Advanced computer programs for drug dosing that combine pharmacokinetic and symbolic modeling of patients.

In this paper, we describe our design for advanced drug dosing programs that "reason" using a combination of Bayesian pharmacokinetic modeling and symbolic modeling of patient status and drug response. Our design is similar to the design of the Digitalis Therapy Advisor program, but extends this previous work by incorporating a Bayesian pharmacokinetic model, performing a "meta-level" analysis of drug concentrations to identify sampling errors and changes in pharmacokinetics, and including the results of this analysis in reasoning for dosing and therapeutic monitoring recommendations. The design has been implemented in a program for aminoglycoside antibiotics called Aminoglycoside Therapy Manager. The program is user-friendly and runs on low-cost general-purpose hardware. The initial validation study showed that the program was as accurate in predicting future drug concentrations as an expert using commercial Bayesian forecasting software and that its dosing recommendations were similar to those of an expert.     

A pocket calculator program for pharmacokinetic dosing of drugs exhibiting single compartment first-order elimination and zero-order or first-order absorption

A pocket computer program has been designed to assist clinicians in the appropriate administration of most drugs exhibiting single compartment first-order elimination and either zero-order (intravenous infusions) or first-order (intramuscular and oral) absorption. The program utilizes well-established pharmacokinetic parameters to calculate an optimal drug dose and dosing interval based upon a patient's demographic characteristics and the drug half-life, volume of distribution, and absorption rate constant or infusion time. It also allows the user to estimate peak and trough drug serum concentrations. When measured serum concentrations are available during steady state, it is possible to determine individual patient drug half-life and volume of distribution for more accurate adjustments in dose and/or dosing interval. Usage of this program should enable clinicians to better select effective but safe drug dosing regimens based on individual patient needs and characteristics.     

Nonparametric identification of population models via Gaussian processes

Population models are used to describe the dynamics of different subjects belonging to a population and play an important role in drug pharmacokinetics. A nonparametric identification scheme is proposed in which both the average impulse response of the population and the individual ones are modelled as Gaussian stochastic processes. Assuming that the average curve is an integrated Wiener process, it is shown that its estimate is a cubic spline. An empirical Bayes algorithm for estimating both the average and the individual curves is worked out. The model is tested on simulated data sets as well as on xenobiotics pharmacokinetic data.     

Open-loop stochastic control of pharmacokinetic systems: a new method for design of dosing regimens.

On the basis stochastic control techniques, an algorithm for the design of dosing regimens is developed. The essence of the method relies on a constrained model for the population and on a first-order approximation in the evaluation of the performance cost function. Since it does not require detailed information on the probability distribution of the model parameters, the method can be used in a wide range of practical applications. The application of the design technique is illustrated in two typical situations: lacking a probability model for the pharmacokinetic parameters (etomidate) and having a probability model for the pharmacokinetic parameters (theophylline).     

Control of Drug Administration During Monitored Anesthesia Care

Monitored anesthesia care (MAC) is increasingly used to provide patient comfort for diagnostic and minor surgical procedures. The drugs used in this setting can cause profound respiratory depression even in the therapeutic concentration range. Titration to effect suffers from the difficulty to predict adequate analgesia prior to application of a stimulus, making titration to a continuously measurable side effect an attractive alternative. Exploiting the fact that respiratory depression and analgesia occur at similar drug concentrations, we suggest to administer opioids and propofol during MAC using a feedback control system with transcutaneously measured partial pressures of CO₂(P_tcCO2) as the controlled variable. To investigate this dosing paradigm, we developed a comprehensive model of human metabolism and cardiorespiratory regulation, including a compartmental pharmacokinetic and a pharmacodynamic model for the fast acting opioid remifentanil. Model simulations are in good agreement with ventilatory experimental data, both in presence and absence of drug. Closed-loop simulations show that the controller maintains a predefined CO₂ target in the face of surgical stimulation and variable patient sensitivity. It prevents dangerous hypoventilation and delivers concentrations associated with analgosedation. The proposed control system for MAC could improve clinical practice titrating drug administration to a surrogate endpoint and actively limiting the occurrence of hypercapnia/hypoxia.     

A program for individual and population optimal design for univariate and multivariate response pharmacokinetic-pharmacodynamic models

The design of pharmacokinetic and pharmacodynamic experiments concerns a number of issues, among which are the number of observations and the times when they are taken. Often a model is used to describe these data and the pharmacokinetic-pharmacodynamic behavior of a drug. Knowledge of the data analysis model at the design stage is beneficial for collecting patient data for parameter estimation. A number of criteria for model-oriented experiments, which maximize the information content of the data, are available. In this paper we present a program, Popdes, to investigate the D-optimal design of individual and population multivariate response models, such as pharmacokinetic-pharmacodynamic, physiologically based pharmacokinetic, and parent drug and metabolites models. A pre-clinical and clinical pharmacokinetic-pharmacodynamic model describing the concentration-time profile and effect of an oncology compound in development is used for illustration.     

A mathematical model for HIV treatment with time-varying antiretroviral therapy

In treating the human immunodeficiency virus (HIV) infection, strict adherence to drug therapy is crucial for maintaining a low viral load, but the high dosages required for this often have toxic side effects which make perfect adherence to antiretroviral therapy (ART) unsustainable. Even in the presence of drug therapy, ongoing viral replication can lead to the emergence of drug resistance. In this paper, we investigate the effect of immune effectors in modelling HIV pathogenesis during ART, showing a higher rebound for healthy T-cell concentration than drug therapy alone. A periodic model of bang–bang type and a pharmacokinetic model are employed to estimate the drug efficacies. We numerically investigate how time-varying drug efficacy due to drug dosing regimen and/or suboptimal adherence affects the antiviral response and how it affects the emergence of drug resistance. Moreover, we qualitatively characterize successful drugs or drug combination scenarios.     

Application of a pharmacokinetic simulation program in pharmacy courses

A model which illustrates aspects of drug absorption, distribution and elimination in the body has been developed at McMaster University and St Bartholomew's Hospital Medical College over the past eight years. It is a multi-compartment model in which drug concentrations are determined by the solution of a system of non-linear differential equations with physiological and biochemical data defining the patient and drugs. The model has been used in course work for final year B.Pharm. students for examining plasma levels and distributions of several drugs following simple and multiple doses by various routes. Third year students carried out investigations using their prior knowledge of dosing regimens and pharmaco-kinetics to design suitable dosage schemes to maintain effective levels of nortryptiline, propranolol, high dose aspirin and kanamycin. In pharmacy courses, posology is taught traditionally as a series of doses to be learnt by rote, while pharmacokinetics course work consists of the interpretation of computer generated data. The model has been found to offer a more interesting and dynamic teaching method for both these subjects.     

Stability and control of a class of compartmental systems with application to cell proliferation and cancer therapy

This paper concerns a systematic application of a variety of concepts and tools of control theory to the study of the stability and control of a class of compartmental systems arising in several application areas where population kinetics are of significant importance. To provide a focus to the development, the specific area of cell proliferation kinetics is selected for detailed study. A multicompartmental model which portrays the progression of a population of cells through the different phases of the ceil cycle is developed and a model reference adaptive algorithm for estimating model parameters is presented. An exponential stability framework is developed for quantifying the control effects of an administered drug protocol and is used to design efficient treatment strategies for cancer chemotherapy by application of optimization concepts. Since the toxic effects of anticancer drugs on the normal cell populations of the body are the bottlenecks in successful chemotherapy, determination of dosing strategies that minimize toxicity while maximizing the therapeutic effects are of great importance. A mathematical formulation of this problem leads to the optimization of bilinear systems under exponential stability constraints for which a solution procedure is presented.     

Modelling the Double Peak Phenomenon in pharmacokinetics

Two methods of modelling the Double Peak Phenomenon in pharmacokinetics are described; both are based on compartmental models. The first method assumes that the absorption of the drug from the gut to the systemic plasma varies with the location of the drug in the gut, with negligible absorption through the jejunum. It has the advantage of clear physiological interpretation, but there are a comparatively large number of parameters to be estimated. The second method assumes simultaneous input via two parallel pathways, and has been developed with the aim of reducing the number of parameters in the model. However, this approach lacks the direct relationship to physiology. The two methods are used to model two data sets provided by AstraZeneca and a further data set from the literature, describing the pharmacokinetics of veralipride. For all three data sets, the measurement is of concentration of drug in the systemic plasma following oral administration in solution form.     

Simulation of compartmental models for kinetic data from a positron emission tomograph.

Linear compartmental models are used to describe the disposition of radio-labelled compounds in regions of interest in the mammalian body, based on a time sequence of measurements from a positron emission tomograph (PET). In this paper we show how closed form solutions for the model equations have been incorporated into a computer program for simulation and parameter estimation. A typical PET data example is included to illustrate the implementation and compare the closed form method with a numerical ode solution method.     

A fast algorithm for the computation of the plasma concentration time curve and confidence limits in linear pharmacokinetics

An algorithm is developed for the computation of the plasma concentration time curve for a drug administration regime involving fast injection (bolus) and/or continuous infusion. The effect of the pharmacokinetic model parameter variations on the plasma concentration time curve is analyzed and efficient algorithms for the computation of the parameter-induced first-order variation and confidence bounds of the plasma concentration time curve are also presented. The application of the method is illustrated with pharmacokinetic data for the etomidate.     

APIS: a software for model identification, simulation and dosage regimen calculations in clinical and experimental pharmacokinetics.

APIS is a software package based on mathematical modelling which provides a reliable approach in optimizing drug therapy. It was designed to assist clinicians in interpreting blood drug levels so that drug therapy may be better and more cost-effective. It is a methodological approach to describe, predict and control the kinetic behaviour of a drug. This software incorporates the principle of Bayesian procedures, i.e. one can use all available patient information (population) to determine patient-specific parameter estimates. These estimates can then be used to design an optimal and individualized drug regimen. APIS is an attractive and useful tool for clinical and experimental pharmacokinetics. APIS may be used on any IBM compatible computer using the Microsoft-Windows environment. The software is menu driven to provide a very user-friendly tool for analysing pharmacokinetic data and for designing dosage regimens.     

Design and pharmacokinetic application of an analog computer program (MULS) for multiple dose simulation

MULS is a simulation program developed on an analog computer equipped with logic elements. It is designed for multiple dose simulation of commonly encountered dosing schemes: equal or unequal dosing intervals, bolus and/or constant rate drug input, with or without loading dose. Appropriate pharmacokinetic models are defined independently of dosage regimen selection. The program can be used in routine operation for visualization of drug accumulation and optimum dosage regimen. Examples of the program outputs are presented.     

Maxsim2—Real-time interactive simulations for computer-assisted teaching of pharmacokinetics and pharmacodynamics

We developed a computer program for use in undergraduate and graduate courses in pharmacology, pharmacokinetics and pharmacodynamics. This program can also be used in environmental and toxicological studies and preclinical simulation, to facilitate communication between modeling pharmacokineticists and project leaders or other decision-makers in the pharmaceutical industry. The program simulates the drug delivery and transport by means of (I) a six-compartment physiological pharmacokinetic flow model, (II) a system of traditional compartment models, or (III) a target-mediated drug disposition system. The program also can be used to simulate instantaneous equilibria between concentration and pharmacodynamic response, or as temporal delays between concentration and response. The latter is done by means of turnover models (indirect response models). Drug absorption, distribution, and elimination are represented by differential equations, which are described by organ and tissue volumes or other volumes of distribution, blood flows, clearance terms, and tissue-to-blood partition coefficients. The user can control and adjust these parameters by means of a slider in real time. By interactively changing the parameter values and simultaneously displaying the resulting concentration–time and/or response–time profiles, users can understand the major mechanisms that govern the disposition or the pharmacological response of the drug in the organism in real time. Schedule dependence is typically seen in clinical practice with a non-linear concentration–response relationship, and is difficult to communicate except via simulations. Here, we sought to illustrate the potential advantages of this approach in teaching pharmacology, pharmacokinetics, and pharmacodynamics to undergraduate pharmacy-, veterinary-, and medical students or to project teams in drug discovery/development.     

Dynamical dosage regimen calculations in linear pharmacokinetics

The objective of this analysis of a linear compartment system is to compute drug input functions that are optimal in producing nontoxic pharmacological responses of maximal therapeutic efficacy. Pharmacokinetics should underlie the rational use of drugs and when a therapeutic range is known, the achievement of safe and effective target concentrations may be assured by a dosage regimen computed for a given administration schedule. The method developed herein is based on linearity and superimposition principles applicable to the class of systems considered. This method requires estimated values of model individual parameters and computes optimum dosage regimens in an iterative scheme, corresponding to a real time dynamical context. An interactive computer program has been developed to perform dosage regimen calculations.     

水厂混凝投药大滞后过程的数据驱动直接控制方法

以自来水厂混凝投药大时滞过程为研究对象,在迭代反馈整定(IFT)方法的基础上,结合Smith预估控制结构,提出了一种混凝投药过程数据驱动直接控制算法.着重针对过程大时滞的特点,在性能指标中加入了预估误差惩罚因子.提出了一种新的步长设置方法,使得步长的下降速率可调.设计了3个闭环实验来求取性能指标梯度向量的无偏估计,完全...