Balancing efficacy and reduction in renal function to optimize initial gentamicin dosing in children with cancer
Carolina Llanos-Paez, Christine Staatz, Stefanie Hennig.
School of Pharmacy, The University of Queensland, Brisbane QLD, Australia
Background: Children with cancer often receive long courses of gentamicin on multiple occasions alongside nephrotoxic chemotherapy. Achieving sufficient exposure for optimal efficacy is crucial in this immune-compromised population. Pharmacokinetic (PK) exposure targets are currently not achieved by 54% of patients, even after dose adjustment (1). Use of gentamicin is associated with nephrotoxicity and ototoxicity as a result of drug accumulation in the renal cortex and inner ear, which may be complicated by concurrent chemotherapy. Our research team previously developed a population PK model of gentamicin in 423 children with cancer (median body weight: 19.4 kg and age: 5.2 years) (2).
Objectives: To apply our population PK model in i) a utility function approach that balanced the probability of efficacy against potential reduction in renal function related to gentamicin accumulation in the renal cortex and ii) in semi-mechanistic pharmacodynamic (PD) models to simulate bacterial killing over time; to predict optimal initial dosing of gentamicin in this population.
Methods: Our previously developed population PK model (2) included an influence of patient age, fat-free mass (FFM) and serum creatinine concentration on gentamicin clearance (CL); and an influence of FFM on gentamicin central (V1) and peripheral (V2) volume of distribution and inter-compartmental CL (Q). Typical PK parameter estimates were: CL (L/h/70kg) = 5.77; V1 (L/70kg) = 21.6; Q (L/h/70kg) = 0.62 and V2 (L/70kg) = 13.8 (2), when standardised for FFM of 70 kg and serum creatinine of 37.4 µmol/L. The PK model was used to predict gentamicin exposure over 24 hours after a single IV-infusion (30 min) after drug administration and this information was then incorporated into a utility function and two semi-mechanistic PD models (3, 4).
Within the utility function the probability of efficacy (PEFF) was balanced against the extent of gentamicin accumulation in the renal cortex and potential reduction in renal function. Efficacy probability at different Cmax/MIC and AUC24/MIC values were obtained from previous publications (5, 6). Patients were considered to have a 100% chance of efficacy when Cmax/MIC reached 10 and AUC24/MIC reached 100. The importance of achieving both Cmax/MIC and AUC24/MIC targets was weighted equally according to equation 1:
PEFF = (Probability of Cmax/MIC ≥ 10 + Probability of AUC24/MIC ≥ 100)/2 Equation 1
Accumulation of gentamicin in the renal cortex (CR) (mg/kg kidney weight) was predicted using a previous model which allowed for non-linear uptake (7) and linear elimination of gentamicin from the kidneys (8). A threshold concentration (CRthreshold) of accumulated gentamicin (8) (42.5 mg/kg kidney weight) was allowed based on patient age-predicted kidney weight (9), below which no side effects occurred. Gentamicin accumulation beyond this threshold had a detrimental effect on renal function, which was described by EGFR (mM) and was calculated using equation 2 (6). Patient’s baseline renal function prior to gentamicin usage (GFR0, mL/min) was calculated using an equation proposed by Rhodin et al. (10). Patient renal function after gentamicin exposure (GFRnew) was predicted based on patient renal function prior to gentamicin usage and the detrimental effect of gentamicin accumulation given by another Emax model (equation 3). The percentage reduction in renal function (PGFR) calculated according to equation 4 was included in the utility function.
If CR < CRthreshold EGFR(t) = 0 Equation 2
If CR > CRthreshold EGFR(t) = Emax × CRγ/(AR50γ + CRγ)
GFRnew = GFR0 - (GFRmax × EGFRδ/(EGFR50δ + EGFRδ)) Equation 3
PGFR = (GFR0 - GFRnew)/((GFR0 + GFRnew)/2) Equation 4
Where Emax is the maximum accumulation effect observed and was fixed to 190 mM; AR50 is the amount of gentamicin in the renal cortex when EGFR is equal to Emax/2 and was fixed to 55.4 mg; γ is the Hill coefficient and was fixed to 2.5; GFRmax is the maximum decrease in renal function and was fixed to 41 mL/min; EGFR50 is the accumulation effect value for which GFRnew is equal to GFRmax/2 and was fixed to 33.5 mM; δ is the Hill coefficient and was fixed to 5.5.
NONMEM® version 7.3 was used to estimate an optimal dose of gentamicin for different microorganism’s MICs using a logit function (equation 5) under which PEFF was maximised towards 1, while PGFR was minimised towards 0.
f(P) = log(PEFF ) - log(1 - PGFR ) Equation 5
Bacterial kill curves for the estimated optimal initial gentamicin doses were then evaluated, given different microorganism MICs using two semi-mechanistic pharmacodynamic (PD) models (3, 4). R© studio software version 3.1 (http://www.r-project.org./) was used to simulate bacterial count over time.
Results: Based on the utility function, the optimal initial dose for gentamicin ranged from 7.2 mg/kg/24 hours (MIC = 0.5 mg/L) to 9.6 mg/kg/24 hours (MIC = 1, 2 and 4 mg/L). These doses provided a 92% (MIC = 0.5 mg/L), 87% (MIC = 1 mg/L), 79% (MIC = 2 mg/L) and 72% (MIC = 4 mg/L) probability of achieving Cmax/MIC ≥ 10 and AUC24/MIC ≥ 100. Baseline GFR prior to gentamicin usage was on average 40.8 mL/min. An average reduction in the GFR of 0.51% and 1.6% was predicted with an initial dose of gentamicin of 7.2 mg/kg and 9.6 mg/kg, respectively. Our utility function model predicted that the currently commonly administered initial gentamicin dose of 7.0 mg/kg/24 hours (1) achieved probability of efficacy of 91%, 83%, 76% and 67% for microorganisms with an MIC of 0.5, 1, 2 and 4 mg/L. When tested in the semi-mechanistic PD model (MIC = 2 mg/L) the estimated optimal dose of 9.6 mg/kg/24 hours given to the typical patient produced rapid initial bacterial eradication with 11 log killing and no bacterial regrowth for at least 11 hours. A dose of 7.0 mg/kg/24 hours produced initial bacterial eradication with 10 log killing and no bacterial regrowth for at least 9 hours. The bacterial count did not reach the starting initial inocula at 24 hours post-dose with any of the two doses.
Conclusions: This study utilised the first population pharmacokinetic model for gentamicin in oncology children with febrile neutropenia to obtain data that will assist in the personalisation of therapy. Using a novel utility function, an initial dose of 9.6 mg/kg/24 hours was identified as optimal to fight microorganisms with an MIC of 1, 2 and 4 mg/L providing 87%, 79% and 72% probability of efficacy, respectively, with a predicted 1.6% reduction in GFR. Simulations from two semi-mechanistic PD models showed that this dose provides acceptable bacterial killing in the typical patient.
References:
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