment models express the relationship between amounts and concentrations by volumes of distribution, which are fundamental parameters of the models. For a recirculation model, the amount of drug in the body is given by the convolution of the measured blood concentration with a function, termed the retention function, which is a characteristic of the system. The amount of drug in the body can be partitioned into rapidly recirculating and slowly recirculating portions, which are analogous to the amounts of drug in the central and peripheral compartments of a compartment model. A method of calculating absorption rates is presented that is comparable with the Wagner-Nelson and Loo-Riegelman methods, but makes fewer assumptions.     

Maximum entropy and its application to the calculation of drug absorption rates

A new method is presented for calculating the rate at which a drug enters the bloodstream after dosing, given the concentration of the drug in blood at various times. The method is based on the principle of maximum entropy, which has not been applied previously to pharmacokinetic problems. The resulting input rate functions are smooth and physiologically realistic, free of spurious oscillations yet still showing small-scale structure where there is evidence for it in the data. Blood samples do not need to be taken at equal intervals, and no preliminary smoothing or interpolation of the data is required.This work was supported by Beecham Products.     

Linear systems approach to the analysis of an induced drug removal process. Phenobarbital removal by oral activated charcoal

The theory of linear systems analysis is applied to the evaluation of induced drug removal processes. The rate and extent of removal are determined by deconvolution for the case of phenobarbital removal from the systemic circulation by orally administered activated charcoal. The proposed method is model independent in the sense that no specific models of intrinsic or induced pharmacokinetic processes are required, and it is readily adapted to the analysis of most types of induced removal processes (hemodialysis, peritoneal dialysis, etc.). Application of the approach indicates that phenobarbital was removed from the systemic circulation to an extent of 25–53% following multiple oral doses of activated charcoal in healthy human subjects.     

Development and Characterization of Gastroretentive High-Density Pellets Lodged With Zero Valent Iron Nanoparticles

The objective of the present study is to improve iron bioavailability using high-density gastroretentive pellets of zero valent iron nanoparticles (ZVINPs). ZVINPs were prepared by the chemical reduction method and were characterized for surface morphology, surface charge, and thermal properties. High-density gastroretentive pellets of iron nanoparticles were prepared using spheronization technique. Pellets were characterized for its micromeritic properties, in vitro drug release, and ex vivo permeability. The pharmacokinetic parameters, organ distribution, and toxicity of the optimized pellets were investigated in Wistar rats. In vivo results revealed more than 2-fold increases in oral bioavailability of iron by pellets compared to plane ferrous sulfate. Toxicological studies of the carriers indicated no evidence of liver damage in acute treatment; however, few complications were observed in chronic treatment groups. These results indicated that ZVINPs pellets successfully improve the oral iron bioavailability but need to obtain more information on repeated dose toxicity to initiate the clinical evaluation of investigational products.     

Clinical pharmacokinetics of sisomicin: Two-compartment model analysis of serum data after I.V. and I.M. administration

Summary The pharmacokinetics of sisomicin, a new single component aminoglycoside antibiotic related to gentamicin c_1a, were determined in four healthy volunteers after intravenous and intramuscular administration of a 1 mg/kg dose. The elimination profile of this antibiotic follows two-compartment model kinetics after I.V. administration. The fast () and slow () disposition rate constants averaged 0.072 and 0.004 min^–1, respectively. The volume of distribution at the steady-state averaged 0.185 liters/kg which approximately corresponds to the volume of extracellular space. The physiological availability of an intramuscular dose appeared to be complete. A method of administration adapted to the kinetic properties of the drug is proposed.     

Modeling of Subcutaneous Absorption Kinetics of Infusion Solutions in the Elderly Using Technetium

Absorption kinetics of solutes given with the subcutaneous administration of fluids is ill-defined. The gamma emitter, technitium pertechnetate, enabled estimates of absorption rate to be estimated independently using two approaches. In the first approach, the counts remaining at the site were estimated by imaging above the subcutaneous administration site, whereas in the second approach, the plasma technetium concentration-time profiles were monitored up to 8 hr after technetium administration. Boluses of technetium pertechnetate were given both intravenously and subcutaneously on separate occasions with a multiple dosing regimen using three doses on each occasion. The disposition of technetium after iv administration was best described by biexponential kinetics with a V_ss of 0.30±0.11 L/kg and a clearance of 30.0±13.1 ml/min. The subcutaneous absorption kinetics was best described as a single exponential process with a half-life of 18.l6±3.97min by image analysis and a half-life of 11.58±2.48 min using plasma technetium time data. The bioavailability of technetium by the subcutaneous route was estimated to be 0.96±0.12. The absorption half-life showed no consistent change with the duration of the subcutaneous infusion. The amount remaining at the absorption site with time was similar when analyzed using image analysis, and plasma concentrations assuming multiexponential disposition kinetics and a first-order absorption process. Profiles of fraction remaining at the absorption site generated by deconvolution analysis, image analysis, and assumption of a constant first-order absorption process were similar. Slowing of absorption from the subcutaneous administration site is apparent after the last bolus dose in three of the subjects and can be associated with the stopping of the infusion. In a fourth subject, the retention of technetium at the subcutaneous site is more consistent with accumulation of technetium near the absorption site as a result of systemic recirculation.     

线性降解程序变湿法研究青霉素钾的稳定性

报道了一种新的研究湿度对固体药物稳定性影响的试验方法——线性降解程序变湿法。按照这一变湿规律进行程序变湿药物稳定性试验能最大限度地使药物在高湿和低湿范围内降解程度一致，提高了试验的精密度。作者以青霉素钾为模型药物，采用线性降解程序变湿法和指数程序变温法进行试验，求得了E_a，m，A和t_0.9等动力学参数。结果表明，新方法测定结果的精密度明显优于文献报道的程序变湿变温法。     

A double-peak phenomenon in the pharmacokinetics of veralipride after oral administration: A double-site model for drug absorption

Equal doses of veralipride have been given to 12 healthy volunteers by three different administrations-intravenous infusion, oral solution, and oral capsule-in a randomized cross-over design. After the intake of the solution, but not after infusion or capsules, two maximum plasma concentrations have been observed and interpreted, according to a double-site model for drug absorption.     

Bioequivalence: Performance of Several Measures of Extent of Absorption

The determination of the area under the concentration–time curve (AUC) is the method most commonly used by regulatory agencies to assess extent of drug absorption after single-dose administration of oral products. Using simulations, several approaches toward measuring the actual area, in whole or part, were tested. In addition, the performance of the peak concentration (C _max), usually taken as a measure of the rate of absorption was assessed evaluating extent. Model scenarios for drugs with typical mean characteristics and statistical distributions were investigated. Using different kinetic models of disposition, the time course of the drug concentration in plasma was simulated. Intraindividual and interindividual variability and assay error were modeled using Monte Carlo techniques. The accuracy, precision, and ease of use of the various measures of extent were evaluated, and statistical power analyses were performed. Among the measures tested, the most reliable were the AUC computed up to the time of the last quantifiable concentration, without extrapolation, and C _max. However, being also sensitive to rate, C _max as a measure of extent is of limited potential.