**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 (V_{1}) and peripheral (V_{2}) volume of distribution and inter-compartmental CL (Q). Typical PK parameter estimates were: CL (L/h/70kg) = 5.77; V_{1} (L/70kg) = 21.6; Q (L/h/70kg) = 0.62 and V_{2} (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 AUC_{24}/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 AUC_{24}/MIC reached 100. The importance of achieving both C_{max}/MIC and AUC_{24}/MIC targets was weighted equally according to equation 1:

P_{EFF }= (Probability of C_{max}/MIC ≥ 10 + Probability of AUC_{24}/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 (GFR_{0}, 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 }= GFR_{0 }- (GFR_{max }× E_{GFR}^{δ}/(E_{GFR50}^{δ }+ E_{GFR}^{δ})) Equation 3

P_{GFR }= (GFR_{0} - GFR_{new})/((GFR_{0 }+ 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 AUC_{24}/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.

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