Intrapulmonary pharmacokinetics of high doses of tigecycline in patients with ventilator-associated pneumonia

Tigecycline is commonly used for infections by multidrug-resistant bacteria. However, it is not approved for ventilator-associated pneumonia (VAP) as increased mortality has been reported in VAP patients treated with conventional doses. The purpose of this study was to prospectively evaluate the intrapulmonary pharmacokinetics of off-label high-dose tigecycline in patients with VAP. Nine mechanically ventilated patients received tigecycline intravenously (loading dose 200 mg followed by 100 mg every 12 h). After ≥5 doses, two bronchoscopies were performed in each patient on consecutive days and eight blood samples were collected. Tigecycline concentrations in plasma and bronchoalveolar lavage fluid were determined by liquid chromatography. The urea dilution method was used to calculate epithelial lining fluid (ELF) concentrations. A two-compartmental pharmacokinetic (PK) model with linear elimination was used to estimate PK parameters. Mean patient age was 69 ± 11.86 years and mean APACHE II score was 21. The estimated population mean PK parameters (relative standard error) were: clearance, 11.64 L/h (54%); volume of distribution in central compartment, 79.01 L (37%); volume of distribution in peripheral compartment, 92.95 L (17%); intercompartmental clearance, 62.81 L/h (34%); and ELF penetration ratio, 2.41 (40%). C_max, C_min, plasma AUC_0-12, plasma fAUC_0-12 and ELF AUC_0-12 were 1.99 ± 1.82 μg/mL, 0.81 ± 1.27 μg/mL, 12.89 ± 17.25 μg•h/mL, 3.24 ± 3.09 μg•h/mL and 7.13 ± 2.61 μg•h/mL, respectively. The increased plasma and ELF AUC_0-12 achieved with a 200 mg daily tigecycline dose, combined with high ELF penetration, support the effectiveness of off-label high-dose tigecycline in VAP.

Dose individualization of intravenous busulfan in pediatric patients undergoing bone marrow transplantation: impact and in vitro evaluation of infusion lag-time

OBJECTIVES

To apply therapeutic drug monitoring and dose-individualization of intravenous Busulfan to paediatric patients and evaluate the impact of syringe-pump induced Busulfan infusion lag-time after in vitro estimation.

METHODS

76 children and adolescents were administered 2 h intravenous Busulfan infusion every 6 h (16 doses). Busulfan plasma levels, withdrawn by an optimized sampling scheme and measured by a validated HPLC-PDA method, were used to estimate basic PK parameters, AUC, Cmax, kel, t1/2, applying Non-Compartmental Analysis. In vivo infusion lag-time was simulated in vitro and used to evaluate its impact on AUC estimation.

KEY FINDINGS

Mean (%CV) Busulfan AUC, Cmax, clearance and t1/2 for pediatric population were found 962.3 μm × min (33.1), 0.95 mg/L (41.4), 0.27 L/h/kg (33.3), 2.2 h (27.8), respectively. TDM applied to 76 children revealed 6 (7.9%) being above and 25 (32.9%) below therapeutic-range (AUC: 900-1350 μm × min). After dose correction, all patients were measured below toxic levels (AUC < 1500 μm × min), no patient below 900 μm × min. Incorporation of infusion lag-time revealed lower AUCs with 17.1% more patients and 23.1% more younger patients, with body weight <16 kg, being below the therapeutic-range.

CONCLUSIONS

TDM, applied successfully to 76 children, confirmed the need for Busulfan dose-individualization in paediatric patients. Infusion lag-time was proved clinically significant for younger, low body-weight patients and those close to the lower therapeutic-range limit.

Pharmacokinetics of doripenem in CSF of patients with non-inflamed meninges

OBJECTIVES

To investigate intact blood-brain barrier (BBB) penetration by doripenem and characterize doripenem pharmacokinetics in CSF using a pharmacokinetic model.

PATIENTS AND METHODS

Thirty-eight neurological patients with no active neurological disease or CNS infection received a single 500 mg doripenem dose before pump implantation surgery, or lumbar puncture, for intrathecal baclofen administration. In most cases single CSF and blood samples were collected per patient and analysed for doripenem with HPLC. A two-stage pharmacokinetic analysis was performed to estimate: (i) empirical Bayesian estimates (EBEs) of individual doripenem plasma pharmacokinetic parameters, using plasma doripenem concentrations and literature population priors for a two-compartment model; and (ii) doripenem CSF pharmacokinetic parameters using simulated plasma concentrations from stage (i) as a forcing function. The mean values of the structural model parameters, k(CSF) (distribution rate constant) and PC (CSF/plasma partition coefficient), and the residual variability were estimated.

RESULTS

The mean estimates of the parameters were k(CSF)= 0.105 h(-1) and PC= 0.053, corresponding to mean steady-state doripenem CSF concentrations of 0.20 mg/L and 0.40 mg/L for regimens of 3 × 500 mg daily and 3 × 1000 mg daily, respectively, and a mean equilibrium half-life of 6.6 h. The model was validated internally using a visual predictive check (VPC) and bootstrap. Simulating two dosing scenarios gave doripenem levels in the CSF above or close to the literature MIC values.

CONCLUSIONS

The present NONMEM software analysis shows that doripenem crosses intact BBB significantly and suggests that the drug should be further evaluated as a candidate to treat certain CNS infections, since drug penetration through BBB is enhanced by meningeal inflammation.

Proper lumping in systems biology models

An algorithm for automatic order reduction of models defined by large systems of differential equations is presented. The algorithm was developed with systems biology models in mind and the motivation behind it is to develop mechanistic pharmacokinetic/pharmacodynamic models from already available systems biology models. The approach used for model reduction is proper lumping of the system's states and is based on a search through the possible combinations of lumps. To avoid combinatorial explosion, a heuristic, greedy search strategy is employed and comparison with the full exhaustive search provides evidence that it performs well. The method takes advantage of an apparent property of this kind of systems that lumps remain consistent over different levels of order reduction. Advantages of the method presented include: the variables and parameters of the reduced model retain a specific physiological meaning; the algorithm is automatic and easy to use; it can be used for nonlinear models and can handle parameter uncertainty and constraints. The algorithm was applied to a model of NF-B signalling pathways in order to demonstrate its use and performance. Significant reduction was achieved for the example model, while agreement with the original model was proportional to the size of the reduced model, as expected. The results of the model reduction were compared with a published, intuitively reduced model of NF-B signalling pathways and were found to be in agreement, in terms of the identified key species for the system's kinetic behaviour. The method may provide useful insights which are complementary to the intuitive reduction approach, especially in large systems.

Nonlinear dynamics and chaos theory: concepts and applications relevant to pharmacodynamics

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological systems. It is widely appreciated that chaotic behavior dominates physiological systems. This is suggested by experimental studies and has also been encouraged by very successful modeling. Pharmacodynamics are very tightly associated with complex physiological processes, and the implications of this relation demand that the new approach of nonlinear dynamics should be adopted in greater extent in pharmacodynamic studies. This is necessary not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale, fundamentally different from the classic approach. In this work the basic principles of dynamical systems are presented and applications of nonlinear dynamics in topics relevant to drug research and especially to pharmacodynamics are reviewed. Special attention is focused on three major fields of physiological systems with great importance in pharmacotherapy, namely cardiovascular, central nervous, and endocrine systems, where tools and concepts from nonlinear dynamics have been applied.

An alternative method for the estimation of the terminal slope when a few data points are available

Phase plane plots are graphical expressions for differential equations plotting the state derivative dc/dt versus the state c. Using these plots, we developed a novel method for the estimation of the terminal slope from time-concentration data. The values of the derivatives used for the construction of the phase plane plots were calculated by two different methods of numerical differentiation. The first method (D1) is based on the classical calculation of slope of the line connecting two successive data points. The alternative method (D2) relies on an initial second-order polynomial interpolation utilizing three successive data points followed by the calculation of the derivative at each one of the concentration values. A forced-through-zero linear regression of the phase plane plot data is used to derive an estimate for the slope. For comparative purposes, the standard approach based on the semilogarithmic plot was also applied. For a hypothetical drug absorbed by first-order process into a one-compartment model, simulated time-concentration data disturbed by a Gaussian zero mean random error with various coefficients of variation were generated. Various sampling schedules, with two, three, four, or five data points, were utilized for the estimation of the terminal slope. Performances of the proposed methods on simulated data were expressed by means of root-mean-squared error, bias, and standard deviation. In all cases, D2 was superior to D1. The D2 method outperforms the standard method in that it furnishes estimates closer to the real values in all cases when two data points and in most cases when three data points were used. All methods behave similarly when four or five data points were used.

Modeling of supersaturated dissolution data

A recursion equation which relies on the population growth model of dissolution is used for the analysis of supersaturated dissolution data. The concentration-time data of dissolution experiments are initially transformed to fractions of dose dissolved-generations by adopting an appropriate time interval as the time step of the recursion equation. A computer program is used to derive estimates for the maximum fraction of dose dissolved and the fraction of dose remaining in solution at steady state. Good fittings were observed when this equation was applied to phenytoin and nifedipine supersaturated dissolution data obtained from literature.

Investigation of absorption kinetics by the phase plane method

PURPOSE

To develop a simple approach for investigating absorption kinetics, which does not require modeling assumption or intravenous data.

METHODS

The concentration (C) -time (t) data are plotted as a phase plane plot (dCldt versus C). Errorless C,t data were generated from one and two compartment models employing first-order, zero-order and Michaelis-menten input kinetics, and the phase plane plots were constructed. A simple test based on the ratio of slopes of the separate linear regression analyses of absorption and elimination data of the phase plane plot is proposed to justify or not the presence of zero order input kinetics. Errant data were used to assess the performance of the test developed. Literature data of theophylline and nitroglycerin formulations were analyzed using the phase plane plot. Input rate-time profiles were constructed for one compartment model drugs utilizing the data of the phase plane plot.

RESULTS

The geometric forms of the phase plane plots derived form the errorless data of the various pharmacokinetic models were found to be indicative of the absorption kinetics. Very good resulted were obtained when the test for he discernment of absorption kinetics was applied to errant data. Zero-order absorption kinetics were justified (i) for the transdermal absorption of nitroglycerin and (ii) only for a certain period of time, for the gastrointestinal absorption of theophylline.

CONCLUSIONS

Investigation of absorption kinetics can be accomplished with the phase plane method. The cumulative character of the classical percent absorbed versus time plots can be misleading in justifying the presence of zero-order input kinetics.

A population growth model of dissolution

PURPOSE

To develop a new approach for describing drug dissolution which does not require the presuppositions of time continuity and Fick's law of diffusion and which can be applied to both homogeneous and heterogeneous media.

METHODS

The mass dissolved is considered to be a function of a discrete time index specifying successive "generations" (n). The recurrence equation: phi n + 1 = phi n + r(1 - phi n)(1 - phi n X0/theta) was derived for the fractions of dose dissolved phi n and phi n+1, between generations n and n + 1, where r is a dimensionless proportionality constant, X0 is the dose and theta is the amount of drug corresponding to the drug's solubility in the dissolution medium.

RESULTS

The equation has two steady state solutions, phi ss = 1 when (X0/theta) < or = 1 and phi ss = theta/X0 when (X0/theta) > 1 and the usual behavior encountered in dissolution studies, i.e, a monotonic exponential increase of phi n reaching asymptotically the steady state when either r < theta/X0 < 1 or r < 1 < theta/X0. Good fits were obtained when the model equation was applied to danazol data after appropriate transformation of the time scale to "generations". The dissolution process is controlled by the two dimensionless parameters theta/X0 and r, which were found to be analogous to the fundamental parameters dose and dissolution number, respectively. The model was also used for the prediction of fraction of dose absorbed for highly permeable drugs.

CONCLUSIONS

The model does not rely on diffusion principles and therefore it can be applied under both homogeneous and non-homogeneous conditions. This feature will facilitate the correlation of in vitro dissolution data obtained under homogeneous conditions and in vivo observations adhering to the heterogeneous milieu of the GI tract.