New Perspectives in Clinical Pharmacokinetics-1: the Importance of Updating the Teaching in Pharmacokinetics that both Clearance and Elimination Rate Constant Approaches Are Mathematically Proven Equally Valid

The healing professions have only about four main therapeutic tools at their disposal-surgery, drugs, physical therapy, and psychotherapy. For the general profession of internal medicine, drug therapy is its primary tool. Providing an understanding of the state-of-the-art in therapeutic methods, grounded in solid scientific and mathematical rigor, is therefore of the utmost clinical importance for both physicians and clinical pharmacists. This is particularly true where rapidly evolving scientific changes require an up-to-date education upon which students can rely. Unfortunately, relatively little attention has been paid to training clinical pharmacokineticists and physicians to manage drug therapy optimally for patients under their care in their everyday practice. In this paper, we discuss one of these basic deficiencies from the perspective of the longstanding controversy in pharmacokinetic modeling: whether the volume and clearance approach or the volume and rate constant approach is somehow "better". We examine this controversy using the mathematical principle of invariance, which to our knowledge has not been done before. The conclusion of this analysis is that both approaches are rigorously proven mathematically to be equally valid. We also discuss some implications of these equally valid approaches from the framework of mechanistic and non-compartmental models. Ultimately, the conclusion is that the choice of one parameterization over the other is based on preference or usefulness for research or clinical practice, but no longer, because of this analysis, on science.

Accurately Achieving Target Busulfan Exposure in Children and Adolescents With Very Limited Sampling and the BestDose Software

BACKGROUND

Busulfan dose adjustment is routinely guided by plasma concentration monitoring using 4-9 blood samples per dose adjustment, but a pharmacometric Bayesian approach could reduce this sample burden.

METHODS

The authors developed a nonparametric population model with Pmetrics. They used it to simulate optimal initial busulfan dosages, and in a blinded manner, they compared dosage adjustments using the model in the BestDose software to dosage adjustments calculated by noncompartmental estimation of area under the time-concentration curve at a national reference laboratory in a cohort of patients not included in model building.

RESULTS

Mean (range) age of the 53 model-building subjects was 7.8 years (0.2-19.0 years) and weight was 26.5 kg (5.6-78.0 kg), similar to nearly 120 validation subjects. There were 16.7 samples (6-26 samples) per subject to build the model. The BestDose cohort was also diverse: 10.2 years (0.25-18 years) and 46.4 kg (5.2-110.9 kg). Mean bias and imprecision of the 1-compartment model-predicted busulfan concentrations were 0.42% and 9.2%, and were similar in the validation cohorts. Initial dosages to achieve average concentrations of 600-900 ng/mL were 1.1 mg/kg (≤12 kg, 67% in the target range) and 1.0 mg/kg (>12 kg, 76% in the target range). Using all 9 concentrations after dose 1 in the Bayesian estimation of dose requirements, the mean (95% confidence interval) bias of BestDose calculations for the third dose was 0.2% (-2.4% to 2.9%, P = 0.85), compared with the standard noncompartmental method based on 9 concentrations. With 1 optimally timed concentration 15 minutes after the infusion (calculated with the authors' novel MMopt algorithm) bias was -9.2% (-16.7% to -1.5%, P = 0.02). With 2 concentrations at 15 minutes and 4 hours bias was only 1.9% (-0.3% to 4.2%, P = 0.08).

CONCLUSIONS

BestDose accurately calculates busulfan intravenous dosage requirements to achieve target plasma exposures in children up to 18 years of age and 110 kg using only 2 blood samples per adjustment compared with 6-9 samples for standard noncompartmental dose calculations.

Two general methods for population pharmacokinetic modeling: non-parametric adaptive grid and non-parametric Bayesian

Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org.

Noninvasive Hemodynamic Monitoring for Combat Casualties

The aims of this study were to develop and to test a noninvasive hemodynamic monitoring system that could be applied to combat casualties to supplement conventional vital signs, to use an advanced information system to predict outcomes, and to evaluate the relative effectiveness of various therapies with instant feedback information during acute emergency conditions. In a university-run inner city public hospital, we evaluated 1,000 consecutively monitored trauma patients in the initial resuscitation period, beginning shortly after admission to the emergency department. In addition to conventional vital signs, we used noninvasive monitoring devices (cardiac index by bioimpedance with blood pressure and heart rate to measure cardiac function, arterial hemoglobin oxygen saturation by pulse oximetry to reflect changes in pulmonary function, and tissue oxygenation by transcutaneous oxygen tension indexed to fractional inspired oxygen concentration and carbon dioxide tension to evaluate tissue perfusion). The cardiac index, mean arterial pressure, pulse oximetry (arterial hemoglobin oxygen saturation), and transcutaneous oxygen tension/fractional inspired oxygen concentration were significantly higher in survivors, whereas the heart rate and carbon dioxide tension were higher in nonsurvivors. The calculated survival probability was a useful outcome predictor that also served as a measure of severity of illness. The rate of misclassification of survival probability was 13.5% in the series as a whole but only 6% for patients without severe head injuries and brain death. Application of noninvasive hemodynamic monitoring to acute emergency trauma patients in the emergency department is feasible, safe, and inexpensive and provides accurate hemodynamic patterns in continuous, on-line, real-time, graphical displays of the status of cardiac, pulmonary, and tissue perfusion functions. Combined with an information system, this approach provided an early outcome predictor and evaluated, with an objective individualized method, the relative efficacy of alternative therapies for specific patients.

Continuous noninvasive monitoring of cardiac performance and tissue perfusion in pediatric trauma patients

PURPOSE

The aim of this study was to assess the accuracy of a continuous survival probability prediction using noninvasive measures of cardiac performance and tissue perfusion in severely injured pediatric patients.

METHODS

Review of all patients entered into a prospective noninvasive monitoring protocol. Cardiac index (CI) was measured using a thoracic bioimpedance device and tissue perfusion was assessed by transcutaneous carbon dioxide (Ptcco(2)) tension and oxygen tension indexed to the fraction of inspired oxygen (Ptco(2)/Fio(2)). Survival probability (SP) was continuously calculated using a stochastic analysis program.

RESULTS

There were 45 patients with a total of 953 data sets. The mean age was 11 years (range, 1-16 years) with a mean Injury Severity Score of 24 (+/-16). There was no difference between survivors (n = 32) and nonsurvivors (n = 13) at study entry for heart rate, blood pressure, CI, or pulse oximetry (all P > .05). However, survivors demonstrated higher Ptcco(2) (45 vs 35), higher Ptco(2)/Fio(2) (236 vs 156), and higher predicted SP (89% vs 62%) compared with nonsurvivors at study entry and throughout the monitoring period (all P < .01). For the entire data set, the strongest independent predictors of survival were Ptco(2)/Fio(2) and SP. The area under the receiver operating characteristic curve for mortality prediction was 0.83 for SP and 0.71 for Ptco(2)/Fio(2), compared with 0.6 for heart rate, 0.51 for blood pressure, and 0.53 for CI. Similar hemodynamic patterns were observed for all injury patterns with the exception of those with severe brain injury.

CONCLUSIONS

Thoracic bioimpedance and transcutaneous monitoring give critical real-time hemodynamic and tissue perfusion data that can provide early identification of pathologic flow patterns and accurately predict survival.

Achieving target goals most precisely using nonparametric compartmental models and "multiple model" design of dosage regimens

Multiple model (MM) design and stochastic control of dosage regimens permit essentially full use of all the information contained in either a Bayesian prior nonparametric EM (NPEM) population pharmacokinetic model or in an MM Bayesian posterior updated parameter set, to achieve and maintain selected therapeutic goals with optimal precision (least predicted weighted squared error). The regimens are visibly more precise in the achievement of desired target goals than are current methods using mean or median population parameter values. Bayesian feedback has now also been incorporated into the MM software. An evaluation of MM dosage design using an NPEM population model versus dosage design based on conventional mean population parameter values is presented, using a population model of vancomycin. Further feedback control was also evaluated, incorporating realistic simulated uncertainties in the clinical environment such as those in the preparation and administration of doses.

Model-based, goal-oriented, individualised drug therapy. Linkage of population modelling, new 'multiple model' dosage design, bayesian feedback and individualised target goals

This article examines the use of population pharmacokinetic models to store experiences about drugs in patients and to apply that experience to the care of new patients. Population models are the Bayesian prior. For truly individualised therapy, it is necessary first to select a specific target goal, such as a desired serum or peripheral compartment concentration, and then to develop the dosage regimen individualised to best hit that target in that patient. One must monitor the behaviour of the drug by measuring serum concentrations or other responses, hopefully obtained at optimally chosen times, not only to see the raw results, but to also make an individualised (Bayesian posterior) model of how the drug is behaving in that patient. Only then can one see the relationship between the dose and the absorption, distribution, effect and elimination of the drug, and the patient's clinical sensitivity to it; one must always look at the patient. Only by looking at both the patient and the model can it be judged whether the target goal was correct or needs to be changed. The adjusted dosage regimen is again developed to hit that target most precisely starting with the very next dose, not just for some future steady state. Nonparametric population models have discrete, not continuous, parameter distributions. These lead naturally into the multiple model method of dosage design, specifically to hit a desired target with the greatest possible precision for whatever past experience and present data are available on that drug--a new feature for this goal-oriented, model-based, individualised drug therapy. As clinical versions of this new approach become available from several centers, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

Pharmaco-informatics: more precise drug therapy from "multiple model" (MM) stochastic adaptive control regimens: evaluation with simulated vancomycin therapy

MM stochastic control of dosage regimens permits essentially full use of information, either in a population pharmacokinetic model or a Bayesian updated MM parameter set, to achieve and maintain selected therapeutic goals with optimal precision. The regimens are visibly more precise than those developed using mean parameter values. Bayesian MM feedback has now also been implemented.