Steady-state dosage regimen calculations in linear pharmacokinetics

Kinetic nomograms assist individualization of drug regimens

BACKGROUND AND OBJECTIVES

Therapeutic drug monitoring is applied to a range of drugs. To predict an appropriate dosing regimen, models based on Bayesian techniques have been used. However, this approach requires a well trained professional and sophisticated software. The objectives of this study were first to develop kinetic nomograms as a useful tool to achieve individual drug blood concentrations within the therapeutic window, using few samples and in a short period of time; and second to evaluate the performance of these nomograms in dosage adjustment and compare them with the Bayesian procedure by use of simulation.

METHODS

Kinetic nomograms involve collection of concentration-time profiles following repeated administrations of a fixed identification protocol and targeting of a steady-state concentration. The profiles divide the concentration-time space into several areas, each of them corresponding to a given adjusted drug dose. Kinetic nomograms are grounded on the statistical description of the interindividual variability provided by population pharmacokinetic approaches. To use them, the assayed drug concentration in a blood sample is first located in the kinetic nomogram and then the dose corresponding to the area containing this location is read. Evaluation of performance and comparison with the traditional Bayesian procedure were done by a simulation study using the immunosuppressant drug sirolimus (rapamycin). All calculations were performed by use of Matlab software.

RESULTS

The simulation study confirmed the need for individual dosage adjustment; 71.6% of individuals underwent modification of the identification protocol of 1 mg twice daily in order to reach steady-state trough concentrations of 8 ng/mL. When the regimens were adjusted by kinetic nomograms and the Bayesian procedure, the steady-state trough concentrations of sirolimus showed low variability (coefficients of variation [CVs] of 23.4% and 24.0%, respectively) as compared with those obtained by standard recommended protocols of 4 mg once daily (CV 68.6%). The doses adjusted by kinetic nomograms and the Bayesian procedure were linearly linked and highly correlated (r = 0.96), and both provided simultaneous control of minimum and maximum drug concentrations (63.9% and 68.7% of cases between 6 and 20 ng/mL, respectively).

CONCLUSION

Kinetic nomograms allow rapid and reliable dosage adjustment after the start of drug therapy. They are interesting alternatives to the cumbersome Bayesian procedure, and they provide dosage adjustment even for drugs that exhibit large intraindividual variability. In the clinical context, kinetic nomograms render individual dosage adjustment a simplified bedside application, and they could assist population studies aiming at dose individualization.

Therapeutic drug monitoring for dose individualization of Cisplatin in testicular cancer patients based upon total platinum measurement in plasma

Cisplatin (CDDP) is an anticancer agent widely used in testicular cancer, for which pharmacokinetic (PK)/pharmacodynamic relationships have usually been based upon measurement of its unbound fraction in plasma. Because it has been shown that free CDDP clearance can be related to patient's body surface area (BSA), dosage is mostly adjusted a priori using only this single parameter, with mixed results for accurately predicting CDDP exposure and reducing toxicities. In contrast, the authors present here an original, 5-day continuous infusion schedule, coupled to a daily Bayesian adaptive dosing with feedback strategy, based upon the rapid assay of total, rather than free, CDDP in plasma. Nineteen patients (66 therapeutic courses) were treated with platinum-based combinational therapy. Plasma samples were analyzed to allow real-time Bayesian estimation of individual PK parameters with subsequent prospective dose adjustment in order to reach a target Cmax (Cend) of 1.95 mg/L of total platinum. Performance of the Bayesian dosing method was evaluated by comparing target Cmax with achieved Cmax. The mean+/-SD Cmax achieved was 1.93+/-0.16 mg/L. No statistically significant difference was observed between experimental and target values (P>0.05, t test), and Cend achievement was done with an overall 6.6% precision, a performance to be compared with the initial 54% interpatient variability observed in CDDP clearance. A nonlinear mixed effect model population PK analysis was subsequently performed to identify retrospectively the covariates associated with PK parameters of total CDDP. It showed a good correlation (r=0.84, P=0.004) between total platinum clearance and therapeutic course number. A weaker correlation (r=0.59) was found between BSA and total CDDP clearance and, importantly, no additional relationship was established with BSA when successive therapeutic courses, and not only the first one, were considered. This highlights the critical importance of total drug accumulation on CDDP pharmacokinetics when several infusions are to be administered in a row and, therefore, the need for real-time dose individualization that takes into account the course number, rather than BSA. Finally, doses of CDDP administered during each course were significantly higher (+20%, P<0.01) than the ones classically normalized with BSA, thus leading to an overall greater drug exposure in the patients. It is noteworthy that despite these markedly higher doses, little severe toxicity was reported, and all of the patients presented in this study were still alive and disease free after a follow-up of up to 15 years.

Dose Individualization of Carboplatin After a 120-hour Infusion Schedule: Higher Dose Intensity but Fewer Toxicities

Carboplatin (CBDCA) is a widely used anticancer agent for which dose-effect and dose-toxicity relationships have been demonstrated, thus stressing the need for a controlled exposure to this drug. So far, carboplatin administration could only be individualized a priori following 2 classic methods, which are based on the evaluation of renal clearance: Calvert's and Chatelut's formulas. This study was designed to develop and evaluate the performance of an alternative CBDCA 120-hour schedule coupled to a Bayesian adaptive dosing with feedback strategy. Precision of the dosing method was assessed in 84 patients (256 courses performed during a 10-year period), by comparing CBDCA plasma concentrations observed at the end of the infusion with initial target values. A comprehensive monitoring of treatment-related toxicities also was performed. Finally, the authors compared doses actually delivered following the dose-tailoring method with the theoretical, standard, ones calculated retrospectively with Calvert's and Chatelut's formulas. No significant differences were found between experimental and theoretical concentrations. According to the target exposure chosen (3 levels), the mean doses administered to our patients were 517, 719, and 902 mg of CBDCA compared with 550, 509, and 538 or 657, 604, and 644 mg, which would have been given following Calvert or Chatelut formulas, respectively. These results showed that our Bayesian method led to the administration of up to 60% higher doses of carboplatin compared with those based only on the evaluation of renal clearance. Despite the markedly higher doses administered, no severe toxicities were reported in the patients treated following this new schedule. It is noteworthy that neither hematologic growth factors nor stem cells, usually associated with high-dose regimen, were used as support in this study. These data strongly suggest that it is possible to deliver higher dose- intensities of carboplatin, even in elderly, unselected patients, without increasing toxicities and with no growth factor support, provided that a therapeutic drug monitoring strategy with real-time tailored dosing is performed.

Dosage regimen calculations with optimal control theory

In clinical pharmacokinetics, dosage regimen calculation involves determination of either: (1) the drug amount to be administered according to a set time schedule, or (2) the time schedule to be used for appropriate drug amounts. The goal is to guarantee that the time profile of circulating drug levels is between the thresholds of toxicity and efficacy. For the first case, solutions are obtained by using the property of linearity when it holds. Herein, we present several results concerning the second case. The optimal control theory allows determination of switching times between the minimal and maximal input rates in order to ensure the fastest transition from an initial state to the therapeutic levels. Fundamental results are reported and the approach is developed for drugs administered by intravenous infusion. By means of the phase trajectories, general graphical rules are presented to design the optimal control and to determine the reachable areas. A numerical example is given, comparisons of the method with others are attempted and potential developments are pointed out.

Pharmacokinetics of high-dose methotrexate in adult osteogenic sarcoma

The pharmacokinetics of 222 infusions of high-dose methotrexate (MTX) with leucovorin rescue were studied in 22 adults with osteosarcoma. To reduce the variability of plasma concentration, we individualized dose regimens using a Bayesian method to reach a concentration of 10(-3) M MTX at the end of an 8-h infusion. The mean concentration observed at the end of the infusion was 1016 +/- 143 mumol/l. The mean dose delivered was 13.2 +/- 2 g/m2. The clearance was 49.1 +/- 11.7 ml min-1 m-2. The decay of the plasma concentration of MTX after completion of the infusion followed a two-compartment model with a t1/2 alpha of 2.66 +/- 0.82 h and a t1/2 beta of 15.69 +/- 8.63 h. The volume of distribution was 0.32 +/- 0.08 l/kg. As compared with previously published data, the interindividual and intraindividual variations in the concentration at the end of the infusion were reduced, with values of 14% and 5.9%-21%, respectively, being obtained. Severe toxicities were avoided, and there were only 3 hematologic and 8 digestive grade 3 side effects and no grade 4 complication. The t1/2 alpha and the MTX plasma concentrations at 23 and 47 h were correlated with renal toxicity (P < 0.001). However, no correlation was found between the pharmacokinetic parameters and other signs of toxicity. There was no significant difference in pharmacokinetics between the toxic and nontoxic groups. In the same manner, the parameters of the group of patients sensitive to MTX were not statistically significant different from those of the group of nonsensitive patients.

Pharmacokinetics and metabolism of epirubicin administered as i.v. bolus and 48-h infusion in patients with advanced soft-tissue sarcoma

We have studied the pharmacokinetics of epirubicin after its administration in sarcoma patients either as an i.v. bolus or as a 48-h infusion (5 courses each; 9 patients in total). Bolus injection was followed by a three exponential decay in plasma, with half-lives of 2.43 min, 1.95 h and 21.7 h; 48-h infusions were characterized by the very rapid establishment of a plasma plateau concentration followed by a biexponential decay after stopping the infusion. Pharmacokinetic parameters such as total plasma clearance, total volume of distribution, mean residence time and elimination half-life were similar, irrespective of the duration of the administration. In contrast, the relative amounts of the metabolites of epirubicin were reduced when the drug was administered over 48 h; in particular, the plasma levels of epirubicin glucuronide never exceeded those of epirubicin, which always occur after bolus injection. This may result from a lower availability of epirubicin for metabolism. These results now require validation in a larger group of patients using a cross-over design.

Pharmacokinetics of navelbine after oral administration in cancer patients

The pharmacokinetic behavior of navelbine was investigated in 19 patients presenting with advanced cancers (mainly women with breast cancer). Navelbine was given orally at seven dose levels of up to 200 mg/week. For a given dose, patients received four successive weekly treatments. Five subjects also received two different doses. After drug administration, plasma was collected for 48 or 72 h and monitored for navelbine concentration by radioimmunoassay. Absorption of navelbine was very rapid after oral administration: maximal drug concentrations were reached within the first 1 or 2 h (Tmax, 0.9-1.75 h; cmax, 70.9-832.6 ng/ml), with absorption constants ranging from 0.85 to 2.42 l/h. A comparison of dose-normalised plasma concentration profiles revealed significant time dependence in six evaluable patients (P less than 0.001). Only four subjects who received low doses (less than or equal to 100 mg/week) exhibited time-independent kinetics. All of the five patients who were treated at different doses displayed apparent dose dependence (P less than 0.001). No individual profile was characterised by both time- and dose-independent pharmacokinetics. In all, 18 patients presented biphasic plasma concentration-decay patterns, and only 1 subject exhibited monophasic decay kinetics. The navelbine pharmacokinetic parameters obtained following oral administration were similar to those observed after i.v. bolus injection and were characterised by high oral clearance (0.43-1.45 1 h-1 kg-1), a large apparent volume of distribution (27.4-45.9 1/kg), and a long terminal half-life (24.2-56.5 h). Large intra- and inter-individual variations in pharmacokinetic parameters were observed. Moreover, after a high dose of 200 mg, an enterohepatic cycle and/or a delay in navelbine's absorption at a distal intestinal site as evidenced by a marked plasma level rebound was observed.

High-dose cytosine arabinoside and mitoxantrone in previously-treated acute leukemia patients

35 patients with refractory or relapsed acute leukemia received salvage chemotherapy using high-dose cytosine arabinoside 2 g/m2 intravenously for 3 hours every 12 h, in 8 doses, followed by continuous infusion of mitoxantrone 12 mg/m2/day for 2 d. 9 patients had acute myeloblastic leukemia (AML), (4 relapsed, 5 refractory), 20 had acute lymphoblastic leukemia (ALL) (11 relapsed, 9 refractory) and 6 had chronic myelogenous leukemia (CML) in the blastic phase (BP). 4 out of 9 AML and 16 out of 20 ALL achieved complete remission. Median survival was 6 months for all patients and 10 months for responders. A short (1.5 months) chronic phase was achieved in 3 patients with CML. The main toxic effect was hematologic. A pharmacokinetic study was performed on mitoxantrone. No correlation was found with clinical response. The combination of mitoxantrone and ara-C is an effective antileukemic regimen, especially in ALL.

Population pharmacokinetics of mitoxantrone performed by a NONMEM method

To date, the pharmacokinetics of mitoxantrone (1,4-dihydroxy-5,8-bis[[2-[(2- hydroxyethyl)amino]ethyl]amino]anthraquinone) has been described either by an open two- or three-compartment model, showing high interindividual variability. In order to evaluate this variability, residual intraindividual variability, and measurement error, we carried out a population study. A sensitive HPLC method allowed analysis of blood samples drawn from 21 patients with breast cancer or acute nonlymphocytic leukemia. Individual data treatment (22 kinetics) using weighted nonlinear least squares regression confirmed the huge interindividual variability whatever the administration protocol of mitoxantrone: bi- or tri-exponential models fitted the data. The NONMEM population method used herein describes all concentration-time curves by a single three-compartment model, considering biphasic kinetics as fragmentary data. Residual intraindividual variability was 21.4%. Population mean values (+/- interindividual SD) of clearance, terminal half-life, and total volume of distribution were, respectively, 23.40 (+/- 10.76) L/h, 46.87 (+/- 12.18) h, and 385.49 (+/- 196.60) L. These results are of particular interest in clinical routines to calculate dosage regimens by Bayesian estimation methods.

Multiple-dose pharmacokinetics of the new H1-receptor antagonist tazifylline in healthy volunteers

The multiple-dose pharmacokinetics of the new H1-receptor antagonist, tazifylline, were investigated in healthy volunteers. From single-dose data, tazifylline appeared to be rapidly absorbed (median tmax of 0.6 h) and eliminated (t1/2 = 1.0 +/- 0.2 h). However, plasma levels measured on days 3 and 8 of the multiple-dose regimen (10 mg b.i.d. for 8 days) indicated moderate accumulation. A two-compartment model best described multiple-dose data with a terminal half-life of 15.6 +/- 7.6 h consistent with twice-daily dosing of tazifylline.

Naproxen kinetics in synovial fluid of patients with osteoarthritis

1. The kinetics of naproxen in synovial fluid were studied in 407 osteoarthritic outpatients with knee effusion requiring aspiration, following a single 1100 mg oral dose of naproxen sodium. 2. The drug concentration-time profiles were described by a biexponential function. Naproxen entered synovial fluid rapidly, reaching a maximum concentration of 36 mg l-1 (Cmax) at 7.5 h. The first order input rate constant (kOs) was 0.41 +/- 0.15 h-1 with a lag time (tlag) of 0.24 +/- 0.36 h. 3. Elimination from the fluid was slow (t1/2 = 31 +/- 12 h) and appreciable drug concentrations were still measurable (27 mg l-1) after 24 h. 4. During once daily dosing of naproxen sodium, naproxen should accumulate in synovial fluid, a steady-state being achieved within a week of treatment. The predicted accumulation ratio based on trough concentration was 2.4.

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.