Per individual on average (range) 13 plasma concentrations (3–15, n = 39 individuals), 14 microdialysate collections in ISF of adipose tissue (6–28, n = 28 individuals) and 11 in ISF of muscle (6–12, n = 24 individuals) were obtained after the start of the levofloxacin administration. The geometric mean and 10th–90th percentiles of the maximum levofloxacin concentration (Cmax) in plasma were 8.25 mg/l, 7.04–13.5 mg/l (Fig. 1b), but observations at the end of the infusion were only available for lung surgery patients (n = 5, 12.8% of all patients). The geometric mean of Cmax in ISF of adipose tissue (4.65 mg/l, 7.50–23.0 mg/l) and muscle (4.83 mg/l, 1.52–11.1 mg/l) were comparable and delayed in comparison to plasma (tmax = 1.64 h, 0.796–11.4 h, and tmax = 3.48 h, 1.17–11.0 h, respectively).
Precision and Plausibility of Parameter Estimates
While the NCA approach did not necessitate structural model development, the same final PK model structure was identified for integral-CA and midpoint-CA: A mammillary four-compartment model with clearance from the central compartment (Fig. 2). Plasma concentrations were related to the central compartment and target-site concentrations were attributed to distinct peripheral compartments.
Total volume of distribution (Vtot) differed between NCA (Vtot,mean = 104 l, at steady-state) and population estimates from the NLME approaches midpoint-CA (Vtot = 82.7 l) and integral-CA (Vtot = 81.1 l, Table II). Both population estimates of Vtot were in accordance with the NLME model based on plasma concentrations only (Vtot = 86 l, Tab. AI). However, compared to the central volume of distribution (V1) in integral-CA and the plasma only model (15.5 l and 21.7 l, respectively), V1 was largely decreased in midpoint-CA (4.82 l, Tab. AII). Clearance obtained from all three approaches (7.35–8.26 l/h) was comparable.
Volumes of distribution associated with ISF of adipose tissue and muscle and the sum of intercompartmental flows were comparable between midpoint-CA and integral-CA (Table II). In contrast, ratios of rate constants into and from the target site were similar for ISF of adipose tissue (1.51 for midpoint-CA and 2.14 for integral-CA) but differed largely for muscle (4.44 for midpoint-CA and 1.03 for integral-CA).
Identical relationships between PK parameters and patient characteristics were identified for the three approaches: Clearance increased by 9.00%–12.6% for each 10 ml/min increase of CLCR (Table II), and was reduced by 43.4%–52.8% in sepsis patients. The intercompartmental flow (not available for NCA due to the lack of mass transfer descriptions) associated with ISF of adipose tissue increased by 7.25%–8.19% for each g/l increase in serum albumin concentration. The inclusion of these covariate relationships decreased the overall interindividual variability in the NLME models substantially (relative reduction of coefficient of variation ≤30.1% for midpoint-CA and ≤43.7% for integral-CA).
On average, estimates of interindividual variability (not available for NCA) were higher in midpoint-CA versus integral-CA (Δ%CVmean = 27.1%). Only integral-CA allowed discrimination of residual variability attributed to microdialysis, retrodialysis and plasma measurements (8.83%–28.3%CV, Tab. AII). Here, residual variability on retrodialysis (18.4%–24.9%CV) and microdialysis (25.4%–28.3%CV) was higher than for plasma observations (8.83%CV).
Parameter precision of the structural parameter estimates was comparable between midpoint-CA (relative standard error (RSE): 10.9%–48.3%) and integral-CA (RSE: 3.89%–61.7%) but parameter precision of interindividual variability of the key PK parameters clearance and V1 was lower for midpoint-CA (RSE: 62.5% and 71.2%, respectively) versus integral-CA (RSE: 38.3% and 34.2%, respectively; Tab. AII), highlighting an important advantage of integral-CA (Table III).
Goodness-of-Fit and Predictive Performance of Nonlinear Mixed-Effects Modelling Approaches
In contrast to midpoint-CA, which demonstrated trends indicating model overpredictions (plasma and adipose tissue) and underpredictions (muscle) in the middle of the measured concentration range (Fig. A1), no pronounced trends were evident for integral-CA (Fig. A2), showing superiority of integral-CA (Table III).
After accounting for interindividual differences in RR, remaining differences between predicted retrodialysate concentrations (used in integral-CA model to calculate RR) and observed ones (used in midpoint-CA and NCA to calculate RR) were evident (Fig. A2b2 and b4). This divergence was quantified as residual unexplained variability (Table AII).
Whereas all data points were evaluated in the NLME approaches, NCA predictions were limited to the terminal phase of the levofloxacin concentration-time profile in all matrices employed for log-linear regression (Fig. A3).
In the visual predictive check of the integral-CA, the median of the simulated concentration-time profiles corresponded with the median of the observed data of all matrices, whereas the 5th and 95th percentile of simulations were lower and higher, respectively, than observed ones. Yet, observed percentiles lay within the 95% confidence intervals of simulated ones, indicating an overall good predictive model performance (Fig. 3b and Fig. A4). In contrast, for midpoint-CA the 5th and 95th percentile of the simulated concentration-time profile diverged from those of observations for numerous sampling time points in plasma and ISF of muscle (Fig. 3a), indicating over prediction of PK-related variability. In addition, for ISF of muscle the median simulated midpoint-CA profile indicated model misspecifications. The less accurate predictive performance compromised the applicability of midpoint-CA for Monte Carlo simulations (Table III) and therefore the subsequent PK/PD evaluation through PTA analysis.
Comparison of Levofloxacin Exposure between Approaches
A comparison of individual exposure ranges determined via NCA, midpoint-CA and integral-CA (Fig. 4a-b) revealed differences in AUC from 0 to 8 h (AUC0–8) and AUC0–24 in plasma between NCA (AUC0–8,range = 22.0–48.6 mg∙h/l, AUC0–24,range = 34.1–114 mg∙h/l) and integral-CA (AUC0–8,range = 22.8–57.1 mg∙h/l, AUC0–24,range = 34.7–112 mg∙h/l), versus midpoint-CA (AUC0–8,range = 21.7–103 mg∙h/l, AUC0–24,range = 33.1–173 mg∙h/l). This divergence of midpoint-CA was further substantiated by the low concordance (Lin’s concordance correlation coefficient ≤ 0.546) of individual plasma AUC estimates between the midpoint-CA versus integral-CA and NCA (Fig. A5-A6). The median plasma Cmax (10.6 mg/l) was lower for NCA compared to midpoint-CA (12.7 mg/l) and integral-CA (12.3 mg/l, Fig. A7), since for most individuals sampling times did not include the end of the infusion (hence tmax was not covered), highlighting a well-known inherent limitation of NCA versus NLME approaches based on the sampling design.
Variability of individual AUC at target site was larger for NCA (69.1%CV-79.2%CV) and midpoint-CA (52.3%CV-56.0%CV) compared to integral-CA (32.6%CV-32.9%CV, Fig. 4) and the accordance of estimates between the different methods was low (Fig. A5-A7). By design, individual AUC determined via NCA and midpoint-CA in both matrices was dependent on RR, whereas no dependency was evident for integral-CA (p = 0.0895 and p = 0.265, Fig. A8), highlighting an advantage of integral-CA (Table III). Importantly, NCA measures of AUC had a large proportion (>20% ) of AUC extrapolated until infinity in plasma (45.7%), ISF of adipose tissue (23.5%) and ISF of muscle (38.2%).
The larger variability associated with exposure simulations from midpoint-CA compared to integral-CA led to broader 95% CI bands obtained from Monte Carlo simulations for all three matrices (Fig. 5). The difference between rate constants associated with ISF of muscle tissue estimated via midpoint-CA and integral-CA manifested in differences in predicted Cmax (Cmax,median = 5.38 mg/l versus 7.49 mg/l, respectively, Fig. 5c). Similarly, penetration indices (AUCISF/AUCplasma) were relatively similar for both approaches for ISF of adipose tissue but differed largely for muscle tissue (Fig. 6). Whereas penetration indices obtained from NLME approached 100% towards the end of the sampling time, penetration indices obtained via NCA yielded penetration indices>100% (Fig. 6). The implausibility of penetration indices>100% indicated a further disadvantage of NCA (Table III).
Pharmacokinetic/Pharmacodynamic Evaluation of Levofloxacin Dosing Regimens Based on Nonlinear Mixed-Effects Modelling Approaches
Monte-Carlo simulations of levofloxacin plasma concentrations following dosing regimens recommended for the treatment of CAP (once- and twice-daily 500 mg levofloxacin short-term infusions of 0.5 h ) were performed covering the 5th to 95th percentile of study CLCR (37.3–146 ml/min) of individuals without sepsis.
PTA was lower at higher CLCR and PTA calculated via integral-CA (PTAintegral-CA) was higher than PTA determined via midpoint-CA (PTAmidpoint-CA) when PTA≥90% (relevant PTA range for the evaluation of adequacy of dosing regimens, Fig. 7): For the epidemiological cut-off value (ECOFF) of Staphylococcus aureus (MIC = 0.5 mg/l) the administration of 500 mg once-daily to an individual with healthy/elevated renal function (CLCR = 146 ml/min) was only deemed adequate via integral-CA but not midpoint-CA (Fig. 7a). The same applied to the ECOFF of Streptococcus pneumoniae (MIC = 2.0 mg/l) and the twice-daily administration of 500 mg levofloxacin to an individual with severe renal impairment (CLCR = 37.3 ml/min, Fig. 7b). At low PTA (⪅50%), midpoint-CA yielded larger PTA than integral-CA.
When considering species-specific MIC distributions via CFR analysis of the most common CAP associated pathogens, both NLME approaches evaluated the once-daily dosing regimen as adequate to cover Haemophilus influenzae but not Staphylococcus aureus (Fig. 8a). Adequate CFR to Streptococcus pneumoniae for all investigated individuals was only achieved by a twice-daily dosing regimen and for CLCR<146 ml/min (Fig. 8b). Integral-CA showed higher CFR than midpoint-CA for Streptococcus pneumoniae (up to 10.4% points).