### Introduction

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- References

Infection by *P. aeruginosa* can seriously jeopardise the prognosis for burn patients and necessitates rapid antibiotic treatment. Among the antibiotics available, ceftazidime remains the drug of choice, but its pharmacokinetics may be modified in such patients. Like other β-lactam antibiotics, the pharmacokinetics of ceftazidime are defined by high renal excretion and a volume of distribution similar to that of the extracellular space [1]. As ceftazidime is completely excreted by the kidneys, following glomelurar filtration, 88% of the dose is recovered in the urine over 24 h [2]. Consequently, the changes in the glomerular filtration in the hypermetabolic phase after a burn injury probably affect the pharmacokinetics of ceftazidime [3].

During the hypermetabolic phase, beginning 48 h after the thermal injury, cardiac output increases as long as adequate intensive care has been given. This is accompanied by an increase in blood flow to the kidneys (with a corresponding increase in glomerular filtration rate) and liver [4]. There are few studies on the pharmacokinetics of ceftazidime in burn patients and in most cases only in a small number of patients. Only one study has investigated the pharmacokinetics of ceftazidime in burn patients using a population pharmacokinetic approach [5] in which substantial differences compared with other patients were observed, with high interindividual variability. The aim of our study was to evaluate the disposition of ceftazidime in burn patients who were in the hypermetabolic phase, and to identify clinical and biological determinants of its pharmacokinetics.

### Results

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- References

Fifty burn patients, with a total of 237 serum ceftazidime concentrations were included in the analysis, corresponding to a mean of 4.7 measurements per patient. Figure 1 shows the individual concentrations normalized to the mean daily dose kg^{−1} over time. The population characteristics are presented in Table 1. The patients were relatively old (age 52 ± 21 years) and badly injured (UBS = 65 ± 50), with mechanical ventilation being required in 32% of cases. Mean ± SD serum creatinine was in the normal range (76.5 ± 21.8 µmol l^{−1}) as was the mean creatinine clearance (105 ± 39.3 ml min^{−1}) which showed considerable interindividual variability (range 33–191).

Table 1. Characteristics of the burn patients studied (*n* = 50) | **Mean ± SD** | **Range** | **CODE** |
---|

*Quantitative variables* |

Age (years) | 52.3 ± 20.7 | 15–90 | AGE |

Body weight (kg) | 71.3 ± 13.5 | 50–108 | WT |

Burned surface area (% of the total body surface) | 23.0 ± 13.5 | 10–62 | BSA |

Baux index | 75.6 ± 22.4 | 30–122 | BAUX |

UBS index | 64.8 ± 50.0 | 10–233 | UBS |

Tobiasen index | 7.0 ± 1.8 | 4–11 | TOBI |

Serum creatinine (µmol l^{−1}) | 76.5 ± 21.8 | 35–141 | CREA |

Creatinine clearance (ml min^{−1}) | 105.3 ± 39.3 | 33–191 | CLCR |

Proteinaemia (g l^{−1}) | 56.8 ± 7.1 | 38–69 | PROT |

BUN (mmol l^{−1}) | 7.3 ± 3.6 | 2–19 | BUN |

*Qualitative variables* |

Gender |

Men = 0; women = 1 | 38 | 12 | SEX |

Mechanical ventilation |

Without = 0; with = 1 | 34 | 16 | VENT |

The initial values of the pharmacokinetic parameters that were used to initiate iteration algorithms were obtained from the work of Walstad *et al.*[13] on the pharmacokinetics of ceftazidime in burn patients.

Two models, a one-compartment model (ADVAN1-TRANS2) and a two-compartment model (ADVAN3-TRANS4), were studied.

The one-compartment model incorporating an error model showed a marked bias (−11.7 mg l^{−1}) described by the equation:

where DV is the observed concentrations and PRED the predicted concentrations. The relationship between individual predicted concentrations (IPRED) and the observed concentrations follows the equation:

with a bias of −2.93 mg l^{−1}. This model had an objective function of 1824.628.

Figure 2 represents the regression lines between the observed concentrations (DV or dependant variable) and predicted concentrations (PRED) starting from the population and individual (IPRED) parameters using a two-compartment model. The following equations describe this second model:

- (1)

- (2)

- (3)

- (4)

where CL = total body clearance in l h^{−1}, *V*1 = the distribution volume of the central compartment in l, *V*2 = the distribution volume of the peripheral compartment in l and Q = the distribution clearance describing ceftazidime exchange between the central and peripheral compartments.

The two-compartment model showed a less marked bias (−5.97 mg l^{−1}) of the adjustment than the preceding model, and is described by the equation;

The two-compartment model based on the individual predicted concentrations is described by the equation:

with a bias of −1.88 mg l^{−1}. This model had an objective function of 1749.280 and showed a greater homogeneity in the distribution of the concentrations about the identity line. Overall, the two-compartment model gave the best fit to the data.

For this model, two tests of modelling of the error were carried out. The additive error model was described by the following equation:

where η is the interindividual variance. In this model IPRED = 0.6498 × DV + 10.057 (*r*^{2} = 0.7829) with a bias of +1.91 mg l^{−1}. However, the additive error model described the variability in the concentrations poorly.

The proportional error model was described by the equation:

The distribution of the residues (RES) (Figure 3A) and the weighted residues (WRES) (Figure 3B) according to the predicted concentrations (PRED) from the two-compartment model incorporating a proportional error model, is shown in Figure 3. In this model IPRED = 0.7141 × DV + 10.968 (*r*^{2} = 0.8362). The residues show a horizontal funnel-shaped distribution, typical of a multiplicative variability. The respective precisions were 20.5 for the additive model and 17.6 for the multiplicative model. The objective function was lower and the proportional error model was more accurate in describing residual and interpatient variability.

Our basic pharmaco-statistical model is a two-compartment model with a proportional error. It is characterized by the parameters given in Table 2. Mean clearance was 4.03 l h^{−1} with an interindividual variability of 27%, the distribution volume of the central compartment was 20.7 l (interindividual variability of 23%), intercompartmental clearance was 3.57 l h^{−1} (interindividual variability: 363%), and the distribution volume of the peripheral compartment was 128 l (interindividual variability: 190%). The residual variability including intraindividual variability and errors of measurement (sampling time, measured concentrations.) was 38%.

Table 2. Pharmacokinetic parameters obtained from the basic pharmaco-statistical model **Pharmacokinetic parameters** | **Mean** | **Interindividual variability** | **Confidence interval** |
---|

Clearance (l h^{−1}) | 4.03 | 27% | 2.89–5.17 |

Distribution volume of the central compartment (l) | 20.7 | 23% | 17.4–24.0 |

Inter-compartmental clearance (l h^{−1}) | 3.57 | 363% | 1.05–6.09 |

Distribution volume of the peripheral compartment (l) | 128 | 190% | 35–221 |

In a preliminary screening, the influence of covariates was examined one by one in this structural model. Many covariates decreased the objective function and the interindividual variability in the pharmacokinetic parameter. These were age, Baux index, creatinine clearance, serum creatinine, Na, pCO_{2}, SaO_{2}, alkaline phosphatases, body weight, proteinaemia, BUN, alkaline reserve, gender, transaminase, burned area, Tobiasen index and mechanical ventilation.

In the forward multivariate model-building, CL was mainly influenced by age, Baux index, creatinine clearance, gender, Tobiasen index, and mechanical ventilation. Age and gender were excluded because they were correlated with the creatinine clearance for which the best estimates were obtained. *V*1 was influenced by age, Baux index and alkaline reserve and *V*2 by creatinine clearance, serum creatinine, gender, mechanical ventilation, burned surface area and alkaline reserve. Q did not seem to be influenced by any of the covariates. In the backward elimination phase, only creatinine clearance influenced ceftazidime clearance, exceeding the objective function cut-off value of 10.83, when it was omitted individually from the model. *V*2 was influenced by gender, mechanical ventilation and creatinine clearance. The final model had an objective function of 1618.37 and is described by the following equations:

These equations can be transformed to:

with SEX = 0 for men and 1 for women, VENT = 1 if the burn patient was mechanically ventilated and =0 if not.

Interindividual variability in the clearance was decreased to 16% and that of the central volume of distribution to 13%. Mean values for the pharmacokinetic parameters based on creatinine clearance are shown in Table 3.

Table 3. Mean pharmacokinetic parameters calculated from creatinine clearance data in ventilated and nonventilated patients **Parameters** | **Without mechanical ventilation** | **With mechanical ventilation** |
---|

**Males** | **Females** | **Males** | **Females** |
---|

*n* | 27 | 7 | 11 | 5 |

Creatinine clearance (ml min^{−1}) | 114 | 103 | 93 | 87 |

Clearance (l h^{−1}) | 7.2 | 6.6 | 6.1 | 5.7 |

Distribution volume of the central compartment (l) | 18.8 | 18.8 | 18.8 | 18.8 |

Inter-compartmental clearance (l h^{−1}) | 6.9 | 6.9 | 6.9 | 6.9 |

Distribution volume of the peripheral compartment (l) | 4.0 | 9.3 | 12.8 | 30.6 |

Volume of distribution (l) | 22.8 | 28.1 | 31.6 | 49.4 |

Elimination rate (h^{−1}) | 0.384 | 0.350 | 0.323 | 0.305 |

Half-life (h) | 1.81 | 1.98 | 2.15 | 2.27 |

### Discussion

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- References

The data collected in this study over the dosing interval were best described by a two-compartment model, which is in agreement with previous observations [14].

Like Dailly *et al.*[5], we showed that a one proportional error model was the best predictor of residual and interpatient variability. A multiplicative model is usually better adapted when the variation in the concentrations is greater than a factor of 10. In the present study, the measured concentrations were between 1 mg l^{−1}, the limit of quantification of the method, and 214.7 mg l^{−1}.

In a previous study [15] we reported high interindividual variability in the trough concentrations of ceftazidime and its influence on glomerular filtration. In the current study, we found a total clearance and a volume of distribution close to that observed by Walstad *et al.*[13], corresponding to an increase in these parameters compared with healthy subjects. In the pharmacokinetic study of Walstad *et al.*[13], eight burn patients were studied at the beginning of the hypermetabolic phase. It found a linear relationship between creatinine clearance and renal clearance of ceftazidime, but not between creatinine clearance and the total ceftazidime clearance, indicating an enhanced extra-renal clearance of the drug (32%). We found no relationship between ceftazidime clearance and the burned area and the depth of burn injury. In the study of Walstad *et al.*, blood samples were taken during surgical procedures and in four of the patients, blood loss was considerable (more than 5 l replacement liquid was required) which may have led to a loss of drug and perturbation of renal function. The authors noted that the blood loss could have distorted the interpretation of the results.

The *trans*-burned area clearance described in burn patients [16–19] does not seem sufficiently important in our study to be statistically significant. Zong *et al.*[16] demonstrated that concentrations of ceftazidine (1 to 21 mg l^{−1}) are well distributed in the exudates from the burn injury and are generally comparable with the blood concentrations. Whatever the fluid loss from these burned areas, the excretion of ceftazidime through exudates is numerically negligible compared with a clearance from 4 to 8 l h^{−1 }.

Values for pharmacokinetic parameters obtained in the present study are different from those obtained from a population pharmacokinetic approach in 41 burn patients by Dailly *et al.*[5]. These authors showed an inverse linear relationship between the total clearance of ceftazidime and serum creatinine concentration. Such findings raise the question of the validity of using plasma creatinine concentrations in burn patients [20, 21]. In our study, the Bayesian approach showed a clear and significant relationship between ceftazidime clearance and creatinine clearance, which emphasizes the importance of renal function.

An elevated volume of distribution has also been reported in burns patients [5] and explained by an increase in the extracellular fluid volume. However, in the work of Dailly *et al.*[5], the average time between the burn injury and the administration of ceftazidime was 31.7 days, i.e. during the hypermetabolic phase. Extracellular fluid volume is significantly increased during the acute phase of the injury (the first 48 h) and decreases over the whole hypermetabolic phase. Our values of volume of distribution are in agreement with those in the literature [13, 16] in burn patients, corresponding to a two fold increase, compared with healthy subjects.

Moreover, it appears that mechanical ventilation also has an influence on the pharmacokinetics of ceftazidime. Such changes in the pharmacokinetics have been described [22], particularly by Triginer during the use of gentamycin in critically ill adults without burn injuries [23]. The consequence of mechanical ventilation on ceftazidime disposition can be attributed to its effect on positive expiratory pressure (PEP), which could lead to a decrease in glomerular filtration rate [24] and an increase in the secretion of antidiuretic hormone responsible for the formation of oedema. This could also explain the variation in the volume of distribution. Mechanical ventilation increased the peripheral volume of distribution by a factor of 2.5 in both males and females. Mechanically ventilated patients are severely injured, and therefore the severity of the burn injury may be a confounding factor.

The distribution of the female population as a function of the area of the burn was homogenous; whereas the males were less badly injured than the females and were not similarly distributed according to the burned area. Even if gender is included in the Cockcroft formula, these parameters are poorly related (*r *= 0.38). The deletion of the covariable SEX led to a loss of information since it increased the objective function by 22.5, which correspond to a probability of 2 × 10^{−6}. As shown in Table 3, an influence of gender on the volume of distribution was found in all groups of burned patients in that the value was 1.2 times higher in females than males in nonmechanically ventilated patients, and 1.5 times higher in mechanically ventilated patients.

The maximum variation in half-life (22%) was observed between the nonmechanically ventilated women and men, whereas mechanical ventilation increased the half-life by 15% on average for both genders. Since the time necessary to reach steady state was only slightly altered and the half-life of ceftazidime was short, these differences are not clinically relevant.

This study highlights the complexity of ceftazidime pharmacokinetics in burn patients. We have shown that gender, mechanical ventilation and creatinine clearance significantly influence ceftazidime disposition in these patients.

These easily measurable covariates should be used to establish an optimal dosage regimen for ceftazidime. In particular, glomerular filtration rate is increased in burn patients, exposing them to the risk of plasma concentrations that are insufficient to exceed the MIC of many pathogens. In burn patients, the interindividual variability in ceftazidime pharmacokinetic parameters is significant, emphasizing the need for therapeutic monitoring.