Oral: Drug/Disease modelling

D-09 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 (P_EFF) was balanced against the extent of gentamicin accumulation in the renal cortex and potential reduction in renal function. Efficacy probability at different C_max/MIC and AUC₂₄/MIC values were obtained from previous publications (5, 6). Patients were considered to have a 100% chance of efficacy when C_max/MIC reached 10 and AUC₂₄/MIC reached 100. The importance of achieving both C_max/MIC and AUC₂₄/MIC targets was weighted equally according to equation 1:

P_EFF = (Probability of C_max/MIC ≥ 10 + Probability of AUC₂₄/MIC ≥ 100)/2                 Equation 1

Accumulation of gentamicin in the renal cortex (C_R) (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 (C_Rthreshold) 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 E_GFR (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 (GFR_new) was predicted based on patient renal function prior to gentamicin usage and the detrimental effect of gentamicin accumulation given by another E_max model (equation 3). The percentage reduction in renal function (P_GFR) calculated according to equation 4 was included in the utility function.

If C_R < C_Rthreshold   E_GFR(t) = 0                                                                               Equation 2

If C_R > C_Rthreshold   E_GFR(t) = E_max × C_R^γ/(A_R50^γ + C_R^γ)

GFR_new = GFR₀ - (GFR_max × E_GFR^δ/(E_GFR50^δ + E_GFR^δ))                                              Equation 3

P_GFR = (GFR₀ - GFR_new)/((GFR₀ + GFR_new)/2)                                                          Equation 4

Where E_max is the maximum accumulation effect observed and was fixed to 190 mM; A_R50 is the amount of gentamicin in the renal cortex when E_GFR is equal to E_max/2 and was fixed to 55.4 mg; γ is the Hill coefficient and was fixed to 2.5; GFR_max is the maximum decrease in renal function and was fixed to 41 mL/min; E_GFR50 is the accumulation effect value for which GFR_new is equal to GFR_max/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 P_EFF was maximised towards 1, while P_GFR was minimised towards 0. 

f(P) = log(P_EFF ) - log(1 - P_GFR )                                                                              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 C_max/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:
[1] Bialkowski S, Staatz CE, Clark J et al. Gentamicin Pharmacokinetics and Monitoring in Pediatric Febrile Neutropenic Patients. Therapeutic drug monitoring 2016. 2.              
[2] Llanos-Paez CC, Staatz CE, Lawson R and Hennig S (2016). Population pharmacokinetic model of gentamicin in paediatric oncology patients. In: World Conference of Pharmacometrics, Brisbane, Australia. August 21-24, 2016.
[3] Mohamed AF, Nielsen EI, Cars O, Friberg LE. 2012. Pharmacokinetic-pharmacodynamic model for gentamicin and its adaptive resistance with predictions of dosing schedules in newborn infants. Antimicrob Agents Chemother 56:179-188.
[4] Zhuang L, He Y, Xia H, Liu Y, Sy SK, Derendorf H. 2016. Gentamicin dosing strategy in patients with end-stage renal disease receiving haemodialysis: evaluation using a semi-mechanistic pharmacokinetic/pharmacodynamic model. J Antimicrob Chemother 71:1012-1021.
[5] Moore RD, Lietman PS, Smith CR. 1987. Clinical response to aminoglycoside therapy: importance of the ratio of peak concentration to minimal inhibitory concentration. J Infect Dis 155:93-99.
[6] Kashuba AD, Nafziger AN, Drusano GL, Bertino JS, Jr. 1999. Optimizing aminoglycoside therapy for nosocomial pneumonia caused by gram-negative bacteria. Antimicrob Agents Chemother 43:623-629.
[7] Giuliano RA, Verpooten GA, Verbist L, Wedeen RP, De Broe ME. 1986. In vivo uptake kinetics of aminoglycosides in the kidney cortex of rats. J Pharmacol Exp Ther 236:470-475.
[8] Rougier F, Claude D, Maurin M et al. Aminoglycoside nephrotoxicity: modeling, simulation, and control. Antimicrobial agents and chemotherapy 2003; 47: 1010-6.
[9] Shankle WR, Landing BH, Gregg J. Normal organ weights of infants and children: graphs of values by age, with confidence intervals. Pediatric pathology 1983; 1: 399-408.
[10] Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M, Chatelut E, Grubb A, Veal GJ, Keir MJ, Holford NH. 2009. Human renal function maturation: a quantitative description using weight and postmenstrual age. Pediatr Nephrol 24:67-76.